Tables of Second Virial Coefficients and Their First and Second Derivatives for the Stockmayer (m, 6, 3) Potential Function

Abstract

Expressions are developed for the second virial coefficient and its first two temperature derivatives for polar molecules on the Stockmayer model of a dipole imbedded in a spherical core. In the case considered, the core molecules interact according to an (m, 6) intermolecular potential function. Terms describing the dependence of these quantities on the polarizability of the dipole are also included. Tables are given for the cases m = 9, 12, 18, 24, 36, and 60. These tables can be used to calculate the first density corrections to all of the thermodynamic properties of a fluid of polar molecules. The adequacy and accuracy of the tables are discussed in some detail.

1. Introduction

Effects on the thermodynamic properties of non-spherical molecules due to the presence of angular dependent terms in the potential function can be quite important. In some cases, these effects cause large deviations from two parameter corresponding states. Such angular dependent terms can be placed in two categories. There are those which are due to “permanent” orientation dependent forces resulting from the shape of the isolated molecules. In addition, there are induced nonspherical forces which arise from the change in the shape of a molecule due to the proximity of a second molecule. The former can be quite large while the latter are generally small. A significant difference between the two types of terms is associated with the fact that the relevant coefficients in the former (e.g., the dipole moment) are, in principle, usually measureable in experiments based on isolated atom effects (e.g. spectrocopy, see for example [1]¹) while those for the latter can rarely be determined separately and so are most often investigated with the help of a model and a parameter. Effects due to permanent orientation dependent forces are thus much more useful in the study of such effects on thermodynamic properties both because they are large and because they do not involve additional parameterization.

The formalism for including orientational effects of both the permanent and induced variety in the potential function has been developed by several authors [2, 3, 4, 5, 6, 7]. In the case of molecules with permanent dipole moments, Stockmayer accounted for effects of the first kind by using as a model a point dipole embedded in a spherical molecule of the Lennard-Jones type, and calculated the angularly dependent interaction between such molecules. Effects of the second type were added to this model later [2, 3]. For the case of the dipole interactions this can be done by introducing an effective dipole moment which is the sum of the permanent dipole moment of the isolated molecule and an induced dipole moment resulting from the proximity of the other polar molecule. The induced field can be written as an expansion in powers of the polarizability (which we shall regard here as isotropic and hence will use a mean value). Effects due to higher order permanent moments have been formulated [2, 3] but we shall not include them here mainly because these properties are usually, at best, only poorly known, and thus would require additional parameterization. Although Stockmayer actually only made use of the two functions corresponding to m = 24 and m = ∞, his name is often associated with the general (m, 6, 3) function family.

The particular Stockmayer potential function which corresponds to the value m = 12 (i.e., the (12, 6, 3) function) has been given a position of importance in the study of the intermolecular potential functions of polar substances which is out of all proportion to its validity. One of the reasons for this distortion is due to the paucity of published tables for other functional forms. One of the purposes of this work is to correct that situation by providing tables for several members of the (m, 6, 3) Stockmayer family of intermolecular potential functions. These tables were thought to be necessary for several reasons: first of all, in order to study the effect of the intermolecular repulsive forces, secondly, to provide additional flexibility in the fitting of experimental data for polar substances and thirdly, to provide a means for extending to polar molecular models studies of the sensitivity of thermodynamic properties to the details of the potential function. The studies were previously applied only to spherical molecules [9]. Results of such studies as applied to polar potentials will be published separately.

A feature of the tables presented here not present in other tabulations for polar potential functions [3, 8, 10, 11, 12] is the inclusion of directly calculated tables of both the first and second derivatives with respect to temperature of the functions from which the second virial coefficients are calculated.² These should allow for the correlation and prediction of other thermodynamic properties of polar gases such as the Joule-Thomson coefficient and the specific heats at low densities.

The choice of the (m, 6, 3) potential function family was, of course, somewhat arbitrary. A study of the sensitivity of thermodynamic properties to the potential function in the case of spherical molecules (i.e. nonpolar in the present context) showed all reasonable three parameter functions to be equivalent when it came to predicting such properties [9]. Subsequently a very successful new correlation of nonpolar second virial coefficients was produced in which the authors arbitrarily chose to base their correlation entirely on the (m, 6) function [13]. Furthermore, tables of collision integrals have now been published for the spherical (m, 6) potential function [14]. The spherical (m, 6) function has also been extended to quantum fluids with the preparation of tables of Wigner-Kirkwood corrections to the second virial coefficient for the (m, 6) family [15]. It thus seemed appropriate to select the (m, 6) as the form for the central part of the potential. With the publication of the present tables, there becomes available an extensive set of tables for the study of various variations on the (m, 6) potential model.

2. Mathematical Preliminaries

Most of the details needed for the derivation of the required expressions are contained in the papers of Buckingham and Pople [3], of Stockmayer [7], and of Lennard-Jones [16] and will not be repeated here except to facilitate the connection with the work of those authors and to indicate departures from their approaches.

We choose to define the (m, 6, 3) potential function in reduced form in terms of the parameters ϵ/k and σ of the spherical core through the expression

$${\Psi }^{*}\left(r^{*}\right)=a\left[{\left(\frac{1}{r^{*}}\right)}^m-{\left(\frac{1}{r^{*}}\right)}^6\right]+\left(\frac{{\mu }^2}{ϵ{\sigma }^3{r}^{*3}}\right)X+\left(\frac{\alpha {\mu }^2}{ϵ{\sigma }^6{r}^{*6}}\right)Y+\left(\frac{{\alpha }^2{\mu }^2}{ϵ{\sigma }^9{r}^{*9}}\right)Z+\dots$$ (1)

where r* = r/σ,

$$a=\left(\frac{6}{m-6}\right){\left(\frac{m}{6}\right)}^{\frac{m}{m-6}},$$

$$X=2\text{cos}{\theta }_1\text{cos}{\theta }_2+\text{sin}{\theta }_1\text{sin}{\theta }_2\text{cos}\left({\Phi }_1+{\Phi }_2\right),$$

$$Y=-\left[3{\text{cos}}^2{\theta }_1+3{\text{cos}}^2{\theta }_2-2\right]/2=1-\frac{3}{2}\left({\text{cos}}^2{\theta }_1+{\text{cos}}^2{\theta }_2\right)$$

and

$$Z=8\text{cos}{\theta }_1\text{cos}{\theta }_2+\text{sin}{\theta }_1\text{sin}{\theta }_2\text{cos}\left({\Phi }_1+{\Phi }_2\right)$$

with the angles defined as in figure 1, where μ is the dipole moment and α is the mean polarizability of the molecule, assumed to be isotropic. It should be noted that σ is that value of r for which the spherical part of the potential function vanishes while ϵ/k is the well depth for this same spherical core (i.e., it is the well depth for the (m, 6) and not for the (m, 6, 3)). This is consistent with the definition of Stockmayer [7] but is not consistent with that of Saxena and Joshi [10]. The latter made use in the (18, 6, 3) potential of a coefficient α which is appropriate to the Stockmayer (12, 6, 3) function. Because of this, their parameter ϵ/k does not have a clear meaning.

Figure 1.

The nonspherical terms in (1) have a strong effect on the potential function. Rowlinson [12] has plotted the potential (1) for m = 12 for different dipole strengths including in the potential only the spherical and dipole terms, the latter for dipoles in the end-on position. His results show that the actual well depth for this end-on configuration for a reduced dipole moment τ(= μ²/ϵσ³) of 4.0 is eight times the well depth for the nonpolar (12, 6) potential. In addition, he found that the polar part of the potential has the effect of making the sides of the potential well much steeper. In particular, Rowlinson found that the ratio of the coordinate at the potential minimum to that at the potential zero (i.e., r_min/σ) changed from 1.414 for τ = 0 to 1.002 for τ = 4.0.

These strong modifications of the spherical part of the potential function result directly from the inclusion of the effect of the dipole moment and so indicate a strong sensitivity of the predicted second virial coefficient to the magnitude of the dipole moment used.

2 Reference [11] contains such tables calculated using numerical difference methods.

2.1. The Calculation of the Second Virial Coefficient

The second virial coefficient for angular dependent potential functions can be written:

$$\begin{array}{l}B(T)=\frac{N{\sigma }^3}{8\pi }{\int }_0^{\infty }{r}^{*2}d{r}^{*}{\int }_0^{\pi }\text{sin}{\theta }_{1}d{\theta }_1{\int }_0^{2\pi }d{\varphi }_1\\ {\int }_0^{\pi }\text{sin}{\theta }_{2}d{\theta }_2{\int }_0^{2\pi }d{\Phi }_2\left[1-\text{exp}\left(-\frac{ϵ{\Psi }^{*}\left(r^{*}\right)}{kT}\right)\right].\end{array}$$

Following Buckingham and Pople [3], the exponential of the angular dependent part of the potential can be expanded by means of the exponential series and the integration over angles carried out. This is easily shown to lead to the series

$$\begin{gathered} B(T)=b_0{B}^{*}\left(T^{*}\right)=\frac{3b_0}{16{\pi }^2}{\int }_0^{\infty }{r}^{*2}d{r}^{*}{\int }_0^{\pi }\text{sin}{\theta }_{1}d{\theta }_1 \\ {\int }_0^{2\pi }d{\Phi }_1{\int }_0^{\pi }\text{sin}{\theta }_{2}d{\theta }_2{\int }_0^{2\pi }d{\Phi }_2 \\ [1-\text{exp}\left(-{\Psi }_0^{*}\left(r^{*}\right)/T^{*}\right)\sum _{l,s,t=0}^{\infty }\frac{{(-1)}^{l+s+t}}{l!s!t!}{\left(\frac{\tau }{T^{*}}\right)}^{l+s+t} \\ {q}^{s+2t}{X}^l{Y}^s{Z}^t{r}^{*-3(l+2s+3t)}] \end{gathered}$$ (2)

where $b_0=\frac{2\pi N}{3}{\sigma }^3$ is the classical hard sphere second virial coefficient and Ψ₀ is the spherical part of the potential (e.g., the first term of (1), where we have defined a reduced dipole moment $\tau =\frac{{\mu }^2}{ϵ{\sigma }^3}$ and a reduced mean polarizability $q=\frac{\alpha }{{\sigma }^3}$.

Following an implicit assumption of Buckingham and Pople, we consider the effect of polarizability to be small. This can be considered to be part of our molecular model, i.e., our model is now that of a point dipole of small polarizability imbedded in the center of a spherical molecule. According to this model, the second virial coefficient can be written in the form

$$B(T,\mu ,\alpha )=b_0{B}^{*}\left(T^{*},\tau ,q\right)=b_0\sum _{p=0}^{\infty }{A}_p\left(T^{*},\tau \right)q_p$$ (3)

where the coefficients A_p contain the integrations over r and over angles, and where the effect of the dipole itself is evaluated to all orders of the reduced dipole moment in each term of the power series in the dipole polarizability.

2.2. The Coefficients A_p

According to (2), the coefficients A_p are given by

$$A_p\left(T^{*},\tau \right)=3{\int }_0^{\infty }{r}^{*2}d{r}^{*}[1-\text{exp}\left(-\frac{{\Psi }_0^{*}\left(r^{*}\right)}{T^{*}}\right)\sum _{l=0}^{\infty }\sum _{[s,t]}^{*}{\left(\frac{\tau }{T^{*}}\right)}^{l+s+t}{r}^{*-3(l+2s+3t)}{Q}_{lst}]$$ (4)

where $\sum _{[s,t]}^{*}$ indicates that the summation extends over values of s and t such that s + 2t = p and where, according to appendix A, Q_lst is given by

$$\begin{gathered} Q_{lst}=\sum _{h=0}^l\sum _{i=0}^s\sum _{j=0}^i\sum _{k=0}^t{C}_{\beta }^{\gamma } \\ \frac{(h+k)!\left(\frac{v_1}{2}\right)!\left(\frac{v_2}{2}\right)!}{\left(v_1+1\right)!\left(v_2+1\right)!\left(\frac{v_1-h-h}{2}\right)!} \\ \frac{\left(v_1-h-k\right)!\left(v_2-h-k\right)!}{\left(\frac{v_2-h-k}{2}\right)!} \end{gathered}$$ (5)

where h + k is even and

$$C_{\beta }^{\gamma }=C_{hlst}^{ijk}=\left(\begin{array}{l}l\hfill \\ h\hfill \end{array}\right)\left(\begin{array}{l}s\hfill \\ i\hfill \end{array}\right)\left(\begin{array}{l}i\hfill \\ j\hfill \end{array}\right)\left(\begin{array}{l}t\hfill \\ k\hfill \end{array}\right)2^{(l-i+3t-2k)}\frac{{(-3)}^i}{l!s!t!}{(-1)}^{l+s+t}.$$

Here v₁ = l + t + 2i − 2j and v₂ = l + t + 2j.

According to our model, the index l (and hence h in eq (5)) must be summed over all its values for each value of p. It should be noted that stopping the series (3) at p = 0 is equivalent to the assumption that the molecule is not polarizable. The resulting model is referred to as the rigid dipole model by Buckingham and Pople. Within the p = 0 coefficient, it is convenient to exhibit the l = 0 term for p = 0 separately since this is the contribution of the spherical core. On designating this spherical contribution as B₀(T*), (4) becomes, for p = 0,

$$\begin{array}{l}{A}_0\left(T^{*},\tau \right)=B_0\left(T^{*}\right)-D_0\left(T^{*}\right),\\ D_0\left(T^{*},\tau \right)=-3\sum _{\begin{array}{c}l=2\\ l\text{ even }\end{array}}^{\infty }{\int }_0^{\infty }{\left(r^{*}\right)}^{-3l}\\ \text{exp}\left[-{\Psi }_0\left(r^{*}\right)/T^{*}\right]{\left(\frac{\tau }{T^{*}}\right)}^{\prime }{Q}_{100}{r}^{*2}d{r}^{*}\end{array}$$ (6)

whereas for p ≠ 0

$$\begin{array}{l}{A}_{p\ne 0}=D_{p\ne 0}\left(T^{*},\tau \right)=-3\sum _{\begin{array}{c}l=2\\ \text{ leven }\end{array}}^{\infty }\sum _{[s,t]}^{*}{\int }_0^{\infty }{\left(r^{*}\right)}^{-3(l+2s+t)}\\ \text{exp}\left[-{\Psi }_0\left(r^{*}\right)/T^{*}\right]{\left(\frac{\tau }{T^{*}}\right)}^{l+s+t}\times Q_{lst}{r}^{*2}d{r}^{*}.\end{array}$$ (6a)

These can be combined as

$$A_p\left(T^{*},\tau \right)=B_0\left(T^{*}\right){\delta }_{p0}+D_p\left(T^{*},\tau \right)$$

where δ_p0 is the Kronecker delta.

Following Buckingham and Pople [3], we define the functions $H_k^{(m,n)}\left(T^{*}\right)$ through the relation

$$\begin{array}{l}\frac{1}{m}{\left(T^{*}/a\right)}^2{H}_k^{(m,n)}\left(T^{*}\right)-{\int }_0^{\infty }{\left(\frac{1}{r^{*}}\right)}^k\\ \text{exp}\left[-{\Psi }_0\left(r^{*}\right)/T^{*}\right]r^{*2}d{r}^{*}.\end{array}$$ (7)

Since we shall ultimately deal only with an (m, 6) potential for the spherical core and shall never consider more than one value of m at a time, the superscripts (m, n) can be dropped without introducing any ambiguity. With this definition for H_k(T*), D_p(T*, τ) becomes

$$D_p\left(T*,\tau \right)=-3\underset{l\text{even}}{{\displaystyle \sum }_{l=2}^{\infty }{\displaystyle \sum }_{\left[s,t\right]}^{*}}{H}_{v3}\left(T*\right)\frac{1}{m}{\left(\frac{T*}{a}\right)}^2{\left(\frac{\tau }{T*}\right)}^{l+s+t}Qlst$$

where v₃ = 3(l + 2s + 3t). With the help of this last eqs and (5) and (6) it is easy to show that the coefficient of the zeroth power of the dipole polarizability (corresponding to the rigid dipole) is given by

$$\begin{gathered} A_0\left(T^{*},\tau \right)=B_0\left(T^{*}\right)+D_0\left(T^{*},\tau \right) \\ =B_0\left(T^{*}\right)-\frac{3}{m}\sum _{i=1}^{\infty }{\left[\frac{i!2^i}{(2i+1)!}\right]}^2{\tau }^{2i}\frac{{\left(T^{*}\right)}^{2-2i}}{a^2} \\ {H}_{6i}\left(T^{*}\right)\sum _{j=0}^i\frac{(2j)!}{{(j!)}^2} \end{gathered}$$ (8)

which, on the substitution of the values m= 12 and a = 4 as appropriate to the (12, 6, 3) potential, reduces to (3.10) of Buckingham and Pople. It should be noted that Buckingham and Pople introduce the variable y which for the (m, 6) potential can be defined as $y={\left(\frac{a}{T^{*}}\right)}^{1/2}$. Substitution of T* = ay² in (8) above will yield the factor required for converting the quantity in the square bracket to the corresponding quantity in eq (3.10) of reference [3].

The variable y is the proper variable for eq (8) for describing convergence behavior. Since, however, we are concerned here only with the functional dependence of the equation and not its analytic behavior, we shall continue to use T* here. (In the tables, both y and T* are given).

A considerable simplification is obtained for the user of our tables if in D₀(T*, τ) all factors independent of the dipole moment are combined. To this end, we define a set of functions I_k(T*) related to the H_k(T*) as follows:

$$I_k\left(T^{*}\right)=F(k)T^{*2-2k}{H}_{6k}\left(T^{*}\right)$$ (9)

where

$$F(k)=\frac{3}{a^{2}m}{(4)}^k{\left[\frac{k!}{(2k+1)!}\right]}^2\sum _{i=0}^k\frac{(2i)!}{{(i!)}^2}.$$

With the help of (9), (8) can then be written simply as

$$A_0\left(T^{*},\tau \right)=B_0\left(T^{*}\right)-\sum _{k=1}^{\infty }{I}_k\left(T^{*}\right){\tau }^{2k}.$$ (10a)

The coefficients A_p for p ≠ 0 are somewhat more complicated due to the relaxation of the requirement that s = t = 0. This adds more terms to the summation $\sum _{[s,t]}^{*}$ in (4). Thus, for example, for p = 1, there is the requirement s + 2t = 1 which can only be satisfied for s = 1, t = 0 while for p = 2 there is the requirement s + 2t = 2 which can be met by both s = 2, t = 0 and s = 0, t = 1. After some laborious algebra, the following results are obtained for p ≠ 0:

$$\begin{gathered} A_p\left(T^{*},\tau \right)={\left(\frac{T^{*}}{4}\right)}^p\sum _{i=0}^{\infty }{\tau }^{(2i+p)}{I}_{i+p}\left(T^{*}\right) \\ \frac{{[(2i+2p+1)!]}^2}{2^{2i}{[(i+p)!]}^2{S}_p}\left(\sum _{i,s,t}^{*}{Q}_{2i,s,t}+\sum _{i,s,t}^{**}{Q}_{2i+1,s,t}\right) \end{gathered}$$

where

$$S_p=\sum _{j=0}^{i+p}\frac{(2j)!}{{(j!)}^2}.$$

Here $\sum ^{*}$ and $\sum ^{**}$ each indicate s + 2t = p with the former requiring t to be even in the sum and the latter t to be odd.

For convenience to the users of the tables, we choose now to define a set of coefficients α_ip through the relation

$$A_p\left(T^{*},\tau \right)={\left(T^{*}\right)}^p\sum _{i=0}^{\infty }{\alpha }_{ip}{\tau }^{2i+p}{I}_{i+p}\left(T^{*}\right).$$ (10b)

Specifically

$$\begin{array}{l}{\alpha }_{ip}\equiv \frac{4-(p+i){[(2i+2p+1)!]}^2}{[(i+p)!]S_p}\\ \left(\sum _{i,s,t}^{*}{Q}_{2i,s,t}+\sum _{i,s,t}^{**}{Q}_{2i+1,s,t}\right)\end{array}$$

Table 1 contains values of α_ip for p through 10, with, in each case, values of i running from 0 through 20. The adequacy of the number of coefficients presented in table 1 is discussed below in some detail.

Table 1.

i╲p	αip
	1	2	3	4	5
0	0.0000000	0.5500000 + 02	0.5141379 + 03	0.4120200 + 05	0.9707331 + 06
1	.3333333 + 01	.2505517 + 03	.4902545 + 04	.9966838 + 06	.4517405 + 08
2	.1158621 + 02	.7093636 + 03	.2273954 + 05	.8103094 + 07	.5670964 + 09
3	.2454545 + 02	.1607692 + 04	.7373551 + 05	.4047887 + 08	.3986518 + 10
4	.4174359 + 02	.3174600 + 04	.1926622 + 06	.1512202 + 09	.1978868 + 11
5	.6295059 + 02	.5687897 + 04	.4353661 + 06	.4639890 + 09	.7753931 + 11
6	.8810707 + 02	.9472656 + 04	.8857678 + 06	.1233316 + 10	.2556091 + 12
7	.1172156 + 03	.1490127 + 05	.1663803 + 07	.2937157 + 10	.7380649 + 12
8	.1502905 + 03	.2239381 + 05	.2934303 + 07	.6411564 + 10	.1918456 + 13
9	.1873439 + 03	.3241823 + 05	.4916837 + 07	.1303864 + 11	.4577321 + 13
10	.2283835 + 03	.4549046 + 05	.7896500 + 07	.2500028 + 11	.1017038 + 14
11	.2734141 + 03	.6217445 + 05	.1223568 + 08	.4561151 + 11	.2127683 + 14
12	.3224384 + 03	.8308218 + 05	.1838677 + 08	.7974850 + 11	.4227211 + 14
13	.3754584 + 03	.1088736 + 06	.2690586 + 08	.1343878 + 12	.8030724 + 14
14	.4324750 + 03	.1402568 + 06	.3846735 + 08	.2192745 + 12	.1466975 + 15
15	.4934892 + 03	.1779876 + 06	.5387958 + 08	.3477383 + 12	.2588470 + 15
16	.5585013 + 03	.2228701 + 06	.7410138 + 08	.5376780 + 12	.4428640 + 15
17	.6275119 + 03	.2757563 + 06	.1002596 + 09	.8127364 + 12	.7370506 + 15
18	.7005212 + 03	.3375462 + 06	.1336675 + 09	.1203687 + 13	.1196489 + 16
19	.7775295 + 03	.4091877 + 06	.1758444 + 09	.1750062 + 13	.1898981 + 16
20	.8585368 + 03	.4916769 + 06	.2285359 + 09	.2502037 + 13	.2952648 + 16
i╲p	6	7	8	9	10
0	0.1294197 + 09	0.7545577 + 10	0.8413075 + 12	0.6715625 + 14	0.1332794 + 17
1	.4053737 + 10	.2842242 + 12	.6556027 + 14	.8180735 + 16	.1272523 + 19
2	.5249590 + 11	.4324812 + 13	.1495321 + 16	.2490697 + 18	.4064630 + 20
3	.4167055 + 12	.3991419 + 14	.1848105 + 17	.3884674 + 19	.7041412 + 21
4	.2394359 + 13	.2646274 + 15	.1548148 + 18	.3973430 + 20	.8116767 + 22
5	.1090498 + 14	.1381173 + 16	.9849835 + 18	.3016918 + 21	.6958387 + 23
6	.4164352 + 14	.6004971 + 16	.5093509 + 19	.1829913 + 22	.4752964 + 24
7	.1384478 + 15	.2258767 + 17	.2237911 + 20	.9302205 + 22	.2709267 + 25
8	.4114908 + 15	.7550668 + 17	.8616638 + 20	.4097642 + 23	.1331826 + 26
9	.1114870 + 16	.2288022 + 18	.2973750 + 21	.1602723 + 23	.5785209 + 26
10	.2794339 + 16	.6380513 + 18	.9357272 + 21	.5669677 + 24	.2262244 + 27
11	.6553784 + 16	.1656904 + 19	.2720343 + 22	.1840128 + 25	.8080441 + 27
12	.1451445 + 17	.4044583 + 19	.7384036 + 22	.5541970 + 25	.2667265 + 128
13	.3057591 + 17	.9351958 + 19	.1887349 + 23	.1563154 + 26	.8213929 + 28
14	.6163506 + 17	.2061175 + 20	.4574366 + 23	.4160481 + 26	.2378431 + 29
15	.1194817 + 18	.4352991 + 20	.1057434 + 24	.1051535 + 27	.6518220 + 29
16	.2236701 + 18	.8847902 + 20	.2342845 + 24	.2537146 + 27	.1700086 + 30
17	.4057697 + 18	.1737424 + 21	.4995829 + 24	.5870413 + 27	.4240033 + 30
18	.7155269 + 18	.3306632 + 21	.1028951 + 25	.1307604 + 28	.1015292 + 31
19	.1229633 + 19	.6116365 + 21	.2053262 + 25	.2813350 + 28	.2342442 + 31
20	.2063989 + 19	.1102261 + 22	.3980369 + 25	.5863817 + 28	.5223271 + 31

2.3. Recursion Relations for the I_k(T*)

Recursion relations for the H_k(T*) have been published for the particular cases m = 12, [3], and m = 18, [10]. The generalization of these to include all of the (m, 6, 3) functions is

$$H_{6k}=\frac{T^{*}}{a}\left(\frac{6k-3-m}{m}\right)H_{6k-m}+\frac{6}{m}{H}_{6k-m+6}.$$ (11)

Using (11) and (9), recursion relations can be derived for the I_k(T*). To avoid confusion between the functional dependence on T* and the explicit appearance of T*, we shall not indicate the argument of the I_k in what follows.

$$\begin{gathered} I_k=\left(\frac{6k-3-m}{am}\right)\frac{F(k)}{F\left(k-\frac{m}{6}\right)}{\left(T^{*}\right)}^{\left(1-\frac{m}{3}\right)}{I}_{k-\frac{m}{6}} \\ +\frac{6}{m}\frac{F(k)}{F\left(k-\frac{m}{6}+1\right)}{\left(T^{*}\right)}^{\left(2-\frac{m}{3}\right)}{I}_{k-\frac{m}{6}+1} \end{gathered}$$

which, for later convenience, we shall write

$$I_k=K_1{T}^{*}{}^{\left(1-\frac{m}{3}\right)}{I}_{k-\frac{m}{6}}+K_2{T}^{*}{}^{\left(2-\frac{m}{3}\right)}{I}_{k-\frac{m}{6}+1}.$$ (12)

By applying this recursion relation to the $I_{k-\frac{m}{6}}$ and the $I_{k-\frac{m}{6}+1}$ in the right side of (12), it is possible to obtain a recursion relation for values of m which are odd multiples of three. This avoids the necessity for tables of the I_k for half integral multiples of k as would otherwise have been required, for example, for m = 9 with (12). The recursion relation obtained is

$$\begin{gathered} I_k=\left(\frac{6k-3-m^{\prime }}{am}\right)\left(\frac{6k-3-2m}{am}\right)\frac{F(k)}{F\left(k-\frac{m}{3}\right)}{T}^{*\left(2-\frac{2m}{3}\right)}{I}_{k-\frac{m}{3}} \\ +\frac{6}{m}\left(\frac{12k-3m}{am}\right)\frac{F(k)}{F\left(k-\frac{m}{3}+1\right)}{T}^{*}{}^{\left(3-\frac{2m}{3}\right)}{I}_{k-\frac{m}{3}+1} \\ +\frac{36}{m^2}\frac{F(k)}{F\left(k-\frac{m}{3}+2\right)}{T}^{*\left(4-\frac{2m}{3}\right)}{I}_{k-\frac{m}{3}+2} \end{gathered}$$

which, for later convenience, we shall write

$$I_k=K_1{T}^{*\left(2-\frac{2m}{3}\right)}{I}_{k-\frac{m}{3}}+K_2{T}^{*\left(3-\frac{2m}{3}\right)}{I}_{k-\frac{m}{3}+1}+K_3{T}^{*\left(4-\frac{2m}{3}\right)}{I}_{k-\frac{m}{3}+2}$$ (12a)

These relations makes it unnecessary to tabulate the functions I_k for values of k beyond $k=\frac{m}{6}$ for those potentials for which m is an exact multiple of 6 or for values of k beyond $k=\frac{m}{3}$ for those potentials for which m is an odd multiple of 3. For convenience in using (12), we have included in table 2, values of the coefficients K₁ and K₂ for 20 values of k for those values of m which are exact multiples of six along with values of the coefficients K₁, K₂, and K₃ for m = 9 for use with (12a).

Table 2.

Values of the coefficients for eq (12)

K	K1	K2
(12, 6) a = 4.000000
3	0.49319728 − 03	0.32879819 − 01
4	.51965231 − 03	.21072797 − 01
5	.38591246 − 03	.14650639 − 01
6	.27553766 − 03	.10746978 − 01
7	.19837657 − 03	.82039216 − 02
8	.14575616 − 03	.64605980 − 02
9	.10952479 − 03	.52162255 − 02
10	.84076210 − 04	.42981889 − 02
11	.65800490 − 04	.36020911 − 02
12	.52390291 − 04	.30619811 − 02
13	.42352551 − 04	.26346187 − 02
14	.34702435 − 04	.22907323 − 02
15	.28776600 − 04	.20099494 − 02
16	.24118928 − 04	.17777436 − 02
17	.20409609 − 04	.15835346 − 02
18	.17420300 − 04	.14194704 − 02
19	.14985220 − 04	.12796253 − 02
20	.12982149 − 04	.11594599 − 02
(18, 6) a = 2.5980762
4	0.21334855 − 04	0.92382632 − 03
5	.15628463 − 04	.41163991 − 03
6	.85137709 − 05	.20993346 − 03
7	.46403348 − 05	.11755649 − 03
8	.26309339 − 05	.70669652 − 04
9	.15607384 − 05	.44933248 − 04
10	.96637297 − 06	.29893763 − 04
11	.62169112 − 06	.20643291 − 04
12	.41359804 − 06	.14706047 − 04
13	.28334491 − 06	.10756203 − 04
14	.19915937 − 06	.80469414 − 05
15	.14318315 − 06	.61390079 − 05
16	.10501599 − 06	.47642327 − 05
17	.78402951 − 07	.37534913 − 05
18	.59471361 − 07	.29970408 − 05
19	.45759922 − 07	.24218537 − 05
20	.35666926 − 07	.19782322 − 05
(24, 6) a = 2.1165347
5	0.57552474 − 06	0.20301968 − 04
6	.30925759 − 06	.66358277 − 05
7	.12860599 − 06	.25834164 − 05
8	.55200089 − 07	.11392278 − 05
9	.25268767 − 07	.55294326 − 06
10	.12351888 − 07	.28969738 − 06
11	.64093976 − 08	.16152009 − 06
12	.35050556 − 08	.94814050 − 07
13	.20063837 − 08	.58117237 − 07
14	.11951090 − 08	.36959374 − 07
15	.73706131 − 09	.24260917 − 07
16	.46868253 − 09	.16370373 − 07
17	.30619686 − 09	.11316491 − 07
18	.20491630 − 09	.79919549 − 08
19	.14012268 − 09	.57526337 − 08
20	.97691942 − 10	.42120633 − 08
(36, 6) a = 1.7171629
7	0.16678404 − 09	0.47732562 − 08
8	.53876233 − 10	.93790327 − 09
9	.14245343 − 10	.23216258 − 09
10	.40678439 − 11	.68111613 − 10
11	.12858991 − 11	.22829137 − 10
12	.44778876 − 12	.85206064 − 11
13	.16994959 − 12	.34746859 − 11
14	.69529587 − 13	.15259262 − 11
15	.30363797 − 13	.71356436 − 12
16	.14036033 − 13	.35216612 − 12
17	.68199773 − 14	.18212628 − 12
18	.34627036 − 14	.98125349 − 13
19	.18280688 − 14	.54813772 − 13
20	.99930413 − 15	.31619886 − 13
(60, 6) a = 1.4350552
11	0.99962681 − 18	0.23908666 − 16
12	.15304192 − 18	.22265289 − 17
13	.20438429 − 19	.27837096 − 18
14	.31104820 − 20	.43525293 − 19
15	.54865676 − 21	.81403008 − 20
16	.11092608 − 21	.17639573 − 20
17	.25304070 − 22	.43235742 − 21
18	.64149301 − 23	.11765568 − 21
19	.17835120 − 23	.35027587 − 22
20	.53771351 − 24	.11274862 − 22

k	K1	K2	K3
(9, 6) a = 6.7500000
4	0.32441637 − 05	0.63869474 − 03	0.18731375 − 01
5	.35646803 − 05	.44721373 − 03	.13022790 − 01
6	.25891966 − 05	.31101253 − 03	.95528695 − 02
7	.17640155 − 05	.22059983 − 03	.72923747 − 02
8	.12001742 − 05	.16053353 − 03	.57427537 − 02
9	.83063691 − 06	.11982199 − 03	.46366449 − 02
10	.58778410 − 06	.91526584 − 04	.38206124 − 02
11	.42540270 − 06	.71359524 − 04	.32018588 − 02
12	.31445720 − 06	.56645513 − 04	.27217610 − 02
13	.23696881 − 06	.45680666 − 04	.23418832 − 02
14	.18170424 − 06	.37353703 − 04	.20362065 − 02
15	.14152017 − 06	.30922410 − 04	.17866217 − 02
16	.11178063 − 06	.25879783 − 04	.15802165 − 02
17	.89414252 − 07	.21872196 − 04	.14075863 − 02
18	.72345403 − 07	.18648254 − 04	.12617515 − 02
19	.59144896 − 07	.16026093 − 04	.11374447 − 02
20	.48811399 − 07	.13872048 − 04	.10306310 − 02

3. The First and Second Derivatives of B(T)

The first and second derivatives of the second virial coefficient are of considerable utility. These appear in expressions for the first density correction of the various thermodynamic functions (e.g., Joule-Thomson coefficient, specific heat, etc.).

According to (3) and (10), the derivatives of B with respect to temperature can be evaluated given expressions for the derivatives of the I_k(T*) with respect to the temperature. Thus,

$$T\frac{dB}{dT}=b_0{T}^{*}\frac{d{B}^{*}}{d{T}^{*}}=\sum _{p=0}^{\infty }{T}^{*}\frac{d{A}_p}{d{T}^{*}}{q}^p.$$ (13)

Where A_p depends on T* and τ. Now, according to (10b),

$$T^{*}\frac{d{A}_p}{d{T}^{*}}={\left(T^{*}\right)}^p\sum _{i=0}^{\infty }{\alpha }_{ip}{\tau }^{2i+p}\left[p{I}_{i+p}+T^{*}\frac{d{I}_{i+p}}{d{T}^{*}}\right]$$ (14a)

with the relation for p = 0 given by

$$T^{*}\frac{d{A}_0}{d{T}^{*}}=T^{*}\frac{d{B}_0^{*}}{d{T}^{*}}-\sum _{k=1}^{\infty }{T}^{*}\frac{d{I}_k}{d{T}^{*}}{\tau }^{2k}.$$ (14b)

The second derivative required is given by

$$T^2\frac{d^{2}B}{d{T}^2}=b_0{\left(T^{*}\right)}^2\frac{d^2{B}^{*}}{d{T}^{*2}}=b_0\sum _{p=0}^{\infty }{\left(T^{*}\right)}^2\frac{d^2{A}_p}{d{T}^{*2}}{q}^p$$ (15)

where

$$T^{*2}\frac{d^2{A}_p}{d{T}^{*2}}=T^{*p}\sum _{i=0}^{\infty }{\alpha }_{ip}{\tau }^{2i+p}[p(p-1)I_{i+p}+(p+1)T^{*}\frac{d{I}_{i+p}}{d{T}^{*}}+T^{*2}\frac{d^2{I}_{i+p}}{d{T}^{*2}}]$$ (16a)

with the relation for p = 0 given by

$$T^{*}\frac{d^2{A}_0^{*}}{d{T}^{*2}}=T^{*2}\frac{d^2{B}_0^{*}}{d{T}^{*2}}-\sum _{k=1}^{\infty }{T}^{*2}\frac{d^2{I}_k}{d{T}^{*2}}{\tau }^{2k}.$$ (16b)

Thus, given the first and second derivatives of the I_k(T*) integrals, the first and second derivatives of the second virial coefficient are easily evaluated.

It is clear from (9) that a knowledge of the temperature derivatives of the H_k(T*) is equivalent to a knowledge of such derivatives for the I_k(T*). Now, for a potential function made up of a sum of inverse powers of the intermolecular potential function, the derivatives of the H_k(T*) can be written in terms of the H_k(T*) themselves. Thus, according to (7) and reference [17], for the (m, 6) function,

$$\begin{array}{l}{T}^{*}\frac{d{H}_k}{d{T}^{*}}=\frac{a}{T^{*}}\left[H_{k+m}-H_{k+6}\right]-2H_k\\ T^{*2}\frac{d^2{H}_k}{d{T}^2}={\left(\frac{a}{T^{*}}\right)}^2\left\{H_{k+2m}+H_{k+12}-2H_{k+m+6}\right\}\\ -6\frac{a}{T^{*}}\left\{H_{k+m}-H_{k+6}\right\}+6H_k.\end{array}$$ (17)

On differentiating (9) and making use of (17) one easily obtains expressions for the derivatives of the I_k(T*) in terms of the I_k(T*) functions themselves. Thus

$$T^{*}\frac{d{I}_k}{d{T}^{*}}=-2k{I}_k+\left(\frac{a}{T^{*}}\right)\left[T^{*}\frac{m}{3}\frac{F(k)}{F{\left(k+\frac{m}{6}\right)}^{k+\frac{m}{6}}}-T^{*2}\frac{F(k)}{F(k+1)}{I}_{k+1}\right]$$ (18)

and

$$\begin{gathered} T^{*2}\frac{d^2{I}_k}{d{T}^{*2}}=2k(2k+1)I_k+(2+4k)\frac{a}{T^{*}} \\ \left[T^{*2}\frac{F(k)}{F(k+1)}{I}_{k+1}-T^{*}\frac{m}{3}\frac{F(k)}{F{\left(k+\frac{m}{6}\right)}^{\mathrm{I}}{}^{{}_{k+\frac{m}{6}}}}\right] \\ +{\left(\frac{a}{T^{*}}\right)}^2[T^{*2}\frac{m}{3}\frac{F(k)}{F{\left(k+\frac{m}{3}\right)}^{k+\frac{m}{3}}}{I}_{k+\frac{m}{3}}+T^{*4}\frac{F(k)}{F(k+2)}{I}_{k+2}-2T^{*}\left(\frac{m}{3}+2\right)\frac{F(k)}{F\left(k+\frac{m}{6}+1\right)}{I}_{k+\frac{m}{6}+1}] \end{gathered}$$ (19)

Obviously, the recursion relation (12), can be used to develop recursion relations for the derivatives using (18) and (19).

4. Numerical Methods

The integral which appears on the right-hand side of (7) is the basic quantity which needs to be evaluated numerically. An extensive number of such evaluations is required, however. In particular, one such integral needs to be calculated for each value of k, at each T* with the entire set of T* values being repeated for each potential function. An automatic method for testing the accuracy of the numerical procedure is clearly required.

The accuracy of numerical integration depends directly on the spacing of the grid of points used to represent the integrand numerically. This depends, in turn, on the rapidity with which the integrand varies as a function of its argument. The potential functions of interest vary rapidly with intermolecular distance for small distances. For large distances, they are characterized by a much slower dependence on distance. As a result, a grid of points which is adequate for small intermolecular separations becomes excessive for large separations. This behavior led us to choose to divide the overall integration range into more than one part and to attempt to optimize the grid spacing separately in each such part. We have, in fact, divided the total range into a total of five parts and, for flexibility, have defined the limits of each part in the input data.

A Gaussian integration scheme was employed in each integration segment with the number of points to be used also supplied in the input. This integration was actually performed, in each interval, at each temperature, both for the given number of integration points for that interval and for half that number of points. The two results were then compared and required to agree within a preassigned tolerance. When the tolerance was not satisfied in an interval at any temperature, the basic number of integration points was doubled and new integrations carried out in that interval at that temperature for both the new basic number of points and for half that number of points. A comparison was made between these two new results to the same tolerance. This procedure was continued until either a requirement that there be 128 points in the interval was reached or until the tolerance was satisfied, whichever came first. The ability to redefine the integration intervals guaranteed that the tolerance would always ultimately be satisfied. This occasionally required the use of quite small intervals for small r.

A second accuracy problem is that associated with the choice of a practical upper limit for the integral in (7). At large values of r the repulsive term in Ψ₀ will be small compared to the attractive term and can be neglected. Then, expanding the exponential in eq (7) we have

$$e^{-{\Psi }_0(r*)}=\left[1-\frac{a}{r^6}\cdot \mathrm{..}\right].$$

Clearly, for $r_f^{*}$ the second term on the right will be negligible to our desired accuracy and we can replace $e_0^{-\Psi }(r*)$ in eq (7) by unity. The integral can then be evaluated analytically from $r_f^{*}$ to infinity yielding $\left[{\left(r_f^{*}\right)}^{3-k}/(3-k)\right]$, independent of particular choice of the repulsive power in the potential function.

Once the integrals in (7) were evaluated as described, the functions I_k could be calculated using (9). The derivatives of the I_k were then obtained through the use of eqs (18) and (19). The ability to calculate these derivatives directly resulted in a sensitive check on the tabulated functions. This was accomplished by computing these same derivatives from the I_k by a numerical difference method and comparing the results with the directly calculated values. The result of such a comparison is described below.

5. The Tables, Their Use, Accuracy, and Adequacy

This paper contains sufficient information to allow the calculation of the first density correction to all of the thermodynamic properties of a fluid whose molecules are polarizable point dipoles imbedded in spherically symmetric bodies which, in the absence of the dipole moment, would interact with each other according to an (m, 6) force law. The main part of the paper consists of tables of second virial coefficients and their first and second derivatives for a spherically symmetric (m, 6) potential and of the functions I_k and their first and second derivatives for the corresponding potential. Tables are included for m = 9, 12, 18, 24, 36, and 60. These tables have been examined very carefully for errors and in order to estimate their accuracy and adequacy. The tables were differenced in order to flush out obvious errors, to produce an estimate of internal accuracy, and to determine a spacing of the temperature argument such that a third order interpolation formula might easily suffice at all temperatures. In this process the tables were found to have been calculated to an accuracy of at least one part in 10,000.

5.1. The Use of the Tables

The tables included in this paper are designed for the calculation of the second virial coefficient and its first two temperature derivatives for a molecular model which consists of a polarizable dipole imbedded in a spherical core. Inclusion of tables of these quantities for the central core potential allows these tables to be used for nondipolar molecules as well.

The tables are designed for use with eqs (3), (13), and (15). The left hand members of those equations refer to the quantities of interest at an experimental temperature T, with a dipole moment μ and a polarizability α. As will become clear below, the right-hand members of these equations can be calculated for a given experimental temperature, dipole moment and polarizability through the use of the tables included in this publication for particular choices of the intermolecular potential parameters ϵ/k and σ. It should be noted that where μ and/or α are not known, they can also be used as parameters. In most applications, the quantities calculated using eqs (3), (13), and (15) are to be compared with corresponding experimental quantities in order to establish “best” values for the unknown parameters ϵ/k and σ (and, on occasion either, or both, α and μ). Methods for doing this have been described [5, 8]. We shall consider the discussion of such methods to be outside the scope of this paper. We wish to point out, however, that methods generally used can be improved on considerably through the use of recently developed nonlinear search methods [18].

The purpose of the present section is to describe the way in which actual computations are to be carried out using tables 1–3. Equations (10a), (10b), (14a), (14b), (16a), and (16b) are the actual working equations associated with (3), (13), and (15). Each of these working equations contains the quantity α_ip along with appropriate combinations of the quantities I_i+p, $T^{*}\frac{d{I}_{i+p}}{d{T}^{*}}$ and $T^{*2}\frac{d^2{I}_{i+p}}{d{T}^{*2}}$.

Table 3.

Second virial coefficients, I_k integrals and their first and second derivatives for (m, 6, 3) potential function

T*	$B_0^{*}$	$T^{*}\frac{\partial B_0^{*}}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{B}_0^{*}}{\partial T^{*2}}$
.300	−35.02383	95.03544	−441.53292
.305	−33.49930	89.51898	−411.00451
.310	−32.08515	84.47750	−383.39190
.315	−30.77079	79.85993	−358.35783
.320	−29.54683	75.62140	−335.60807
.325	−28.40491	71.72246	−314.88603
.330	−27.33762	68.12842	−295.96795
.335	−26.33835	64.80877	−278.65859
.340	−25.40121	61.73662	−262.78743
.345	−24.52094	58.88826	−248.20528
.350	−23.69283	56.24269	−234.78135
.360	−22.17665	51.48757	−210.96160
.370	−20.82369	47.34560	−190.56018
.380	−19.61030	43.71629	−172.97251
.390	−18.51697	40.51853	−157.71741
.400	−17.52753	37.68635	−144.40919
.410	−16.56525	35.21820	−132.67749
.420	−15.80865	32.91327	−122.45387
.430	−15.06465	30.88332	−113.35011
.440	−14.36934	29.06873	−105.24893
.450	−13.73356	27.42187	−98.01626
.460	−13.14882	25.92441	−91.53557
.470	−12.60641	24.56175	−85.70413
.480	−12.10223	23.31776	−80.43915
.490	−11.63326	22.17792	−75.67087
.500	−11.19594	21.13078	−71.33917
.510	−10.78714	20.16642	−67.39226
.520	−10.40427	19.27607	−63.78611
.530	−10.04502	18.45213	−60.48263
.540	−9.70732	17.68794	−57.44885
.550	−9.38934	16.97768	−54.65614
.560	−9.08944	16.31621	−52.07950
.580	−8.53818	15.12204	−47.48972
.600	−8.04357	14.07499	−43.53455
.620	−7.59742	13.15092	−40.10097
.640	−7.19311	12.33052	−37.10002
.660	−6.82509	11.59815	−34.46082
.680	−6.48879	10.94106	−32.12645
.700	−6.18032	10.34878	−30.05075
.720	−5.89642	9.81260	−28.19598
.740	−5.63432	9.32527	−26.53105
.760	−5.39162	8.88069	−25.03020
.780	−5.16628	8.47371	−23.67190
.800	−4.95652	8.09995	−22.43807
.820	−4.76080	7.75565	−21.31342
.840	−4.57778	7.43760	−20.28496
.860	−4.40626	7.14301	−19.34161
.880	−4.24522	6.86948	−18.47383
.900	−4.09371	6.61488	−17.67341
.920	−3.95097	6.37741	−16.93328
.940	−3.81622	6.15543	−16.24721
.960	−3.68883	5.94753	−15.60982
.980	−3.56822	5.75244	−15.01638
1.000	−3.45387	5.56906	−14.46272
1.025	−3.31897	5.35484	−13.82190
1.050	−3.19241	5.15554	−13.22959
1.075	−3.07330	4.96978	−12.68253
1.100	−2.96105	4.79638	−12.17645
1.150	−2.75493	4.48175	−11.26809
1.200	−2.57017	4.20403	−10.47769
1.250	−2.40360	3.95717	−9.78448
1.300	−2.25283	3.73642	−9.17220
1.350	−2.11558	3.53788	−8.62791
1.400	−1.99024	3.35843	−8.14123
1.450	−1.87527	3.19547	−7.70376
1.500	−1.76949	3.04686	−7.30858
1.550	−1.67183	2.91081	−6.95003
1.600	−1.58142	2.78581	−6.62337
1.650	−1.49748	2.67057	−6.32463
1.700	−1.41936	2.56401	−6.05045
1.750	−1.34648	2.46520	−5.79800
1.800	−1.27833	2.37331	−5.56486
1.850	−1.21449	2.28767	−5.34893
1.900	−1.15455	2.20765	−5.14841
2.000	−1.04509	2.06243	−4.78756
2.100	−.94763	1.93410	−4.47204
2.200	−.86034	1.81990	−4.19395
2.300	−.78174	1.71763	−3.94708
2.400	−.71062	1.62551	−3.72651
2.500	−.64598	1.54211	−3.52832
2.600	−.58700	1.46626	−3.34928
2.700	−.53298	1.39697	−3.18678
2.800	−.48334	1.33343	−3.03865
2.900	−.43758	1.27495	−2.90307
3.000	−.39528	1.22097	−2.77853
3.100	−.35607	1.17096	−2.66375
3.200	−.31964	1.12453	−2.55761
3.300	−.28570	1.08128	−2.45921
3.400	−.25403	1.04092	−2.36771
3.500	−.22441	1.00315	−2.28242
3.600	−.19665	.96774	−2.20273
3.700	−.17059	.93447	−2.12811
3.800	−.14609	.90316	−2.05809
3.900	−.12302	.87363	−1.99227
4.000	−.10125	.84575	−1.93027
4.250	−.05192	.78242	−1.78999
4.500	−.00881	.72670	−1.66751
4.750	.01469	.67744	−1.55966
5.000	.06274	.63353	−1.46398
5.250	.09268	.59415	−1.37850
5.500	.11949	.55863	−1.30170
5.750	.14360	.52643	−1.23229
6.000	.16537	.49712	−1.16928
6.250	.18511	.47031	−1.11181
6.500	.20308	.44571	−1.05918
6.750	.21946	.42304	−1.01081
7.000	.23447	.40209	−.96620
7.250	.24823	.38268	−.92492
7.500	.26090	.36465	−.88662
7.750	.27258	.34784	−.85099
8.000	.28337	.33215	−.81775
8.250	.29337	.31746	−.78667
8.500	.30264	.30368	−.75756
9.000	.31927	.27855	−.70451
9.500	.33372	.25619	−.65739
10.000	.34634	.23619	−.61527
10.500	.35742	.21818	−.57740
11.000	.36719	.20189	−.54315
11.500	.37583	.18709	−.51204
12.000	.38351	.17358	−.48365
12.500	.39034	.16120	−.45765
13.000	.39643	.14982	−.43374
13.500	.40189	.13932	−.41168
14.000	.40678	.12961	−.39127
15.000	.41511	.11223	−.35470
16.000	.42186	.09713	−.32288
17.000	.42735	.08389	−.29496
18.000	.43180	.07220	−.27026
19.000	.43542	.06181	−.24825
20.000	.43835	.05252	−.22853
T*	Y	I1	$T^{*}\frac{\partial I_1}{\partial T^{*}}$
.300	4.74342	41.16584	−196.6320
.305	4.70438	38.05780	−179.7159
.310	4.66628	35.26002	−164.6504
.315	4.62910	32.73492	−151.1948
.320	4.59279	30.45021	−139.1444
.325	4.55733	28.37804	−128.3244
.330	4.52267	26.49430	−118.5846
.335	4.48879	24.77807	−109.7963
.340	4.45566	23.21113	−101.8481
.345	4.42326	21.77758	−94.64379
.350	4.39155	20.46349	−88.09971
.360	4.33013	18.14623	−76.71063
.370	4.27121	16.17794	−67.20218
.380	4.21464	14.49494	−59.20609
.390	4.16025	13.04697	−52.43624
.400	4.10792	11.79402	−46.66835
.410	4.05751	10.70397	−41.72505
.420	4.00892	9.750872	−37.46498
.430	3.96203	8.913570	−33.77462
.440	3.91675	8.174732	−30.56216
.450	3.87298	7.520055	−27.75283
.460	3.83065	6.937671	−25.28539
.470	3.78968	6.417676	−23.10936
.480	3.75000	5.951758	−21.18288
.490	3.71154	5.532912	−19.47109
.500	3.67423	5.155199	−17.94477
.510	3.63803	4.813568	−16.57935
.520	3.60288	4.503699	−15.35404
.530	3.56873	4.221884	−14.25118
.540	3.53553	3.964931	−13.25572
.550	3.50325	3.730076	−12.35479
.560	3.47183	3.514921	−11.53729
.580	3.41144	3.135627	−10.11571
.600	3.35410	2.813284	−8.928811
.620	3.29956	2.537263	−7.929473
.640	3.24760	2.299262	−7.081512
.660	3.19801	2.092730	−6.356843
.680	3.15063	1.912447	−5.733442
.700	3.10529	1.754215	−5.193872
.720	3.06186	1.614634	−4.724203
.740	3.02020	1.490923	−4.313216
.760	2.98020	1.380796	−3.951805
.780	2.94174	1.282359	−3.632523
.800	2.90474	1.194032	−3.349242
.820	2.86910	1.114493	−3.096885
.840	2.83473	1.042623	−2.871222
.860	2.80158	.9774777	−2.668707
.880	2.76956	.9182495	−2.486117
.900	2.73861	.8642490	−2.321627
.920	2.70868	.8148829	−2.172381
.940	2.67971	.7696391	−2.036773
.960	2.65165	.7280740	−1.913225
.980	2.62445	.6898014	−1.800376
1.000	2.59808	.6544843	−1.697048
1.025	2.56620	.6140476	−1.579734
1.050	2.53546	.5772706	−1.473997
1.075	2.50581	.5437257	−1.378386
1.100	2.47717	.5130462	−1.291669
1.150	2.42272	.4590593	−1.140851
1.200	2.37171	.4132469	−1.014767
1.250	2.32379	.3740391	−.9083500
1.300	2.27866	.3402245	−.8177530
1.350	2.23607	.3108563	−.7400177
1.400	2.19578	.2851868	−.6728405
1.450	2.15758	.2626185	−.6144066
$T^{*2}\frac{{\partial }^2{I}_1}{\partial T^{*2}}$	I2	$T^{*}\frac{\partial I_2}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_2}{\partial T^{*2}}$
1272.544	2.275951+01	−1.557715+02	1.297592+03
1152.507	2.033421+01	−1.380636+02	1.141989+03
1046.518	1.821655+01	−1.227242+02	1.008138+03
952.6499	1.636175+01	−1.093927+02	8.926015+02
869.2750	1.473235+01	−9.776955+01	7.925412+02
795.0145	1.329684+01	−8.760514+01	7.056078+02
728.6952	1.202868+01	−7.869042+01	6.298477+02
669.3161	1.090540+01	−7.084982+01	5.636304+02
616.0196	9.907907+00	−6.393529+01	5.055896+02
568.0693	9.019952+00	−5.782163+01	4.545768+02
524.8303	8.227641+00	−5.240254+01	4.096231+02
450.3649	6.883986+00	−4.329929+01	3.347364+02
389.0477	5.800208+00	−3.604769+01	2.757344+02
338.1643	4.918997+00	−3.022166+01	2.288290+02
295.6331	4.197100+00	−2.550351+01	1.912267+02
259.8423	3.601554+00	−2.165400+01	1.608452+02
229.5328	3.107005+00	−1.849120+01	1.361168+02
203.7127	2.693782+00	−1.587550+01	1.158503+02
181.5943	2.346502+00	−1.369889+01	9.913255+01
162.5475	2.053043+00	−1.187709+01	8.525746+01
146.0647	1.803782+00	−1.034388+01	7.367505+01
131.7342	1.591027+00	−9.046851+00	6.395361+01
119.2202	1.408594+00	−7.944222+00	5.575194+01
108.2469	1.251476+00	−7.002495+00	4.879854+01
98.58659	1.115600+00	−6.194639+00	4.287603+01
90.05044	9.976294−01	−5.498719+00	3.780930+01
82.48085	8.948223−01	−4.896834+00	3.345652+01
75.74570	8.049101−01	−4.374305+00	2.970214+01
69.73379	7.260080−01	−3.919029+00	2.645158+01
64.35104	6.565438−01	−3.520983+00	2.362701+01
59.51758	5.951994−01	−3.171829+00	2.116412+01
55.16529	5.408657−01	−2.864597+00	1.900947+01
47.67921	4.496239−01	−2.353440+00	1.545399+01
41.51735	3.768893−01	−1.950862+00	1.268357+01
36.39905	3.183399−01	−1.630494+00	1.050117+01
32.11181	2.707841−01	−1.373099+00	8.764601+00
28.49285	2.318351−01	−1.164463+00	7.369866+00
25.41612	1.996887−01	−9.939583−01	6.239977+00
22.78300	1.729660−01	−8.535507−01	5.317278+00
20.51564	1.506035−01	−7.371047−01	4.558132+00
18.55203	1.317726−01	−6.398894−01	3.929183+00
16.84237	1.158230−01	−5.582250−01	3.404695+00
15.34638	1.022399−01	−4.892244−01	2.964641+00
14.03120	9.061252−02	−4.306052−01	2.593305+00
12.86991	8.061122−02	−3.805494−01	2.278262+00
11.84026	7.196932−02	−3.375992−01	2.009619+00
10.92379	6.446993−02	−3.005775−01	1.779440+00
10.10442	5.793551−02	−2.685280−01	1.581324+00
9.371097	5.221998−02	−2.406698−01	1.410072+00
8.710998	4.720247−02	−2.163609−01	1.261439+00
8.115483	4.278246−02	−1.950712−01	1.131941+00
7.576656	3.887600−02	−1.763606−01	1.018699+00
7.087762	3.541260−02	−1.598621−01	9.193291−01
6.643000	3.233285−02	−1.452682−01	8.318416−01
6.141554	2.894680−02	−1.293139−01	7.366824−01
5.692978	2.600020−02	−1.155149−01	6.548271−01
5.290289	2.342580−02	−1.035297−01	5.841035−01
4.927597	2.116808−02	−9.307822−02	5.227419−01
4.302962	1.742620−02	−7.589308−02	4.225573−01
3.787273	1.448989−02	−6.254442−02	3.454438−01
3.357085	1.215793−02	−5.204352−02	2.852950−01
2.994839	1.028563−02	−4.368723−02	2.378099−01
2.687194	8.767360−03	−3.696740−02	1.999084−01
2.423887	7.524919−03	−3.151141−02	1.693509−01
2.196922	6.499647−03	−2.704232−02	1.444860−01
T*	Y	I1	$T^{*}\frac{\partial I_1}{\partial T^{*}}$
1.50	2.12132	.2426699	−.5632725
1.55	2.08683	.2249493	−.5182783
1.60	2.05396	.2091357	−.4784841
1.65	2.02260	.1949637	−.4431223
1.70	1.99263	.1822127	−.4115609
1.75	1.96396	.1706979	−.3832760
1.80	1.93649	.1602636	−.3578307
1.85	1.91014	.1507780	−.3348581
1.90	1.88484	.1421287	−.3140484
2.00	1.83712	.1269678	−.2779049
2.10	1.79284	.1141605	−.2477223
2.20	1.75162	.1032404	−.2222581
2.30	1.71312	.09385154	−.2005767
2.40	1.67705	.08571814	−.1819632
2.50	1.64317	.07862413	−.1658636
2.60	1.61126	.07239814	−.1518436
2.70	1.58114	.06690282	−.1395585
2.80	1.55265	.06202708	−.1287325
2.90	1.52564	.05768024	−.1191423
3.00	1.50000	.05378771	−.1106063
3.10	1.47561	.05028764	−.1029738
3.20	1.45237	.04712843	−.09612128
3.30	1.43019	.04426672	−.08994536
3.40	1.40900	.04166611	−.08435977
3.50	1.38873	.03929512	−.07929017
3.60	1.36931	.03712715	−.07467484
3.70	1.35068	.03513947	−.07046067
3.80	1.33278	.03331237	−.06660213
3.90	1.31559	.03162880	−.06305997
4.00	1.29904	.03007391	−.05980024
4.25	1.26025	.02666853	−.05270202
4.50	1.22474	.02382761	−.04682596
4.75	1.19208	.02143152	−.04190451
5.00	1.16189	.01939088	−.03773977
5.25	1.13389	.01763784	−.03418276
5.50	1.10782	.01612008	−.03111962
5.75	1.08347	.01479675	−.02846206
6.00	1.06066	.01363555	−.02614074
6.25	1.03923	.01261066	−.02410064
6.50	1.01905	.01170126	−.02229759
6.75	1.00000	.01089036	−.02069581
7.00	.98198	.01016403	−.01926605
7.25	.96490	.009510715	−.01798425
7.50	.94868	.008920805	−.01683041
7.75	.93326	.008386222	−.01578783
8.00	.91856	.007900147	−.01484246
8.25	.90453	.007456790	−.01398243
8.50	.89113	.007051205	−.01319761
9.00	.86603	.006336966	−.01182029
9.50	.84293	.005729951	−.01065476
10.00	.82158	.005209400	−.009659161
10.50	.80178	.004759386	−.008801569
11.00	.78335	.004367513	−.008057256
11.50	.76613	.004024020	−.007406837
12.00	.75000	.003721126	−.006834932
12.50	.73485	.003452570	−.006329209
13.00	.72058	.003213261	−.005879683
13.50	.70711	.002999028	−.005478200
14.00	.69437	.002806424	−.005118042
15.00	.67082	.002475095	−.004500329
16.00	.64952	.002201394	−.003991941
17.00	.63013	.001972476	−.003568156
18.00	.61237	.001778920	−.003210915
19.00	.59604	.001613677	−.002906770
20.00	.58095	.001471387	−.002645533
$T^{*2}\frac{{\partial }^2{I}_1}{\partial T^{*2}}$	I2	$T^{*}\frac{\partial I_2}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_2}{\partial T^{*2}}$
2.000004	5.647029−03	−2.335172−02	1.240807−01
1.828130	4.932911−03	−2.028102−02	1.072031−01
1.677280	4.330820−03	−1.770824−02	9.314162−02
1.544204	3.820048−03	−1.553865−02	8.134685−02
1.426246	3.384251−03	−1.369799−02	7.139100−02
1.321226	3.010423−03	−1.212758−02	6.293788−02
1.227338	2.688138−03	−1.078065−02	5.572116−02
1.143076	2.408979−03	−9.619685−03	4.952818−02
1.067181	2.166100−03	−8.614351−03	4.418797−02
.9364011	1.767786−03	−6.976355−03	3.553787−02
.8282741	1.459170−03	−5.717743−03	2.894065−02
.7378838	1.216743−03	−4.736638−03	2.383335−02
.6615707	1.023941−03	−3.961903−03	1.982607−02
.5965679	8.688800−04	−3.342941−03	1.664346−02
.5407526	7.428988−04	−2.843158−03	1.408786−02
.4924767	6.395899−04	−2.435703−03	1.201521−02
.4504420	5.541501−04	−2.100537−03	1.031853−02
.4136189	4.829345−04	−1.822595−03	8.917958−03
.3811807	4.231483−04	−1.590371−03	7.752812−03
.3524601	3.726239−04	−1.395025−03	6.776655−03
.3269058	3.296524−04	−1.229594−03	5.953192−03
.3040700	2.928983−04	−1.088675−03	5.254311−03
.2835797	2.612927−04	−9.679661−04	4.657740−03
.2651252	2.339778−04	−8.640292−04	4.145757−03
.2484422	2.102598−04	−7.740966−04	3.704153−03
.2333116	1.895740−04	−6.959248−04	3.321454−03
.2195458	1.714579−04	−6.276832−04	2.988330−03
.2069848	1.555299−04	−5.678688−04	2.697145−03
.1954916	1.414742−04	−5.152404−04	2.441618−03
.1849478	1.290273−04	−4.687674−04	2.216548−03
.1621037	1.035855−04	−3.742048−04	1.760427−03
.1433204	8.430543−05	−3.029863−04	1.418802−03
.1276847	6.944910−05	−2.484175−04	1.158359−03
.1145267	5.783074−05	−2.059623−04	9.566670−04
.1033459	4.862338−05	−1.724775−04	7.982664−04
.09376251	4.123947−05	−1.457423−04	6.722922−04
.08548385	3.525382−05	−1.241585−04	5.709620−04
.07828154	3.035400−05	−1.065575−04	4.886108−04
.07197523	2.630713−05	−9.207226−05	4.210531−04
.06642095	2.293736−05	−8.005091−05	3.651536−04
.06150264	2.011027−05	−6.999722−05	3.185346−04
.05712584	1.772199−05	−6.152920−05	2.793718−04
.05321312	1.569148−05	−5.434982−05	2.462513−04
.04970045	1.395486−05	−4.822581−05	2.180661−04
.04653451	1.246136−05	−4.297238−05	1.939416−04
.04367064	1.117033−05	−3.844194−05	1.731812−04
.04107117	1.004892−05	−3.451569−05	1.552257−04
.03870416	9.070452−06	−3.109731−05	1.396229−04
.03456247	7.458836−06	−2.548375−05	1.140683−04
.03107067	6.202596−06	−2.112461−05	9.429075−05
.02809808	5.209746−06	−1.769142−05	7.876232−05
.02554548	4.415287−06	−1.495307−05	6.641197−05
.02333638	3.772447−06	−1.274393−05	5.647469−05
.02141107	3.247012−06	−1.094326−05	4.839469−05
.01972232	2.813576−06	−9.461710−06	4.176188−05
.01823240	2.453016−06	−8.232255−06	3.626946−05
.01691087	2.150762−06	−7.203960−06	3.168493−05
.01573294	1.895584−06	−6.337682−06	2.783004−05
.01467824	1.678735−06	−5.603014−06	2.456665−05
.01287392	1.333937−06	−4.438076−06	1.940454−05
.01139362	1.076507−06	−3.571325−06	1.557546−05
.01016317	8.806125−07	−2.913825−06	1.267880−05
.009128588	7.290302−07	−2.406506−06	1.044939−05
.008249831	6.099869−07	−2.009132−06	8.707139−06
.007496661	5.152557−07	−1.693675−06	7.326975−06
T*	I3	$T^{*}\frac{\partial I_3}{\partial T^{*}}$	$T^{{*}_2}\frac{{\partial }^2{I}_3}{\partial T^{*2}}$
.300	8.523708+00	−7.423520+01	7.500989+02
.305	7.384336+00	−6.389539+01	6.417862+02
.310	6.418004+00	−5.518305+01	5.510661+02
.315	5.595476+00	−4.781441+01	4.747840+02
.320	4.892929+00	−4.155968+01	4.104013+02
.325	4.290866+00	−3.623205+01	3.558658+02
.330	3.773263+00	−3.167892+01	3.095109+02
.335	3.326903+00	−2.777519+01	2.699780+02
.340	2.940837+00	−2.441788+01	2.361546+02
.345	2.605969+00	−2.152190+01	2.071264+02
.350	2.314707+00	−1.901665+01	1.821392+02
.360	1.838617+00	−1.495314+01	1.418950+02
.370	1.472943+00	−1.186365+01	1.115810+02
.380	1.189416+00	−9.491467+00	8.851227+01
.390	9.676377−01	−7.653213+00	7.078841+01
.400	7.927207−01	−6.216368+00	5.704846+01
.410	6.536890−01	−5.084142+00	4.630692+01
.420	5.423714−01	−4.185131+00	3.784270+01
.430	4.526288−01	−3.466154+00	3.112310+01
.440	3.798089−01	−2.887251+00	2.575083+01
.450	3.203574−01	−2.418140+00	2.142711+01
.460	2.715377−01	−2.035688+00	1.792533+01
.470	2.312277−01	−1.722094+00	1.507228+01
.480	1.977701−01	−1.463555+00	1.273460+01
.490	1.698621−01	−1.249303+00	1.080889+01
.500	1.464733−01	−1.070874+00	9.214423+00
.510	1.267839−01	−9.215833−01	7.887792+00
.520	1.101376−01	−7.961128−01	6.778880+00
.530	9.600659−02	−6.902125−01	5.847853+00
.540	8.396407−02	−6.004658−01	5.062871+00
.550	7.366304−02	−5.241127−01	4.398350+00
.560	6.482022−02	−4.589126−01	3.833631+00
.580	5.062072−02	−3.549909−01	2.939638+00
.600	3.995235−02	−2.776671−01	2.280355+00
.620	3.184152−02	−2.194189−01	1.787893+00
.640	2.560730−02	−1.750372−01	1.415663+00
.660	2.076666−02	−1.408617−01	1.131211+00
.680	1.697253−02	−1.142858−01	9.116147−01
.700	1.397246−02	−9.342996−02	7.404734−01
.720	1.158077−02	−7.692287−02	6.059114−01
.740	9.659428−03	−6.375315−02	4.992326−01
.760	8.104817−03	−5.316729−02	4.140022−01
.780	6.838434−03	−4.459845−02	3.454114−01
.800	5.800278−03	−3.761640−02	2.898331−01
.820	4.944119−03	−3.189183−02	2.445081−01
.840	4.234059−03	−2.717066−02	2.073197−01
.860	3.642019−03	−2.325539−02	1.766319−01
.880	3.145885−03	−1.999137−02	1.511704−01
.900	2.728128−03	−1.725671−02	1.299364−01
.920	2.374765−03	−1.495473−02	1.121412−01
.940	2.074578−03	−1.300827−02	9.715880−02
.960	1.818516−03	−1.135539−02	8.448876−02
.980	1.599236−03	−9.946105−03	7.372917−02
1.000	1.410754−03	−8.739846−03	6.455533−02
1.025	1.211075−03	−7.467739−03	5.492115−02
1.050	1.044202−03	−6.409839−03	4.694536−02
1.075	9.040446−04	−5.525498−03	4.030698−02
1.100	7.857674−04	−4.782598−03	3.475365−02
1.150	6.001468−04	−3.624074−03	2.614369−02
1.200	4.645734−04	−2.784819−03	1.995335−02
1.250	3.640391−04	−2.167218−03	1.542991−02
1.300	2.884509−04	−1.706184−03	1.207539−02
1.350	2.308963−04	−1.357498−03	9.554010−03
1.400	1.865624−04	−1.090605−03	7.635304−03
1.450	1.520459−04	−8.840533−04	6.158546−03
1.500	1.249069−04	−7.225655−04	5.009967−03
1.550	1.033730−04	−5.951148−04	4.107934−03
1.600	8.614117−05	−4.936434−04	3.393121−03
1.650	7.224271−05	−4.121957−04	2.821909−03
1.700	6.094996−05	−3.463217−04	2.361872−03
1.750	5.171100−05	−2.926641−04	1.988658−03
1.800	4.410336−05	−2.486655−04	1.683804−03
1.850	3.780092−05	−2.123612−04	1.433186−03
1.900	3.254987−05	−1.822291−04	1.225909−03
2.000	2.444793−05	−1.359828−04	9.093255−04
2.100	1.865255−05	−1.031267−04	6.858086−04
2.200	1.443269−05	−7.935276−05	5.250091−04
2.300	1.131041−05	−6.186537−05	4.073648−04
2.400	8.966457−06	−4.880821−05	3.199616−04
2.500	7.183423−06	−3.892611−05	2.541205−04
2.600	5.810765−06	−3.135472−05	2.038942−04
2.700	4.742128−06	−2.548622−05	1.651252−04
2.800	3.901650−06	−2.089037−05	1.348811−04
2.900	3.234411−06	−1.725635−05	1.110539−04
3.000	2.700075−06	−1.435711−05	9.211023−05
3.100	2.268695−06	−1.202486−05	7.692120−05
3.200	1.917806−06	−1.013421−05	6.464645−05
3.300	1.630378−06	−8.590496−06	5.465377−05
3.400	1.393381−06	−7.321550−06	4.646287−05
3.500	1.196760−06	−6.271879−06	3.970560−05
3.600	1.032692−06	−5.398444−06	3.409730−05
3.700	8.950390−07	−4.667604−06	2.941614−05
3.800	7.789555−07	−4.052864−06	2.548790−05
3.900	6.805864−07	−3.533219−06	2.217483−05
4.000	5.968460−07	−3.091899−06	1.936723−05
4.250	4.363235−07	−2.249111−06	1.402403−05
4.500	3.251938−07	−1.668682−06	1.036167−05
4.750	2.465496−07	−1.259876−06	7.793433−06
5.000	1.897974−07	−9.661575−07	5.955586−06
5.250	1.481218−07	−7.513373−07	4.616379−06
5.500	1.170329−07	−5.916871−07	3.624510−06
5.750	9.350976−08	−4.713092−07	2.879009−06
6.000	7.547982−08	−3.793425−07	2.311150−06
6.250	6.149659−08	−3.082342−07	1.873304−06
6.500	5.053413−08	−2.526466−07	1.531920−06
6.750	4.185416−08	−2.087514−07	1.263005−06
7.000	3.491825−08	−1.737651−07	1.049165−06
7.250	2.932881−08	−1.456385−07	8.776283−07
7.500	2.478890−08	−1.228452−07	7.389070−07
7.750	2.107438−08	−1.042362−07	6.258747−07
8.000	1.801437−08	−8.893771−08	5.331248−07
8.250	1.547741−08	−7.627908−08	4.565164−07
8.500	1.336150−08	−6.574104−08	3.928501−07
9.000	1.009045−08	−4.949180−08	2.949086−07
9.500	7.742942−09	−3.786869−08	2.250603−07
10.000	6.027027−09	−2.939845−08	1.742991−07
10.500	4.751976−09	−2.312206−08	1.367810−07
11.000	3.790373−09	−1.840091−08	1.086263−07
11.500	3.055363−09	−1.480101−08	8.720551−08
12.000	2.486647−09	−1.202188−08	7.070253−08
12.500	2.041663−09	−9.852006−09	5.784234−08
13.000	1.689908−09	−8.140175−09	4.771522−08
13.500	1.409217−09	−6.776753−09	3.966305−08
14.000	1.183274−09	−5.681219−09	3.320343−08
15.000	8.500320−10	−4.069306−09	2.371978−08
16.000	6.243580−10	−2.981041−09	1.733471−08
17.000	4.676023−10	−2.227216−09	1.292298−08
18.000	3.562639−10	−1.693155−09	9.804561−09
19.000	2.756077−10	−1.307167−09	7.555499−09
20.000	2.161412−10	−1.023196−09	5.904069−09
T*	$B_0^{*}$	$T^{*}\frac{\partial B_0^{*}}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{B}_0^{*}}{\partial T^{*2}}$
.300	−27.88058	76.60725	−356.87677
.305	−26.65829	72.17876	−332.37589
.310	−25.51878	68.10205	−310.01275
.315	−24.45686	64.35313	−289.63388
.320	−23.46734	60.90802	−271.08578
.325	−22.54504	57.74275	−254.21500
.330	−21.68477	54.83334	−238.86804
.335	−20.88134	52.15582	−224.89144
.340	−20.12957	49.68620	−212.13170
.345	−19.41961	47.37721	−200.27843
.350	−18.75279	45.23749	−189.39784
.360	−17.53534	41.40722	−170.19200
.370	−16.44618	38.05678	−153.64931
.380	−15.47213	35.13298	−139.46209
.390	−14.59278	32.54850	−127.10256
.400	−13.79883	30.26708	−116.36602
.410	−13.07640	28.23177	−106.91833
.420	−12.41877	26.41727	−98.62002
.430	−11.81624	24.78531	−91.25262
.440	−11.26387	23.31785	−84.71897
.450	−10.75472	21.98847	−78.87212
.460	−10.28508	20.78407	−73.64303
.470	−9.84986	19.68598	−68.93034
.480	−9.44623	18.68450	−64.68407
.490	−9.07046	17.76639	−60.83397
.500	−8.72020	16.92369	−57.33951
.510	−8.39283	16.14750	−54.15482
.520	−8.08631	15.43102	−51.24558
.530	−7.79875	14.76810	−48.58097
.540	−7.52850	14.15338	−46.13431
.550	−7.27408	13.58215	−43.88243
.560	−7.03419	13.05026	−41.80512
.580	−6.59336	12.09027	−38.10566
.600	−6.19797	11.24885	−34.90536
.620	−5.84148	10.50651	−32.13996
.640	−5.51852	9.84766	−29.72374
.660	−5.22466	9.25970	−27.59943
.680	−4.95620	8.73234	−25.72102
.700	−4.71004	8.25712	−24.05124
.720	−4.48356	7.82704	−22.55959
.740	−4.27452	7.43624	−21.22100
.760	−4.08101	7.07983	−20.01463
.780	−3.90139	6.75364	−18.92313
.800	−3.73423	6.45414	−17.93190
.820	−3.57830	6.17832	−17.02860
.840	−3.43251	5.92358	−16.20277
.860	−3.29592	5.68769	−15.44544
.880	−3.16771	5.46870	−14.74896
.900	−3.04712	5.26492	−14.10668
.920	−2.93350	5.07487	−13.51289
.940	−2.82629	4.89727	−12.96260
.960	−2.72495	4.73095	−12.45146
.980	−2.62902	4.57491	−11.97566
1.000	−2.53808	4.42826	−11.53185
1.025	−2.43087	4.25694	−11.01760
1.050	−2.33022	4.09767	−10.54370
1.075	−2.23556	3.94925	−10.10581
1.100	−2.14638	3.81064	−9.70016
1.150	−1.98265	3.55930	−8.97290
1.200	−1.83595	3.33749	−8.34033
1.250	−1.70378	3.14041	−7.78576
1.300	−1.58411	2.96421	−7.29612
1.350	−1.47526	2.80578	−6.86099
1.400	−1.37585	2.66262	−6.47205
1.450	−1.28472	2.53265	−6.12254
1.500	−1.20088	2.41414	−5.80691
1.550	−1.12352	2.30567	−5.52061
1.600	−1.05191	2.20602	−5.25985
1.650	−.98545	2.11418	−5.02143
1.700	−.92362	2.02926	−4.80267
1.750	−.86594	1.95053	−4.60129
1.800	−.81203	1.87733	−4.41535
1.850	−.76154	1.80911	−4.24317
1.900	−.71415	1.74537	−4.08331
2.000	−.62763	1.62972	−3.79571
2.100	−.55063	1.52755	−3.54433
2.200	−.48171	1.43663	−3.32284
2.300	−.41968	1.35522	−3.12626
2.400	−.36358	1.28190	−2.95068
2.500	−.31261	1.21553	−2.79294
2.600	−.26613	1.15517	−2.65048
2.700	−.22359	1.10004	−2.52120
2.800	−.18451	1.04948	−2.40337
2.900	−.14850	1.00296	−2.29555
3.000	−.11523	.96000	−2.19653
3.100	−.08441	.92022	−2.10527
3.200	−.05579	.88328	−2.02090
3.300	−.02914	.84887	−1.94268
3.400	−.00428	.81676	−1.86996
3.500	.01896	.78671	−1.80218
3.600	.04072	.75854	−1.73886
3.700	.06114	.73208	−1.67957
3.800	.08033	.70716	−1.62395
3.900	.09839	.68367	−1.57165
4.000	.11542	.66148	−1.52240
4.250	.15397	.61105	−1.41097
4.500	.18762	.56675	−1.31370
4.750	.21719	.52755	−1.22806
5.000	.24334	.49260	−1.15207
5.250	.26660	.46124	−1.08420
5.500	.28739	.43296	−1.02321
5.750	.30607	.40732	−.96810
6.000	.32290	.38397	−.91806
6.250	.33814	.36262	−.87242
6.500	.35197	.34301	−.83063
6.750	.36457	.32495	−.79221
7.000	.37609	.30826	−.75679
7.250	.38663	.29278	−.72400
7.500	.39631	.27840	−.69358
7.750	.40522	.26500	−.66528
8.000	.41343	.25248	−.63888
8.250	.42102	.24076	−.61419
8.500	.42804	.22977	−.59106
9.000	.44060	.20970	−.54890
9.500	.45145	.19185	−.51146
10.000	.46088	.17587	−.47798
10.500	.46910	.16148	−.44786
11.000	.47631	.14845	−.42063
11.500	.48264	.13661	−.39588
12.000	.48822	.12580	−.37330
12.500	.49316	.11589	−.35260
13.000	.49752	.10678	−.33358
13.500	.50139	.09837	−.31601
14.000	.50483	.09059	−.29976
15.000	.51059	.07665	−.27063
16.000	.51514	.06453	−.24528
17.000	.51873	.05390	−.22301
18.000	.52154	.04450	−.20331
19.000	.52371	.03614	−.18575
20.000	.52537	.02866	−.17000
T*	Y	I1	$T^{*}\frac{\partial I_1}{\partial T^{*}}$
.300	3.65148	38.68728	−183.7527
.305	3.62143	35.78234	−168.0008
.310	3.59211	33.16651	−153.9687
.315	3.56348	30.80484	−141.4332
.320	3.53553	28.66728	−130.2041
.325	3.50823	26.72794	−120.1191
.330	3.48155	24.96436	−111.0389
.335	3.45547	23.35707	−102.8438
.340	3.42997	21.88912	−95.43027
.345	3.40503	20.54569	−88.70898
.350	3.38062	19.31380	−82.60223
.360	3.33333	17.14046	−71.97054
.370	3.28798	15.29321	−63.09020
.380	3.24443	13.71270	−55.61877
.390	3.20256	12.35204	−49.29015
.400	3.16228	11.17390	−43.89564
.410	3.12348	10.14831	−39.27017
.420	3.08607	9.251022	−35.28215
.430	3.04997	8.462273	−31.82584
.440	3.01511	7.765863	−28.81573
.450	2.98142	7.148420	−26.18215
.460	2.94884	6.598842	−23.86802
.470	2.91730	6.107858	−21.82626
.480	2.88675	5.667690	−20.01784
.490	2.85714	5.271774	−18.41024
.500	2.82843	4.914546	−16.97618
.510	2.80056	4.591271	−15.69273
.520	2.77350	4.297897	−14.54047
.530	2.74721	4.030948	−13.50291
.540	2.72166	3.787426	−12.56600
.550	2.69680	3.564737	−11.71769
.560	2.67261	3.360629	−10.94762
.580	2.62613	3.000556	−9.607687
.600	2.58199	2.694265	−8.488049
.620	2.54000	2.431758	−7.544586
.640	2.50000	2.205217	−6.743408
.660	2.46183	2.008468	−6.058196
.680	2.42536	1.836589	−5.468297
.700	2.39046	1.685620	−4.957351
.720	2.35702	1.552348	−4.512280
.740	2.32495	1.434147	−4.122547
.760	2.29416	1.328854	−3.779593
.780	2.26455	1.234677	−3.476416
.800	2.23607	1.150121	−3.207251
.820	2.20863	1.073932	−2.967317
.840	2.18218	1.005050	−2.752632
.860	2.15666	.9425787	−2.559853
.880	2.13201	.8857519	−2.386164
.900	2.10819	.8339146	−2.229178
.920	2.08514	.7865031	−2.086864
.940	2.06284	.7430306	−1.957487
.960	2.04124	.7030748	−1.839553
.980	2.02031	.6662683	−1.731776
1.000	2.00000	.6322901	−1.633045
1.025	1.97546	.5933692	−1.520887
1.050	1.95180	.5579540	−1.419739
1.075	1.92897	.5256370	−1.328225
1.100	1.90693	.4960679	−1.245179
1.150	1.86501	.4440044	−1.100633
1.200	1.82574	.3997919	−.9796721
1.250	1.78885	.3619283	−.8774831
1.300	1.75412	.3292536	−.7904098
1.350	1.72133	.3008603	−.7156370
1.400	1.69031	.2760308	−.6509703
1.450	1.66091	.2541916	−.5946797
$T^{*2}\frac{{\partial }^2{I}_1}{\partial T^{*2}}$	I2	$T^{*}\frac{\partial I_2}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_2}{\partial T^{*2}}$
1185.505	2.320998+01	−1.592469+02	1.328510+03
1073.954	2.073082+01	−1.411148+02	1.169009+03
975.4404	1.856657+01	−1.254104+02	1.031822+03
888.1764	1.667137+01	−1.117638+02	9.134210+02
810.6532	1.500682+01	−9.986779+01	8.108927+02
741.5921	1.354066+01	−8.946640+01	7.218267+02
679.9048	1.224569+01	−8.034528+01	6.442180+02
624.6628	1.109891+01	−7.232441+01	5.763935+02
575.0705	1.008076+01	−6.525204+01	5.169516+02
530.4446	9.174612+00	−5.899982+01	4.647142+02
490.1960	8.366242+00	−5.345879+01	4.186873+02
420.8617	6.995789+00	−4.415291+01	3.420272+02
363.7485	5.890877+00	−3.674230+01	2.816437+02
316.3363	4.992877+00	−3.079045+01	2.336525+02
276.6918	4.257551+00	−2.597199+01	1.951898+02
243.3179	3.651197+00	−2.204193+01	1.641214+02
215.0448	3.147896+00	−1.881402+01	1.388405+02
190.9506	2.727551+00	−1.614536+01	1.181268+02
170.3031	2.374446+00	−1.392542+01	1.010446+02
152.5163	2.076201+00	−1.206798+01	8.687082+01
137.1184	1.822989+00	−1.050531+01	7.504226+01
123.7262	1.606963+00	−9.183809+00	6.511692+01
112.0273	1.421809+00	−8.060755+00	5.674547+01
101.7650	1.262423+00	−7.101914+00	4.965006+01
92.72740	1.124649+00	−6.279659+00	4.360824+01
84.73860	1.005087+00	−5.571579+00	3.844086+01
77.65182	9.009415−01	−4.959391+00	3.400282+01
71.34402	8.099015−01	−4.428101+00	3.017596+01
65.71155	7.300475−01	−3.965354+00	2.686356+01
60.66677	6.597785−01	−3.560919+00	2.398606+01
56.13518	5.977527−01	−3.206283+00	2.147770+01
52.05327	5.428416−01	−2.894339+00	1.928390+01
45.02867	4.506947−01	−2.375611+00	1.566528+01
39.24266	3.773085−01	−1.967361+00	1.284726+01
34.43328	3.182912−01	−1.642711+00	1.062862+01
30.40210	2.704012−01	−1.382063+00	8.864209+00
26.99702	2.312161−01	−1.170942+00	7.447924+00
24.10023	1.989058−01	−9.985304−01	6.301235+00
21.61951	1.720728−01	−8.566553−01	5.365353+00
19.48203	1.496393−01	−7.390774−01	4.595806+00
17.62974	1.307668−01	−6.409884−01	3.958608+00
16.01601	1.147972−01	−5.586497−01	3.427550+00
14.60310	1.012101−01	−4.891299−01	2.982240+00
13.36024	8.959036−02	−4.301126−01	2.606689+00
12.26215	7.960512−02	−3.797535−01	2.288256+00
11.28798	7.098529−02	−3.365743−01	2.016880+00
10.42040	6.351211−02	−2.993823−01	1.784495+00
9.644915	5.700666−02	−2.672088−01	1.584598+00
8.949357	5.132182−02	−2.392630−01	1.411907+00
8.323455	4.633591−02	−2.148953−01	1.262113+00
7.758495	4.194785−02	−1.935696−01	1.131679+00
7.247052	3.807322−02	−1.748409−01	1.017686+00
6.782769	3.464122−02	−1.583383−01	9.177154−01
6.360189	3.159221−02	−1.437512−01	8.297506−01
5.883492	2.824339−02	−1.278172−01	7.341346−01
5.456804	2.533251−02	−1.140481−01	6.519464−01
5.073541	2.279221−02	−1.020995−01	5.809870−01
4.728151	2.056690−02	−9.168922−02	5.194655−01
4.132834	1.688481−02	−7.459403−02	4.191269−01
3.640834	1.400182−02	−6.133860−02	3.420066−01
3.229995	1.171721−02	−5.092922−02	2.819392−01
2.883713	9.886898−02	−4.266010−02	2.345864−01
2.589360	8.405848−03	−3.602178−02	1.968444−01
2.337212	7.196417−03	−3.064113−02	1.664585−01
2.119686	6.200460−03	−2.624117−02	1.417682−01
T*	Y	I1	$T^{*}\frac{\partial I_1}{\partial T^{*}}$
1.50	1.63299	.2348799	−.5453879
1.55	1.60644	.2177192	−.5019873
1.60	1.58114	.2024004	−.4635799
1.65	1.55700	.1886680	−.4294314
1.70	1.53393	.1763096	−.3989370
1.75	1.51186	.1651468	−.3715950
1.80	1.49071	.1550296	−.3469866
1.85	1.47043	.1458307	−.3247600
1.90	1.45095	.1374417	−.3046180
2.00	1.41421	.1227345	−.2696149
2.10	1.38013	.1103084	−.2403650
2.20	1.34840	.09971227	−.2156733
2.30	1.31876	.09060140	−.1946388
2.40	1.29099	.08270886	−.1765725
2.50	1.26491	.07582523	−.1609402
2.60	1.24035	.06978434	−.1473224
2.70	1.21716	.06445300	−.1353863
2.80	1.19523	.05972342	−.1248652
2.90	1.17444	.05550756	−.1155430
3.00	1.15470	.05173303	−.1072437
3.10	1.13592	.04833977	−.09982207
3.20	1.11803	.04527763	−.09315812
3.30	1.10096	.04250452	−.08715157
3.40	1.08465	.03998481	−.08171823
3.50	1.06904	.03768826	−.07678701
3.60	1.05409	.03558902	−.07229753
3.70	1.03975	.03366488	−.06819822
3.80	1.02598	.03189670	−.06444212
3.90	1.01274	.03026789	−.06099933
4.00	1.00000	.02876404	−.05782862
4.25	.97014	.02547215	−.05092486
4.50	.94281	.02272808	−.04521082
4.75	.91766	.02041552	−.04042619
5.00	.89443	.01844764	−.03637839
5.25	.87287	.01675848	−.03292237
5.50	.85280	.01529725	−.02994738
5.75	.83406	.01402425	−.02736718
6.00	.81650	.01290813	−.02511435
6.25	.80000	.01192403	−.02313557
6.50	.78446	.01105139	−.02138726
6.75	.76980	.01027390	−.01983480
7.00	.75593	.009578063	−.01844971
7.25	.74278	.008952678	−.01720853
7.50	.73030	.008388432	−.01609178
7.75	.71842	.007877507	−.01508320
8.00	.70711	.007413303	−.01416911
8.25	.69631	.006990218	−.01333792
8.50	.68599	.006603472	−.01257981
9.00	.66667	.005923159	−.01125030
9.50	.64889	.005345823	−.01012633
10.00	.63246	.004851430	−.009167177
10.50	.61721	.004424625	−.008341773
11.00	.60302	.004053471	−.007626090
11.50	.58977	.003728570	−.007001281
12.00	.57735	.003442438	−.006452406
12.50	.56569	.003189068	−.005967503
13.00	.55470	.002963571	−.005536880
13.50	.54433	.002761948	−.005152628
14.00	.53452	.002580896	−.004808236
15.00	.51640	.002269967	−.004218326
16.00	.50000	.002013688	−.003733654
17.00	.48507	.001799801	−.003330311
18.00	.47140	.001619325	−.002990852
19.00	.45883	.001465554	−.002702300
20.00	.44721	.001333394	−.002454836
$T^{*2}\frac{{\partial }^2{I}_1}{\partial T^{*2}}$	I2	$T^{*}\frac{\partial I_2}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_2}{\partial T^{*2}}$
1.930812	5.373921−03	−2.261372−02	1.215344−01
1.765834	4.683049−03	−1.960056−02	1.048220−01
1.620935	4.101723−03	−1.708012−02	9.091731−02
1.493022	3.609540−03	−1.495810−02	7.927003−02
1.379568	3.190421−03	−1.316069−02	6.945203−02
1.278495	2.831592−03	−1.162961−02	6.112720−02
1.188083	2.522826−03	−1.031848−02	5.402949−02
1.106896	2.255877−03	−9.190136−03	4.794674−02
1.033732	2.024054−03	−8.214553−03	4.270849−02
.9075639	1.644885−03	−6.628573−03	3.423973−02
.8031537	1.352152−03	−5.413574−03	2.779743−02
.7157970	1.123004−03	−4.469244−03	2.282268−02
.6419886	9.413824−04	−3.725694−03	1.892907−02
.5790752	7.957999−04	−3.133321−03	1.584435−02
.5250199	6.779041−04	−2.656331−03	1.337332−02
.4782382	5.815330−04	−2.268496−03	1.137386−02
.4374837	5.020790−04	−1.950331−03	9.741019−03
.4017650	4.360544−04	−1.687177−03	8.396233−03
.3702857	3.807889−04	−1.467873−03	7.280018−03
.3424009	3.342171−04	−1.283833−03	6.346822−03
.3175830	2.947254−04	−1.128383−03	5.561407−03
.2953979	2.610424−04	−9.962881−04	4.896251−03
.2754856	2.321575−04	−8.834086−04	4.329672−03
.2575454	2.072613−04	−7.864416−04	3.844444−03
.2413245	1.857008−04	−7.027338−04	3.426779−03
.2266097	1.669458−04	−6.301383−04	3.065558−03
.2132197	1.505625−04	−5.669066−04	2.751758−03
.2009919	1.361944−04	−5.116055−04	2.478006−03
.1898161	1.235464−04	−4.630539−04	2.238244−03
.1795553	1.123733−04	−4.202724−04	2.027463−03
.1573198	8.962729−05	−3.335301−04	1.601664−03
.1390330	7.248913−05	−2.685330−04	1.284206−03
.1238086	5.935620−05	−2.189766−04	1.043269−03
.1109958	4.914026−05	−1.806027−04	8.574756−04
.1001081	4.108601−05	−1.504760−04	7.121697−04
.09077701	3.465975−05	−1.265336−04	5.970967−04
.08271642	2.947558−05	−1.072845−04	5.048849−04
.07570466	2.525113−05	−9.165314−05	4.302312−04
.06956694	2.177786−05	−7.884132−05	3.692164−04
.06416147	1.889841−05	−6.825087−05	3.189140−04
.05937588	1.649301−05	−5.942804−05	2.771114−04
.05511815	1.446941−05	−5.202470−05	2.421161−04
.05131277	1.275590−05	−4.577099−05	2.126200−04
.04789733	1.129618−05	−4.045566−05	1.876018−04
.04481986	1.004565−05	−3.591190−05	1.662571−04
.04203679	8.968693−06	−3.200683−05	1.479468−04
.03951140	8.036664−06	−2.863384−05	1.321593−04
.03721253	7.226349−06	−2.570676−05	1.184818−04
.03319191	5.898492−06	−2.092237−05	9.617731−05
.02980434	4.870378−06	−1.722990−05	7.901348−05
.02692238	4.063046−06	−1.433892−05	6.561111−05
.02444927	3.421028−06	−1.204614−05	5.500809−05
.02231044	2.904628−06	−1.020659−05	4.652033−05
.02044763	2.484961−06	−8.715107−06	3.965302−05
.01881482	2.140692−06	−7.494227−06	3.404267−05
.01737527	1.855841−06	−6.486102−06	2.941847−05
.01609930	1.618292−06	−5.646973−06	2.557602−05
.01496276	1.418749−06	−4.943349−06	2.235923−05
.01394582	1.250006−06	−4.349325−06	1.964759−05
.01220786	9.835387−07	−3.413401−06	1.538397−05
.01078394	7.863749−07	−2.722856−06	1.224621−05
.009601930	6.376173−07	−2.203178−06	9.890298−06
.008609380	5.234416−07	−1.805234−06	8.090018−06
.007767409	4.344680−07	−1.495783−06	6.692747−06
.007046677	3.641886−07	−1.251825−06	5.593116−06
T*	$B_0^{*}$	$T^{*}\frac{\partial B_0^{*}}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{B}_0^{*}}{\partial T^{*2}}$
.300	−21.20540	58.61918	−272.49826
.305	−20.26497	55.21349	−253.64084
.310	−19.39277	52.10189	−236.59096
.315	−18.58219	49.25225	−221.13542
.320	−17.82738	46.63658	−207.09039
.325	−17.12318	44.23046	−194.29682
.330	−16.46500	42.01248	−182.61664
.335	−15.84879	39.96386	−171.92964
.340	−15.27091	38.06803	−162.13085
.345	−14.72812	36.31037	−153.12833
.350	−14.21752	34.67794	−144.84136
.360	−13.22272	31.74403	−130.13795
.370	−12.44860	29.18859	−117.54536
.380	−11.70056	26.94951	−106.68972
.390	−11.02657	24.97678	−97.27429
.400	−10.41668	23.22975	−89.06153
.410	−9.86255	21.67517	−81.85975
.420	−9.35722	20.28563	−75.51307
.430	−8.89476	19.03839	−69.89392
.440	−8.47017	17.91447	−64.89715
.450	−8.07915	16.89795	−60.43556
.460	−7.71801	15.97535	−56.43640
.470	−7.38358	15.13527	−52.83866
.480	−7.07310	14.36795	−49.59091
.490	−6.78417	13.66507	−46.64955
.500	−6.51469	13.01943	−43.97747
.510	−6.26282	12.42482	−41.54292
.520	−6.02693	11.87587	−39.31864
.530	−5.80561	11.36787	−37.28114
.540	−5.59756	10.89673	−35.41004
.550	−5.40167	10.45885	−33.68768
.560	−5.21692	10.05106	−32.09684
.580	−4.87735	9.31488	−29.26819
.600	−4.57267	8.66943	−26.82924
.620	−4.29788	8.09881	−24.71207
.640	−4.04886	7.59412	−22.86174
.660	−3.82222	7.14270	−21.23456
.680	−3.61511	6.73770	−19.79538
.700	−3.42515	6.37264	−18.51574
.720	−3.25034	6.04218	−17.37234
.740	−3.08895	5.74183	−16.34601
.760	−2.93952	5.46783	−15.42086
.780	−2.80078	5.21701	−14.58362
.800	−2.67164	4.98666	−13.82311
.820	−2.55115	4.77448	−13.12993
.840	−2.43848	4.57847	−12.49605
.860	−2.33290	4.39692	−11.91464
.880	−2.23377	4.22834	−11.37982
.900	−2.14053	4.07144	−10.88652
.920	−2.05266	3.92510	−10.43041
.940	−1.96973	3.78830	−10.00761
.960	−1.89133	3.66017	−9.61481
.980	−1.81711	3.53994	−9.24911
1.000	−1.74674	3.42693	−8.90793
1.025	−1.66376	3.29487	−8.51253
1.050	−1.58585	3.17208	−8.14806
1.075	−1.51258	3.05764	−7.81123
1.100	−1.44352	2.95073	−7.49913
1.150	−1.31672	2.75682	−6.93941
1.200	−1.20308	2.58565	−6.45240
1.250	−1.10068	2.43350	−6.02529
1.300	−1.00793	2.29743	−5.64804
1.350	−.92356	2.17505	−5.31268
1.400	−.84649	2.06443	−5.01283
1.450	−.77583	1.96397	−4.74328
1.500	−.71082	1.87235	−4.49981
1.550	−.65081	1.78846	−4.27890
1.600	−.59526	1.71139	−4.07764
1.650	−.54370	1.64033	−3.89357
1.700	−.49572	1.57462	−3.72464
1.750	−.45097	1.51368	−3.56910
1.800	−.40913	1.45702	−3.42545
1.850	−.36994	1.40419	−3.29240
1.900	−.33315	1.35483	−3.16885
2.000	−.26598	1.26524	−2.94650
2.100	−.20621	1.18607	−2.75209
2.200	−.15269	1.11560	−2.58072
2.300	−.10452	1.05247	−2.42858
2.400	−.06095	.99561	−2.29266
2.500	−.02136	.94412	−2.17051
2.600	.01474	.89728	−2.06016
2.700	.04779	.85448	−1.96000
2.800	.07814	.81524	−1.86868
2.900	.10611	.77911	−1.78511
3.000	.13196	.74575	−1.70833
3.100	.15590	.71484	−1.63756
3.200	.17814	.68614	−1.57212
3.300	.19884	.65940	−1.51144
3.400	.21815	.63444	−1.45502
3.500	.23620	.61108	−1.40242
3.600	.25310	.58917	−1.35327
3.700	.26896	.56858	−1.30724
3.800	.28386	.54921	−1.26405
3.900	.29789	.53093	−1.22345
4.000	.31111	.51366	−1.18520
4.250	.34105	.47440	−1.09863
4.500	.36717	.43991	−1.02304
4.750	.39012	.40937	−.95647
5.000	.41041	.38213	−.89740
5.250	.42846	.35769	−.84461
5.500	.44458	.33564	−.79716
5.750	.45904	.31564	−.75428
6.000	.47209	.29741	−.71533
6.250	.48389	.28074	−.67981
6.500	.49459	.26543	−.64726
6.750	.50434	.25132	−.61735
7.000	.51325	.23828	−.58975
7.250	.52140	.22618	−.56420
7.500	.52887	.21493	−.54050
7.750	.53575	.20444	−.51843
8.000	.54208	.19465	−.49786
8.250	.54793	.18547	−.47861
8.500	.55333	.17687	−.46057
9.000	.56299	.16115	−.42769
9.500	.57132	.14715	−.39847
10.000	.57854	.13461	−.37234
10.500	.58483	.12331	−.34882
11.000	.59033	.11308	−.32755
11.500	.59515	.10377	−.30821
12.000	.59938	.09527	−.29056
12.500	.60311	.08747	−.27438
13.000	.60640	.08029	−.25949
13.500	.60930	.07366	−.24575
14.000	.61187	.06753	−.23303
15.000	.61615	.05652	−.21021
16.000	.61948	.04694	−.19035
17.000	.62207	.03852	−.17289
18.000	.62405	.03107	−.15743
19.000	.62555	.02443	−.14364
20.000	.62665	.01848	−.13127
T*	Y	I1	$T^{*}\frac{\partial I_1}{\partial T^{*}}$
.300	2.94283	35.33701	−166.2731
.305	2.91861	32.70767	−152.1056
.310	2.89498	30.33868	−139.4799
.315	2.87191	28.19866	−128.1960
.320	2.84938	26.26062	−118.0840
.325	2.82738	24.50133	−108.9985
.330	2.80588	22.90058	−100.8149
.335	2.78486	21.44089	−93.42592
.340	2.76431	20.10700	−86.73896
.345	2.74420	18.88559	−80.67392
.350	2.72453	17.76499	−75.16117
.360	2.68642	15.78639	−65.55785
.370	2.64987	14.10286	−57.53000
.380	2.61477	12.66089	−50.77037
.390	2.58103	11.41822	−45.04009
.400	2.54857	10.34113	−40.15173
.410	2.51729	9.402550	−35.95693
.420	2.48715	8.580565	−32.33737
.430	2.45806	7.857301	−29.19799
.440	2.42996	7.218093	−26.46175
.450	2.40281	6.650828	−24.06597
.460	2.37655	6.145439	−21.95918
.470	2.35113	5.693521	−20.09896
.480	2.32651	5.288007	−18.45011
.490	2.30265	4.922942	−16.98326
.500	2.27951	4.593261	−15.67382
.510	2.25705	4.294663	−14.50104
.520	2.23524	4.023457	−13.44739
.530	2.21405	3.776476	−12.49796
.540	2.19346	3.550990	−11.64002
.550	2.17342	3.344633	−10.86267
.560	2.15393	3.155347	−10.15654
.580	2.11647	2.821049	−8.926637
.600	2.08090	2.536273	−7.897581
.620	2.04706	2.291863	−7.029326
.640	2.01482	2.080657	−6.291086
.660	1.98406	1.896992	−5.658930
.680	1.95466	1.736346	−5.114055
.700	1.92654	1.595077	−4.641557
.720	1.89959	1.470226	−4.229513
.740	1.87374	1.359374	−3.868302
.760	1.84892	1.260526	−3.550106
.780	1.82507	1.172024	−3.268523
.800	1.80211	1.092489	−3.018278
.820	1.78000	1.020756	−2.794982
.840	1.75868	.9558473	−2.594996
.860	1.73811	.8969294	−2.415249
.880	1.71824	.8432917	−2.253154
.900	1.69904	.7943253	−2.106518
.920	1.68047	.7495066	−1.973474
.940	1.66250	.7083819	−1.852421
.960	1.64509	.6705579	−1.741987
.980	1.62822	.6356923	−1.640984
1.000	1.61185	.6034856	−1.548387
1.025	1.59208	.5665690	−1.443110
1.050	1.57301	.5329531	−1.348081
1.075	1.55461	.5022571	−1.262030
1.100	1.53684	.4741528	−1.183874
1.150	1.50306	.4246236	−1.047680
1.200	1.47142	.3825159	−.9335348
1.250	1.44169	.3464183	−.8369666
1.300	1.41369	.3152386	−.7545735
1.350	1.38726	.2881221	−.6837319
1.400	1.36227	.2643911	−.6223938
1.450	1.33857	.2435039	−.5689427
$T^{*2}\frac{{\partial }^2{I}_1}{\partial T^{*2}}$	I2	$T^{*}\frac{\partial I_2}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_2}{\partial T^{*2}}$
1067.080	2.343779+01	−1.610717+02	1.344799+03
967.1021	2.093035+01	−1.427159+02	1.183257+03
878.7802	1.874167+01	−1.268188+02	1.044322+03
800.5186	1.682529+01	−1.130056+02	9.244155+02
730.9708	1.514235+01	−1.009653+02	8.205895+02
668.9944	1.366016+01	−9.043855+01	7.303999+02
613.6173	1.235120+01	−8.120811+01	6.518163+02
564.0102	1.119218+01	−7.309174+01	5.831428+02
519.4624	1.016329+01	−6.593571+01	5.229603+02
479.3626	9.247712+00	−5.961000+01	4.700745+02
443.1846	8.431034+00	−5.400435+01	4.234787+02
380.8329	7.046783+00	−4.459105+01	3.458775+02
329.4386	5.931058+00	−3.709618+01	2.847595+02
286.7465	5.024541+00	−3.107773+01	2.361903+02
251.0262	4.282464+00	−2.620625+01	1.972691+02
220.9366	3.670733+00	−2.223372+01	1.658343+02
195.4297	3.163133+00	−1.897156+01	1.402587+02
173.6791	2.739337+00	−1.627514+01	1.193064+02
155.0281	2.383452+00	−1.403258+01	1.020298+02
138.9513	2.082962+00	−1.215662+01	8.769682+01
125.0249	1.827935+00	−1.057872+01	7.573723+01
112.9051	1.610437+00	−9.244632+00	6.570343+01
102.3112	1.424091+00	−8.111153+00	5.724191+01
93.01248	1.263737+00	−7.143643+00	5.007127+01
84.81846	1.125179+00	−6.314150+00	4.396642+01
77.57096	1.004983+00	−5.600017+00	3.874603+01
71.13790	9.003261−01	−4.982751+00	3.426324+01
65.40854	8.088746−01	−4.447193+00	3.039848+01
60.28954	7.286924−01	−3.980850+00	2.705388+01
55.70193	6.581626−01	−3.573379+00	2.414895+01
51.57860	5.959326−01	−3.216180+00	2.161716+01
47.86226	5.408630−01	−2.902067+00	1.940329+01
41.46131	4.485073−01	−2.379945+00	1.575261+01
36.18302	3.750177−01	−1.969258+00	1.291078+01
31.79070	3.159682−01	−1.642862+00	1.067433+01
28.10503	2.680942−01	−1.380968+00	8.896512+00
24.98844	2.289571−01	−1.168967+00	7.470087+00
22.33423	1.967154−01	−9.959455−01	6.315712+00
20.05887	1.699636−01	−8.536575−01	5.373988+00
18.09632	1.476186−01	−7.358130−01	4.599999+00
16.39390	1.288380−01	−6.375651−01	3.959428+00
14.90927	1.129609−01	−5.551477−01	3.425818+00
13.60813	9.946504−02	−4.856076−01	2.978590+00
12.46251	8.793432−02	−4.266127−01	2.601608+00
11.44937	7.803492−02	−3.763068−01	2.282125+00
10.54975	6.949726−02	−3.332027−01	2.009993+00
9.747838	6.210238−02	−2.961010−01	1.777082+00
9.030424	5.567124−02	−2.640279−01	1.576837+00
8.386396	5.005669−02	−2.361888−01	1.403938+00
7.806376	4.513715−02	−2.119311−01	1.254043+00
7.282399	4.081165−02	−1.907167−01	1.123592+00
6.807670	3.699591−02	−1.720989−01	1.009647+00
6.376377	3.361932−02	−1.557058−01	9.097716−01
5.983519	3.062240−02	−1.412259−01	8.219396−01
5.539973	2.733434−02	−1.254215−01	7.265276−01
5.142590	2.447970−02	−1.117767−01	6.445716−01
4.785327	2.199143−02	−9.994667−02	5.738631−01
4.463085	1.981432−02	−8.964902−02	5.126019−01
3.906975	1.621825−02	−7.276125−02	4.127924−01
3.446628	1.340929−02	−5.969041−02	3.361887−01
3.061627	1.118858−02	−4.944459−02	2.766098−01
2.736649	9.413619−03	−4.132019−02	2.297102−01
2.460022	7.980688−03	−3.480987−02	1.923839−01
2.222745	6.813238−03	−2.954250−02	1.623766−01
2.017793	5.854049−03	−2.524293−02	1.380294−01
T*	Y	I1	$T^{*}\frac{\partial I_1}{\partial T^{*}}$
1.50	1.31607	.2250225	−.5220897
1.55	1.29467	.2085906	−.4807969
1.60	1.27428	.1939149	−.4442223
1.65	1.25483	.1807532	−.4116760
1.70	1.23624	.1689034	−.3825894
1.75	1.21845	.1581963	−.3564904
1.80	1.20141	.1484888	−.3329844
1.85	1.18506	.1396599	−.3117395
1.90	1.16936	.1316062	−.2924755
2.00	1.13975	.1174825	−.2589703
2.10	1.11229	.1055451	−.2309437
2.20	1.08671	.09536320	−.2072633
2.30	1.06283	.08660698	−.1870743
2.40	1.04045	.07902087	−.1697222
2.50	1.01943	.07240422	−.1546985
2.60	.99963	.06659769	−.1416039
2.70	.98094	.06147347	−.1301210
2.80	.96327	.05692807	−.1199951
2.90	.94651	.05287694	−.1110199
3.00	.93060	.04925046	−.1030271
3.10	.91547	.04599094	−.09587766
3.20	.90105	.04305014	−.08945669
3.30	.88730	.04038753	−.08366808
3.40	.87415	.03796885	−.07843107
3.50	.86157	.03576498	−.07367749
3.60	.84952	.03375104	−.06934931
3.70	.83796	.03190564	−.06539702
3.80	.82686	.03021035	−.06177813
3.90	.81619	.02864920	−.05845594
4.00	.80593	.02720830	−.05539873
4.25	.78186	.02405606	−.04874240
4.50	.75984	.02143076	−.04323390
4.75	.73957	.01922034	−.03862239
5.00	.72084	.01734116	−.03472213
5.25	.70347	.01572969	−.03139326
5.50	.68730	.01433701	−.02852869
5.75	.67219	.01312493	−.02604542
6.00	.65804	.01206326	−.02387819
6.25	.64474	.01112790	−.02197523
6.50	.63222	.01029942	−.02029497
6.75	.62040	.009561993	−.01880371
7.00	.60922	.008902635	−.01747393
7.25	.59863	.008310601	−.01628297
7.50	.58857	.007776950	−.01521201
7.75	.57900	.007294179	−.01424532
8.00	.56988	.006855960	−.01336969
8.25	.56118	.006456924	−.01257394
8.50	.55286	.006092494	−.01184856
9.00	.53728	.005452278	−.01057757
9.50	.52295	.004909926	−.009504322
10.00	.50971	.004446286	−.008589520
10.50	.49743	.004046699	−.007803205
11.00	.48599	.003699781	−.007122197
11.50	.47531	.003396582	−.006528351
12.00	.46530	.003129984	−.006007272
12.50	.45590	.002894267	−.005547444
13.00	.44705	.002684795	−.005139541
13.50	.43869	.002497775	−.004775967
14.00	.43079	.002330074	−.004450460
15.00	.41618	.002042664	−.003893732
16.00	.40296	.001806405	−.003437298
17.00	.39093	.001609733	−.003058221
18.00	.37992	.001444194	−.002739812
19.00	.36978	.001303483	−.002469679
20.00	.36042	.001182827	−.002238432
$T^{*2}\frac{{\partial }^2{I}_1}{\partial T^{*2}}$	I2	$T^{*}\frac{\partial I_2}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_2}{\partial T^{*2}}$
1.839624	5.059820−03	−2.170460−02	1.181061−01
1.683821	4.397440−03	−1.877070−02	1.016741−01
1.546834	3.841324−03	−1.632093−02	8.802259−02
1.425781	3.371517−03	−1.426205−02	7.660408−02
1.318307	2.972323−03	−1.252117−02	6.699292−02
1.222473	2.631286−03	−1.104084−02	5.885525−02
1.136672	2.338455−03	−9.775371−03	5.192714−02
1.059561	2.085816−03	−8.688183−03	4.599826−02
.9900146	1.866877−03	−7.749795−03	4.089983−02
.8699520	1.509860−03	−6.228055−03	3.267428−02
.7704562	1.235343−03	−5.066165−03	2.643467−02
.6871061	1.021305−03	−4.166085−03	2.162989−02
.6166021	8.523163−04	−3.459671−03	1.787970−02
.5564421	7.173742−04	−2.898677−03	1.491671−02
.5047028	6.085021−04	−2.448370−03	1.254959−02
.4598867	5.198311−04	−2.083360−03	1.063932−02
.4208133	4.469868−04	−1.784830−03	9.083411−03
.3865429	3.866669−04	−1.538654−03	7.805313−03
.3563202	3.363500−04	−1.334101−03	6.747168−03
.3295322	2.940914−04	−1.162937−03	5.864758−03
.3056773	2.583759−04	−1.018775−03	5.123939−03
.2843420	2.280126−04	−8.966161−04	4.498097−03
.2651838	2.020576−04	−7.925153−04	3.966302−03
.2479158	1.797570−04	−7.033332−04	3.511958−03
.2322967	1.605039−04	−6.265520−04	3.121802−03
.2181230	1.438067−04	−5.601394−04	2.785163−03
.2052212	1.292645−04	−5.024436−04	2.493394−03
.1934432	1.165483−04	−4.521137−04	2.239441−03
.1826619	1.053869−04	−4.080381−04	2.017520−03
.1727676	9.555501−05	−3.692977−04	1.822859−03
.1513193	7.563357−05	−2.910743−04	1.431079−03
.1336732	6.072458−05	−2.328092−04	1.140543−03
.1189782	4.937391−05	−1.886398−04	9.211718−04
.1066087	4.059965−05	−1.546287−04	7.528650−04
.09609697	3.372387−05	−1.280713−04	6.218790−04
.08708710	2.826926−05	−1.070719−04	5.186213−04
.07930482	2.389378−05	−9.027775−05	4.362734−04
.07253570	2.034833−05	−7.670740−05	3.699060−04
.06661037	1.744887−05	−6.563831−05	3.159022−04
.06139345	1.505759−05	−5.653132−05	2.715709−04
.05677570	1.307005−05	−4.897901−05	2.348847−04
.05266825	1.140620−05	−4.266998−05	2.042983−04
.04899814	1.000404−05	−3.736381−05	1.786213−04
.04570503	8.815120−06	−3.287297−05	1.569276−04
.04273865	7.801211−06	−2.904993−05	1.384901−04
.04005689	6.931910−06	−2.577759−05	1.227331−04
.03762422	6.182847−06	−2.296234−05	1.091968−04
.03541054	5.534367−06	−2.052872−05	9.751177−05
.03154093	4.478113−06	−1.657294−05	7.855426−05
.02828302	3.666780−06	−1.354224−05	6.406504−05
.02551353	3.034529−06	−1.118604−05	5.282504−05
.02313880	2.535422−06	−9.330019−06	4.398901−05
.02108677	2.136801−06	−7.850605−06	3.695879−05
.01930100	1.815054−06	−6.658674−06	3.130433−05
.01773704	1.552846−06	−5.688951−06	2.671121−05
.01635933	1.337271−06	−4.892945−06	2.294648−05
.01513918	1.158599−06	−4.234120−06	1.983453−05
.01405329	1.009408−06	−3.684787−06	1.724326−05
.01308249	8.839752−07	−3.223524−06	1.507002−05
.01142514	6.875071−07	−2.502287−06	1.167737−05
.01006965	5.436819−07	−1.975445−06	9.204144−06
.008946254	4.362610−07	−1.582707−06	7.363731−06
.008004423	3.546099−07	−1.284676−06	5.969383−06
.007206784	2.915777−07	−1.055022−06	4.896548−06
.006525001	2.422132−07	−8.753972−07	4.058518−06
T*	I3	$T^{*}\frac{\partial I_3}{\partial T^{*}}$	$T^{{*}_2}\frac{{\partial }^2{I}_3}{\partial T^{*2}}$
.300	1.000280+01	−8.846354+01	9.041886+02
.305	8.646330+00	−7.599426+01	7.722942+02
.310	7.498101+00	−6.550538+01	6.619889+02
.315	6.522629+00	−5.664906+01	5.693772+02
.320	5.691052+00	−4.914416+01	4.913292+02
.325	4.979778+00	−4.276231+01	4.253165+02
.330	4.369455+00	−3.731732+01	3.692894+02
.335	3.844135+00	−3.265664+01	3.215781+02
.340	3.390639+00	−2.865496+01	2.808176+02
.345	2.998025+00	−2.520881+01	2.458870+02
.350	2.657181+00	−2.223254+01	2.158631+02
.360	2.101576+00	−1.741655+01	1.676095+02
.370	1.676416+00	−1.376681+01	1.313676+02
.380	1.347989+00	−1.097351+01	1.038669+02
.390	1.092031+00	−8.815848+00	8.279819+01
.400	8.908944−01	−7.134704+00	6.651154+01
.410	7.316014−01	−5.814156+00	5.381487+01
.420	6.045202−01	−4.768903+00	4.383803+01
.430	5.024356−01	−3.935579+00	3.593958+01
.440	4.198951−01	−3.266683+00	2.964228+01
.450	3.527450−01	−2.726315+00	2.458798+01
.460	2.977967−01	−2.287117+00	2.050566+01
.470	2.525841−01	−1.928087+00	1.718864+01
.480	2.151869−01	−1.632984+00	1.447812+01
.490	1.840999−01	−1.389163+00	1.225126+01
.500	1.581357−01	−1.186716+00	1.041235+01
.510	1.363520−01	−1.017830+00	8.886378+00
.520	1.179973−01	−8.763100−01	7.614202+00
.530	1.024681−01	−7.572126−01	6.548892+00
.540	8.927786−02	−6.565754−01	5.653026+00
.550	7.803233−02	−5.712049−01	4.896599+00
.560	6.841034−02	−4.985139−01	4.255428+00
.580	5.303302−02	−3.831351−01	3.244187+00
.600	4.155396−02	−2.977712−01	2.502209+00
.620	3.288211−02	−2.338249−01	1.950745+00
.640	2.625839−02	−1.853702−01	1.535979+00
.660	2.114713−02	−1.482617−01	1.220572+00
.680	1.716534−02	−1.195604−01	9.782559−01
.700	1.403587−02	−9.715668−02	7.903123−01
.720	1.155589−02	−7.951782−02	6.432393−01
.740	9.575345−03	−6.551848−02	5.271887−01
.760	7.982156−03	−5.432375−02	4.349010−01
.780	6.691809−03	−4.530824−02	3.609719−01
.800	5.640021−03	−3.799929−02	3.013407−01
.820	4.777492−03	−3.203661−02	2.529098−01
.840	4.066121−03	−2.714335−02	2.133862−01
.860	3.476247−03	−2.310519−02	1.808992−01
.880	2.984613−03	−1.975501−02	1.540630−01
.900	2.572868−03	−1.696162−02	1.317794−01
.920	2.226443−03	−1.462136−02	1.131850−01
.940	1.933697−03	−1.265181−02	9.759618−02
.960	1.685280−03	−1.098710−02	8.446897−02
.980	1.473643−03	−9.574260−03	7.336771−02
1.000	1.292656−03	−8.370478−03	6.394179−02
1.025	1.101998−03	−7.107388−03	5.408823−02
1.050	9.436547−04	−6.062845−03	4.597221−02
1.075	8.114794−04	−5.194488−03	3.925104−02
1.100	7.006143−04	−4.468990−03	3.365636−02
1.150	5.281406−04	−3.346459−03	2.504415−02
1.200	4.036417−04	−2.541843−03	1.891173−02
1.250	3.123739−04	−1.955835−03	1.447283−02
1.300	2.445188−04	−1.522799−03	1.121143−02
1.350	1.934165−04	−1.198527−03	8.782239−03
1.400	1.544732−04	−9.527243−04	6.950123−03
1.450	1.244709−04	−7.643018−04	5.552313−03
1.500	1.011229−04	−6.183600−04	4.474453−03
1.550	8.278298−05	−5.042316−04	3.635082−03
1.600	6.825157−05	−4.141823−04	2.975428−03
1.650	5.664435−05	−3.425397−04	2.452580−03
1.700	4.730268−05	−2.850978−04	2.034861−03
1.750	3.973106−05	−2.387065−04	1.698642−03
1.800	3.355334−05	−2.009845−04	1.426134−03
1.850	2.848143−05	−1.701152−04	1.203813−03
1.900	2.429293−05	−1.447015−04	1.021320−03
2.000	1.791144−05	−1.061460−04	7.455637−04
2.100	1.342318−05	−7.917584−05	5.536588−04
2.200	1.020810−05	−5.995272−05	4.175227−04
2.300	7.866680−06	−4.601766−05	3.192658−04
2.400	6.135780−06	−3.576003−05	2.472303−04
2.500	4.838632−06	−2.810335−05	1.936620−04
2.600	3.854342−06	−2.231480−05	1.533052−04
2.700	3.098849−06	−1.788712−05	1.225369−04
2.800	2.512821−06	−1.446372−05	9.882032−05
2.900	2.053796−06	−1.179037−05	8.035315−05
3.000	1.690985−06	−9.683416−06	6.583800−05
3.100	1.401808−06	−8.008590−06	5.432933−05
3.200	1.169508−06	−6.666615−06	4.513012−05
3.300	9.815310−07	−5.583311−06	3.772107−05
3.400	8.283777−07	−4.702711−06	3.171145−05
3.500	7.027936−07	−3.982198−06	2.680447−05
3.600	5.991937−07	−3.389044−06	2.277275−05
3.700	5.132433−07	−2.897910−06	1.944073−05
3.800	4.415530−07	−2.489032−06	1.667168−05
3.900	3.814538−07	−2.146877−06	1.435845−05
4.000	3.308300−07	−1.859162−06	1.241646−05
4.250	2.354529−07	−1.318563−06	8.776909−06
4.500	1.710447−07	−9.548546−07	6.336905−06
4.750	1.265365−07	−7.043670−07	4.661836−06
5.000	9.514299−08	−5.282309−07	3.487403−06
5.250	7.258995−08	−4.020507−07	2.648310−06
5.500	5.611789−08	−3.101307−07	2.038545−06
5.750	4.390588−08	−2.421463−07	1.588581−06
6.000	3.472815−08	−1.911667−07	1.251873−06
6.250	2.774452−08	−1.524545−07	9.966882−07
6.500	2.236957−08	−1.227167−07	8.010178−07
6.750	1.818911−08	−9.962919−08	6.493633−07
7.000	1.490606−08	−8.152826−08	5.306537−07
7.250	1.230454−08	−6.720758−08	4.368764−07
7.500	1.022584−08	−5.578187−08	3.621621−07
7.750	8.551941−09	−4.659415−08	3.021624−07
8.000	7.194230−09	−3.915180−08	2.536220−07
8.250	6.085494−09	−3.308187−08	2.140799−07
8.500	5.174309−09	−2.809942−08	1.816587−07
9.000	3.794692−09	−2.056778−08	1.327254−07
9.500	2.831507−09	−1.532038−08	9.869983−08
10.000	2.145774−09	−1.159157−08	7.456436−08
10.500	1.648931−09	−8.894562−09	5.713598−08
11.000	1.283207−09	−6.912452−09	4.434660−08
11.500	1.010108−09	−5.434517−09	3.482368−08
12.000	8.034940−10	−4.317844−09	2.763739−08
12.500	6.453000−10	−3.463979−09	2.214924−08
13.000	5.228424−10	−2.803785−09	1.791063−08
13.500	4.270856−10	−2.288108−09	1.460331−08
14.000	3.515048−10	−1.881506−09	1.199812−08
15.000	2.430342−10	−1.298779−09	8.269380−09
16.000	1.721883−10	−9.188623−10	5.842406−09
17.000	1.246249−10	−6.641655−10	4.217733−09
18.000	9.191592−11	−4.892701−10	3.103589−09
19.000	6.893949−11	−3.665713−10	2.322900−09
20.000	5.249002−11	−2.788300−10	1.765249−09
T*	$B_0^{*}$	$T^{*}\frac{\partial B_0^{*}}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{B}_0^{*}}{\partial T^{*2}}$
.300	−17.93726	49.47168	−228.79492
.305	−17.15247	46.66943	−213.30859
.310	−16.41125	44.06421	−199.11621
.315	−15.72773	41.68213	−186.26172
.320	−15.08829	39.48920	−174.51831
.325	−14.49091	37.46426	−163.79614
.330	−13.93338	35.59863	−154.00153
.335	−13.41112	33.87363	−145.02933
.340	−12.92118	32.27675	−136.79972
.345	−12.46084	30.79570	−129.23615
.350	−12.02771	29.41992	−122.27254
.360	−11.23441	26.94653	−109.91423
.370	−10.52616	24.79128	−99.32657
.380	−9.89064	22.90208	−90.19633
.390	−9.31772	21.23692	−82.27485
.400	−8.79901	19.76168	−75.36300
.410	−8.32750	18.44844	−69.30005
.420	−7.89729	17.27415	−63.95534
.430	−7.50340	16.21972	−59.22183
.440	−7.14158	15.26920	−55.01132
.450	−6.80823	14.40917	−51.25063
.460	−6.50021	13.62833	−47.87873
.470	−6.21486	12.91708	−44.84440
.480	−5.94983	12.26720	−42.10444
.490	−5.70309	11.67169	−39.62226
.500	−5.47288	11.12449	−37.36667
.510	−5.25762	10.62038	−35.31102
.520	−5.05596	10.15482	−33.43239
.530	−4.86667	9.72386	−31.71104
.540	−4.68869	9.32404	−30.12985
.550	−4.52104	8.95233	−28.67396
.560	−4.36288	8.60606	−27.33041
.580	−4.07203	7.98067	−24.93632
.600	−3.81092	7.43203	−22.87233
.620	−3.57529	6.94759	−21.07975
.640	−3.36164	6.51728	−19.51236
.660	−3.16708	6.13296	−18.13334
.680	−2.98921	5.78798	−16.91309
.700	−2.82599	5.47689	−15.82762
.720	−2.67572	5.19513	−14.85731
.740	−2.53693	4.93895	−13.98598
.760	−2.40836	4.70513	−13.20022
.780	−2.28895	4.49101	−12.48883
.800	−2.17777	4.29429	−11.84240
.820	−2.07399	4.11300	−11.25296
.840	−1.97691	3.94548	−10.71375
.860	−1.88591	3.79025	−10.21900
.880	−1.80045	3.64607	−9.76373
.900	−1.72003	3.51183	−9.34368
.920	−1.64423	3.38658	−8.95514
.940	−1.57267	3.26946	−8.59486
.960	−1.50500	3.15973	−8.26005
.980	−1.44091	3.05674	−7.94824
1.000	−1.38015	2.95990	−7.65724
1.025	−1.30847	2.84760	−7.31989
1.050	−1.24115	2.74141	−7.00882
1.075	−1.17780	2.64325	−6.72123
1.100	−1.11810	2.55153	−6.45467
1.150	−1.00843	2.38503	−5.97640
1.200	−.91009	2.23806	−5.55999
1.250	−.82143	2.10732	−5.19458
1.300	−.74110	1.99033	−4.87166
1.350	−.66799	1.88507	−4.58445
1.400	−.60119	1.78988	−4.32751
1.450	−.53991	1.70340	−4.09644
1.500	−.48351	1.62450	−3.88762
1.550	−.43144	1.55224	−3.69807
1.600	−.38322	1.48582	−3.52531
1.650	−.33845	1.42456	−3.36726
1.700	−.29677	1.36790	−3.22215
1.750	−.25789	1.31533	−3.08849
1.800	−.22153	1.26644	−2.96501
1.850	−.18746	1.22086	−2.85061
1.900	−.15547	1.17825	−2.74433
2.000	−.09705	1.10089	−2.55301
2.100	−.04502	1.03249	−2.38562
2.200	.00158	.97159	−2.23801
2.300	.04354	.91701	−2.10691
2.400	.08151	.86784	−1.98972
2.500	.11602	.82329	−1.88437
2.600	.14751	.78276	−1.78917
2.700	.17635	.74572	−1.70272
2.800	.20284	.71174	−1.62389
2.900	.22727	.68046	−1.55171
3.000	.24984	.65156	−1.48539
3.100	.27076	.62479	−1.42425
3.200	.29020	.59991	−1.36769
3.300	.30830	.57674	−1.31524
3.400	.32520	.55510	−1.26645
3.500	.34099	.53485	−1.22096
3.600	.35579	.51585	−1.17845
3.700	.36968	.49800	−1.13863
3.800	.38273	.48119	−1.10126
3.900	.39503	.46534	−1.06612
4.000	.40662	.45036	−1.03302
4.250	.43288	.41629	−.95807
4.500	.45580	.38635	−.89261
4.750	.47597	.35983	−.83494
5.000	.49381	.33618	−.78375
5.250	.50969	.31495	−.73799
5.500	.52390	.29578	−.69686
5.750	.53665	.27840	−.65968
6.000	.54816	.26256	−.62591
6.250	.55858	.24806	−.59509
6.500	.56805	.23475	−.56686
6.750	.57668	.22247	−.54090
7.000	.58456	.21112	−.51695
7.250	.59178	.20059	−.49478
7.500	.59841	.19080	−.47421
7.750	.60452	.18167	−.45505
8.000	.61015	.17314	−.43719
8.250	.61536	.16515	−.42047
8.500	.62017	.15766	−.40481
9.000	.62879	.14396	−.37625
9.500	.63624	.13176	−.35087
10.000	.64271	.12082	−.32816
10.500	.64837	.11097	−.30773
11.000	.65332	.10204	−.28924
11.500	.65767	.09391	−.27243
12.000	.66151	.08648	−.25708
12.500	.66490	.07967	−.24301
13.000	.66790	.07340	−.23006
13.500	.67056	.06760	−.21811
14.000	.67292	.06223	−.20704
15.000	.67688	.05260	−.13719
16.000	.68000	.04420	−.16990
17.000	.68245	.03682	−.15470
18.000	.68437	.03028	−.14123
19.000	.68585	.02445	−.12922
20.000	.68696	.01922	−.11843
T*	Y	I1	$T^{*}\frac{\partial I_1}{\partial T^{*}}$
.300	2.65615	33.12951	−154.6953
.305	2.63429	30.68268	−141.5814
.310	2.61295	28.47708	−129.8904
.315	2.59213	26.48373	−119.4383
.320	2.57180	24.67768	−110.0683
.325	2.55194	23.03743	−101.6466
.330	2.53254	21.54432	−94.05819
.335	2.51357	20.18215	−87.20421
.340	2.49502	18.93682	−80.99928
.345	2.47687	17.79598	−75.36946
.350	2.45911	16.74882	−70.25055
.360	2.42472	14.89870	−61.32876
.370	2.39173	13.32310	−53.86554
.380	2.36005	11.97243	−47.57707
.390	2.32959	10.80743	−42.24262
.400	2.30029	9.796834	−37.68891
.410	2.27207	8.915477	−33.77872
.420	2.24485	8.142985	−30.40255
.430	2.21860	7.462736	−27.47235
.440	2.19324	6.861081	−24.91683
.450	2.16873	6.326737	−22.67786
.460	2.14503	5.850328	−20.70774
.470	2.12209	5.424013	−18.96713
.480	2.09987	5.041204	−17.42336
.490	2.07833	4.696337	−16.04917
.500	2.05744	4.384687	−14.82171
.510	2.03717	4.102229	−13.72172
.520	2.01749	3.845517	−12.73290
.530	1.99836	3.611587	−11.84137
.540	1.97977	3.397882	−11.03530
.550	1.96169	3.202185	−10.30455
.560	1.94410	3.022572	−9.640383
.580	1.91029	2.705088	−8.482650
.600	1.87818	2.434330	−7.512964
.620	1.84764	2.201704	−6.693970
.640	1.81854	2.000476	−5.996927
.660	1.79077	1.825317	−5.399472
.680	1.76424	1.671967	−4.884029
.700	1.73886	1.536994	−4.436651
.720	1.71454	1.417606	−4.046169
.740	1.69121	1.311518	−3.703569
.760	1.66881	1.216843	−3.401518
.780	1.64727	1.132015	−3.134008
.800	1.62655	1.055726	−2.896083
.820	1.60659	.9868747	−2.683628
.840	1.58735	.9245321	−2.493208
.860	1.56879	.8679079	−2.321937
.880	1.55086	.8163273	−2.167380
.900	1.53353	.7692121	−2.027470
.920	1.51677	.7260634	−1.900445
.940	1.50054	.6864503	−1.784798
.960	1.48483	.6499983	−1.679229
.980	1.46960	.6163809	−1.582621
1.000	1.45483	.5853125	−1.494001
1.025	1.43698	.5496828	−1.393183
1.050	1.41977	.5172216	−1.302118
1.075	1.40316	.4875648	−1.219603
1.100	1.38713	.4603990	−1.144613
1.150	1.35664	.4124917	−1.013818
1.200	1.32807	.3717291	−.9040757
1.250	1.30124	.3367582	−.8111352
1.300	1.27597	.3065311	−.7317600
1.350	1.25212	.2802266	−.6634510
1.400	1.22956	.2571935	−.6042555
1.450	1.20817	.2369100	−.5526306
$T^{*2}\frac{{\partial }^2{I}_1}{\partial T^{*2}}$	I2	$T^{*}\frac{\partial I_2}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_2}{\partial T^{*2}}$
988.3657	2.332806+01	−1.603109+02	1.338057+03
896.1057	2.083242+01	−1.420474+02	1.177390+03
814.5780	1.865396+01	−1.262292+02	1.039198+03
742.3162	1.674646+01	−1.124840+02	9.199260+02
678.0817	1.507126+01	−1.005023+02	8.166433+02
620.8239	1.359585+01	−9.002610+01	7.269208+02
569.6487	1.229284+01	−8.083974+01	6.487394+02
523.7926	1.113906+01	−7.276171+01	5.804141+02
482.6014	1.011481+01	−6.563920+01	5.205333+02
445.5129	9.203337+00	−5.934287+01	4.679101+02
412.0422	8.390318+00	−5.376300+01	4.215434+02
354.3327	7.012238+00	−4.439254+01	3.443183+02
306.7384	5.901480+00	−3.693129+01	2.834913+02
267.1810	4.998991+00	−3.093949+01	2.351492+02
234.0652	4.260218+00	−2.608935+01	1.964071+02
206.1545	3.651223+00	−2.213404+01	1.651147+02
182.4817	3.145906+00	−1.888592+01	1.396533+02
162.2842	2.724030+00	−1.620102+01	1.187932+02
144.9559	2.369774+00	−1.396799+01	1.015918+02
130.0112	2.070675+00	−1.209998+01	8.732055+01
117.0587	1.816844+00	−1.052875+01	7.541187+01
105.7806	1.600381+00	−9.200308+00	6.542045+01
95.91727	1.414935+00	−8.071624+00	5.699433+01
87.25539	1.255370+00	−7.108212+00	4.985353+01
79.61869	1.117505+00	−6.282253+00	4.377393+01
72.86070	9.979219−01	−5.571174+00	3.857501+01
66.85915	8.938093−01	−4.956564+00	3.411061+01
61.51143	8.028436−01	−4.423327+00	3.026165+01
56.73108	7.230960−01	−3.959023+00	2.693072+01
52.44488	6.529573−01	−3.553351+00	2.403765+01
48.59060	5.910797−01	−3.197744+00	2.151620+01
45.11510	5.363294−01	−2.885048+00	1.931138+01
39.12482	4.445277−01	−2.365325+00	1.567571+01
34.18054	3.714998−01	−1.956578+00	1.284564+01
30.06246	3.128394−01	−1.631770+00	1.061856+01
26.60383	2.652961−01	−1.371192+00	8.848311+00
23.67666	2.264425−01	−1.160293+00	7.428067+00
21.18165	1.944455−01	−9.882027−01	6.278790+00
19.04098	1.679065−01	−8.467092−01	5.341321+00
17.19308	1.457474−01	−7.295474−01	4.570914+00
15.58885	1.271301−01	−6.318907−01	3.933386+00
14.18875	1.113974−01	−5.499879−01	3.402379+00
12.96076	9.802965−02	−4.808988−01	2.957396+00
11.87872	8.661302−02	−4.223011−01	2.582363+00
10.92113	7.681566−02	−3.723471−01	2.264581+00
10.07022	6.836960−02	−3.295559−01	1.993943+00
9.311205	6.105720−02	−2.927336−01	1.762352+00
8.631700	5.470055−02	−2.609110−01	1.563276+00
8.021300	4.915349−02	−2.332972−01	1.391420+00
7.471207	4.429524−02	−2.092431−01	1.242458+00
6.973949	4.002554−02	−1.882128−01	1.112844+00
6.523149	3.626074−02	−1.697623−01	9.996534−01
6.113347	3.293074−02	−1.535215−01	9.004610−01
5.739841	2.997653−02	−1.391806−01	8.132481−01
5.317873	2.673699−02	−1.235337−01	7.185320−01
4.939556	2.392611−02	−1.100302−01	6.371972−01
4.599203	2.147743−02	−9.832751−02	5.670443−01
4.292009	1.933620−02	−8.814492−02	5.062831−01
3.761364	1.580246−02	−7.145610−02	4.073319−01
3.321562	1.304545−02	−5.855029−02	3.314345−01
2.953320	1.086840−02	−4.844265−02	2.724429−01
2.642147	9.130401−03	−4.043484−02	2.260362−01
2.376999	7.728975−03	−3.402364−02	1.891270−01
2.149345	6.588550−03	−2.884110−02	1.594753−01
1.952523	5.652667−01	−2.461457−02	1.354333−01
T*	Y	I1	$T^{*}\frac{\partial I_1}{\partial T^{*}}$
1.50	1.18786	.2189547	−.5073447
1.55	1.16855	.2029836	−.4674054
1.60	1.15015	.1887141	−.4320064
1.65	1.13258	.1759122	−.4004871
1.70	1.11580	.1643828	−.3723022
1.75	1.09975	.1539621	−.3469987
1.80	1.08437	.1445120	−.3241977
1.85	1.06961	.1359151	−.3035804
1.90	1.05545	.1280714	−.2848769
2.00	1.02872	.1143123	−.2523270
2.10	1.00393	.1026796	−.2250792
2.20	.98085	.09275520	−.2020417
2.30	.95929	.08421890	−.1823894
2.40	.93909	.07682236	−.1654885
2.50	.92012	.07037047	−.1508513
2.60	.90225	.06470823	−.1380873
2.70	.88538	.05971124	−.1268903
2.80	.86943	.05527872	−.1170134
2.90	.85431	.05132833	−.1082566
3.00	.83995	.04779224	−.1004562
3.10	.82629	.04461417	−.09347757
3.20	.81328	.04174711	−.08720879
3.30	.80086	.03915155	−.08155649
3.40	.78899	.03679405	−.07644213
3.50	.77764	.03464622	−.07179933
3.60	.76676	.03268375	−.06757164
3.70	.75633	.03088579	−.06371081
3.80	.74631	.02923435	−.06017544
3.90	.73668	.02771383	−.05692979
4.00	.72742	.02631066	−.05394292
4.25	.70570	.02324195	−.04743957
4.50	.68581	.02068741	−.04205776
4.75	.66752	.01853766	−.03755264
5.00	.65062	.01671098	−.03374283
5.25	.63494	.01514537	−.03049165
5.50	.62034	.01379304	−.02769446
5.75	.60671	.01261671	−.02527011
6.00	.59393	.01158692	−.02315482
6.25	.58193	.01068014	−.02129793
6.50	.57063	.009877409	−.01965879
6.75	.55996	.009163287	−.01820444
7.00	.54987	.008525109	−.01690796
7.25	.54031	.007952403	−.01574716
7.50	.53123	.007436447	−.01470364
7.75	.52259	.006969930	−.01376202
8.00	.51436	.006546687	−.01290937
8.25	.50651	.006161489	−.01213476
8.50	.49900	.005809875	−.01142888
9.00	.48494	.005192640	−.01019265
9.50	.47201	.004670274	−.009149451
10.00	.46006	.004224155	−.008260852
10.50	.44897	.003840035	−.007497566
11.00	.43865	.003506856	−.006836942
11.50	.42901	.003215929	−.006261246
12.00	.41997	.002960349	−.005756426
12.50	.41149	.002734571	−.005311229
13.00	.40350	.002534102	−.004916561
13.50	.39595	.002355267	−.004565000
14.00	.38882	.002195038	−.004250446
15.00	.37564	.001920753	−.003712981
16.00	.36371	.001695629	−.003272847
17.00	.35285	.001508503	−.002907739
18.00	.34291	.001351221	−.002601413
19.00	.33376	.001217712	−.002341811
20.00	.32531	.001103382	−.002119828
$T^{*2}\frac{{\partial }^2{I}_1}{\partial T^{*2}}$	I2	$T^{*}\frac{\partial I_2}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_2}{\partial T^{*2}}$
1.781272	4.878649−03	−2.113949−02	1.157736−01
1.631394	4.233881−03	−1.826065−02	9.957054−02
1.499513	3.693181−03	−1.585902−02	8.611885−02
1.382884	3.236928−03	−1.384242−02	7.487556−02
1.279265	2.849694−03	−1.213885−02	6.541871−02
1.186807	2.519255−03	−1.069155−02	5.741753−02
1.103974	2.235844−03	−9.455423−03	5.061058−02
1.029486	1.991609−03	−8.394406−03	4.478965−02
.9622649	1.780187−03	−7.479424−03	3.978769−02
.8461249	1.435988−03	−5.997588−03	3.172646−02
.7497832	1.171903−03	−4.868170−03	2.562043−02
.6690016	9.664397−04	−3.994778−03	2.092538−02
.6006132	8.045630−04	−3.310500−03	1.726617−02
.5422071	6.755565−04	−2.767866−03	1.437852−02
.4919554	5.717031−04	−2.333308−03	1.207617−02
.4483938	4.872803−04	−1.981531−03	1.022025−02
.4103923	4.180618−04	−1.694299−03	8.710741−03
.3770446	3.608545−04	−1.457824−03	7.472490−03
.3476214	3.132245−04	−1.261649−03	6.448756−03
.3215304	2.732966−04	−1.097756−03	5.596214−03
.2982868	2.396127−04	−9.599334−04	4.881442−03
.2774909	2.110279−04	−8.433270−04	4.278417−03
.2588105	1.866365−04	−7.441091−04	3.766690−03
.2419679	1.657156−04	−6.592374−04	3.330066−03
.2267295	1.476845−04	−5.862757−04	2.955616−03
.2128975	1.320734−04	−5.232591−04	2.632944−03
.2003038	1.184996−04	−4.685925−04	2.353635−03
.1888047	1.066496−04	−4.209728−04	2.110834−03
.1782766	9.626501−05	−3.793292−04	1.898922−03
.1686130	8.713189−05	−3.427771−04	1.713270−03
.1476592	6.867476−05	−2.691425−04	1.340387−03
.1304145	5.491341−05	−2.144770−04	1.064685−03
.1160503	4.447440−05	−1.731695−04	8.571136−04
.1039574	3.643303−05	−1.414611−04	6.983070−04
.09367940	3.015283−05	−1.167766−04	5.750523−04
.08486935	2.518701−05	−9.731549−05	4.781483−04
.07725943	2.121623−05	−8.179593−05	4.010679−04
.07064034	1.800861−05	−6.929033−05	3.391032−04
.06484654	1.539325−05	−5.911731−05	2.888063−04
.05974576	1.324253−05	−5.076959−05	2.476177−04
.05523122	1.145998−05	−4.386468−05	2.136125−04
.05121601	9.971837−06	−3.811093−05	1.853267−04
.04762876	8.721109−06	−3.328361−05	1.616346−04
.04441044	7.663353−06	−2.920780−05	1.416620−04
.04151189	6.763595−06	−2.574616−05	1.247238−04
.03889190	5.994081−06	−2.278993−05	1.102786−04
.03651568	5.332618−06	−2.025229−05	9.789506−05
.03435375	4.761328−06	−1.806347−05	8.722685−05
.03057570	3.833944−06	−1.451665−05	6.996908−05
.02739619	3.124767−06	−1.181045−05	5.682949−05
.02469450	2.574481−06	−9.714851−06	4.667419−05
.02237896	2.141860−06	−8.070401−06	3.871917−05
.02037893	1.797703−06	−6.764443−06	3.241180−05
.01863925	1.520973−06	−5.715995−06	2.735563−05
.01711637	1.296281−06	−4.865934−06	2.326181−05
.01577548	1.112207−06	−4.170473−06	1.991678−05
.01458852	9.601685−07	−3.596764−06	1.716062−05
.01353265	8.336395−07	−3.119870−06	1.487209−05
.01258914	7.276034−07	−2.720649−06	1.295828−05
.01097976	5.622721−07	−2.099093−06	9.982731−06
.009664615	4.419605−07	−1.647607−06	7.825060−06
.008575688	3.526088−07	−1.312843−06	6.227662−06
.007663608	2.850508−07	−1.060099−06	5.023292−06
.006891816	2.331535−07	−8.661977−07	4.100465−06
.006232762	1.927176−07	−7.152984−07	3.383105−06
T*	I3	$T^{*}\frac{\partial I_3}{\partial T^{*}}$	$T^{{*}_2}\frac{{\partial }^2{I}_3}{\partial T^{*2}}$
.300	1.045960+01	−9.284472+01	9.515266+02
.305	9.036270+00	−7.972130+01	8.124037+02
.310	7.831999+00	−6.868642+01	6.960926+02
.315	6.809384+00	−5.937275+01	5.984718+02
.320	5.938019+00	−5.148335+01	5.162298+02
.325	5.193057+00	−4.477716+01	4.466937+02
.330	4.554119+00	−3.905764+01	3.876960+02
.335	4.004424+00	−3.416392+01	3.374722+02
.340	3.530103+00	−2.996378+01	2.945797+02
.345	3.119648+00	−2.634813+01	2.578346+02
.350	2.763479+00	−2.322667+01	2.262616+02
.360	2.183283+00	−1.817864+01	1.755438+02
.370	1.739715+00	−1.435605+01	1.374767+02
.380	1.397380+00	−1.143272+01	1.086107+02
.390	1.130829+00	−9.176378+00	8.651104+01
.400	9.215582−01	−7.419711+00	6.943891+01
.410	7.559744−01	−6.040910+00	5.613891+01
.420	6.239949−01	−4.950394+00	4.569504+01
.430	5.180716−01	−4:081654+00	3.743241+01
.440	4.325047−01	−3.384870+00	3.084920+01
.450	3.629556−01	−2.822405+00	2.556896+01
.460	3.060953−01	−2.365599+00	2.130702+01
.470	2.593516−01	−1.992462+00	1.784637+01
.480	2.207225−01	−1.685998+00	1.502038+01
.490	1.886402−01	−1.432984+00	1.270020+01
.500	1.618684−01	−1.223064+00	1.078550+01
.510	1.394273−01	−1.048077+00	9.197699+00
.520	1.205352−01	−9.015554−01	7.874850+00
.530	1.045654−01	−7.783424−01	6.767843+00
.540	9.101292−02	−6.743060−01	5.837527+00
.550	7.946861−02	−5.861181−01	5.052529+00
.560	6.959958−02	−5.110845−01	4.387579+00
.580	5.384748−02	−3.921178−01	3.339838+00
.600	4.210888−02	−3.042299−01	2.572082+00
.620	3.325615−02	−2.384903−01	2.002202+00
.640	2.650574−02	−1.887498−01	1.574140+00
.660	2.130546−02	−1.507121−01	1.249039+00
.680	1.726109−02	−1.213348−01	9.995962−01
.700	1.408769−02	−9.843636−02	8.063706−01
.720	1.157702−02	−8.043376−02	6.553555−01
.740	9.575225−03	−6.616598−02	5.363441−01
.760	7.967537−03	−5.477266−02	4.418201−01
.780	6.667527−03	−4.561004−02	3.661936−01
.800	5.609540−03	−3.819213−02	3.052684−01
.820	4.743290−03	−3.214889−02	2.558675−01
.840	4.029963−03	−2.719631−02	2.155648−01
.860	3.439377−03	−2.311474−02	1.824941−01
.880	2.947904−03	−1.973311−02	1.552085−01
.900	2.536919−03	−1.691726−02	1.325789−01
.920	2.191651−03	−1.456130−02	1.137181−01
.940	1.900317−03	−1.258116−02	9.792470−02
.960	1.653465−03	−1.090969−02	8.464077−02
.980	1.443468−03	−9.492955−03	7.342007−02
1.000	1.264145−03	−8.287405−03	6.390372−02
1.025	1.075542−03	−7.024265−03	5.396842−02
1.050	9.191857−04	−5.981338−03	4.579675−02
1.075	7.888982−04	−5.115680−03	3.903904−02
1.100	6.798073−04	−4.393564−03	3.342184−02
1.150	5.105185−04	−3.278761−03	2.479242−02
1.200	3.887319−04	−2.482104−03	1.866457−02
1.250	2.997483−04	−1.903616−03	1.424093−02
1.300	2.338062−04	−1.477384−03	1.099935−02
1.350	1.843026−04	−1.159122−03	8.591229−03
1.400	1.466955−04	−9.185559−04	6.779665−03
1.450	1.178112−04	−7.346574−04	5.401029−03
1.500	9.540094−05	−5.926078−04	4.340602−03
1.550	7.784962−05	−4.818205−04	3.516831−03
1.600	6.398331−05	−3.946377−04	2.871000−03
1.650	5.293890−05	−3.254553−04	2.360326−03
1.700	4.407505−05	−2.701274−04	1.953289−03
1.750	3.691049−05	−2.255557−04	1.626427−03
1.800	3.108070−05	−1.894028−04	1.362105−03
1.850	2.630718−05	−1.598896−04	1.146947−03
1.900	2.237541−05	−1.356505−04	9.707242−04
2.000	1.640741−05	−9.900284−05	7.052857−04
2.100	1.223093−05	−7.348509−05	5.213471−04
2.200	9.253708−06	−5.537839−05	3.914031−04
2.300	7.095716−06	−4.230968−05	2.979944−04
2.400	5.507715−06	−3.273049−05	2.297833−04
2.500	4.322955−06	−2.560969−05	1.792539−04
2.600	3.427841−06	−2.024793−05	1.413295−04
2.700	2.743696−06	−1.616280−05	1.125219−04
2.800	2.215198−06	−1.301635−05	9.039626−05
2.900	1.802897−06	−1.056846−05	7.322836−05
3.000	1.478295−06	−8.646262−06	5.978077−05
3.100	1.220562−06	−7.123768−06	4.915440−05
3.200	1.014298−06	−5.908123−06	4.068842−05
3.300	8.480008−07	−4.930163−06	3.389194−05
3.400	7.129961−07	−4.137866−06	2.839663−05
3.500	6.026822−07	−3.491738−06	2.392353−05
3.600	5.119922−07	−2.961537−06	2.025952−05
3.700	4.370057−07	−2.523918−06	1.724043−05
3.800	3.746668−07	−2.160723−06	1.473882−05
3.900	3.225763−07	−1.857724−06	1.265504−05
4.000	2.788380−07	−1.603698−06	1.091063−05
4.250	1.968610−07	−1.128735−06	7.656552−06
4.500	1.419151−07	−8.114381−07	5.489578−06
4.750	1.042170−07	−5.943935−07	4.011520−06
5.000	7.780963−08	−4.427666−07	2.981638−06
5.250	5.896374−08	−3.348246−07	2.250215−06
5.500	4.528677−08	−2.566661−07	1.721760−06
5.750	3.520915−08	−1.991968−07	1.333970−06
6.000	2.768034−08	−1.563455−07	1.045355−06
6.250	2.198424−08	−1.239834−07	8.277625−07
6.500	1.762455−08	−9.925520−08	6.617638−07
6.750	1.425196−08	−8.015560−08	5.337405−07
7.000	1.161716−08	−6.525596−08	4.340085−07
7.250	9.539906−09	−5.352519−08	3.555903−07
7.500	7.888280−09	−4.420999−08	2.933963−07
7.750	6.564671−09	−3.675381−08	2.436718−07
8.000	5.496091−09	−3.074111−08	2.036176−07
8.250	4.627434−09	−2.585861−08	1.711258−07
8.500	3.916719−09	−2.186791−08	1.445948−07
9.000	2.847343−09	−1.587162−08	1.047829−07
9.500	2.106922−09	−1.172715−08	7.731238−08
10.000	1.583949−09	−8.804499−09	5.796996−08
10.500	1.207901−09	−6.705998−09	4.410126−08
11.000	9.331036−10	−5.174563−09	3.399318−08
11.500	7.293370−10	−4.040372−09	2.651589−08
12.000	5.762136−10	−3.189036−09	2.090948−08
12.500	4.597357−10	−2.542123−09	1.665358−08
13.000	3.701359−10	−2.044976−09	1.338605−08
13.500	3.004973−10	−1.658938−09	1.085100−08
14.000	2.458543−10	−1.356287−09	8.865178−09
15.000	1.680709−10	−9.259559−10	6.044671−09
16.000	1.178053−10	−6.482627−10	4.227089−09
17.000	8.440310−11	−4.639660−10	3.022289−09
18.000	6.165493−11	−3.385965−10	2.203613−09
19.000	4.582161−11	−2.514262−10	1.634946−09
20.000	3.458491−11	−1.896206−10	1.232113−09
T*	I4	$T^{*2}\frac{\partial I_4}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_4}{\partial T^{*2}}$
.300	3.241264+00	−3.506965+01	4.254119+02
.305	2.711704+00	−2.919046+01	3.523856+02
.310	2.277263+00	−2.439233+01	2.930797+02
.315	1.919386+00	−2.045980+01	2.447050+02
.320	1.623412+00	−1.722352+01	2.050805+02
.325	1.377701+00	−1.454975+01	1.724917+02
.330	1.172970+00	−1.233233+01	1.455849+02
.335	1.001781+00	−1.048667+01	1.232858+02
.340	8.581502−01	−8.945036+00	1.047384+02
.345	7.372472−01	−7.652984+00	8.925760+01
.350	6.351512−01	−6.566551+00	7.629289+01
.360	4.752088−01	−4.874769+00	5.621876+01
.370	3.591494−01	−3.656876+00	4.187594+01
.380	2.740108−01	−2.770214+00	3.150879+01
.390	2.109145−01	−2.117863+00	2.393357+01
.400	1.637034−01	−1.633133+00	1.834179+01
.410	1.280586−01	−1.269589+00	1.417441+01
.420	1.009168−01	−9.945339−01	1.104048+01
.430	8.008357−02	−7.847019−01	8.663580+00
.440	6.397097−02	−6.233719−01	6.846309+00
.450	5.141972−02	−4.984125−01	5.446300+00
.460	4.157606−02	−4.009443−01	4.359952+00
.470	3.380597−02	−3.244122−01	3.511212+00
.480	2.763497−02	−2.639386−01	2.843793+00
.490	2.270535−02	−2.158665−01	2.315711+00
.500	1.874547−02	−1.774334−01	1.895412+00
.510	1.554769−02	−1.465387−01	1.559021+00
.520	1.295228−02	−1.215744−01	1.288343+00
.530	1.083560−02	−1.013017−01	1.069428+00
.540	9.101342−03	−8.476047−02	8.915106−01
.550	7.674143−03	−7.120244−02	7.462371−01
.560	6.494656−03	−6.004113−02	6.270866−01
.580	4.700622−03	−4.315645−02	4.477677−01
.600	3.446845−03	−3.144019−02	3.241807−01
.620	2.558162−03	−2.319127−02	2.377241−01
.640	1.919962−03	−1.730487−02	1.764019−01
.660	1.456039−03	−1.305156−02	1.323461−01
.680	1.114966−03	−9.942337−03	1.003155−01
.700	8.615499−04	−7.644667−03	7.676759−02
.720	6.713950−04	−5.929426−03	5.927504−02
.740	5.273829−04	−4.636758−03	4.615369−02
.760	4.173650−04	−3.653833−03	3.622093−02
.780	3.326273−04	−2.900140−03	2.863710−02
.800	2.668564−04	−2.317637−03	2.279971−02
.820	2.154346−04	−1.864073−03	1.827218−02
.840	1.749541−04	−1.508410−03	1.473519−02
.860	1.428790−04	−1.227653−03	1.195313−02
.880	1.173067−04	−1.004620−03	9.750674−03
.900	9.679909−05	−8.263770−04	7.996355−03
.920	8.026136−05	−6.831159−04	6.590822−03
.940	6.685419−05	−5.673448−04	5.458474−03
.960	5.592996−05	−4.733044−04	4.541387−03
.980	4.698591−05	−3.965385−04	3.794894−03
1.000	3.962935−05	−3.335787−04	3.184336−03
1.025	3.220263−05	−2.702138−04	2.571662−03
1.050	2.631527−05	−2.201490−04	2.089124−03
1.075	2.161920−05	−1.803413−04	1.706616−03
1.100	1.785130−05	−1.484987−04	1.401537−03
1.150	1.234518−05	−1.021609−04	9.593642−04
1.200	8.687832−06	−7.154856−05	6.687723−04
1.250	6.212051−06	−5.093034−05	4.739974−04
1.300	4.506897−06	−3.679636−05	3.410787−04
1.350	3.313759−06	−2.694967−05	2.488678−04
1.400	2.466647−06	−1.998725−05	1.839236−04
1.450	1.857077−06	−1.499639−05	1.375417−04
1.500	1.412954−06	−1.137324−05	1.039872−04
1.550	1.085619−06	−8.711923−06	7.942101−05
1.600	8.417595−07	−6.735629−06	6.123447−05
1.650	6.582598−07	−5.253012−06	4.763077−05
1.700	5.188817−07	−4.130115−06	3.735616−05
1.750	4.120843−07	−3.272047−06	2.952537−05
1.800	3.295752−07	−2.610840−06	2.350620−05
1.850	2.653355−07	−2.097306−06	1.884244−05
1.900	2.149535−07	−1.695496−06	1.520158−05
2.000	1.435428−07	−1.127788−06	1.007327−05
2.100	9.790430−08	−7.664557−07	6.822144−06
2.200	6.806119−08	−5.310687−07	4.711919−06
2.300	4.813884−08	−3.744759−07	3.312774−06
2.400	3.458719−08	−2.682991−07	2.367025−06
2.500	2.520988−08	−1.950463−07	1.716412−06
2.600	1.861860−08	−1.436994−07	1.261578−06
2.700	1.391841−08	−1.071786−07	9.388809−07
2.800	1.052195−08	−8.085161−08	7.067971−07
2.900	8.037267−09	−6.163562−08	5.377702−07
3.000	6.198782−09	−4.744738−08	4.132244−07
3.100	4.823950−09	−3.685853−08	3.204542−07
3.200	3.785635−09	−2.887661−08	2.506512−07
3.300	2.994196−09	−2.280338−08	1.976316−07
3.400	2.385696−09	−1.814186−08	1.570028−07
3.500	1.914038−09	−1.453443−08	1.256099−07
3.600	1.545647−09	−1.172112−08	1.011638−07
3.700	1.255836−09	−9.511116−09	8.198701−08
3.800	1.026293−09	−7.763111−09	6.683935−08
3.900	8.433148−10	−6.371537−09	5.479576−08
4.000	6.965663−10	−5.256901−09	4.516072−08
4.250	4.410838−10	−3.320167−09	2.845104−08
4.500	2.870033−10	−2.155306−09	1.842734−08
4.750	1.913107−10	−1.433640−09	1.223211−08
5.000	1.303068−10	−9.746050−10	8.299978−09
5.250	9.049545−11	−6.756474−10	5.744130−09
5.500	6.396018−11	−4.767569−10	4.046851−09
5.750	4.593230−11	−3.418645−10	2.897631−09
6.000	3.346926−11	−2.487590−10	2.105637−09
6.250	2.471514−11	−1.834575−10	1.550948−09
6.500	1.847579−11	−1.369788−10	1.156669−09
6.750	1.396863−11	−1.034466−10	8.725686−10
7.000	1.067208−11	−7.895043−11	6.652658−10
7.250	8.233073−12	−6.084691−11	5.122284−10
7.500	6.409141−12	−4.732306−11	3.980219−10
7.750	5.031519−12	−3.711861−11	3.119300−10
8.000	3.981275−12	−2.934644−11	2.464181−10
8.250	3.173611−12	−2.337473−11	1.961256−10
8.500	2.547403−12	−1.874858−11	1.571967−10
9.000	1.673114−12	−1.229700−11	1.029664−10
9.500	1.124743−12	−8.256300−12	6.904902−11
10.000	7.720126−13	−5.660611−12	4.728869−11
10.500	5.399329−13	−3.954823−12	3.300528−11
11.000	3.840856−13	−2.810607−12	2.343441−11
11.500	2.774739−13	−2.028668−12	1.690027−11
12.000	2.033021−13	−1.485168−12	1.236273−11
12.500	1.508963−13	−1.101495−12	9.162235−12
13.000	1.133404−13	−8.267637−13	6.872305−12
13.500	8.607244−14	−6.274421−13	5.212143−12
14.000	6.603353−14	−4.810663−13	3.993805−12
15.000	3.995777−14	−2.907711−13	2.411337−12
16.000	2.498852−14	−1.816580−13	1.505007−12
17.000	1.608514−14	−1.168284−13	9.670606−13
18.000	1.062189−14	−7.708556−14	6.375835−13
19.000	7.175581−15	−5.203660−14	4.300941−13
20.000	4.947267−15	−3.585305−14	2.961410−13
T*	$B_0^{*}$	$T^{*}\frac{\partial B_0^{*}}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{B}_0^{*}}{\partial T^{*2}}$
.300	−14.65940	40.28430	−184.79590
.305	−14.01284	37.98229	−172.14785
.310	−13.41250	35.87770	−160.70990
.315	−12.85402	33.94891	−150.33361
.320	−12.33350	32.17720	−140.89920
.325	−11.84743	30.54626	−132.29991
.330	−11.39270	29.04180	−124.44590
.335	−10.96654	27.65128	−117.25442
.340	−10.56650	26.36360	−110.65850
.345	−10.19040	25.16897	−104.59418
.350	−9.83630	24.05870	−99.00980
.360	−9.18730	22.06130	−89.09280
.370	−8.60710	20.31930	−80.59050
.380	−8.08590	18.79100	−73.25340
.390	−7.61560	17.44280	−66.88320
.400	−7.18940	16.24740	−61.32110
.410	−6.80152	15.18233	−56.43877
.420	−6.44730	14.22926	−52.13195
.430	−6.12270	13.37279	−48.31515
.440	−5.82426	12.60013	−44.91786
.450	−5.54906	11.90052	−41.88158
.460	−5.29457	11.26485	−39.15748
.470	−5.05861	10.68542	−36.70459
.480	−4.83928	10.15563	−34.48832
.490	−4.63494	9.66981	−32.47935
.500	−4.44415	9.22312	−30.65270
.510	−4.26562	8.81133	−28.98700
.520	−4.09825	8.43078	−27.46388
.530	−3.94105	8.07829	−26.06748
.540	−3.79314	7.75107	−24.78407
.550	−3.65373	7.44668	−23.60173
.560	−3.52213	7.16294	−22.51003
.580	−3.27992	6.65007	−20.56321
.600	−3.06222	6.19964	−18.88309
.620	−2.86556	5.80149	−17.42246
.640	−2.68707	5.44746	−16.14409
.660	−2.52438	5.13097	−15.01830
.680	−2.37550	4.84661	−14.02124
.700	−2.23877	4.58994	−13.13352
.720	−2.11278	4.35728	−12.33930
.740	−1.99633	4.14556	−11.62551
.760	−1.88838	3.95217	−10.98131
.780	−1.78805	3.77493	−10.39762
.800	−1.69456	3.61197	−9.86683
.820	−1.60724	3.46169	−9.38249
.840	−1.52551	3.32273	−8.93910
.860	−1.44885	3.19388	−8.53199
.880	−1.37682	3.07412	−8.15712
.900	−1.30900	2.96255	−7.81102
.920	−1.24503	2.85839	−7.49067
.940	−1.18462	2.76094	−7.19345
.960	−1.12746	2.66958	−6.91707
.980	−1.07330	2.58379	−6.65932
1.000	−1.02193	2.50307	−6.41903
1.025	−.96130	2.40868	−6.14006
1.050	−.90432	2.32083	−5.88265
1.075	−.85068	2.23887	−5.64452
1.100	−.80009	2.16225	−5.42366
1.150	−.70711	2.02309	−5.02703
1.200	−.62366	1.90007	−4.68131
1.250	−.54836	1.79056	−4.37761
1.300	−.48008	1.69248	−4.10895
1.350	−.41789	1.60417	−3.86977
1.400	−.36102	1.52425	−3.65562
1.450	−.30882	1.45159	−3.46286
1.500	−.26074	1.38526	−3.28852
1.550	−.21632	1.32447	−3.13016
1.600	−.17517	1.26856	−2.98571
1.650	−.13693	1.21697	−2.85347
1.700	−.10132	1.16923	−2.73199
1.750	−.06807	1.12492	−2.62002
1.800	−.03697	1.08368	−2.51651
1.850	−.00780	1.04520	−2.42060
1.900	.01958	1.00926	−2.33139
2.000	.06965	.94392	−2.17073
2.100	.11428	.88612	−2.03004
2.200	.15429	.83462	−1.90587
2.300	.19036	.78844	−1.79550
2.400	.22302	.74861	−1.69677
2.500	.25273	.70909	−1.60796
2.600	.27986	.67474	−1.52765
2.700	.30473	.64335	−1.45469
2.800	.32760	.61453	−1.38812
2.900	.34869	.58800	−1.32715
3.000	.36821	.56348	−1.27109
3.100	.38631	.54076	−1.21939
3.200	.40314	.51964	−1.17155
3.300	.41882	.49996	−1.12716
3.400	.43347	.48158	−1.08587
3.500	.44718	.46438	−1.04735
3.600	.46004	.44823	−1.01134
3.700	.47211	.43306	−.97761
3.800	.48347	.41877	−.94594
3.900	.49417	.40529	−.91615
4.000	.50427	.39255	−.88808
4.250	.52721	.36351	−.82468
4.500	.54722	.33811	−.76893
4.750	.56489	.31553	−.72000
5.000	.58055	.26539	−.67652
5.250	.59451	.27730	−.63765
5.500	.60703	.26097	−.60269
5.750	.61830	.24617	−.57108
6.000	.62849	.23266	−.54237
6.250	.63775	.22027	−.51622
6.500	.64615	.20895	−.49215
6.750	.65380	.19855	−.46993
7.000	.66087	.18880	−.44969
7.250	.66740	.17971	−.43106
7.500	.67330	.17147	−.41331
7.750	.67869	.16386	−.39660
8.000	.68387	.15640	−.38180
8.250	.68877	.14927	−.36829
8.500	.69295	.14317	−.35423
9.000	.70079	.13148	−.32991
9.500	.70762	.12105	−.30829
10.000	.71358	.11171	−.28895
10.500	.71883	.10328	−.27154
11.000	.72345	.09564	−.25578
11.500	.72755	.08869	−.24146
12.000	.73119	.08233	−.22838
12.500	.73443	.07649	−.21639
13.000	.73732	.07112	−.20535
13.500	.73991	.06615	−.19516
14.000	.74223	.06155	−.18572
15.000	.74619	.05329	−.16879
16.000	.74939	.04608	−.15404
17.000	.75199	.03974	−.14107
18.000	.75410	.03412	−.12958
19.000	.75581	.02910	−.11932
20.000	.75719	.02459	−.11011
T*	Y	I1	$T^{*}\frac{\partial I_1}{\partial T^{*}}$
.300	2.39246	30.33122	−139.9341
.305	2.37277	28.11705	−128.1696
.310	2.35356	26.11964	−117.6753
.315	2.33480	24.31307	−108.2875
.320	2.31649	22.67504	−99.86678
.325	2.29860	21.18627	−92.29377
.330	2.28112	19.83005	−85.46614
.335	2.26404	18.59187	−79.29574
.340	2.24733	17.45908	−73.70644
.345	2.23098	16.42059	−68.63230
.350	2.21499	15.46671	−64.01602
.360	2.18401	13.77963	−55.96360
.370	2.15429	12.34092	−49.22010
.380	2.12576	11.10592	−43.53183
.390	2.09833	10.03930	−38.70130
.400	2.07193	9.112846	−34.57332
.410	2.04651	8.303853	−31.02497
.420	2.02200	7.593913	−27.95803
.430	1.99835	6.967994	−25.29350
.440	1.97551	6.413740	−22.96733
.450	1.95344	5.920928	−20.92726
.460	1.93209	5.481054	−19.13041
.470	1.91142	5.087002	−17.54135
.480	1.89141	4.732785	−16.13065
.490	1.87201	4.413341	−14.87375
.500	1.85319	4.124373	−13.75002
.510	1.83493	3.862212	−12.74207
.520	1.81721	3.623715	−11.83517
.530	1.79998	3.406177	−11.01680
.540	1.78324	3.207263	−10.27624
.550	1.76695	3.024948	−9.604300
.560	1.75110	2.857468	−8.993079
.580	1.72065	2.561058	−7.926352
.600	1.69173	2.307858	−7.031470
.620	1.66422	2.089978	−6.274494
.640	1.63801	1.901225	−5.629276
.660	1.61300	1.736693	−5.075448
.680	1.58910	1.592452	−4.596980
.700	1.56623	1.465333	−4.181136
.720	1.54433	1.352754	−3.817708
.740	1.52332	1.252600	−3.498444
.760	1.50314	1.163120	−3.216626
.780	1.48374	1.082862	−2.966743
.800	1.46508	1.010609	−2.744243
.820	1.44710	.9453366	−2.545344
.840	1.42977	.8861799	−2.366885
.860	1.41305	.8324015	−2.206208
.880	1.39690	.7833716	−2.061067
.900	1.38129	.7385497	−1.929554
.920	1.36619	.6974694	−1.810042
.940	1.35158	.6597270	−1.701137
.960	1.33743	.6249715	−1.601636
.980	1.32371	.5928968	−1.510503
1.000	1.31041	.5632347	−1.426838
1.025	1.29433	.5291937	−1.331573
1.050	1.27882	.4981569	−1.245441
1.075	1.26387	.4697812	−1.167324
1.100	1.24942	.4437713	−1.096268
1.150	1.22196	.3978599	−.9721832
1.200	1.19623	.3587499	−.8679052
1.250	1.17206	.3251614	−.7794634
1.300	1.14930	.2961015	−.7038273
1.350	1.12782	.2707907	−.6386536
1.400	1.10749	.2486101	−.5821084
1.450	1.08823	.2290635	−.5327406
$T^{*2}\frac{{\partial }^2{I}_1}{\partial T^{*2}}$	I2	$T^{*}\frac{\partial I_2}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_2}{\partial T^{*2}}$
887.6048	2.286542+01	−1.568903+02	1.307549+03
805.2622	2.042278+01	−1.390449+02	1.150792+03
732.4625	1.829016+01	−1.235857+02	1.015935+03
667.9051	1.642243+01	−1.101495+02	8.995178+02
610.4911	1.478184+01	−9.843485+01	7.986862+02
559.2882	1.333666+01	−8.819020+01	7.110755+02
513.5025	1.206011+01	−7.920502+01	6.347195+02
472.4561	1.092957+01	−7.130245+01	5.679767+02
435.5677	9.925780+00	−6.433333+01	5.094716+02
402.3377	9.032372+00	−5.817150+01	4.580479+02
372.3349	8.235338+00	−5.270985+01	4.127299+02
320.5689	6.884062+00	−4.353561+01	3.372318+02
277.8364	5.794601+00	−3.622820+01	2.777444+02
242.2871	4.909184+00	−3.035810+01	2.304516+02
212.4996	4.184212+00	−2.560505+01	1.925382+02
187.3713	3.586458+00	−2.172783+01	1.619057+02
166.0395	3.090367+00	−1.854296+01	1.369740+02
147.8232	2.676115+00	−1.590970+01	1.165421+02
132.1810	2.328202+00	−1.371907+01	9.968917+01
118.6788	2.034411+00	−1.188612+01	8.570339+01
106.9665	1.785050+00	−1.034404+01	7.403002+01
96.75971	1.572372+00	−9.039979+00	6.423368+01
87.82582	1.390148+00	−7.931802+00	5.597018+01
79.97368	1.233339+00	−6.985724+00	4.896567+01
73.04522	1.097845+00	−6.174489+00	4.300084+01
66.90905	9.803091−01	−5.475976+00	3.789906+01
61.45536	8.779726−01	−4.872139+00	3.351722+01
56.59200	7.885544−01	−4.348177+00	2.973877+01
52.24123	7.101603−01	−3.891891+00	2.646827+01
48.33721	6.412100−01	−3.493178+00	2.362723+01
44.82392	5.803798−01	−3.143633+00	2.115073+01
41.65353	5.265559−01	−2.836237+00	1.898490+01
36.18317	4.363080−01	−2.325258+00	1.541279+01
31.66150	3.645188−01	−1.923328+00	1.263149+01
27.89008	3.068576−01	−1.603900+00	1.044229+01
24.71824	2.601288−01	−1.347616+00	8.701798+00
22.03019	2.219458−01	−1.140180+00	7.305190+00
19.73600	1.905060−01	−9.709084−01	6.174868+00
17.76513	1.644338−01	−8.317315−01	5.252744+00
16.06170	1.426689−01	−7.164893−01	4.494867+00
14.58108	1.243869−01	−6.204358−01	3.867653+00
13.28736	1.089413−01	−5.398818−01	3.345202+00
12.15135	9.582083−02	−4.719354−01	2.907368+00
11.14925	8.461853−02	−4.143121−01	2.538349+00
10.26144	7.500790−02	−3.651938−01	2.225657+00
9.471702	6.672536−02	−3.231237−01	1.959355+00
8.766515	5.955681−02	−2.869268−01	1.731477+00
8.134566	5.332728−02	−2.556494−01	1.535600+00
7.566329	4.789300−02	−2.285131−01	1.366511+00
7.053742	4.313520−02	−2.048790−01	1.219957+00
6.589956	3.895530−02	−1.842198−01	1.092446+00
6.169119	3.527105−02	−1.660985−01	9.811007−01
5.786215	3.201352−02	−1.501507−01	8.835341−01
5.436924	2.912473−02	−1.360716−01	7.977592−01
5.041941	2.595832−02	−1.207141−01	7.046163−01
4.687456	2.321228−02	−1.074644−01	6.246446−01
4.368228	2.082129−02	−9.598513−02	5.556786−01
4.079825	1.873161−02	−8.600013−02	4.959560−01
3.580964	1.528561−02	−6.964312−02	3.987237−01
3.166780	1.259994−02	−5.700268−02	3.241760−01
2.819417	1.048156−02	−4.711007−02	2.662601−01
2.525432	8.792282−03	−3.927852−02	2.207221−01
2.274563	7.431674−03	−3.301330−02	1.845227−01
2.058873	6.325721−03	−2.795282−02	1.554571−01
1.872153	5.419174−03	−2.382922−02	1.319042−01
T*	Y	I1	$T^{*}\frac{\partial I_1}{\partial T^{*}}$
1.50	1.06994	.2117490	−.4893897
1.55	1.05254	.1963389	−.4511206
1.60	1.03597	.1825629	−.4171710
1.65	1.02015	.1701977	−.3869170
1.70	1.00504	.1590566	−.3598421
1.75	.99057	.1489827	−.3355172
1.80	.97672	.1398436	−.3135827
1.85	.96343	.1315268	−.2937360
1.90	.95067	.1239364	−.2757205
2.00	.92660	.1106161	−.2443418
2.10	.90427	.09934915	−.2180474
2.20	.88348	.08973313	−.1957959
2.30	.86406	.08145959	−.1767988
2.40	.84586	.07428901	−.1604509
2.50	.82877	.06803305	−.1462812
2.60	.81268	.06254203	−.1339189
2.70	.79749	.05769570	−.1230690
2.80	.78312	.05339657	−.1134939
2.90	.76950	.04956497	−.1050013
3.00	.75656	.04613524	−.09743365
3.10	.74426	.04305285	−.09066109
3.20	.73254	.04027226	−.08457576
3.30	.72135	.03775517	−.07908758
3.40	.71067	.03546914	−.07412065
3.50	.70044	.03338665	−.06961089
3.60	.69064	.03148412	−.06550368
3.70	.68125	.02974131	−.06175239
3.80	.67222	.02814075	−.05831693
3.90	.66355	.02666730	−.05516272
4.00	.65520	.02530779	−.05225977
4.25	.63564	.02233547	−.04593857
4.50	.61773	.01986234	−.04070718
4.75	.60126	.01778214	−.03632802
5.00	.58603	.01601549	−.03262499
5.25	.57191	.01450215	−.02946531
5.50	.55876	.01319570	−.02674728
5.75	.54648	.01205991	−.02439200
6.00	.53497	.01106618	−.02233743
6.25	.52416	.01019166	−.02053430
6.50	.51398	.009417927	−.01894303
6.75	.50438	.008730000	−.01753156
7.00	.49529	.008115584	−.01627368
7.25	.48667	.007564515	−.01514779
7.50	.47849	.007068335	−.01413598
7.75	.47071	.006619953	−.01322327
8.00	.46330	.006213392	−.01239708
8.25	.45622	.005843580	−.01164676
8.50	.44947	.005506197	−.01096326
9.00	.43680	.004914421	−.009766832
9.50	.42515	.004414136	−.008757935
10.00	.41439	.003987324	−.007899171
10.50	.40440	.003620204	−.007162038
11.00	.39510	.003302090	−.006524508
11.50	.38642	.003024589	−.005969331
12.00	.37828	.002781039	−.005482848
12.50	.37064	.002566089	−.005054124
13.00	.36344	.002375410	−.004674321
13.50	.35665	.002205460	−.004336235
14.00	.35022	.002053326	−.004033944
15.00	.33835	.001793224	−.003517937
16.00	.32760	.001580094	−.003095929
17.00	.31782	.001403217	−.002746301
18.00	.30887	.001254775	−.002453326
19.00	.30063	.001128955	−.002205338
20.00	.29302	.001021361	−.001993533
$T^{*2}\frac{{\partial }^2{I}_1}{\partial T^{*2}}$	I2	$T^{*}\frac{\partial I_2}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_2}{\partial T^{*2}}$
1.709489	4.670261−03	−2.044152−02	1.126553−01
1.566963	4.047128−03	−1.763746−02	9.680079−02
1.441411	3.525173−03	−1.530019−02	8.364670−02
1.330266	3.085242−03	−1.333934−02	7.265918−02
1.231420	2.712290−03	−1.168429−02	6.342350−02
1.143139	2.394401−03	−1.027943−02	5.561464−02
1.063978	2.122066−03	−9.080609−03	4.897578−02
.9927318	1.887642−03	−8.052516−03	4.330245−02
.9283853	1.684943−03	−7.166710−03	3.843070−02
.8170882	1.355488−03	−5.733976−03	3.058729−02
.7246361	1.103278−03	−4.643913−03	2.465463−02
.6470188	9.074849−04	−3.802441−03	2.009937−02
.5812343	7.535619−04	−3.144327−03	1.655417−02
.5250010	6.311664−04	−2.623499−03	1.376119−02
.4765597	5.328248−04	−2.206864−03	1.153630−02
.4345374	4.530566−04	−1.870293−03	9.745929−03
.3978499	3.877881−04	−1.595944−03	8.291813−03
.3656320	3.339540−04	−1.370457−03	7.100701−03
.3371868	2.892212−04	−1.183710−03	6.117337−03
.3119478	2.517953−04	−1.027949−03	5.299563−03
.2894509	2.202828−04	−8.971811−04	4.614905−03
.2693126	1.935909−04	−7.867198−04	4.038080−03
.2512146	1.708571−04	−6.928812−04	3.549265−03
.2348900	1.513938−04	−6.127376−04	3.132760−03
.2201145	1.346493−04	−5.439477−04	2.776047−03
.2066978	1.201777−04	−4.846256−04	2.469073−03
.1944782	1.076168−04	−4.332421−04	2.203706−03
.1833173	9.666994−05	−3.885495−04	1.973329−03
.1730960	8.709312−05	−3.495237−04	1.772523−03
.1637116	7.868449−05	−3.153195−04	1.596828−03
.1433554	6.173863−05	−2.465828−04	1.244708−03
.1265949	4.915436−05	−1.957328−04	9.851711−04
.1126289	3.964493−05	−1.574396−04	7.903674−04
.1008679	3.234685−05	−1.281424−04	6.417726−04
.09087004	2.666764−05	−1.054085−04	5.267787−04
.08229886	2.219266−05	−8.754121−05	4.366257−04
.07489462	1.862645−05	−7.333611−05	3.651138−04
.06845413	1.575508−05	−6.192363−05	3.077808−04
.06281665	1.342133−05	−5.266666−05	2.613665−04
.05785362	1.150814−05	−4.509202−05	2.234554−04
.05346127	9.927218−06	−3.884373−05	1.922349−04
.04955505	8.611268−06	−3.365112−05	1.663296−04
.04606554	7.508419−06	−2.930596−05	1.446837−04
.04293532	6.578322−06	−2.564663−05	1.264792−04
.04011652	5.789303−06	−2.254648−05	1.110762−04
.03756901	5.116285−06	−1.990543−05	9.797003−05
.03525894	4.539266−06	−1.764376−05	8.675933−05
.03315757	4.042168−06	−1.569753−05	7.712254−05
.02948643	3.238125−06	−1.255433−05	6.158172−05
.02639820	2.626182−06	−1.016666−05	4.979806−05
.02377525	2.153503−06	−8.325542−06	4.072685−05
.02152824	1.783518−06	−6.886682−06	3.364826−05
.01958835	1.490426−06	−5.748492−06	2.805655−05
.01790183	1.255713−06	−4.838203−06	2.359014−05
.01642622	1.065881−06	−4.102870−06	1.998637−05
.01512762	9.109534−07	−3.503412−06	1.705166−05
.01397869	7.834572−07	−3.010605−06	1.464148−05
.01295718	6.777282−07	−2.602328−06	1.264657−05
.01204484	5.894281−07	−2.261660−06	1.098345−05
.01048983	4.524138−07	−1.733684−06	8.408888−06
.009220422	3.533375−07	−1.352467−06	6.552628−06
.008170439	2.801963−07	−1.071412−06	5.185827−06
.007291867	2.252091−07	−8.603654−07	4.160649−06
.006549166	1.831970−07	−6.992897−07	3.379009−06
.005915574	1.506324−07	−5.745553−07	2.774280−06
T*	I3	$T^{*}\frac{\partial I_3}{\partial T^{*}}$	$T^{{*}_2}\frac{{\partial }^2{I}_3}{\partial T^{*2}}$
.300	1.089813+01	−9.703553+01	9.966130+02
.305	9.410824+00	−8.328906+01	8.506390+02
.310	8.152881+00	−7.173376+01	7.286300+02
.315	7.085093+00	−6.198374+01	6.262524+02
.320	6.175575+00	−5.372721+01	5.400247+02
.325	5.398288+00	−4.671108+01	4.671370+02
.330	4.731877+00	−4.072906+01	4.053114+02
.335	4.158766+00	−3.561231+01	3.526936+02
.340	3.664428+00	−3.122210+01	3.077681+02
.345	3.236817+00	−2.744402+01	2.692913+02
.350	2.865905+00	−2.418335+01	2.362390+02
.360	2.262037+00	−1.891263+01	1.831654+02
.370	1.800732+00	−1.492394+01	1.433513+02
.380	1.444990+00	−1.187555+01	1.131766+02
.390	1.168220+00	−9.524205+00	9.008758+01
.400	9.511009−01	−7.694771+00	7.226092+01
.410	7.794452−01	−6.259801+00	5.838075+01
.420	6.427369−01	−5.125613+00	4.748736+01
.430	5.331073−01	−4.222684+00	3.887391+01
.440	4.446189−01	−3.498964+00	3.201505+01
.450	3.727538−01	−2.915149+00	2.651685+01
.460	3.140484−01	−2.441325+00	2.208151+01
.470	2.658276−01	−2.054550+00	1.848213+01
.480	2.260107−01	−1.737102+00	1.554454+01
.490	1.929691−01	−1.475199+00	1.313413+01
.500	1.654198−01	−1.258053+00	1.114614+01
.510	1.423460−01	−1.077167+00	9.498516+00
.520	1.229373−01	−9.258111−01	8.126635+00
.530	1.065445−01	−7.986204−01	6.979269+00
.540	9.264450−02	−6.913001−01	6.015605+00
.550	8.081402−02	−6.003915−01	5.202949+00
.560	7.070875−02	−5.230969−01	4.514980+00
.580	5.459910−02	−4.006704−01	3.431918+00
.600	4.261392−02	−3.103515−01	2.639212+00
.620	3.359016−02	−2.428883−01	2.051524+00
.640	2.672066−02	−1.919148−01	1.610613+00
.660	2.143733−02	−1.529884−01	1.276158+00
.680	1.733509−02	−1.229667−01	1.019846+00
.700	1.412152−02	−9.959836−02	8.215376−01
.720	1.158318−02	−8.125182−02	6.667366−01
.740	9.562594−03	−6.673154−02	5.448882−01
.760	7.942415−03	−5.515256−02	4.482270−01
.780	6.634393−03	−4.585341−02	3.709832−01
.800	5.571573−03	−3.833527−02	3.088295−01
.820	4.702738−03	−3.221871−02	2.584925−01
.840	3.988402−03	−2.721284−02	2.174751−01
.860	3.397903−03	−2.309293−02	1.838578−01
.880	2.907260−03	−1.968412−02	1.561541−01
.900	2.497600−03	−1.684943−02	1.332048−01
.920	2.153971−03	−1.448088−02	1.141000−01
.940	1.864459−03	−1.249278−02	9.812100−02
.960	1.619520−03	−1.081681−02	8.469666−02
.980	1.411462−03	−9.398116−03	7.337052−02
1.000	1.234058−03	−8.192476−03	6.377587−02
1.025	1.047782−03	−6.931071−03	5.377172−02
1.050	8.936360−04	−5.891252−03	4.555520−02
1.075	7.654231−04	−5.029553−03	3.877009−02
1.100	6.582620−04	−4.311881−03	3.313810−02
1.150	4.923977−04	−3.206473−03	2.450365−02
1.200	3.734919−04	−2.418982−03	1.838932−02
1.250	2.869116−04	−1.848900−03	1.398757−02
1.300	2.229669−04	−1.430128−03	1.077080−02
1.350	1.751220−04	−1.118365−03	8.387520−03
1.400	1.388933−04	−8.833992−04	6.599386−03
1.450	1.111569−04	−7.042997−04	5.242137−03
1.500	8.970483−05	−5.663495−04	4.200853−03
1.550	7.295596−05	−4.590602−04	3.394012−03
1.600	5.976387−05	−3.748626−04	2.763044−03
1.650	4.928791−05	−3.082304−04	2.265359−03
1.700	4.090503−05	−2.550845−04	1.869646−03
1.750	3.414885−05	−2.123835−04	1.552645−03
1.800	2.866703−05	−1.778379−04	1.296910−03
1.850	2.419103−05	−1.497091−04	1.089232−03
1.900	2.051451−05	−1.266655−04	9.195308−04
2.000	1.495589−05	−9.195064−05	6.647649−04
2.100	1.108646−05	−6.789605−05	4.890137−04
2.200	8.342277−06	−5.090820−05	3.653970−04
2.300	6.363121−06	−3.870348−05	2.769162−04
2.400	4.913787−06	−2.979770−05	2.125732−04
2.500	3.837589−06	−2.320647−05	1.651035−04
2.600	3.028237−06	−1.826465−05	1.296176−04
2.700	2.412416−06	−1.451517−05	1.027673−04
2.800	1.938779−06	−1.163901−05	8.222362−05
2.900	1.570857−06	−9.410343−06	6.634286−05
3.000	1.282398−06	−7.667070−06	5.394876−05
3.100	1.054298−06	−6.291573−06	4.419005−05
3.200	8.724767−07	−5.197396−06	3.644263−05
3.300	7.264576−07	−4.320374−06	3.024444−05
3.400	6.083674−07	−3.612397−06	2.524979−05
3.500	5.122351−07	−3.037060−06	2.119771−05
3.600	4.334930−07	−2.566575−06	1.788936−05
3.700	3.686192−07	−2.179556−06	1.517204−05
3.800	3.148769−07	−1.859421−06	1.292756−05
3.900	2.701248−07	−1.593215−06	1.106372−05
4.000	2.326754−07	−1.370749−06	9.508155−06
4.250	1.628730−07	−9.569646−07	6.620741−06
4.500	1.164591−07	−6.826206−07	4.711710−06
4.750	8.485738−08	−4.963140−07	3.418556−06
5.000	6.288225−08	−3.670649−07	2.523484−06
5.250	4.730971−08	−2.756692−07	1.891867−06
5.500	3.608478−08	−2.099184−07	1.438338−06
5.750	2.786788−08	−1.618737−07	1.107518−06
6.000	2.176790−08	−1.262657−07	8.627252−07
6.250	1.718091−08	−9.953044−08	6.792026−07
6.500	1.369083−08	−7.921739−08	5.399566−07
6.750	1.100640−08	−6.361395−08	4.331320−07
7.000	8.920855−09	−5.150650−08	3.503406−07
7.250	7.285481−09	−4.202338−08	2.855670−07
7.500	5.992002−09	−3.453091−08	2.344439−07
7.750	4.960690−09	−2.856308−08	1.937640−07
8.000	4.132216−09	−2.377357−08	1.611463−07
8.250	3.461997−09	−1.990244−08	1.348060−07
8.500	2.916219−09	−1.675275−08	1.133923−07
9.000	2.100450−09	−1.205033−08	8.145783−08
9.500	1.540574−09	−8.827676−09	5.960343−08
10.000	1.148434−09	−6.573486−09	4.433623−08
10.500	8.687249−10	−4.967515−09	3.347195−08
11.000	6.658999−10	−3.804255−09	2.561094−08
11.500	5.166138−10	−2.948915−09	1.983643−08
12.000	4.052293−10	−2.311324−09	1.553583−08
12.500	3.210828−10	−1.830060−09	1.229237−08
13.000	2.567825−10	−1.462596−09	9.817774−09
13.500	2.071272−10	−1.179035−09	7.909565−09
14.000	1.684059−10	−9.580649−10	6.423560−09
15.000	1.137591−10	−6.464976−10	4.330147−09
16.000	7.884474−11	−4.476609−10	2.995651−09
17.000	5.589153−11	−3.170752−10	2.120086−09
18.000	4.041788−11	−2.291218−10	1.530886−09
19.000	2.975147−11	−1.685425−10	1.125386−09
20.000	2.225107−11	−1.259758−10	8.406618−10
T*	I4	$T^{*2}\frac{\partial I_4}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_4}{\partial T^{*2}}$
.300	3.552717+00	−3.867929+01	4.715396+02
.305	2.968936+00	−3.216256+01	3.902382+02
.310	2.490493+00	−2.684891+01	3.242660+02
.315	2.096764+00	−2.249778+01	2.704977+02
.320	1.771467+00	−1.892023+01	2.264911+02
.325	1.501681+00	−1.596714+01	1.903278+02
.330	1.277114+00	−1.352028+01	1.604939+02
.335	1.089525+00	−1.148545+01	1.357889+02
.340	9.322898−01	−9.787319+00	1.152570+02
.345	8.000649−01	−8.365360+00	9.813361+01
.350	6.885188−01	−7.170759+00	8.380474+01
.360	5.140212−01	−5.312920+00	6.164439+01
.370	3.876467−01	−3.977827+00	4.583621+01
.380	2.951207−01	−3.007536+00	3.442800+01
.390	2.266814−01	−2.294893+00	2.610526+01
.400	1.755705−01	−1.766276+00	1.997133+01
.410	1.370545−01	−1.370495+00	1.540704+01
.420	1.077820−01	−1.071561+00	1.197996+01
.430	8.535522−02	−8.438989−01	9.384752+00
.440	6.804251−02	−6.691547−01	7.403618+00
.450	5.458138−02	−5.340318−01	5.879705+00
.460	4.404352−02	−4.288114−01	4.699012+00
.470	3.574065−02	−3.463291−01	3.777958+00
.480	2.915848−02	−2.812610−01	3.054764+00
.490	2.390987−02	−2.296210−01	2.483406+00
.500	1.970130−02	−1.884025−01	2.029342+00
.510	1.630874−02	−1.553224−01	1.666464+00
.520	1.356010−02	−1.286350−01	1.374903+00
.530	1.132238−02	−1.069976−01	1.139444+00
.540	9.492152−03	−8.937092−02	9.483601−01
.550	7.988579−03	−7.494596−02	7.925615−01
.560	6.748112−03	−6.308959−02	6.649626−01
.580	4.866029−03	−4.519415−02	4.733296−01
.600	3.555103−03	−3.281440−02	3.416268−01
.620	2.629026−03	−2.412502−02	2.497526−01
.640	1.966156−03	−1.794295−02	1.847683−01
.660	1.485863−03	−1.348928−02	1.382097−01
.680	1.133884−03	−1.024314−02	1.044513−01
.700	8.731914−04	−7.851258−03	7.969977−02
.720	6.781867−04	−6.070807−03	6.136195−02
.740	5.309565−04	−4.732799−03	4.764268−02
.760	4.188224−04	−3.718250−03	3.728430−02
.780	3.327143−04	−2.942464−03	2.939584−02
.800	2.660780−04	−2.344528−03	2.333943−02
.820	2.141324−04	−1.880209−03	1.865386−02
.840	1.733581−04	−1.517089−03	1.500253−02
.860	1.411427−04	−1.231204−03	1.213763−02
.880	1.155312−04	−1.004693−03	9.875129−03
.900	9.504966−05	−8.241407−04	8.077340−03
.920	7.857860−05	−6.793953−04	6.640428−03
.940	6.526197−05	−5.627218−04	5.485545−03
.960	5.444087−05	−4.681865−04	4.552404−03
.980	4.560492−05	−3.912084−04	3.794607−03
1.000	3.835650−05	−3.282300−04	3.176231−03
1.025	3.106028−05	−2.650185−04	2.557291−03
1.050	2.529504−05	−2.152250−04	2.071191−03
1.075	2.071101−05	−1.757506−04	1.686931−03
1.100	1.704455−05	−1.442672−04	1.381300−03
1.150	1.171062−05	−9.864344−05	9.400617−04
1.200	8.189066−06	−6.867348−05	6.516277−04
1.250	5.819278−06	−4.859951−05	4.593059−04
1.300	4.196522−06	−3.491300−05	3.287298−04
1.350	3.067425−06	−2.542844−05	2.385960−04
1.400	2.270187−06	−1.875673−05	1.754247−04
1.450	1.699588−06	−1.399849−05	1.305250−04
1.500	1.286044−06	−1.056132−05	9.819524−05
1.550	9.828147−07	−8.048868−06	7.463457−05
1.600	7.580511−07	−6.192005−06	5.727121−05
1.650	5.897554−07	−4.805488−06	4.434079−05
1.700	4.625439−07	−3.760183−06	3.461719−05
1.750	3.655313−07	−2.964996−06	2.723802−05
1.800	2.909305−07	−2.354947−06	2.158979−05
1.850	2.331130−07	−1.883198−06	1.723150−05
1.900	1.879711−07	−1.515654−06	1.384291−05
2.000	1.243911−07	−9.994718−07	9.097224−06
2.100	8.410269−08	−6.735930−07	6.111915−06
2.200	5.797445−08	−4.629645−07	4.188731−06
2.300	4.067070−08	−3.239056−07	2.922859−06
2.400	2.899096−08	−2.303114−07	2.073229−06
2.500	2.096932−08	−1.662009−07	1.492745−06
2.600	1.537182−08	−1.215743−07	1.089641−06
2.700	1.140842−08	−9.004772−08	8.055017−07
2.800	8.564002−09	−6.747026−08	6.024398−07
2.900	6.497053−09	−5.109660−08	4.554609−07
3.000	4.977597−09	−3.908246−08	3.478119−07
3.100	3.848533−09	−3.017078−08	2.680981−07
3.200	3.001098−09	−2.349304−08	2.084630−07
3.300	2.359050−09	−1.844164−08	1.634203−07
3.400	1.868319−09	−1.458642−08	1.290933−07
3.500	1.490134−09	−1.161952−08	1.027119−07
3.600	1.196414−09	−9.318307−09	8.227612−08
3.700	9.666195−10	−7.520194−09	6.632767−08
3.800	7.855930−10	−6.105376−09	5.379350−08
3.900	6.420509−10	−4.984795−09	4.387706−08
4.000	5.275260−10	−4.091710−09	3.598219−08
4.250	3.298024−10	−2.552419−09	2.239718−08
4.500	2.119975−10	−1.637438−09	1.434040−08
4.750	1.396787−10	−1.076922−09	9.414952−09
5.000	9.408499−11	−7.242130−10	6.321320−09
5.250	6.464562−11	−4.968662−10	4.330612−09
5.500	4.522331−11	−3.471132−10	3.021359−09
5.750	3.215720−11	−2.465148−10	2.143097−09
6.000	2.320963−11	−1.777177−10	1.543257−09
6.250	1.698208−11	−1.298937−10	1.126784−09
6.500	1.258260−11	−9.614693−11	8.332304−10
6.750	9.431594−12	−7.200251−11	6.234237−10
7.000	7.145972−12	−5.450643−11	4.715365−10
7.250	5.468455−12	−4.167723−11	3.602648−10
7.500	4.223727−12	−3.216618−11	2.778426−10
7.750	3.290679−12	−2.504253−11	2.161590−10
8.000	2.584582−12	−1.965577−11	1.695502−10
8.250	2.045454−12	−1.554579−11	1.340141−10
8.500	1.630360−12	−1.238354−11	1.066907−10
9.000	1.056427−12	−8.015264−12	6.898051−11
9.500	7.010919−13	−5.313948−12	4.568766−11
10.000	4.753438−13	−3.599600−12	3.092063−11
10.500	3.285613−13	−2.486003−12	2.133743−11
11.000	2.311050−13	−1.747286−12	1.498582−11
11.500	1.651592−13	−1.247823−12	1.069478−11
12.000	1.197570−13	−9.042123−13	7.744867−12
12.500	8.799992−14	−6.640357−13	5.684341−12
13.000	6.546165−14	−4.936900−13	4.223829−12
13.500	4.925021−14	−3.712361−13	3.174546−12
14.000	3.744413−14	−2.821080−13	2.411242−12
15.000	2.227090−14	−1.676438−13	1.431656−12
16.000	1.370361−14	−1.030734−13	8.795627−13
17.000	8.686959−15	−6.529475−14	5.568052−13
18.000	5.653821−15	−4.246999−14	3.619448−13
19.000	3.767110−15	−2.828162−14	2.408936−13
20.000	2.563368−15	−1.923470−14	1.637530−13
T*	I5	$T^{*}\frac{\partial I_5}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_5}{\partial T^{*2}}$
.300	8.415836−01	−1.080607+01	1.523791+02
.305	6.809591−01	−8.706192+00	1.222627+02
.310	5.533785−01	−7.045604+00	9.854655+01
.315	4.515741−01	−5.726160+00	7.977955+01
.320	3.699758−01	−4.672979+00	6.485932+01
.325	3.042922−01	−3.828628+00	5.294388+01
.330	2.512005−01	−3.148826+00	4.338675+01
.335	2.081156−01	−2.599265+00	3.568907+01
.340	1.730168−01	−2.153240+00	2.946402+01
.345	1.443177−01	−1.789869+00	2.441027+01
.350	1.207673−01	−1.492744+00	2.029199+01
.360	8.535276−02	−1.048166+00	1.415945+01
.370	6.103004−02	−7.448447−01	1.000202+01
.380	4.411742−02	−5.352618−01	7.146814+00
.390	3.222019−02	−3.887174−01	5.161966+00
.400	2.375929−02	−2.850999−01	3.766314+00
.410	1.768011−02	−2.110605−01	2.774349+00
.420	1.326969−02	−1.576287−01	2.062124+00
.430	1.004053−02	−1.187060−01	1.545830+00
.440	7.655710−03	−9.010008−02	1.168164+00
.450	5.879945−03	−6.889930−02	8.895235−01
.460	4.547363−03	−5.306110−02	6.822653−01
.470	3.539939−03	−4.113926−02	5.269073−01
.480	2.772959−03	−3.210062−02	4.095948−01
.490	2.185114−03	−2.520083−02	3.203894−01
.500	1.731682−03	−1.989930−02	2.521037−01
.510	1.379792−03	−1.580036−02	1.994985−01
.520	1.105112−03	−1.261234−02	1.587265−01
.530	8.895050−04	−1.011866−02	1.269420−01
.540	7.193631−04	−8.157457−03	1.020260−01
.550	5.844127−04	−6.606980−03	8.239029−02
.560	4.768505−04	−5.375077−03	6.683674−02
.580	3.214262−04	−3.602806−03	4.455549−02
.600	2.200333−04	−2.453306−03	3.018444−02
.620	1.527947−04	−1.695152−03	2.075581−02
.640	1.075220−04	−1.187289−03	1.447122−02
.660	7.660497−05	−8.421453−04	1.022023−02
.680	5.521143−05	−6.044108−04	7.305167−03
.700	4.022432−05	−4.385909−04	5.280475−03
.720	2.960344−05	−3.215642−04	3.857277−03
.740	2.199488−05	−2.380578−04	2.845595−03
.760	1.648856−05	−1.778498−04	2.118819−03
.780	1.246529−05	−1.340146−04	1.591511−03
.800	9.498955−06	−1.018051−04	1.205330−03
.820	7.293143−06	−7.793131−05	9.199968−04
.840	5.639567−06	−6.009008−05	7.074065−04
.860	4.390449−06	−4.665285−05	5.477561−04
.880	3.439982−06	−3.645749−05	4.269589−04
.900	2.711753−06	−2.866739−05	3.349057−04
.920	2.150125−06	−2.267526−05	2.642796−04
.940	1.714266−06	−1.803674−05	2.097422−04
.960	1.373989−06	−1.442424−05	1.673687−04
.980	1.106818−06	−1.159448−05	1.342521−04
1.000	8.959015−07	−9.365590−06	1.082248−04
1.025	6.923006−07	−7.219203−06	8.321982−05
1.050	5.386330−07	−5.603434−06	6.444412−05
1.075	4.217972−07	−4.377998−06	5.023874−05
1.100	3.323434−07	−3.441997−06	3.941376−05
1.150	2.099234−07	−2.165214−06	2.469428−05
1.200	1.354505−07	−1.391788−06	1.581464−05
1.250	8.911174−08	−9.124318−07	1.033225−05
1.300	5.967790−08	−6.090597−07	6.874918−06
1.350	4.062490−08	−4.133480−07	4.651900−06
1.400	2.807497−08	−2.848437−07	3.196778−06
1.450	1.967453−08	−1.990828−07	2.228471−06
1.500	1.396721−08	−1.409782−07	1.574207−06
1.550	1.003561−08	−1.010562−07	1.125828−06
1.600	7.292117−09	−7.326705−08	8.144689−07
1.650	5.354530−09	−5.368660−08	5.955807−07
1.700	3.970625−09	−3.973214−08	4.399199−07
1.750	2.971695−09	−2.968050−08	3.280226−07
1.800	2.243464−09	−2.236719−08	2.467662−07
1.850	1.707597−09	−1.699580−08	1.871954−07
1.900	1.309796−09	−1.301546−08	1.431287−07
2.000	7.873676−10	−7.800613−09	8.553000−08
2.100	4.858924−10	−4.800662−09	5.249585−08
2.200	3.070300−10	−3.025877−09	3.300704−08
2.300	1.982181−10	−1.948994−09	2.121205−08
2.400	1.304964−10	−1.280382−09	1.390605−08
2.500	8.746280−11	−8.564582−10	9.283870−09
2.600	5.959124−11	−5.824623−10	6.302443−09
2.700	4.122070−11	−4.022145−10	4.344805−09
2.800	2.891513−11	−2.816912−10	3.038121−09
2.900	2.054797−11	−1.998789−10	2.152589−09
3.000	1.477919−11	−1.435617−10	1.543953−09
3.100	1.075014−11	−1.042865−10	1.120109−09
3.200	7.902024−12	−7.656163−11	8.213211−10
3.300	5.865881−12	−5.676690−11	6.082692−10
3.400	4.394759−12	−4.248287−11	4.547162−10
3.500	3.321269−12	−3.207192−11	3.429275−10
3.600	2.530585−12	−2.441224−11	2.607706−10
3.700	1.943056−12	−1.872661−11	1.998505−10
3.800	1.502842−12	−1.447086−11	1.542960−10
3.900	1.170403−12	−1.126010−11	1.199597−10
4.000	9.174783−13	−8.819530−12	9.388324−11
4.250	5.125584−13	−4.917769−12	5.225176−11
4.500	2.963307−13	−2.838318−12	3.010697−11
4.750	1.766217−13	−1.689118−12	1.788997−11
5.000	1.081818−13	−1.033149−12	1.092740−11
5.250	6.790842−14	−6.477075−13	6.842093−12
5.500	4.358508−14	−4.152273−13	4.381247−12
5.750	2.854437−14	−2.716451−13	2.863225−12
6.000	1.904185−14	−1.810339−13	1.906296−12
6.250	1.291924−14	−1.227124−13	1.291002−12
6.500	8.902590−15	−8.448842−14	8.881196−13
6.750	6.223408−15	−5.901516−14	6.198670−13
7.000	4.408702−15	−4.177566−14	4.384713−13
7.250	3.161924−15	−2.994069−14	3.140383−13
7.500	2.293933−15	−2.170737−14	2.275356−13
7.750	1.682154−15	−1.590836−14	1.666500−13
8.000	1.245965−15	−1.177644−14	1.232954−13
8.250	9.315991−16	−8.800344−15	9.208714−14
8.500	7.027280−16	−6.634882−15	6.939238−14
9.000	4.097562−16	−3.865064−15	4.038570−14
9.500	2.461127−16	−2.319480−15	2.421550−14
10.000	1.518007−16	−1.429520−15	1.491279−14
10.500	9.589678−17	−9.024235−16	9.407499−15
11.000	6.190781−17	−5.821938−16	6.065296−15
11.500	4.076155−17	−3.830994−16	3.988769−15
12.000	2.732638−17	−2.566856−16	2.671109−15
12.500	1.862487−17	−1.748594−16	1.818693−15
13.000	1.288886−17	−1.209490−16	1.257385−15
13.500	9.045680−18	−8.484681−17	8.816807−16
14.000	6.431688−18	−6.030292−17	6.263778−16
15.000	3.368990−18	−3.156346−17	3.276120−16
16.000	1.840739−18	−1.723402−17	1.787624−16
17.000	1.043663−18	−9.765523−18	1.012349−16
18.000	6.114334−19	−5.718104−18	5.924591−17
19.000	3.688147−19	−3.447475−18	3.570270−17
20.000	2.283636−19	−2.133679−18	2.208725−17
T*	I6	$T^{*}\frac{\partial I_6}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_6}{\partial T^{*2}}$
.300	1.512780−01	−2.234974+00	3.576831+01
.305	1.185551−01	−1.744923+00	2.782351+01
.310	9.336261−02	−1.369098+00	2.175326+01
.315	7.386774−02	−1.079359+00	1.709040+01
.320	5.870707−02	−8.548571−01	1.349016+01
.325	4.686070−02	−6.800556−01	1.069657+01
.330	3.756146−02	−5.433122−01	8.518508+00
.335	3.022925−02	−4.358561−01	6.812511+00
.340	2.442321−02	−3.510454−01	5.470309+00
.350	1.612120−02	−2.303300−01	3.568340+00
.345	1.980667−02	−2.838253−01	4.409785+00
.360	1.079196−02	−1.533103−01	2.361990+00
.370	7.320163−03	−1.034259−01	1.585042+00
.380	5.026975−03	−7.065815−02	1.077419+00
.390	3.492499−03	−4.884739−02	7.412649−01
.400	2.453100−03	−3.414798−02	5.158206−01
.410	1.740901−03	−2.412444−02	3.628094−01
.420	1.247570−03	−1.721333−02	2.577828−01
.430	9.023176−04	−1.239807−02	1.849211−01
.440	6.583363−04	−9.009698−03	1.338617−01
.450	4.843231−04	−6.602888−03	9.773732−02
.460	3.591217−04	−4.877993−03	7.194662−02
.470	2.682873−04	−3.631291−03	5.337426−02
.480	2.018622−04	−2.722920−03	3.988987−02
.490	1.529192−04	−2.055960−03	3.002284−02
.500	1.165966−04	−1.562653−03	2.274880−02
.510	8.945426−05	−1.195226−03	1.734809−02
.520	6.903821−05	−9.197218−04	1.331093−02
.530	5.358472−05	−7.118185−04	1.027338−02
.540	4.181691−05	−5.539657−04	7.973684−03
.550	3.280388−05	−4.334089−04	6.222201−03
.560	2.586245−05	−3.408169−04	4.880602−03
.580	1.630543−05	−2.138188−04	3.047276−03
.600	1.046427−05	−1.365882−04	1.937839−03
.620	6.827114−06	−8.872563−05	1.253446−03
.640	4.522859−06	−5.853823−05	8.236679−04
.660	3.039371−06	−3.918524−05	5.492705−04
.680	2.069858−06	−2.658774−05	3.713502−04
.700	1.427294−06	−1.827003−05	2.543082−04
.720	9.957880−07	−1.270439−05	1.762658−04
.740	7.024169−07	−8.933328−06	1.235633−04
.760	5.006317−07	−6.347952−06	8.754577−05
.780	3.603144−07	−4.555693−06	6.265280−05
.800	2.617279−07	−3.300174−06	4.526498−05
.820	1.917820−07	−2.411910−06	3.299722−05
.840	1.416955−07	−1.777562−06	2.425938−05
.860	1.055142−07	−1.320508−06	1.797956−05
.880	7.915934−08	−9.884089−07	1.342765−05
.900	5.980976−08	−7.451628−07	1.010134−05
.920	4.549608−08	−5.656340−07	7.651815−06
.940	3.483144−08	−4.321663−07	5.834665−06
.960	2.683103−08	−3.322525−07	4.477153−06
.980	2.078991−08	−2.569606−07	3.456208−06
1.000	1.619969−08	−1.998634−07	2.683460−06
1.025	1.194938−08	−1.471050−07	1.970895−06
1.050	8.884709−09	−1.091495−07	1.459392−06
1.075	6.656181−09	−8.160901−08	1.089031−06
1.100	5.022610−09	−6.146292−08	8.186574−07
1.150	2.918192−09	−3.558260−08	4.722774−07
1.200	1.738258−09	−2.112502−08	2.794753−07
1.250	1.059228−09	−1.283327−08	1.692674−07
1.300	6.590456−10	−7.961991−09	1.047225−07
1.350	4.179904−10	−5.036343−09	6.606902−08
1.400	2.698360−10	−3.243154−09	4.244129−08
1.450	1.770703−10	−2.123245−09	2.772213−08
1.500	1.179760−10	−1.411552−09	1.839032−08
1.550	7.972355−11	−9.519077−10	1.237681−08
1.600	5.459006−11	−6.505462−10	8.442348−09
1.650	3.784450−11	−4.501637−10	5.831401−09
1.700	2.654101−11	−3.151602−10	4.075616−09
1.750	1.881706−11	−2.230752−10	2.880126−09
1.800	1.347804−11	−1.595321−10	2.056564−09
1.850	9.747357−12	−1.152031−10	1.482944−09
1.900	7.113753−12	−8.395811−11	1.079247−09
2.000	3.886294−12	−4.574646−11	5.865341−10
2.100	2.189841−12	−2.571534−11	3.289303−10
2.200	1.268896−12	−1.486794−11	1.897683−10
2.300	7.541424−13	−8.818598−12	1.123332−10
2.400	4.586905−13	−5.353707−12	6.807154−11
2.500	2.849539−13	−3.320150−12	4.214339−11
2.600	1.804972−13	−2.099689−12	2.660968−11
2.700	1.163985−13	−1.352013−12	1.710903−11
2.800	7.631675−14	−8.852079−13	1.118642−11
2.900	5.081196−14	−5.886020−13	7.428605−12
3.000	3.431772−14	−3.970447−13	5.004939−12
3.100	2.348860−14	−2.714407−13	3.417743−12
3.200	1.627808−14	−1.879087−13	2.363441−12
3.300	1.141337−14	−1.316163−13	1.653739−12
3.400	8.090548−15	−9.320739−14	1.170013−12
3.500	5.794445−15	−6.669341−14	8.364275−13
3.600	4.190410−15	−4.818888−14	6.038338−13
3.700	3.058265−15	−3.514014−14	4.399647−13
3.800	2.251385−15	−2.584840−14	3.233770−13
3.900	1.671015−15	−1.917062−14	2.396560−13
4.000	1.249919−15	−1.432929−14	1.790065−13
4.250	6.241599−16	−7.143567−15	8.909370−14
4.500	3.246397−16	−3.709980−15	4.620236−14
4.750	1.750823−16	−1.998140−15	2.485084−14
5.000	9.753675−17	−1.111781−15	1.381053−14
5.250	5.594691−17	−6.370031−16	7.904130−15
5.500	3.295050−17	−3.747851−16	4.645758−15
5.750	1.987859−17	−2.258898−16	2.797483−15
6.000	1.225863−17	−1.391794−16	1.722160−15
6.250	7.713271−18	−8.750266−17	1.081870−15
6.500	4.943993−18	−5.604477−17	6.924178−16
6.750	3.223609−18	−3.651711−17	4.508487−16
7.000	2.135420−18	−2.417430−17	2.982698−16
7.250	1.435523−18	−1.624110−17	2.002670−16
7.500	9.783254−19	−1.106215−17	1.363290−16
7.750	6.753160−19	−7.631835−18	9.400408−17
8.000	4.717627−19	−5.328743−18	6.560318−17
8.250	3.332797−19	−3.762716−18	4.630162−17
8.500	2.379403−19	−2.685118−18	3.302659−17
9.000	1.248695−19	−1.407951−18	1.730330−17
9.500	6.788893−20	−7.648939−19	9.393308−18
10.000	3.809791−20	−4.289482−19	5.264146−18
10.500	2.199906−20	−2.475343−19	3.035917−18
11.000	1.303589−20	−1.465960−19	1.796928−18
11.500	7.908621−21	−8.888996−20	1.089018−18
12.000	4.902360−21	−5.507381−20	6.744014−19
12.500	3.099438−21	−3.480378−20	4.259967−19
13.000	1.995515−21	−2.239835−20	2.740412−19
13.500	1.306530−21	−1.465920−20	1.792845−19
14.000	8.688430−22	−9.744807−21	1.191376−19
15.000	4.008585−22	−4.492980−21	5.489411−20
16.000	1.945034−22	−2.178790−21	2.660450−20
17.000	9.864462−23	−1.104419−21	1.347874−20
18.000	5.202547−23	−5.822000−22	7.102089−21
19.000	2.841207−23	−3.178152−22	3.875312−21
20.000	1.600919−23	−1.790084−22	2.181928−21
T*	$B_0^{*}$	$T^{*}\frac{\partial B_0^{*}}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{B}_0^{*}}{\partial T^{*2}}$
.300	−11.92776	32.43477	−146.70903
.305	−11.40595	30.61402	−136.79848
.310	−10.92284	28.94770	−127.82393
.315	−10.47201	27.41918	−119.67757
.320	−10.05137	26.01407	−112.26570
.325	−9.65817	24.71966	−105.50644
.330	−9.28998	23.52477	−99.32835
.335	−8.94462	22.41953	−93.66903
.340	−8.62014	21.39526	−88.47393
.345	−8.31481	20.44428	−83.69531
.350	−8.02707	19.55980	−79.29125
.360	−7.49890	17.96684	−71.46363
.370	−7.02602	16.57559	−64.74451
.380	−6.60055	15.35336	−58.93947
.390	−6.21599	14.27372	−53.89356
.400	−5.86692	13.31512	−49.48237
.410	−5.54886	12.46001	−45.60628
.420	−5.25795	11.69383	−42.18303
.430	−4.99100	11.00447	−39.14608
.440	−4.74527	10.38184	−36.44013
.450	−4.51838	9.81741	−34.01921
.460	−4.30832	9.30400	−31.84498
.470	−4.11332	8.83548	−29.88525
.480	−3.93187	8.40665	−28.11286
.490	−3.76263	8.01300	−26.50471
.500	−3.60444	7.65069	−25.04114
.510	−3.45628	7.31636	−23.70530
.520	−3.31724	7.00709	−22.48269
.530	−3.18652	6.72035	−21.36081
.540	−3.06342	6.45392	−20.32883
.550	−2.94729	6.20585	−19.37730
.560	−2.83757	5.97442	−18.49797
.580	−2.63539	5.55556	−16.92798
.600	−2.45339	5.18709	−15.57093
.620	−2.28873	4.86089	−14.38937
.640	−2.13908	4.57040	−13.35373
.660	−2.00249	4.31034	−12.44041
.680	−1.87735	4.07636	−11.63041
.700	−1.76229	3.86490	−10.90829
.720	−1.65614	3.67298	−10.26141
.740	−1.55793	3.49812	−9.67932
.760	−1.46680	3.33822	−9.15336
.780	−1.38201	3.19152	−8.67626
.800	−1.30293	3.05649	−8.24191
.820	−1.22901	2.93184	−7.84514
.840	−1.15976	2.81647	−7.48155
.860	−1.09476	2.70940	−7.14737
.880	−1.03363	2.60979	−6.83936
.900	−.97603	2.51692	−6.55471
.920	−.92167	2.43013	−6.29100
.940	−.87029	.2.34888	−6.04612
.960	−.82164	2.27265	−5.81821
.980	−.77553	2.20101	−5.60565
1.000	−.73175	2.13356	−5.40702
1.025	−.68005	2.05462	−5.17641
1.050	−.63143	1.98109	−4.96342
1.075	−.58562	1.91244	−4.76618
1.100	−.54240	1.84822	−4.58307
1.150	−.46291	1.73107	−4.20864
1.200	−.39141	1.62808	−3.96646
1.250	−.32683	1.53559	−3.72083
1.300	−.26825	1.45335	−3.48963
1.350	−.21483	1.37880	−3.27199
1.400	−.16591	1.31145	−3.11097
1.450	−.12097	1.24997	−2.96763
1.500	−.07956	1.19400	−2.80363
1.550	−.04126	1.14261	−2.66938
1.600	−.00574	1.09524	−2.54959
1.650	.02729	1.05157	−2.44984
1.700	.05807	1.01105	−2.33634
1.750	.08683	.97338	−2.24890
1.800	.11375	.93847	−2.15495
1.850	.13902	.90580	−2.07406
1.900	.16276	.87525	−1.99888
2.000	.20621	.81970	−1.86324
2.100	.24499	.77051	−1.74433
2.200	.27980	.72665	−1.63926
2.300	.31122	.68730	−1.54578
2.400	.33971	.65180	−1.46208
2.500	.36566	.61961	−1.38673
2.600	.38939	.59029	−1.31852
2.700	.41116	.56347	−1.25651
2.800	.43120	.53886	−1.19991
2.900	.44970	.51618	−1.14805
3.000	.46684	.49522	−1.10034
3.100	.48275	.47579	−1.05631
3.200	.49757	.45772	−1.01555
3.300	.51139	.44088	−.97771
3.400	.52432	.42514	−.94248
3.500	.53643	.41041	−.90961
3.600	.54780	.39659	−.87887
3.700	.55848	.38359	−.85006
3.800	.56855	.37135	−.82302
3.900	.57804	.35980	−.79757
4.000	.58701	.34889	−.77359
4.250	.60745	.32410	−.71915
4.500	.62529	.30220	−.67172
4.750	.64109	.28283	−.62983
5.000	.65516	.26556	−.59259
5.250	.66774	.25005	−.55929
5.500	.67904	.23603	−.52935
5.750	.68924	.22331	−.50227
6.000	.69850	.21172	−.47765
6.250	.70693	.20111	−.45518
6.500	.71462	.19136	−.43458
6.750	.72167	.18237	−.41564
7.000	.72815	.17405	−.39816
7.250	.73412	.16634	−.38198
7.500	.73964	.15916	−.36695
7.750	.74475	.15247	−.35296
8.000	.74949	.14621	−.33991
8.250	.75390	.14035	−.32770
8.500	.75801	.13484	−.31675
9.000	.76542	.12478	−.29537
9.500	.77193	.11582	−.27681
10.000	.77766	.10779	−.26021
10.500	.78274	.10054	−.24526
11.000	.78726	.09397	−.23173
11.500	.79130	.08799	−.21943
12.000	.79493	.08252	−.20820
12.500	.79820	.07750	−.19790
13.000	.80115	.07287	−.18842
13.500	.80382	.06859	−.17967
14.000	.80624	.06463	−.17157
15.000	.81045	.05751	−.15703
16.000	.81396	.05130	−.14437
17.000	.81690	.04583	−.13323
18.000	.81938	.04098	−.12336
19.000	.82148	.03664	−.11455
20.000	.82326	.03275	−.10665
T*	Y	I1	$T^{*}\frac{\partial I_1}{\partial T^{*}}$
.300	2.18713	27.39035	−124.3045
.305	2.16912	25.42243	−113.9775
.310	2.15156	23.64525	−104.7573
.315	2.13442	22.03617	−96.50201
.320	2.11767	20.57566	−89.09070
.325	2.10132	19.24686	−82.41980
.330	2.08534	18.03513	−76.40035
.335	2.06972	16.92774	−70.95575
.340	2.05445	15.91359	−66.01978
.345	2.03950	14.98295	−61.53506
.350	2.02488	14.12730	−57.45166
.360	1.99656	12.61182	−50.32023
.370	1.96940	11.31702	−44.33850
.380	1.94331	10.20353	−39.28490
.390	1.91824	9.240141	−34.98674
.400	1.89411	8.401908	−31.30818
.410	1.87086	7.668721	−28.14147
.420	1.84846	7.024254	−25.40043
.430	1.82684	6.455156	−23.01565
.440	1.80596	5.950438	−20.93081
.450	1.78578	5.500996	−19.09990
.460	1.76626	5.099247	−17.48510
.470	1.74737	4.738837	−16.05517
.480	1.72907	4.414412	−14.78411
.490	1.71134	4.121444	−13.65019
.500	1.69414	3.856078	−12.63516
.510	1.67745	3.615024	−11.72360
.520	1.66124	3.395457	−10.90247
.530	1.64549	3.194946	−10.16062
.540	1.63019	3.011386	−9.488539
.550	1.61530	2.842952	−8.878054
.560	1.60081	2.688053	−8.322125
.580	1.57297	2.413475	−7.350362
.600	1.54653	2.178445	−6.533459
.620	1.52138	1.975809	−5.841070
.640	1.49742	1.799941	−5.249775
.660	1.47456	1.646372	−4.741299
.680	1.45271	1.511521	−4.301236
.700	1.43181	1.392490	−3.918120
.720	1.41178	1.286918	−3.582747
.740	1.39257	1.192863	−3.287665
.760	1.37413	1.108720	−3.026797
.780	1.35640	1.033151	−2.795153
.800	1.33934	.9650366	−2.588603
.820	1.32290	.9034320	−2.403713
.840	1.30706	.8475369	−2.237606
.860	1.29177	.7966697	−2.087861
.880	1.27701	.7502472	−1.952432
.900	1.26274	.7077679	−1.829575
.920	1.24894	.6687987	−1.717803
.940	1.23558	.6329643	−1.615840
.960	1.22264	.5999380	−1.522583
.980	1.21010	.5694344	−1.437083
1.000	1.19794	.5412035	−1.358511
1.025	1.18324	.5087782	−1.268950
1.050	1.16907	.4791884	−1.187884
1.075	1.15539	.4521132	−1.114280
1.100	1.14219	.4272757	−1.047259
1.150	1.11708	.3833857	−.9300484
1.200	1.09356	.3459468	−.8313636
1.250	1.07147	.3137538	−.7475211
1.300	1.05066	.2858701	−.6757037
1.350	1.03102	.2615590	−.6137287
1.400	1.01244	.2402347	−.5598845
1.450	.99483	.2214268	−.5128145
$T^{*2}\frac{{\partial }^2{I}_1}{\partial T^{*2}}$	I2	$T^{*}\frac{\partial I_2}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_2}{\partial T^{*2}}$
780.3366	2.195606+01	−1.500621+02	1.246400+03
708.6089	1.961920+01	−1.330553+02	1.097486+03
645.1458	1.757799+01	−1.183158+02	9.693196+02
588.8258	1.578952+01	−1.054994+02	8.586297+02
538.7003	1.421785+01	−9.432008+01	7.627169+02
493.9643	1.283279+01	−8.453940+01	6.793447+02
453.9321	1.160884+01	−7.595751+01	6.066523+02
418.0176	1.052444+01	−6.840648+01	5.430856+02
385.7179	9.561232+00	−6.174466+01	4.873421+02
356.6007	8.703612+00	−5.585218+01	4.383264+02
330.2927	7.938215+00	−5.062722+01	3.951135+02
284.8545	6.639875+00	−4.184561+01	3.230819+02
247.2937	5.592356+00	−3.484575+01	2.662837+02
216.0042	4.740455+00	−2.921870+01	2.210962+02
189.7508	4.042482+00	−2.465932+01	1.848455+02
167.5747	3.466641+00	−2.093764+01	1.555366+02
148.7245	2.988460+00	−1.787861+01	1.316666+02
132.6069	2.588946+00	−1.534784+01	1.120925+02
118.7493	2.253236+00	−1.324126+01	9.593735+01
106.7729	1.969612+00	−1.147763+01	8.252270+01
96.37138	1.728766+00	−9.993088+00	7.131966+01
87.29599	1.523261+00	−8.737026+00	6.191285+01
79.34305	1.347108+00	−7.669110+00	5.397371+01
72.34496	1.195464+00	−6.756969+00	4.724067+01
66.16304	1.064383+00	−5.974475+00	4.150417+01
60.68186	9.506355−01	−5.300415+00	3.659532+01
55.80493	8.515640−01	−4.717471+00	3.237722+01
51.45116	7.649713−01	−4.211435+00	2.873834+01
47.55208	6.890317−01	−3.770587+00	2.558727+01
44.04967	6.222217−01	−3.385222+00	2.284883+01
40.89452	5.632639−01	−3.047259+00	2.046079+01
38.04441	5.110838−01	−2.749946+00	1.837151+01
33.11939	4.235629−01	−2.255495+00	1.492375+01
29.04052	3.539145−01	−1.866333+00	1.223737+01
25.63200	2.979529−01	−1.556882+00	1.012149+01
22.76010	2.525876−01	−1.308479+00	8.438248+00
20.32190	2.155091−01	−1.107330+00	7.086804+00
18.23738	1.849721−01	−9.431214−01	5.992450+00
16.44362	1.596440−01	−8.080564−01	5.099225+00
14.89076	1.384973−01	−6.961812−01	4.364761+00
13.53891	1.207327−01	−6.029058−01	3.756663+00
12.35588	1.057230−01	−5.246604−01	3.249935+00
11.31555	9.297221−02	−4.586454−01	2.825120+00
10.39653	8.208531−02	−4.026481−01	2.466953+00
9.581195	7.274530−02	−3.549070−01	2.163363+00
8.854943	6.469620−02	−3.140099−01	1.904738+00
8.205598	5.773003−02	−2.788174−01	1.683371+00
7.622952	5.167678−02	−2.484044−01	1.493045+00
7.098400	4.639675−02	−2.220156−01	1.328712+00
6.624653	4.177449−02	−1.990308−01	1.186251+00
6.195509	3.771416−02	−1.789381−01	1.062280+00
5.805667	3.413578−02	−1.613130−01	9.540085−01
5.450573	3.097235−02	−1.458016−01	8.591217−01
5.126306	2.816747−02	−1.321076−01	7.756921−01
4.759193	2.509364−02	−1.171704−01	6.850848−01
4.429308	2.242853−02	−1.042838−01	6.072811−01
4.131873	2.010861−02	−9.311965−02	5.401786−01
3.862845	1.808158−02	−8.340946−02	4.820655−01
3.396728	1.474033−02	−6.750484−02	3.874469−01
3.008910	1.213792−02	−5.521697−02	3.149004−01
2.683014	1.008657−02	−4.560314−02	2.585407−01
2.406686	8.451882−03	−3.799493−02	2.142299−01
2.170472	7.136206−03	−3.191074−02	1.790107−01
1.967049	6.067583−03	−2.699857−02	1.507372−01
1.790677	5.192305−03	−2.299763−02	1.278308−01
T*	Y	I1	$T^{*}\frac{\partial I_1}{\partial T^{*}}$
1.50	.97811	.2047538	−.4714322
1.55	.96221	.1899040	−.4348599
1.60	.94705	.1766206	−.4023822
1.65	.93259	.1646904	−.3734114
1.70	.91878	.1539354	−.3474614
1.75	.90556	.1442058	−.3241271
1.80	.89289	.1353751	−.3030691
1.85	.88074	.1273356	−.2840010
1.90	.86908	.1199953	−.2666802
2.00	.84707	.1071076	−.2364822
2.10	.82666	.09620016	−.2111474
2.20	.80765	.08688633	−.1896853
2.30	.78990	.07886948	−.1713452
2.40	.77327	.07191900	−.1555495
2.50	.75764	.06585339	−.1418483
2.60	.74293	.06052822	−.1298868
2.70	.72904	.05582742	−.1193823
2.80	.71590	.05165683	−.1101072
2.90	.70345	.04793940	−.1018768
3.00	.69163	.04461163	−.09453957
3.10	.68038	.04162075	−.08797075
3.20	.66967	.03892266	−.08206651
3.30	.65944	.03648025	−.07674000
3.40	.64967	.03426212	−.07191812
3.50	.64032	.03224156	−.06753898
3.60	.63137	.03039571	−.06354991
3.70	.62278	.02870494	−.05990582
3.80	.61453	.02715231	−.05656800
3.90	.60660	.02572312	−.05350299
4.00	.59897	.02440459	−.05068180
4.25	.58109	.02152244	−.04453758
4.50	.56471	.01912514	−.03945178
4.75	.54965	.01710946	−.03519410
5.00	.53573	.01539829	−.03159370
5.25	.52282	.01393310	−.02852166
5.50	.51080	.01266876	−.02587922
5.75	.49957	.01157008	−.02358968
6.00	.48906	.01060925	−.02159274
6.25	.47918	.009764073	−.01984048
6.50	.46987	.009016656	−.01829439
6.75	.46109	.008352437	−.01692329
7.00	.45278	.007759475	−.01570165
7.25	.44490	.007227901	−.01460846
7.50	.43743	.006749498	−.01362628
7.75	.43031	.006317382	−.01274053
8.00	.42354	.005925753	−.01193896
8.25	.41707	.005569688	−.01121119
8.50	.41089	.005244996	−.01054842
9.00	.39931	.004675863	−.009388765
9.50	.38866	.004195152	−.008411446
10.00	.37882	.003785401	−.007580036
10.50	.36969	.003433259	−.006866838
11.00	.36119	.003128382	−.006250361
11.50	.35325	.002862648	−.005713838
12.00	.34581	.002629613	−.005243980
12.50	.33883	.002424107	−.004830151
13.00	.33225	.002241946	−.004463759
13.50	.32604	.002079712	−.004137800
14.00	.32016	.001934592	−.003846519
15.00	.30931	.001686747	−.003349722
16.00	.29948	.001483943	−.002943875
17.00	.29054	.001315860	−.002608000
18.00	.28236	.001174981	−.002326846
19.00	.27483	.001055718	−.002089107
20.00	.26787	.000953852	7 −.001886259
$T^{*2}\frac{{\partial }^2{I}_1}{\partial T^{*2}}$	I2	$T^{*}\frac{\partial I_2}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_2}{\partial T^{*2}}$
1.636807	4.469815−03	−1.971237−02	1.091155−01
1.501800	3.869146−03	−1.699446−02	9.370459−02
1.382720	3.366421−03	−1.473022−02	8.092259−02
1.277174	2.943050−03	−1.283169−02	7.024950−02
1.183201	2.584438−03	−1.123015−02	6.128138−02
1.099180	2.279031−03	−9.871520−03	5.370164−02
1.023762	2.017612−03	−8.712842−03	4.726016−02
.9558179	1.792775−03	−7.719781−03	4.175781−02
.8943969	1.598533−03	−6.864689−03	3.703493−02
.7880244	1.283220−03	−5.482914−03	2.943622−02
.6995223	1.042251−03	−4.432974−03	2.369405−02
.6251142	8.555049−04	−3.623533−03	1.928937−02
.5619675	7.089437−04	−2.991305−03	1.586481−02
.5079247	5.925992−04	−2.491627−03	1.316966−02
.4613202	4.992760−04	−2.092443−03	1.102494−02
.4208513	4.237039−04	−1.770399−03	9.300924−03
.3854882	3.619703−04	−1.508241−03	7.902201−03
.3544077	3.111343−04	−1.293059−03	6.757700−03
.3269459	2.689605−04	−1.115081−03	5.813840−03
.3025626	2.337314−04	−9.668301−04	5.029774−03
.2808144	2.041147−04	−8.425275−04	4.374046−03
.2613350	1.790677−04	−7.376654−04	3.822202−03
.2438196	1.577672−04	−6.486970−04	3.355060−03
.2280128	1.395583−04	−5.728095−04	2.957453−03
.2136993	1.239161−04	−5.077549−04	2.617292−03
.2006967	1.104170−04	−4.517242−04	2.324875−03
.1888496	9.871707−05	−4.032518−04	2.072363−03
.1780250	8.853502−05	−3.611429−04	1.853377−03
.1681085	7.963979−05	−3.244177−04	1.662702−03
.1590011	7.184040−05	−2.922686−04	1.496046−03
.1392368	5.615845−05	−2.277914−04	1.162626−03
.1229541	4.455124−05	−1.802308−04	9.175014−04
.1093801	3.580814−05	−1.445157−04	7.339753−04
.09794501	2.911894−05	−1.172661−04	5.943262−04
.08822132	2.392916−05	−9.617762−05	4.865146−04
.07988333	1.985170−05	−7.964680−05	4.021909−04
.07267932	1.661145−05	−6.653760−05	3.354566−04
.06641226	1.400967−05	−5.603164−05	2.820743−04
.06092617	1.190066−05	−4.753057−05	2.389534−04
.05609624	1.017619−05	−4.059081−05	2.038081−04
.05182164	8.754800−06	−3.487944−05	1.749265−04
.04802022	7.574544−06	−3.014367−05	1.510113−04
.04462450	6.587781−06	−2.618950−05	1.310687−04
.04157860	5.757527−06	−2.286658−05	1.143299−04
.03883596	5.054808−06	−2.005734−05	1.001945−04
.03635754	4.456734−06	−1.766902−05	8.818987−05
.03411038	3.945081−06	−1.562790−05	7.794054−05
.03206650	3.505230−06	−1.387490−05	6.914627−05
.02849656	2.795927−06	−1.105171−05	5.500120−05
.02549441	2.258234−06	−8.915069−06	4.431301−05
.02294537	1.844343−06	−7.272817−06	3.610981−05
.02076266	1.521824−06	−5.994797−06	2.973417−05
.01887894	1.267117−06	−4.986730−06	2.471127−05
.01724190	1.063836−06	−4.183088−06	2.071131−05
.01581019	8.999652−07	−3.535911−06	1.749334−05
.01455075	7.666484−07	−3.009898−06	1.488024−05
.01343694	6.572726−07	−2.578722−06	1.274009−05
.01244708	5.668399−07	−2.222511−06	1.097343−05
.01156339	4.915315−07	−1.926097−06	9.504413−06
.01005819	3.751475−07	−1.468468−06	7.238648−06
.008830509	2.914333−07	−1.139707−06	5.612884−06
.007815922	2.299419−07	−8.984820−07	4.421274−06
.006967694	1.839324−07	−7.181670−07	3.531395−06
.006251251	1.489385−07	−5.811426−07	2.855738−06
.005640568	1.219307−07	−4.754727−07	2.335088−06
T*	I3	$T^{*}\frac{\partial I_3}{\partial T^{*}}$	$T^{{*}_2}\frac{{\partial }^2{I}_3}{\partial T^{*2}}$
.300	1.112181+01	−9.913713+01	1.018720+03
.305	9.602355+00	−8.508517+01	8.694753+02
.310	8.317346+00	−7.327347+01	7.447318+02
.315	7.226695+00	−6.330753+01	6.400597+02
.320	6.297802+00	−5.486853+01	5.518997+02
.325	5.504047+00	−4.769773+01	4.773795+02
.330	4.823601+00	−4.158419+01	4.141700+02
.335	4.238494+00	−3.635528+01	3.603757+02
.340	3.733876+00	−3.186915+01	3.144467+02
.345	3.297433+00	−2.800881+01	2.751118+02
.350	2.918914+00	−2.467742+01	2.413235+02
.360	2.302798+00	−1.929305+01	1.870713+02
.370	1.832288+00	−1.521914+01	1.463770+02
.380	1.469569+00	−1.210625+01	1.155388+02
.390	1.187471+00	−9.705698+00	9.194505+01
.400	9.662543−01	−7.838426+00	7.373142+01
.410	7.914269−01	−6.374150+00	5.955222+01
.420	6.522485−01	−5.217111+00	4.842607+01
.430	5.406845−01	−4.296251+00	3.963024+01
.440	4.506732−01	−3.558378+00	3.262755+01
.450	3.776035−01	−2.963330+00	2.701524+01
.460	3.179410−01	−2.480543+00	2.248886+01
.470	2.689565−01	−2.086581+00	1.881646+01
.480	2.285282−01	−1.763345+00	1.582001+01
.490	1.949952−01	−1.496760+00	1.336192+01
.500	1.670499−01	−1.275812+00	1.133514+01
.510	1.436560−01	−1.091828+00	9.655833+00
.520	1.239880−01	−9.379356−01	8.257957+00
.530	1.073847−01	−8.086638−01	7.089189+00
.540	9.331343−02	−6.996299−01	6.107839+00
.550	8.134345−02	−6.073067−01	5.280520+00
.560	7.112443−02	−5.288411−01	4.580354+00
.580	5.484617−02	−4.046339−01	3.478595+00
.600	4.274869−02	−3.130797−01	2.672749+00
.620	3.365039−02	−2.447522−01	2.075718+00
.640	2.673188−02	−1.931711−01	1.628112+00
.660	2.141683−02	−1.538161−01	1.288820+00
.680	1.729464−02	−1.234913−01	1.028992+00
.700	1.406913−02	−9.990879−02	8.281132−01
.720	1.152429−02	−8.141133−02	6.714250−01
.740	9.500862−03	−6.678537−02	5.481861−01
.760	7.880281−03	−5.513316−02	4.504982−01
.780	6.573451−03	−4.578413−02	3.724957−01
.800	5.512832−03	−3.823291−02	3.097818−01
.820	4.646803−03	−3.209537−02	2.590319−01
.840	3.935602−03	−2.707719−02	2.177117−01
.860	3.348376−03	−2.295116−02	1.838739−01
.880	2.861019−03	−1.954061−02	1.560115−01
.900	2.454574−03	−1.670725−02	1.329498−01
.920	2.114035−03	−1.434211−02	1.137674−01
.940	1.827459−03	−1.235883−02	9.773696−02
.960	1.585281−03	−1.068854−02	8.428062−02
.980	1.379805−03	−9.276048−03	7.293702−02
1.000	1.204803−03	−8.076847−03	6.333565−02
1.025	1.021282−03	−6.823547−03	5.333391−02
1.050	8.696312−04	−5.791668−03	4.512804−02
1.075	7.436716−04	−4.937589−03	3.835887−02
1.100	6.385413−04	−4.227125−03	3.274604−02
1.150	4.761501−04	−3.134742−03	2.415417−02
1.200	3.600552−04	−2.358401−03	1.808281−02
1.250	2.757515−04	−1.797729−03	1.372117−02
1.300	2.136556−04	−1.386842−03	1.054036−02
1.350	1.673171−04	−1.081664−03	8.188613−03
1.400	1.323208−04	−8.521942−04	6.427779−03
1.450	1.055969−04	−6.776843−04	5.093987−03
1.500	8.498052−05	−5.435737−04	4.072776−03
1.550	6.892443−05	−4.395042−04	3.283083−03
1.600	5.630924−05	−3.580143−04	2.666757−03
1.650	4.631578−05	−2.936659−04	2.181582−03
1.700	3.833819−05	−2.424527−04	1.796572−03
1.750	3.192387−05	−2.013924−04	1.488743−03
1.800	2.673157−05	−1.682443−04	1.240882−03
1.850	2.250171−05	−1.413097−04	1.039983−03
1.900	1.903525−05	−1.192899−04	8.761299−04
2.000	1.381118−05	−8.621505−05	6.308059−04
2.100	1.019047−05	−6.338806−05	4.621863−04
2.200	7.633564−06	−4.732979−05	3.440098−04
2.300	5.797086−06	−3.583668−05	2.597190−04
2.400	4.457643−06	−2.748124−05	1.986333−04
2.500	3.466942−06	−2.131971−05	1.537180−04
2.600	2.724736−06	−1.671642−05	1.202521−04
2.700	2.162111−06	−1.323588−05	9.501196−05
2.800	1.730964−06	−1.057506−05	7.576127−05
2.900	1.397238−06	−8.520072−06	6.092601−05
3.000	1.136504−06	−6.917897−06	4.938326−05
3.100	9.310260−07	−5.657735−06	4.032188−05
3.200	7.677819−07	−4.658428−06	3.314912−05
3.300	6.371087−07	−3.859891−06	2.742714−05
3.400	5.317662−07	−3.217200−06	2.282925−05
3.500	4.462790−07	−2.696452−06	1.910936−05
3.600	3.764706−07	−2.271833−06	1.608050−05
3.700	3.191296−07	−1.923532−06	1.359940−05
3.800	2.717675−07	−1.636223−06	1.155540−05
3.900	2.324420−07	−1.397965−06	9.862432−06
4.000	1.996270−07	−1.199387−06	8.453071−06
4.250	1.387452−07	−8.316519−07	5.847890−06
4.500	9.853262−08	−5.893793−07	4.135812−06
4.750	7.132790−08	−4.258503−07	2.982776−06
5.000	5.252624−08	−3.130650−07	2.189134−06
5.250	3.928104−08	−2.337594−07	1.632101−06
5.500	2.978786−08	−1.770156−07	1.234204−06
5.750	2.287665−08	−1.357694−07	9.454191−07
6.000	1.777305−08	−1.053546−07	7.327690−07
6.250	1.395495−08	−8.263064−08	5.740961−07
6.500	1.106423−08	−6.544718−08	4.542540−07
6.750	8.851462−09	−5.230853−08	3.627233−07
7.000	7.140338−09	−4.215920−08	2.920908−07
7.250	5.804620−09	−3.424432−08	2.370618−07
7.500	4.752780−09	−2.801732−08	1.938070−07
7.750	3.917707−09	−2.307786−08	1.595249−07
8.000	3.249659−09	−1.912956−08	1.321437−07
8.250	2.711405−09	−1.595079−08	1.101157−07
8.500	2.274817−09	−1.337429−08	9.227383−08
9.000	1.625863−09	−9.548229−09	6.580416−08
9.500	1.183739−09	−6.944777−09	4.781449−08
10.000	8.762428−10	−5.136080−09	3.533007−08
10.500	6.583784−10	−3.855882−09	2.650229−08
11.000	5.014143−10	−2.934384−09	2.015367−08
11.500	3.865967−10	−2.260881−09	1.551740−08
12.000	3.014385−10	−1.761739−09	1.208399−08
12.500	2.374733−10	−1.387081−09	9.508658−09
13.000	1.888645−10	−1.102556−09	7.554135−09
13.500	1.515272−10	−8.841389−10	6.054637−09
14.000	1.225618−10	−7.147924−10	4.892666−09
15.000	8.197517−11	−4.776785−10	3.266901−09
16.000	5.628827−11	−3.277512−10	2.239870−09
17.000	3.955154−11	−2.301439−10	1.571782−09
18.000	2.836368−11	−1.649450−10	1.125840−09
19.000	2.071327−11	−1.203903−10	8.212952−10
20.000	1.537463−11	−8.931750−11	6.090267−10
T*	I4	$T^{*2}\frac{\partial I_4}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_4}{\partial T^{*2}}$
.300	3.827353+00	−4.184820+01	5.118746+02
.305	3.195951+00	−3.477395+01	4.233654+02
.310	2.678832+00	−2.900910+01	3.515816+02
.315	2.253566+00	−2.429131+01	2.931074+02
.320	1.902452+00	−2.041459+01	2.452743+02
.325	1.611455+00	−1.721646+01	2.059871+02
.330	1.369397+00	−1.456814+01	1.735931+02
.335	1.167336+00	−1.236711+01	1.467824+02
.340	9.980881−01	−1.053137+01	1.245123+02
.345	8.558589−01	−8.995109+00	1.059491+02
.350	7.359559−01	−7.705260+00	9.042370+01
.360	5.485736−01	−5.701059+00	6.643153+01
.370	4.130555−01	−4.262532+00	4.933501+01
.380	3.139722−01	−3.218339+00	3.701033+01
.390	2.407841−01	−2.452350+00	2.802871+01
.400	1.862023−01	−1.884854+00	2.141634+01
.410	1.451276−01	−1.460484+00	1.650140+01
.420	1.139535−01	−1.140346+00	1.281504+01
.430	9.010287−02	−8.968329−01	1.002652+01
.440	7.171634−02	−7.101501−01	7.900142+00
.450	5.743992−02	−5.659715−01	6.266288+00
.460	4.627914−02	−4.538359−01	5.001794+00
.470	3.749751−02	−3.660397−01	4.016443+00
.480	3.054529−02	−2.968637−01	3.243608+00
.490	2.500914−02	−2.420301−01	2.633695+00
.500	2.057602−02	−1.983154−01	2.149519+00
.510	1.700729−02	−1.632743−01	1.762997+00
.520	1.411981−02	−1.350389−01	1.452776+00
.530	1.177220−02	−1.121740−01	1.202518+00
.540	9.854667−03	−9.356956−02	9.996445−01
.550	8.281469−03	−7.836267−02	8.344118−01
.560	6.985282−03	−6.587849−02	6.992324−01
.580	5.022398−03	−4.706770−02	4.965292−01
.600	3.658829−03	−3.408586−02	3.575203−01
.620	2.698044−03	−2.499507−02	2.607546−01
.640	2.012100−03	−1.854247−02	1.924555−01
.660	1.516357−03	−1.390464−02	1.436250−01
.680	1.153973−03	−1.053203−02	1.082934−01
.700	8.862462−04	−8.052604−03	8.244231−02
.720	6.864758−04	−6.211154−03	6.332940−02
.740	5.360176−04	−4.830400−03	4.905959−02
.760	4.217033−04	−3.785761−03	3.830748−02
.780	3.341323−04	−2.988723−03	3.013573−02
.800	2.665254−04	−2.375748−03	2.387441−02
.820	2.139474−04	−1.900778−03	1.903997−02
.840	1.727731−04	−1.530125−03	1.528008−02
.860	1.403168−04	−1.238930−03	1.233577−02
.880	1.145729−04	−1.008696−03	1.001510−02
.900	9.403209−05	−8.255600−04	8.174643−03
.920	7.755045−05	−6.790469−04	6.706450−03
.940	6.425490−05	−5.611908−04	5.528671−03
.960	5.347465−05	−4.658911−04	4.578822−03
.980	4.469124−05	−3.884471−04	3.808903−03
1.000	3.750146−05	−3.252139−04	3.181801−03
1.025	3.028152−05	−2.618868−04	2.555416−03
1.050	2.459159−05	−2.121244−04	2.064591−03
1.075	2.007925−05	−1.727702−04	1.677472−03
1.100	1.647942−05	−1.414577−04	1.370255−03
1.150	1.126163−05	−9.623662−05	9.281418−04
1.200	7.833908−06	−6.666905−05	6.403919−04
1.250	5.538478−06	−4.695459−05	4.493436−04
1.300	3.974116−06	−3.357301−05	3.201743−04
1.350	2.890711−06	−2.434019−05	2.313771−04
1.400	2.129217−06	−1.787331−05	1.693931−04
1.450	1.586629−06	−1.328046−05	1.255112−04
1.500	1.195101−06	−9.976400−06	9.403693−05
1.550	9.092431−07	−7.570972−06	7.118704−05
1.600	6.982428−07	−5.800233−06	5.441050−05
1.650	5.409016−07	−4.483155−06	4.196302−05
1.700	4.224496−07	−3.493985−06	3.263643−05
1.750	3.324740−07	−2.744317−06	2.558367−05
1.800	2.635529−07	−2.171303−06	2.020416−05
1.850	2.103408−07	−1.729794−06	1.606748−05
1.900	1.689502−07	−1.387033−06	1.286208−05
2.000	1.109605−07	−9.080636−07	8.394332−06
2.100	7.447567−08	−6.077248−07	5.602013−06
2.200	5.097684−08	−4.148761−07	3.814423−06
2.300	3.551804−08	−2.883646−07	2.644956−06
2.400	2.515092−08	−2.037407−07	1.864669−06
2.500	1.807536−08	−1.461219−07	1.334624−06
2.600	1.316804−08	−1.062476−07	9.686049−07
2.700	9.713852−09	−7.823801−08	7.120104−07
2.800	7.249133−09	−5.828985−08	5.296072−07
2.900	5.468115−09	−4.390078−08	3.982647−07
3.000	4.165989−09	−3.339819−08	3.025540−07
3.100	3.203557−09	−2.564757−08	2.320302−07
3.200	2.484934−09	−1.986884−08	1.795245−07
3.300	1.943234−09	−1.551882−08	1.400535−07
3.400	1.531246−09	−1.221473−08	1.101114−07
3.500	1.215279−09	−9.683825−09	8.720364−08
3.600	9.710392−10	−7.729736−09	6.953701−08
3.700	7.808394−10	−6.209680−09	5.580930−08
3.800	6.316821−10	−5.018879−09	4.506618−08
3.900	5.139340−10	−4.079769−09	3.660205−08
4.000	4.203964−10	−3.334459−09	2.989089−08
4.250	2.600326−10	−2.058545−09	1.841843−08
4.500	1.654559−10	−1.307583−09	1.167957−08
4.750	1.079587−10	−8.518711−10	7.597491−09
5.000	7.204516−11	−5.676936−10	5.056059−09
5.250	4.906214−11	−3.861035−10	3.434454−09
5.500	3.402868−11	−2.674843−10	2.376595−09
5.750	2.399813−11	−1.884378−10	1.672511−09
6.000	1.718358−11	−1.347965−10	1.195253−09
6.250	1.247682−11	−9.778570−11	8.663005−10
6.500	9.176208−12	−7.185718−11	6.360684−10
6.750	6.829097−12	−5.343568−11	4.726403−10
7.000	5.138342−12	−4.017679−11	3.551101−10
7.250	3.905729−12	−3.051822−11	2.695603−10
7.500	2.997061−12	−2.340326−11	2.065858−10
7.750	2.320220−12	−1.810717−11	1.597418−10
8.000	1.811152−12	−1.412642−11	1.245545−10
8.250	1.424780−12	−1.110696−11	9.788040−11
8.500	1.129026−12	−8.796992−12	7.748552−11
9.000	7.233966−13	−5.631281−12	4.955634−11
9.500	4.749677−13	−3.694326−12	3.248422−11
10.000	3.187590−13	−2.477469−12	2.176829−11
10.500	2.181880−13	−1.694653−12	1.488006−11
11.000	1.520413−13	−1.180161−12	1.035616−11
11.500	1.076851−13	−8.353869−13	7.326564−12
12.000	7.741145−14	−6.002180−13	5.261341−12
12.500	5.641270−14	−4.371897−13	3.830445−12
13.000	4.162949−14	−3.224769−13	2.824133−12
13.500	3.107862−14	−2.406455−13	2.106614−12
14.000	2.345248−14	−1.815246−13	1.588457−12
15.000	1.375159−14	−1.063637−13	9.301030−13
16.000	8.348885−15	−6.453559−14	5.639890−13
17.000	5.225964−15	−4.037363−14	3.526408−13
18.000	3.360760−15	−2.595103−14	2.265573−13
19.000	2.213921−15	−1.708782−14	1.491145−13
20.000	1.490253−15	−1.149768−14	1.002931−13
T*	I5	$T^{*}\frac{\partial I_5}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_5}{\partial T^{*2}}$
.300	9.505024−01	−1.228546+01	1.742020+02
.305	7.680019−01	−9.885223+00	1.396041+02
.310	6.232342−01	−7.989374+00	1.123889+02
.315	5.078649−01	−6.484795+00	9.087678+01
.320	4.155133−01	−5.285265+00	7.379292+01
.325	3.412694−01	−4.324722+00	6.016455+01
.330	2.813354−01	−3.552284+00	4.924545+01
.335	2.327599−01	−2.928571+00	4.046039+01
.340	1.932387−01	−2.422957+00	3.336371+01
.345	1.609645−01	−2.011521+00	2.760859+01
.350	1.345138−01	−1.675487+00	2.292383+01
.360	9.481057−02	−1.173534+00	1.595864+01
.370	6.761052−02	−8.318594−01	1.124684+01
.380	4.874410−02	−5.963169−01	8.017814+00
.390	3.550512−02	−4.319958−01	5.777845+00
.400	2.611303−02	−3.160717−01	4.206120+00
.410	1.938114−02	−2.334246−01	3.091345+00
.420	1.450892−02	−1.739139−01	2.292605+00
.430	1.095018−02	−1.306589−01	1.714791+00
.440	8.328163−03	−9.893889−02	1.292990+00
.450	6.380369−03	−7.548143−02	9.824211−01
.460	4.922098−03	−5.799533−02	7.518812−01
.470	3.822204−03	−4.486138−02	5.794189−01
.480	2.986744−03	−3.492503−02	4.494508−01
.490	2.347872−03	−2.735604−02	3.508180−01
.500	1.856192−03	−2.155255−02	2.754643−01
.510	1.475474−03	−1.707490−02	2.175279−01
.520	1.178953−03	−1.359955−02	1.727112−01
.530	9.467146−04	−1.088672−02	1.378411−01
.540	7.638499−04	−8.757532−03	1.105588−01
.550	6.191232−04	−7.077663−03	8.909913−02
.560	5.040175−04	−5.745645−03	7.213303−02
.580	3.382056−04	−3.834870−03	4.789408−02
.600	2.304921−04	−2.600430−03	3.231841−02
.620	1.593584−04	−1.789422−03	2.213690−02
.640	1.116588−04	−1.248240−03	1.537503−02
.660	7.921569−05	−8.818440−04	1.081754−02
.680	5.685520−05	−6.304135−04	7.703305−03
.700	4.125196−05	−4.556862−04	5.547805−03
.720	3.023706−05	−3.328213−04	4.037864−03
.740	2.237621−05	−2.454630−04	2.968161−03
.760	1.670863−05	−1.827007−04	2.202279−03
.780	1.258283−05	−1.371653−04	1.648436−03
.800	9.551988−06	−1.038218−04	1.244148−03
.820	7.306309−06	−7.919158−05	9.464002−04
.840	5.628818−06	−6.084689−05	7.252683−04
.860	4.366070−06	−4.707630−05	5.597268−04
.880	3.408550−06	−3.666223−05	4.348626−04
.900	2.677421−06	−2.873079−05	3.400031−04
.920	2.115454−06	−2.264944−05	2.674455−04
.940	1.680783−06	−1.795673−05	2.115853−04
.960	1.342546−06	−1.431341−05	1.683130−04
.980	1.077839−06	−1.146834−05	1.345936−04
1.000	8.695369−07	−9.234215−06	1.081696−04
1.025	6.691683−07	−7.090008−06	8.286488−05
1.050	5.185300−07	−5.481877−06	6.393154−05
1.075	4.044373−07	−4.266703−06	4.965707−05
1.100	3.174146−07	−3.341895−06	3.881704−05
1.150	1.989571−07	−2.086806−06	2.414894−05
1.200	1.274183−07	−1.331803−06	1.535919−05
1.250	8.321995−08	−8.670313−07	9.967520−06
1.300	5.533902−08	−5.748302−07	6.588933−06
1.350	3.741237−08	−3.875384−07	4.429983−06
1.400	2.568163−08	−2.653352−07	3.025337−06
1.450	1.787967−08	−1.842798−07	2.096139−06
1.500	1.261203−08	−1.296927−07	1.471927−06
1.550	9.005420−09	−9.240746−08	1.046562−06
1.600	6.503705−09	−6.660256−08	7.528177−07
1.650	4.747167−09	−4.852234−08	5.474324−07
1.700	3.499729−09	−3.570790−08	4.021499−07
1.750	2.604330−09	−2.652716−08	2.982567−07
1.800	1.955144−09	−1.988276−08	2.231979−07
1.850	1.480002−09	−1.502793−08	1.684463−07
1.900	1.129134−09	−1.144865−08	1.281438−07
2.000	6.717130−10	−6.792428−09	7.582601−08
2.100	4.103733−10	−4.139600−09	4.610042−08
2.200	2.568080−10	−2.584743−09	2.872149−08
2.300	1.642498−10	−1.649768−09	1.829509−08
2.400	1.071591−10	−1.074303−09	1.189130−08
2.500	7.119486−11	−7.125057−10	7.873054−09
2.600	4.809730−11	−4.805710−10	5.301748−09
2.700	3.299722−11	−3.292007−10	3.626415−09
2.800	2.296228−11	−2.287648−10	2.516546−09
2.900	1.619141−11	−1.610978−10	1.769878−09
3.000	1.155806−11	−1.148567−10	1.260329−09
3.100	8.345541−12	−8.283715−11	9.079423−10
3.200	6.090705−12	−6.039031−11	6.612037−10
3.300	4.489829−12	−4.447187−11	4.864242−10
3.400	3.340978−12	−3.306055−11	3.612650−10
3.500	2.508160−12	−2.479678−11	2.707195−10
3.600	1.898683−12	−1.875500−11	2.045834−10
3.700	1.448644−12	−1.429782−11	1.558373−10
3.800	1.113514−12	−1.098159−11	1.196004−10
3.900	8.619510−13	−8.494350−12	9.244410−11
4.000	6.716820−13	−6.614614−12	7.193671−11
4.250	3.699077−13	−3.636866−12	3.948890−11
4.500	2.109655−13	−2.071158−12	2.245620−11
4.750	1.241188−13	−1.216943−12	1.317744−11
5.000	7.508537−14	−7.353148−13	7.952895−12
5.250	4.657578−14	−4.556274−13	4.922651−12
5.500	2.955416−14	−2.888288−13	3.117503−12
5.750	1.914422−14	−1.869250−13	2.015792−12
6.000	1.263690−14	−1.232846−13	1.328403−12
6.250	8.486855−15	−8.273348−14	8.907841−13
6.500	5.791060−15	−5.641351−14	6.069715−13
6.750	4.009999−15	−3.903747−14	4.197421−13
7.000	2.814714−15	−2.738442−14	2.942654−13
7.250	2.000816−15	−1.945477−14	2.089363−13
7.500	1.439082−15	−1.398524−14	1.501156−13
7.750	1.046478−15	−1.016469−14	1.090516−13
8.000	7.688352−16	−7.464317−15	8.004297−14
8.250	5.703181−16	−5.534504−15	5.932241−14
8.500	4.269025−16	−4.141007−15	4.436737−14
9.000	2.452628−16	−2.377221−15	2.545022−14
9.500	1.452515−16	−1.406868−15	1.505127−14
10.000	8.839479−17	−8.556238−16	9.148067−15
10.500	5.512938−17	−5.333202−16	5.698832−15
11.000	3.515508−17	−3.399096−16	3.630230−15
11.500	2.287572−17	−2.210750−16	2.359946−15
12.000	1.516310−17	−1.464735−16	1.562894−15
12.500	1.022271−17	−9.870927−17	1.052813−15
13.000	7.000448−18	−6.756966−17	7.204117−16
13.500	4.863520−18	−4.692694−17	5.001481−16
14.000	3.424372−18	−3.303001−17	3.519190−16
15.000	1.760581−18	−1.697163−17	1.807175−16
16.000	9.452292−19	−9.107002−18	9.692259−17
17.000	5.271396−19	−5.076453−18	5.400183−17
18.000	3.040328−19	−2.926666−18	3.112011−17
19.000	1.806886−19	−1.738680−18	1.848100−17
20.000	1.103094−19	−1.061093−18	1.127489−17
T*	I6	$T^{*}\frac{\partial I_6}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_6}{\partial T^{*2}}$
.300	1.779676−01	−2.651543+00	4.274749+01
.305	1.391819−01	−2.066103+00	3.319095+01
.310	1.093802−01	−1.617949+00	2.590193+01
.315	8.636324−02	−1.273080+00	2.031255+01
.320	6.849807−02	−1.006346+00	1.600435+01
.325	5.456522−02	−7.990370−01	1.266713+01
.330	4.364897−02	−6.371556−01	1.006965+01
.335	3.505813−02	−5.101731−01	8.038586+00
.340	2.826827−02	−4.101292−01	6.443324+00
.345	2.287958−02	−3.309756−01	5.184959+00
.350	1.858575−02	−2.680941−01	4.188206+00
.360	1.239333−02	−1.777895−01	2.762612+00
.370	8.374020−03	−1.195033−01	1.847475+00
.380	5.728819−03	−8.134786−02	1.251511+00
.390	3.965142−03	−5.603707−02	8.581249−01
.400	2.774730−03	−3.903608−02	5.951389−01
.410	1.961917−03	−2.748161−02	4.172110−01
.420	1.400847−03	−1.954112−02	2.954632−01
.430	1.009537−03	−1.402667−02	2.112626−01
.440	7.339469−04	−1.015879−02	1.524381−01
.450	5.380506−04	−7.420144−03	1.109461−01
.460	3.975732−04	−5.463629−03	8.141238−02
.470	2.959916−04	−4.053942−03	6.020795−02
.480	2.219496−04	−3.029998−03	4.485799−02
.490	1.675700−04	−2.280483−03	3.365864−02
.500	1.273418−04	−1.727801−03	2.542636−02
.510	9.737592−05	−1.317387−03	1.933171−02
.520	7.490663−05	−1.010569−03	1.478878−02
.530	5.795173−05	−7.797186−04	1.138033−02
.540	4.508023−05	−6.049554−04	8.807038−03
.550	3.525186−05	−4.718706−04	6.852607−03
.560	2.770528−05	−3.699501−04	5.359663−03
.580	1.735950−05	−2.307269−04	3.327469−03
.600	1.107331−05	−1.465356−04	2.104269−03
.620	7.181549−06	−9.464589−05	1.353669−03
.640	4.729925−06	−6.209530−05	8.847543−04
.660	3.160319−06	−4.133810−05	5.868939−04
.680	2.140119−06	−2.789710−05	3.947277−04
.700	1.467587−06	−1.906803−05	2.689376−04
.720	1.018336−06	−1.319008−05	1.854692−04
.740	7.144849−07	−9.227226−06	1.293720−04
.760	5.065575−07	−6.523659−06	9.121496−05
.780	3.626948−07	−4.658502−06	6.496564−05
.800	2.621169−07	−3.358121−06	4.671423−05
.820	1.911054−07	−2.442422−06	3.389519−05
.840	1.404996−07	−1.791497−06	2.480525−05
.860	1.041157−07	−1.324629−06	1.830100−05
.880	7.773659−08	−9.869188−07	1.360677−05
.900	5.845806−08	−7.406557−07	1.019109−05
.920	4.426134−08	−5.596914−07	7.686322−06
.940	3.373103−08	−4.257350−07	5.835904−06
.960	2.586610−08	−3.258804−07	4.459199−06
.980	1.995304−08	−2.509480−07	3.428007−06
1.000	1.547934−08	−1.943581−07	2.650619−06
1.025	1.135635−08	−1.423052−07	1.936915−06
1.050	8.398913−09	−1.050450−07	1.427081−06
1.075	6.259350−09	−7.814268−08	1.059693−06
1.100	4.698877−09	−5.855899−08	7.927513−07
1.150	2.702737−09	−3.357200−08	4.530181−07
1.200	1.594269−09	−1.974335−08	2.656219−07
1.250	9.623170−10	−1.188398−08	1.594435−07
1.300	5.932559−10	−7.307325−09	9.778940−08
1.350	3.729073−10	−4.582141−09	6.117409−08
1.400	2.386418−10	−2.925741−09	3.897356−08
1.450	1.552754−10	−1.899666−09	2.525278−08
1.500	1.026016−10	−1.252771−09	1.662103−08
1.550	6.877644−11	−8.382087−10	1.110053−08
1.600	4.672432−11	−5.684573−10	7.515219−09
1.650	3.214317−11	−3.904176−10	5.153094−09
1.700	2.237362−11	−2.713328−10	3.575814−09
1.750	1.574621−11	−1.906794−10	2.509263−09
1.800	1.119762−11	−1.354094−10	1.779484−09
1.850	8.041322−12	−9.711284−11	1.274545−09
1.900	5.828334−12	−7.029887−11	9.214848−10
2.000	3.141751−12	−3.780614−11	4.944257−10
2.100	1.747686−12	−2.098612−11	2.738797−10
2.200	1.000229−12	−1.198741−11	1.561422−10
2.300	5.874090−13	−7.027377−12	9.137428−11
2.400	3.531829−13	−4.218325−12	5.476041−11
2.500	2.169767−13	−2.587589−12	3.354062−11
2.600	1.359637−13	−1.619179−12	2.095883−11
2.700	8.676792−14	−1.031962−12	1.334058−11
2.800	5.631543−14	−6.689639−13	8.637549−12
2.900	3.712764−14	−4.405327−13	5.681681−12
3.000	2.483673−14	−2.943825−13	3.792734−12
3.100	1.684192−14	−1.994225−13	2.566755−12
3.200	1.156655−14	−1.368287−13	1.759473−12
3.300	8.038642−15	−9.501025−14	1.220659−12
3.400	5.649521−15	−6.671681−14	8.564437−13
3.500	4.012382−15	−4.734580−14	6.073013−13
3.600	2.878002−15	−3.393470−14	4.349545−13
3.700	2.083707−15	−2.455162−14	3.144659−13
3.800	1.522011−15	−1.792120−14	2.293874−13
3.900	1.121064−15	−1.319167−14	1.687428−13
4.000	8.323125−16	−9.787897−15	1.251270−13
4.250	4.082085−16	−4.793699−15	6.119619−14
4.500	2.087171−16	−2.447921−15	3.121096−14
4.750	1.107439−16	−1.297373−15	1.652285−14
5.000	6.074153−17	−7.108587−16	9.043997−15
5.250	3.432607−17	−4.013421−16	5.101395−15
5.500	1.992999−17	−2.328230−16	2.956868−15
5.750	1.185967−17	−1.384364−16	1.756784−15
6.000	7.217659−18	−8.418992−17	1.067621−15
6.250	4.484043−18	−5.226890−17	6.623889−16
6.500	2.839095−18	−3.307384−17	4.188783−16
6.750	1.829348−18	−2.129859−17	2.695916−16
7.000	1.198002−18	−1.394052−17	1.763615−16
7.250	7.964578−19	−9.263317−18	1.171320−16
7.500	5.369851−19	−6.242549−18	7.889849−17
7.750	3.668185−19	−4.262451−18	5.384886−17
8.000	2.536670−19	−2.946403−18	3.720751−17
8.250	1.774471−19	−2.060285−18	2.600744−17
8.500	1.254770−19	−1.456339−18	1.837697−17
9.000	6.464726−20	−7.498133−19	9.455234−18
9.500	3.453725−20	−4.003365−19	5.045233−18
10.000	1.906094−20	−2.208216−19	2.781373−18
10.500	1.083247−20	−1.254314−19	1.579093−18
11.000	6.321829−21	−7.316810−20	9.207150−19
11.500	3.779676−21	−4.372708−20	5.500124−19
12.000	2.310265−21	−2.671708−20	3.359262−19
12.500	1.441034−21	−1.665888−20	2.093853−19
13.000	9.157891−22	−1.058334−20	1.329781−19
13.500	5.921185−22	−6.840718−21	8.592627−20
14.000	3.890134−22	−4.492960−21	5.641997−20
15.000	1.753847−22	−2.024572−21	2.541026−20
16.000	8.327489−23	−9.608514−22	1.205409−20
17.000	4.137948−23	−4.772547−22	5.984845−21
18.000	2.140584−23	−2.467966−22	3.093747−21
19.000	1.147768−23	−1.322874−22	1.657765−21
20.000	6.355404−24	−7.322824−23	9.173927−22
T*	I7	$T^{*}\frac{\partial I_7}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_7}{\partial T^{*2}}$
.300	2.599300−02	−4.382705−01	7.915025+00
.305	1.967955−02	−3.307385−01	5.954026+00
.310	1.498030−02	−2.509658−01	4.503978+00
.315	1.146265−02	−1.914445−01	3.425455+00
.320	8.815093−03	−1.467084−01	2.618733+00
.325	6.811892−03	−1.131003−01	2.012028+00
.330	5.288515−03	−8.755907−02	1.553352+00
.335	4.124343−03	−6.809677−02	1.204830+00
.340	3.230457−03	−5.319512−02	9.387117−01
.345	2.540963−03	−4.173233−02	7.345543−01
.350	2.006769−03	−3.287512−02	5.772153−01
.360	1.266376−03	−2.064463−02	3.607422−01
.370	8.110211−04	−1.315998−02	2.289105−01
.380	5.266438−04	−8.507760−03	1.473466−01
.390	3.464669−04	−5.573458−03	9.612836−02
.400	2.307498−04	−3.697027−03	6.351299−02
.410	1.554739−04	−2.481388−03	4.246819−02
.420	1.059098−04	−1.684116−03	2.871910−02
.430	7.289948−05	−1.155119−03	1.963007−02
.440	5.067445−05	−8.002427−04	1.355423−02
.450	3.555608−05	−5.596760−04	9.449449−03
.460	2.517091−05	−3.949734−04	6.648273−03
.470	1.797043−05	−2.811424−04	4.718351−03
.480	1.293360−05	−2.017603−04	3.376534−03
.490	9.380380−06	−1.459259−04	2.435482−03
.500	6.853487−06	−1.063318−04	1.770013−03
.510	5.042571−06	−7.803429−05	1.295686−03
.520	3.735170−06	−5.765872−05	9.550354−04
.530	2.784602−06	−4.288215−05	7.086108−04
.540	2.088790−06	−3.209241−05	5.291089−04
.550	1.576146−06	−2.416195−05	3.974835−04
.560	1.196096−06	−1.829622−05	3.003478−04
.580	7.000485−07	−1.066433−05	1.743557−04
.600	4.180938−07	−6.344528−06	1.033355−04
.620	2.544314−07	−3.846955−06	6.243290−05
.640	1.575625−07	−2.374167−06	3.840109−05
.660	9.917675−08	−1.489582−06	2.401676−05
.680	6.338426−08	−9.490925−07	1.525639−05
.700	4.109133−08	−6.135082−07	9.833898−06
.720	2.699833−08	−4.019899−07	6.426085−06
.740	1.796369−08	−2.667731−07	4.253615−06
.760	1.209513−08	−1.791763−07	2.849942−06
.780	8.235548−09	−1.217131−07	1.931447−06
.800	5.667286−09	−8.356856−08	1.323198−06
.820	3.939251−09	−5.796272−08	9.158224−07
.840	2.764280−09	−4.059065−08	6.400439−07
.860	1.957366−09	−2.868557−08	4.514467−07
.880	1.397942−09	−2.044863−08	3.212197−07
.900	1.006593−09	−1.469761−08	2.304692−07
.920	7.304662−10	−1.064737−08	1.666741−07
.940	5.340378−10	−7.771298−09	1.214530−07
.960	3.932097−10	−5.712856−09	8.914241−08
.980	2.914884−10	−4.228480−09	6.588067−08
1.000	2.174886−10	−3.150347−09	4.901164−08
1.025	1.521381−10	−2.199841−09	3.416439−08
1.050	1.074092−10	−1.550460−09	2.403910−08
1.075	7.649734−11	−1.102462−09	1.706585−08
1.100	5.493737−11	−7.905200−10	1.221838−08
1.150	2.900565−11	−4.161651−10	6.413866−09
1.200	1.576321−11	−2.255614−10	3.467129−09
1.250	8.795756−12	−1.255503−10	1.925132−09
1.300	5.028293−12	−7.160900−11	1.095530−09
1.350	2.939353−12	−4.177060−11	6.376910−10
1.400	1.753989−12	−2.487600−11	3.790219−10
1.450	1.066812−12	−1.510192−11	2.296762−10
1.500	6.604602−13	−9.333241−12	1.416988−10
1.550	4.156950−13	−5.864734−12	8.889507−11
1.600	2.657034−13	−3.742831−12	5.664565−11
1.650	1.722991−13	−2.423563−12	3.662650−11
1.700	1.132513−13	−1.590807−12	2.400867−11
1.750	7.539157−14	−1.057627−12	1.594133−11
1.800	5.079237−14	−7.116608−13	1.071360−11
1.850	3.460781−14	−4.843295−13	7.282844−12
1.900	2.383298−14	−3.331676−13	5.004322−12
2.000	1.164379−14	−1.624360−13	2.434879−12
2.100	5.898940−15	−8.213834−14	1.228948−12
2.200	3.088161−15	−4.292658−14	6.411736−13
2.300	1.665573−15	−2.311564−14	3.447289−13
2.400	9.230588−16	−1.279208−14	1.904974−13
2.500	5.244492−16	−7.258264−15	1.079453−13
2.600	3.048689−16	−4.214076−15	6.259480−14
2.700	1.810034−16	−2.499044−15	3.707766−14
2.800	1.095821−16	−1.511327−15	2.239923−14
2.900	6.755545−17	−9.307686−16	1.378107−14
3.000	4.235474−17	−5.830065−16	8.623990−15
3.100	2.697563−17	−3.709865−16	5.482916−15
3.200	1.743514−17	−2.395796−16	3.537892−15
3.300	1.142513−17	−1.568716−16	2.314732−15
3.400	7.584261−18	−1.040577−16	1.534303−15
3.500	5.096226−18	−6.987224−17	1.029532−15
3.600	3.463882−18	−4.746029−17	6.988422−16
3.700	2.380005−18	−3.258900−17	4.795659−16
3.800	1.652102−18	−2.260840−17	3.324981−16
3.900	1.157990−18	−1.583762−17	2.327897−16
4.000	8.191504−19	−1.119729−17	1.644951−16
4.250	3.578409−19	−4.885352−18	7.167980−17
4.500	1.640523−19	−2.237185−18	3.278844−17
4.750	7.851138−20	−1.069583−18	1.566028−17
5.000	3.904759−20	−5.314718−19	7.774499−18
5.250	2.010527−20	−2.734234−19	3.996415−18
5.500	1.068211−20	−1.451623−19	2.120130−18
5.750	5.839902−21	−7.930495−20	1.157469−18
6.000	3.277062−21	−4.447351−20	6.486864−19
6.250	1.883460−21	−2.554561−20	3.723874−19
6.500	1.106611−21	−1.500087−20	2.185541−19
6.750	6.635418−22	−8.990186−21	1.309156−19
7.000	4.054397−22	−5.490606−21	7.991688−20
7.250	2.521084−22	−3.412625−21	4.964958−20
7.500	1.593419−22	−2.156009−21	3.135439−20
7.750	1.022550−22	−1.383043−21	2.010551−20
8.000	6.656201−23	−8.999494−22	1.307794−20
8.250	4.391075−23	−5.934884−22	8.621534−21
8.500	2.933376−23	−3.963393−22	5.755707−21
9.000	1.355404−23	−1.830236−22	2.656313−21
9.500	6.532572−24	−8.816319−23	1.278870−21
10.000	3.269774−24	−4.410705−23	6.394932−22
10.500	1.693372−24	−2.283227−23	3.308911−22
11.000	9.044810−25	−1.219044−23	1.765957−22
11.500	4.968859−25	−6.694446−24	9.694250−23
12.000	2.800763−25	−3.772117−24	5.460552−23
12.500	1.616369−25	−2.176262−24	3.149385−23
13.000	9.533213−26	−1.283164−24	1.856393−23
13.500	5.736615−26	−7.719334−25	1.116477−23
14.000	3.516829−26	−4.731127−25	6.841077−24
15.000	1.390450−26	−1.869684−25	2.702273−24
16.000	5.839039−27	−7.848338−26	1.133870−24
17.000	2.585322−27	−3.473715−26	5.016770−25
18.000	1.199588−27	−1.611281−26	2.326282−25
19.000	5.803380−28	−7.792812−27	1.124760−25
20.000	2.914687−28	−3.912830−27	5.646032−26
T*	I8	$T^{*}\frac{\partial I_8}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_8}{\partial T^{*2}}$
.300	3.043474−03	−5.726215−02	1.144912+00
.305	2.231031−03	−4.185274−02	8.343968−01
.310	1.645203−03	−3.077478−02	6.118212−01
.315	1.220160−03	−2.276066−02	4.512633−01
.320	9.099293−04	−1.692788−02	3.347314−01
.325	6.821938−04	−1.265792−02	2.496529−01
.330	5.140869−04	−9.514406−03	1.871832−01
.335	3.893296−04	−7.187588−03	1.410616−01
.340	2.962635−04	−5.456238−03	1.068285−01
.345	2.264904−04	−4.161424−03	8.128890−02
.350	1.739269−04	−3.188322−03	6.214021−02
.360	1.038935−04	−1.896121−03	3.679534−02
.370	6.307787−05	−1.146388−03	2.215473−02
.380	3.888730−05	−7.039249−04	1.355050−02
.390	2.432163−05	−4.385876−04	8.411210−03
.400	1.541971−05	−2.770516−04	5.294319−03
.410	9.902206−06	−1.772996−04	3.376550−03
.420	6.436648−06	−1.148663−04	2.180412−03
.430	4.232361−06	−7.528939−05	1.424691−03
.440	2.813487−06	−4.989674−05	9.413610−04
.450	1.889775−06	−3.341697−05	6.286385−04
.460	1.281907−06	−2.260447−05	4.240608−04
.470	8.777727−07	−1.543648−05	2.888210−04
.480	6.064512−07	−1.063740−05	1.985210−04
.490	4.225914−07	−7.393942−06	1.376509−04
.500	2.968871−07	−5.182058−06	9.624464−05
.510	2.102096−07	−3.660641−06	6.783279−05
.520	1.499547−07	−2.605515−06	4.817476−05
.530	1.077401−07	−1.867987−06	3.446486−05
.540	7.794300−08	−1.348555−06	2.483015−05
.550	5.675959−08	−9.800680−07	1.800963−05
.560	4.159594−08	−7.168401−07	1.314732−05
.580	2.274590−08	−3.905387−07	7.136598−06
.600	1.272189−08	−2.176716−07	3.964048−06
.620	7.266030−09	−1.239159−07	2.249383−06
.640	4.231684−09	−7.194579−08	1.302032−06
.660	2.509774−09	−4.254656−08	7.677768−07
.680	1.514087−09	−2.559690−08	4.606596−07
.700	9.281092−10	−1.564969−08	2.809203−07
.720	5.775082−10	−9.713896−09	1.739455−07
.740	3.644551−10	−6.115923−09	1.092640−07
.760	2.330804−10	−3.902620−09	6.956903−08
.780	1.509458−10	−2.522032−09	4.486425−08
.800	9.892236−11	−1.649475−09	2.928385−08
.820	6.556213−11	−1.091105−09	1.933396−08
.840	4.391830−11	−7.295551−10	1.290390−08
.860	2.971930−11	−4.928164−10	8.701442−09
.880	2.030562−11	−3.361472−10	5.925306−09
.900	1.400165−11	−2.314140−10	4.072641−09
.920	9.739586−12	−1.607225−10	2.824207−09
.940	6.831668−12	−1.125682−10	1.975129−09
.960	4.830318−12	−7.947718−11	1.392538−09
.980	3.441408−12	−5.654634−11	9.894129−10
1.000	2.469825−12	−4.052833−11	7.082103−10
1.025	1.647533−12	−2.699209−11	4.709312−10
1.050	1.110468−12	−1.816557−11	3.164592−10
1.075	7.558886−13	−1.234725−11	2.147905−10
1.100	5.193760−13	−8.472091−12	1.471764−10
1.150	2.517609−13	−4.096035−12	7.097247−11
1.200	1.260768−13	−2.046285−12	3.537193−11
1.250	6.504451−14	−1.053358−12	1.816823−11
1.300	3.448670−14	−5.573412−13	9.593365−12
1.350	1.875084−14	−3.024523−13	5.196151−12
1.400	1.043488−14	−1.680143−13	2.881386−12
1.450	5.933505−15	−9.537699−14	1.632974−12
1.500	3.442164−15	−5.524372−14	9.443740−13
1.550	2.034484−15	−3.260364−14	5.565366−13
1.600	1.223612−15	−1.958185−14	3.337991−13
1.650	7.480252−16	−1.195525−14	2.035298−13
1.700	4.643366−16	−7.412070−15	1.260311−13
1.750	2.924113−16	−4.662230−15	7.918259−14
1.800	1.866531−16	−2.972723−15	5.043294−14
1.850	1.206765−16	−1.919932−15	3.253823−14
1.900	7.896781−17	−1.255105−15	2.125000−14
2.000	3.497213−17	−5.548137−16	9.376226−15
2.100	1.613804−17	−2.555898−16	4.312194−15
2.200	7.729001−18	−1.222212−16	2.058912−15
2.300	3.828792−18	−6.046036−17	1.017075−15
2.400	1.956060−18	−3.084787−17	5.182583−16
2.500	1.027925−18	−1.619129−17	2.716964−16
2.600	5.543862−19	−8.722635−18	1.462074−16
2.700	3.062403−19	−4.813343−18	8.059743−17
2.800	1.729562−19	−2.715816−18	4.543157−17
2.900	9.971079−20	−1.564276−18	2.614455−17
3.000	5.859491−20	−9.184661−19	1.533789−17
3.100	3.505359−20	−5.490225−19	9.161147−18
3.200	2.132339−20	−3.337251−19	5.564499−18
3.300	1.317576−20	−2.060638−19	3.433484−18
3.400	8.261830−21	−1.291258−19	2.150102−18
3.500	5.252675−21	−8.204340−20	1.365269−18
3.600	3.383323−21	−5.281379−20	8.783440−19
3.700	2.206221−21	−3.441968−20	5.721107−19
3.800	1.455482−21	−2.269504−20	3.770268−19
3.900	9.708438−22	−1.513043−20	2.512302−19
4.000	6.543802−22	−1.019343−20	1.691728−19
4.250	2.546424−22	−3.962167−21	6.568388−20
4.500	1.046835−22	−1.627211−21	2.694862−20
4.750	4.519104−23	−7.018186−22	1.161255−20
5.000	2.038177−23	−3.162705−22	5.228877−21
5.250	9.562338−24	−1.482715−22	2.449549−21
5.500	4.649455−24	−7.204436−23	1.189420−21
5.750	2.335383−24	−3.616472−23	5.966934−22
6.000	1.208412−24	−1.870219−23	3.083974−22
6.250	6.425489−25	−9.939233−24	1.638107−22
6.500	3.503420−25	−5.416578−24	8.922818−23
6.750	1.954974−25	−3.021170−24	4.974561−23
7.000	1.114583−25	−1.721715−24	2.833721−23
7.250	6.482543−26	−1.000970−24	1.646815−23
7.500	3.841015−26	−5.928702−25	9.750398−24
7.750	2.315688−26	−3.573069−25	5.874258−24
8.000	1.418941−26	−2.188681−25	3.597095−24
8.250	8.827968−27	−1.361269−25	2.236554−24
8.500	5.571482−27	−8.588682−26	1.410702−24
9.000	2.308919−27	−3.557377−26	5.839904−25
9.500	1.003971−27	−1.546078−26	2.536867−25
10.000	4.557737−28	−7.015657−27	1.150654−25
10.500	2.151054−28	−3.309761−27	5.426258−26
11.000	1.051587−28	−1.617454−27	2.650807−26
11.500	5.308372−29	−8.162108−28	1.337223−26
12.000	2.759346−29	−4.241438−28	6.946748−27
12.500	1.473443−29	−2.264209−28	3.707335−27
13.000	8.065297−30	−1.239050−28	2.028244−27
13.500	4.516999−30	−6.937638−29	1.135369−27
14.000	2.584012−30	−3.967863−29	6.492070−28
15.000	8.959677−31	−1.375228−29	2.249170−28
16.000	3.327796−31	−5.105995−30	8.347773−29
17.000	1.312942−31	−2.013855−30	3.291385−29
18.000	5.464428−32	−8.379182−31	1.369074−29
19.000	2.385238−32	−3.656582−31	5.972939−30
20.000	1.086611−32	−1.665387−31	2.719732−30
T*	I9	$T^{*}\frac{\partial I_9}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_9}{\partial T^{*2}}$
.300	2.921130−04	−6.064856−03	1.329778−01
.305	2.073528−04	−4.293490−03	9.388992−02
.310	1.481416−04	−3.059445−03	6.673207−02
.315	1.065002−04	−2.193884−03	4.773326−02
.320	7.702529−05	−1.582799−03	3.435414−02
.325	5.603182−05	−1.148645−03	2.487222−02
.330	4.098900−05	−8.383125−04	1.811081−02
.335	3.014733−05	−6.151803−04	1.326065−02
.340	2.228952−05	−4.538325−04	9.761440−03
.345	1.656336−05	−3.365193−04	7.222860−03
.350	1.236862−05	−2.507688−04	5.371275−03
.360	6.994768−06	−1.412461−04	3.013404−03
.370	4.026728−06	−8.100139−05	1.721612−03
.380	2.357207−06	−4.724491−05	1.000549−03
.390	1.401809−06	−2.799868−05	5.909274−04
.400	8.461362−07	−1.684417−05	3.543457−04
.410	5.179613−07	−1.027854−05	2.155527−04
.420	3.213172−07	−6.357016−06	1.329165−04
.430	2.018595−07	−3.982079−06	8.302213−05
.440	1.283411−07	−2.524760−06	5.249457−05
.450	8.253214−08	−1.619275−06	3.357948−05
.460	5.365182−08	−1.049957−06	2.171847−05
.470	3.523927−08	−6.879345−07	1.419554−05
.480	2.337452−08	−4.552365−07	9.371938−06
.490	1.565089−08	−3.041208−07	6.246892−06
.500	1.057390−08	−2.050178−07	4.202144−06
.510	7.205472−09	−1.394127−07	2.851525−06
.520	4.950652−09	−9.559138−08	1.951286−06
.530	3.428362−09	−6.606785−08	1.346015−06
.540	2.392191−09	−4.601248−08	9.356686−07
.550	1.681351−09	−3.228066−08	6.552435−07
.560	1.190012−09	−2.280688−08	4.621319−07
.580	6.080905−10	−1.161495−08	2.345687−07
.600	3.185594−10	−6.065481−09	1.221124−07
.620	1.707860−10	−3.242165−09	6.508077−08
.640	9.355489−11	−1.771057−09	3.545253−08
.660	5.228936−11	−9.872593−10	1.971110−08
.680	2.978054−11	−5.608739−10	1.117048−08
.700	1.726298−11	−3.243553−10	6.444831−09
.720	1.017420−11	−1.907355−10	3.781452−09
.740	6.090658−12	−1.139385−10	2.254148−09
.760	3.700165−12	−6.907929−11	1.363923−09
.780	2.279381−12	−4.247235−11	8.369888−10
.800	1.422740−12	−2.646165−11	5.205237−10
.820	8.991823−13	−1.669464−11	3.278285−10
.840	5.750483−13	−1.065874−11	2.089561−10
.860	3.719122−13	−6.882494−12	1.347119−10
.880	2.431183−13	−4.492173−12	8.779238−11
.900	1.605518−13	−2.962206−12	5.780735−11
.920	1.070599−13	−1.972488−12	3.843930−11
.940	7.205463−14	−1.325748−12	2.580118−11
.960	4.892612−14	−8.990305−13	1.747404−11
.980	3.350398−14	−6.148743−13	1.193622−11
1.000	2.312981−14	−4.239736−13	8.220550−12
1.025	1.471445−14	−2.693293−13	5.214641−12
1.050	9.469350−15	−1.730855−13	3.346632−12
1.075	6.161021−15	−1.124657−13	2.171701−12
1.100	4.050534−15	−7.384675−14	1.424189−12
1.150	1.802904−15	−3.279156−14	6.309256−13
1.200	8.320744−16	−1.510090−14	2.899203−13
1.250	3.969525−16	−7.189552−15	1.377552−13
1.300	1.952197−16	−3.529174−15	6.749516−14
1.350	9.873650−17	−1.781846−15	3.401883−14
1.400	5.124830−17	−9.233494−16	1.760011−14
1.450	2.724633−17	−4.901563−16	9.328875−15
1.500	1.481252−17	−2.660952−16	5.057296−15
1.550	8.222107−18	−1.475062−16	2.799725−15
1.600	4.653446−18	−8.337869−17	1.580586−15
1.650	2.682050−18	−4.799896−17	9.088323−16
1.700	1.572430−18	−2.810927−17	5.316413−16
1.750	9.367932−19	−1.672868−17	3.160631−16
1.800	5.666026−19	−1.010788−17	1.907829−16
1.850	3.476197−19	−6.195436−18	1.168263−16
1.900	2.161627−19	−3.849062−18	7.251589−17
2.000	8.678737−20	−1.542764−18	2.901699−17
2.100	3.648196−20	−6.475242−19	1.216042−17
2.200	1.598592−20	−2.833398−19	5.313699−18
2.300	7.274242−21	−1.287656−19	2.411768−18
2.400	3.426077−21	−6.057526−20	1.133237−18
2.500	1.665380−21	−2.941281−20	5.496557−19
2.600	8.333653−22	−1.470342−20	2.744956−19
2.700	4.283407−22	−7.550276−21	1.408229−19
2.800	2.256890−22	−3.974679−21	7.406851−20
2.900	1.216816−22	−2.141213−21	3.986917−20
3.000	6.702582−23	−1.178536−21	2.192746−20
3.100	3.766508−23	−6.617986−22	1.230438−20
3.200	2.156517−23	−3.786559−22	7.035344−21
3.300	1.256536−23	−2.204898−22	4.094047−21
3.400	7.442898−24	−1.305247−22	2.422123−21
3.500	4.477466−24	−7.847558−23	1.455429−21
3.600	2.733128−24	−4.787699−23	8.874615−22
3.700	1.691499−24	−2.961523−23	5.486761−22
3.800	1.060579−24	−1.855983−23	3.436878−22
3.900	6.732469−25	−1.177616−23	2.179682−22
4.000	4.324047−25	−7.560096−24	1.398704−22
4.250	1.498981−25	−2.618122−24	4.838916−23
4.500	5.526202−26	−9.643264−25	1.780690−23
4.750	2.152035−26	−3.752234−25	6.923088−24
5.000	8.802162−27	−1.533582−25	2.827457−24
5.250	3.763037−27	−6.551826−26	1.207146−24
5.500	1.674506−27	−2.913682−26	5.365039−25
5.750	7.728012−28	−1.343932−26	2.473223−25
6.000	3.687385−28	−6.409162−27	1.178860−25
6.250	1.814028−28	−3.151499−27	5.793886−26
6.500	9.178912−29	−1.593934−27	2.929073−26
6.750	4.766814−29	−8.274217−28	1.519873−26
7.000	2.535860−29	−4.400032−28	8.079213−27
7.250	1.379562−29	−2.392844−28	4.392092−27
7.500	7.663204−30	−1.328729−28	2.438075−27
7.750	4.340440−30	−7.523528−29	1.380050−27
8.000	2.503628−30	−4.338379−29	7.955575−28
8.250	1.469017−30	−2.544849−29	4.665352−28
8.500	8.759077−31	−1.516973−29	2.780258−28
9.000	3.255730−31	−5.635790−30	1.032406−28
9.500	1.277239−31	−2.209973−30	4.046615−29
10.000	5.259049−32	−9.095958−31	1.664873−29
10.500	2.261975−32	−3.910852−31	7.155617−30
11.000	1.012136−32	−1.749357−31	3.199712−30
11.500	4.694870−33	−8.112052−32	1.483310−30
12.000	2.250620−33	−3.887654−32	7.106696−31
12.500	1.111989−33	−1.920320−32	3.509473−31
13.000	5.649156−34	−9.753315−33	1.782038−31
13.500	2.944648−34	−5.082825−33	9.284820−32
14.000	1.571930−34	−2.712781−33	4.954426−32
15.000	4.780099−35	−8.246221−34	1.505466−32
16.000	1.570327−35	−2.708097−34	4.942391−33
17.000	5.520823−36	−9.518095−35	1.736584−33
18.000	2.061072−36	−3.552426−35	6.479733−34
19.000	8.117560−37	−1.398796−35	2.550847−34
20.000	3.354332−37	−5.778858−36	1.053609−34
T*	I10	$T^{*}\frac{\partial I_{10}}{\partial T^{*}}$	$T^{*2}\frac{{\partial }^2{I}_{10}}{\partial T^{*2}}$
.300	2.340906−05	−5.314871−04	1.267881−02
.305	1.609168−05	−3.644461−04	8.672762−03
.310	1.113927−05	−2.516768−04	5.974982−03
.315	7.763193−06	−1.749894−04	4.144805−03
.320	5.445638−06	−1.224711−04	2.894367−03
.325	3.844005−06	−8.626017−05	2.034157−03
.330	2.729936−06	−6.112891−05	1.438472−03
.335	1.950140−06	−4.357658−05	1.023324−03
.340	1.401004−06	−3.124239−05	7.322068−04
.345	1.012031−06	−2.252368−05	5.268428−04
.350	7.349397−07	−1.632528−05	3.811331−04
.360	3.935424−07	−8.709452−06	2.025901−04
.370	2.148404−07	−4.737895−06	1.098254−04
.380	1.194343−07	−2.625080−06	6.064881−05
.390	6.754260−08	−1.479802−06	3.408107−05
.400	3.881917−08	−8.479072−07	1.946931−05
.410	2.265438−08	−4.933895−07	1.129648−05
.420	1.341355−08	−2.913214−07	6.651683−06
.430	8.051851−09	−1.744083−07	3.971761−06
.440	4.896748−09	−1.057963−07	2.403206−06
.450	3.015095−09	−6.498313−08	1.472551−06
.460	1.878524−09	−4.039205−08	9.131809−07
.470	1.183627−09	−2.539297−08	5.728030−07
.480	7.538246−10	−1.613713−08	3.632338−07
.490	4.850365−10	−1.036152−08	2.327483−07
.500	3.151605−10	−6.719041−09	1.506283−07
.510	2.067089−10	−4.398382−09	9.841468−08
.520	1.367997−10	−2.905408−09	6.488902−08
.530	9.131636−11	−1.935919−09	4.315951−08
.540	6.146083−11	−1.300711−09	2.894820−08
.550	4.169578−11	−8.809342−10	1.957318−08
.560	2.850335−11	−6.012299−10	1.333703−08
.580	1.361240−11	−2.862423−10	6.330255−09
.600	6.680125−12	−1.400625−10	3.088591−09
.620	3.362125−12	−7.030157−11	1.546071−09
.640	1.732506−12	−3.613341−11	7.926248−10
.660	9.126273−13	−1.898776−11	4.155172−10
.680	4.907494−13	−1.018695−11	2.224196−10
.700	2.690420−13	−5.572646−12	1.214106−10
.720	1.502002−13	−3.104687−12	6.750371−11
.740	8.530032−14	−1.759743−12	3.818724−11
.760	4.923111−14	−1.013751−12	2.195840−11
.780	2.885034−14	−5.930267−13	1.282279−11
.800	1.715259−14	−3.519821−13	7.598067−12
.820	1.033822−14	−2.118059−13	4.564866−12
.840	6.312468−15	−1.291289−13	2.778765−12
.860	3.902190−15	−7.970655−14	1.712732−12
.880	2.440695−15	−4.978377−14	1.068260−12
.900	1.543737−15	−3.144572−14	6.738604−13
.920	9.868755−16	−2.007653−14	4.296747−13
.940	6.373409−16	−1.294966−14	2.768054−13
.960	4.156285−16	−8.434773−15	1.800842−13
.980	2.735774−16	−5.545613−15	1.182653−13
1.000	1.816874−16	−3.678869−15	7.836933−14
1.025	1.102373−16	−2.229168−15	4.742466−14
1.050	6.773853−17	−1.368046−15	2.906813−14
1.075	4.212840−17	−8.497953−16	1.803473−14
1.100	2.650298−17	−5.339876−16	1.131951−14
1.150	1.083317−17	−2.177950−16	4.606889−15
1.200	4.608201−18	−9.245992−17	1.951867−15
1.250	2.033054−18	−4.071613−17	8.579560−16
1.300	9.275032−19	−1.854330−17	3.900722−16
1.350	4.364051−19	−8.710986−18	1.829518−16
1.400	2.112808−19	−4.211048−18	8.831148−17
1.450	1.050326−19	−2.090495−18	4.377997−17
1.500	5.351500−20	−1.063735−18	2.224830−17
1.550	2.789892−20	−5.538764−19	1.157038−17
1.600	1.485962−20	−2.946673−19	6.148501−18
1.650	8.075030−21	−1.599543−19	3.333989−18
1.700	4.471567−21	−8.848412−20	1.842428−18
1.750	2.520378−21	−4.982520−20	1.036466−18
1.800	1.444492−21	−2.852979−20	5.929356−19
1.850	8.410070−22	−1.659601−20	3.446161−19
1.900	4.969860−22	−9.799127−21	2.033111−19
2.000	1.809086−22	−3.561495−21	7.378034−20
2.100	6.927978−23	−1.361977−21	2.817556−20
2.200	2.777684−23	−5.453671−22	1.126777−20
2.300	1.161107−23	−2.277021−22	4.699029−21
2.400	5.041921−24	−9.876882−23	2.036072−21
2.500	2.267112−24	−4.436714−23	9.136971−22
2.600	1.052660−24	−2.058131−23	4.234604−22
2.700	5.034623−25	−9.835050−24	2.021825−22
2.800	2.474874−25	−4.830731−24	9.922754−23
2.900	1.247944−25	−2.434042−24	4.996000−23
3.000	6.443601−26	−1.255900−24	2.575995−23
3.100	3.401461−26	−6.625281−25	1.358027−23
3.200	1.833094−26	−3.568231−25	7.309509−24
3.300	1.007218−26	−1.959462−25	4.011609−24
3.400	5.635996−27	−1.095830−25	2.242258−24
3.500	3.208187−27	−6.234537−26	1.275030−24
3.600	1.855941−27	−3.604898−26	7.368763−25
3.700	1.090168−27	−2.116497−26	4.324300−25
3.800	6.496642−28	−1.260720−26	2.574681−25
3.900	3.924819−28	−7.613147−27	1.554122−25
4.000	2.402043−28	−4.657459−27	9.503743−26
4.250	7.418473−29	−1.437066−27	2.929669−26
4.500	2.452724−29	−4.747308−28	9.670036−27
4.750	8.616652−30	−1.666519−28	3.392078−27
5.000	3.196290−30	−6.177632−29	1.256561−27
5.250	1.245195−30	−2.405160−29	4.889199−28
5.500	5.071185−31	−9.789718−30	1.988930−28
5.750	2.150446−31	−4.149194−30	8.425365−29
6.000	9.462044−32	−1.824788−30	3.703657−29
6.250	4.306809−32	−8.302159−31	1.684297−29
6.500	2.022435−32	−3.897015−31	7.902831−30
6.750	9.774831−33	−1.882788−31	3.816696−30
7.000	4.852224−33	−9.342837−32	1.893266−30
7.250	2.469153−33	−4.752716−32	9.627896−31
7.500	1.285859−33	−2.474301−32	5.010809−31
7.750	6.842481−34	−1.316273−32	2.664865−31
8.000	3.715422−34	−7.145312−33	1.446212−31
8.250	2.056044−34	−3.953059−33	7.998941−32
8.500	1.158221−34	−2.226313−33	4.503810−32
9.000	3.861402−35	−7.418986−34	1.500182−32
9.500	1.366753−35	−2.624907−34	5.305652−33
10.000	5.104362−36	−9.799554−35	1.980036−33
10.500	2.000825−36	−3.839984−35	7.756260−34
11.000	8.194553−37	−1.572220−35	3.174717−34
11.500	3.492893−37	−6.699654−36	1.352457−34
12.000	1.544203−37	−2.961146−36	5.976128−35
12.500	7.059601−38	−1.353420−36	2.730801−35
13.000	3.328621−38	−6.380008−37	1.287016−35
13.500	1.614878−38	−3.094622−37	6.241398−36
14.000	8.044515−39	−1.541293−37	3.107971−36
15.000	2.145448−39	−4.109164−38	8.283166−37
16.000	0.000000	0.000000	0.000000
17.000	0.000000	0.000000	0.000000
18.000	0.000000	0.000000	0.000000
19.000	0.000000	0.000000	0.000000
20.000	0.000000	0.000000	0.000000

As mentioned earlier, the quantity α_ip is presented in table 1 for values of p from 0 through 10 with, in each case, i running from 0 through 20. Appendix B contains listings of the computer subroutines needed for extending table 1 to still higher values of i and p. For each value of m table 3 contains the second virial coefficient and its first two temperature derivatives for the central potential. This corresponds to the first terms in eqs (10a), (14b), and (16b). Table 3 also contains the quantities

$$I_k,T^{*}\frac{d{I}_k}{d{T}^{*}}\text{ and }{T}^{*2}\frac{d^2{I}_k}{d{T}^{*2}}$$

as required for completing the quantities required for the evaluation of the working equations. It should be noted that table 3 contains only those values of k needed to produce closure in the recursion relations (12) and (12a). This closure in effect includes the quantities $T^{*}\frac{d{I}_k}{d{T}^{*}}$ and $T^{*2}\frac{d^2{I}_k}{d{T}^{*2}}$ when use is made of eqs (18) and (19). As has been pointed out above, (12) and (12a) and (18) and (19) can be used to produce recursion relations for the derivatives themselves.

In summary, eqs (3), (13), and (15) can be evaluated through the use of the working equations (10a, b), (14a, b), and (16a, b) where table 1 (with appendix B used when necessary) contains values of α_ip, table 3 contains terms corresponding to the contribution of the central potential and (with proper use made of (12), (18), and (19) the necessary values of the quantities I_k, $T^{*}\frac{d{I}_k}{d{T}^{*}}$ and $T^{*2}\frac{d^2{I}_k}{d{T}^{*2}}$.

5.2. The Adequacy of Table 1

The adequacy of table 1 for any particular experimental data point will depend on the value of T* associated with that data point as well as on the values of τ and q associated with the substance. In order to examine this adequacy in a general fashion, we calculated the terms of (10) corresponding to each member of table 1 for the particular case m = 12 and for selected values of T* and τ. The calculations were carried out for τ values through 4 in order to be sure to include a representation of the situation for even the most polar substance. In each case, the value of T* = 0.3 was taken as a lower limit in order to include a reduced temperature well below what might be the lowest reached in practice.

Table 1 is, by definition, adequate for those situations for which convergence in (3) occurs when only terms whose values are contained in table 1 are used. Choice of particular criteria for convergence in (3) are somewhat arbitrary. The adequacy of a particular criterion for a given data points depends, first of all, on the accuracy of the experimental data being analyzed. The adequacy for such a data point depends further on the contribution which that data point will make to the entire set of data being analyzed, i.e., on its contribution to the sum of the squares of the deviations summed over all data points. It depends, therefore, on the number of data points and on their distribution.

It is convenient to take different convergence criteria with respect to i and to p. Thus, for the series in i, we consider there to be convergence by a given term when that term contributes less than one part in 10,000 to the sum. With respect to p, we consider there to be convergence by a given term when the ratio of the value of that term to that of the p − 1 term is less than 0.001. These criteria are clearly adequate. Since they may be excessively stringent, we have in the following also inserted remarks appropriate to less stringent criteria. Our results can be summarized as follows:

1. Convergence with respect to i

   1. Convergence in i is only weakly dependent on p.
   2. For T* ⩾ 0.4 convergence always occurs by 20 terms.
   3. For T* = 0.3, 20 terms in i are adequate for τ ⩽ 3. For τ = 4, the term i = 21 contributes approximately one part in a hundred to the sum with indications that at most 25 terms will be needed in order to meet the convergence criteria. Thus table 1 is adequate with respect to i even for τ = 4 when there are a sufficient number of data points so that the contribution of one part in one hundred for a point in the immediate vicinity of T* = 0.3 is negligible.

2. Convergence with respect to p

Convergence with respect to p depends very strongly on the value of q. Values for this parameter are not known with any great certainty. Buckingham and Pople obtained values in the neighborhood of 0.1. This value is of questionable accuracy since it is more than likely that a sufficient number of terms was not included by them. This is partly indicated by the fact that the values of σ, the hard core diameter, reported by them are, in general, unrealistically small for the molecules considered. Because of these small σ values, their values of q might be expected to be too large. Because of this we have only considered q values less than or equal to 0.1. In particular, we have examined convergence with respect to p for q = 0.1, 0.05, and 0.01, the latter being a good lower limit based on reasonable estimates for an upper bound for σ. Our results for convergence with respect to p can be summarized as follows:

1. Convergence is dependent on τ (due to the appearance of a factor τ^p in (10)).

2. For q = 0.01 convergence is obtained within table 1 over the entire range of T* and τ values used.

3. For q = 0.05 convergence is obtained by the last term of table 1 for all T* values included for τ ⩽ 2.0. For this value of q and τ = 3.0, convergence is obtained only for T* ⩾ 0.5 while for τ = 4.0 and q = 0.05 table 1 is adequate only for T* > 0.75.

4. For q = 0.1, there is convergence only for τ ⩽ 1. For this value of q and τ = 2, the series converges within the table for T* ⩾ 0.75. For τ = 3.0, and q = 0.1, convergence is obtained only for T* ⩾ 1.0 whereas for τ = 4.0 and q = 0.1 convergence occurs only for T* ⩾ 2.0.

Table 1 is clearly adequate for all except the most extreme cases. Sufficient terms are presented for almost all situations for substances with values of q less than 0.05. For q = 0.1, the table is adequate for almost all situations for τ ⩽ 2.0 and for many situations for τ even up to 3.0. It is clearly inadequate for the combination τ = 4.0, q = 0.1.

For convenience to the user for those cases where table 1 is inadequate, a computer program for calculating the quantities Q_lst and α_ip (the latter to any order in p) has been included as appendix B. With the help of table 1 and/or appendix B it is possible to calculate A_p(T*, τ) in (11) for as many values of p as are necessary for the proper evaluation of the second virial coefficient according to our model (i.e., according to eq (3)).

The tables were also compared with other published tables with particular emphasis placed on comparisons with those of Saxena et al. [11], for the (18, 6, 3) potential since those tables include functions of the first derivative of the second virial coefficients. In order to avoid the need for interpolation in the less closely spaced tables of Saxena et al., all comparisons were made for values of T* and τ corresponding to values of y and t* contained in [11]. Thus, comparisons were made for y = 0.4 through 2.60 (y being defined as in reference [11]). For each such value of y the comparisons were made for t* = 0.1, in steps of 0.1, to 2.0 where such values were to be found in [11]. This corresponds, according to our definitions, to, approximately, 0.65 < T* < 16 and 0 < τ < 3.6742. It should be realized that this required the calculation of reduced second virial coefficients from our I_k tables.

Agreement to one part in ten thousand was obtained for all values of T* greater than 2.0 and for all values of τ. Under those conditions, the major contributions to the second virial coefficients come from small values of k. For reduced temperatures smaller than 2.0, differences began to appear at the largest values of τ. These differences increased with decreasing T* and reached a maximum of five parts in one thousand for the largest τ values at the two lowest temperatures, T* = 0.65 and 0.802. An examination of the contributions of successive terms showed that these differences could not be attributed to the possibility that Saxena et al. had included an insufficient number of terms in the evaluation of the second virial coefficient and its first derivative.

As mentioned above, the tables were also checked for accuracy and internal consistency by comparing the derivatives of the I_k calculated using a numerical difference scheme with the derivatives calculated using (18) and (19).

Because of these relatively large differences from the values published by Saxena et al., particular attention was paid to the lowest temperatures in this checking. It was a simple matter to carry out these comparisons for each value of m, for each k value and including many more T* values than contained in these tables. Both the first and second derivatives were included in these comparisons.

It was found that the first derivatives calculated using differences and those calculated with (18) and (19) generally agreed to better than one part in 100,000 particularly for T* small. At the higher T* values, there were occasional differences on the order of one part in 10,000. As might be expected the differences between the derivatives calculated using the two methods were larger in the case of the second derivatives. Nevertheless, agreement was generally found to better than five parts in 100,000 with occasional high temperature values showing differences on the order of one part in 10,000 and with some rare cases where there were discrepancies on the order of five parts in 10,000.

Our tables would appear to be internally consistent to much better than the one part in 10,000 required indicating that the differences between our results and those of Saxena et al. are most likely attributable to errors in their calculations.

The tables of I_k values contained herein do not include all of the values which were computed. The values included represent an attempt to strike a compromise between the inclusion of a sufficient number of reduced temperatures to allow for ease in interpolation and the removal of a sufficient number of values to reduce the volume of numbers to manageable size. An attempt was made to include only those values such that the fourth tabular difference at any temperature divided by the value of the function at that temperature lie between 0.001 and 0.0001. It was possible to satisfy these limits for all reduced temperatures less than 4.0. This fraction took on values slightly above 0.001 in the range 4.0 < T* < 4.5 and T* > 11.0 both of which represent quite high reduced temperatures for almost all polar substances. It follows then that a fourth order interpolation formula is guaranteed to produce errors less than one part per thousand over the entire set of tables. A sufficient number of decimal places has been included to allow for the use of still higher order interpolation formulas where necessary for additional accuracy.

Appendix A. The Integration Over Angles

The angular integrals in (4) are of the form

$$\begin{gathered} Q_{\text{lst}}=\frac{{(-1)}^{l+s+t}}{16{\pi }^2}{\int }_0^{\pi }\text{sin}{\theta }_{1}d{\theta }_1{\int }_0^{\pi }\text{sin}{\theta }_{2}d{\theta }_2 \\ {\int }_0^{2\pi }d{\Phi }_1{\int }_0^{2\pi }d{\Phi }_2\frac{X^l{Y}^s{Z}^t}{l!s!t!} \end{gathered}$$ A-1

where l, s, and t are integers and where X, Y, and Z have already been defined. It should be noted that, for spherical molecules without dipole moments, l = s = t = 0 whereas for the nonpolarizable dipole l > 0 and s = t = 0. The introduction of dipole polarizability requires s and/or t to be different from zero.

The integrand in A-1 is a function of the four angular variables. We choose to exhibit this explicitly by defining the function

$$G_{lst}\left({\theta }_1,{\theta }_2,{\Phi }_1,{\Phi }_2\right)=\frac{X^l{Y}^s{Z}^t}{l!s!t!}$$

Introducing the definitions of the functions X, Y, and Z, these become

$$\begin{gathered} G_{lst}\left({\theta }_1,{\theta }_2,{\Phi }_1,{\Phi }_2\right)=(2\text{cos}{\theta }_1\text{cos}{\theta }_2{+\text{sin}{\theta }_1\text{sin}{\theta }_2\text{cos}\left({\Phi }_1+{\Phi }_2\right))}^{\prime } \\ {\left(1-\frac{3}{2}{\text{cos}}^2{\theta }_1-\frac{3}{2}{\text{cos}}^2{\theta }_2\right)}^s(8\text{cos}{\theta }_1\text{cos}{\theta }_2{+\text{sin}{\theta }_1\text{sin}{\theta }_2\text{cos}\left({\Phi }_1+{\Phi }_2\right))}^t\frac{1}{l!s!t!} \end{gathered}$$

On making use of the multinomial expansion, this can be written

$$\begin{gathered} G_{lst}\left({\theta }_1,{\theta }_2,{\Phi }_1,{\Phi }_2\right)=\{\frac{1}{l!}\sum _{h=0}^l(k)2^{l-h}{\left(\text{cos}{\theta }_1\text{cos}{\theta }_2\right)}^{l-h}{\left(\text{sin}{\theta }_1\text{sin}{\theta }_2\right)}^h{\text{cos}}^h\left({\Phi }_1+{\Phi }_2\right)\} \\ \left\{\frac{1}{s!}\sum _{i=0}^s\left(\begin{array}{c}s\\ i\end{array}\right){\left(-\frac{3}{2}\right)}^i\sum _{j=0}^i\left(\begin{array}{c}i\\ j\end{array}\right){\left(\text{cos}{\theta }_1\right)}^{2i-2j}{\left(\text{cos}{\theta }_2\right)}^{2j}\right\} \end{gathered}$$

$$\{\frac{1}{t!}\sum _{k=0}^t\left(\begin{array}{l}t\hfill \\ k\hfill \end{array}\right)8^{t-k}{\left(\text{cos}{\theta }_1\text{cos}{\theta }_2\right)}^{t-k}{\left(\text{sin}{\theta }_1\text{sin}{\theta }_2\text{cos}\left({\Phi }_1+{\Phi }_2\right)\right)}^k\}$$

Equation A-1 then becomes

$$Q_{lst}=\sum _{h=0}^l\sum _{i=0}^s\sum _{j=0}^i\sum _{k=0}^t{C}_{\beta }^{\alpha }{J}_{hk}{F}_{v_1}{F}_{v_2}$$ A-2

where the integrals F_v1 and F_v2 are defined by

$$F_w={\int }_0^{\pi }{(\text{cos}\theta )}^{w-h-k}{(\text{sin}\theta )}^{h+k+1}d\theta$$ A-3

the additional factor of sin θ coming from the volume element in (2). It should be noted that since h + k is even, and since 2i and 2j are necessarily even, both F_v1 and F_V2 vanish unless l + t is even.

The integral in (A-3) can be evaluated by repeated integration by parts with the help of the identities

$${\int }_0^{\pi }{\text{cos}}^{n}X{\text{sin}}^{m}XdX=\frac{m-1}{m+n}{\int }_0^{\pi }{\text{cos}}^{n}X{\text{sin}}^{m-2}XdX$$

and

$$\begin{gathered} {\int }_0^{\pi }{\text{cos}}^{p}X\text{sin}XdX=\frac{2}{p+1}p\text{ even } \\ =0p\text{ odd } \end{gathered}$$

There results

$$F_w=2^{h+k+1}\frac{\left(\frac{w}{2}\right)!(w-h-k)!\left(\frac{h+k}{2}\right)!}{(w+1)!\left(\frac{w-h-k}{2}\right)!}$$

Making use of this result A-2 becomes

$$={\displaystyle \sum }_{h=0}^l{\displaystyle \sum }_{i=0}^s{\displaystyle \sum }_{j=0}^i{\displaystyle \sum }_{k=0}^t\frac{2^{-h}}{16{\pi }^2}{C}_{\text{hlst}}^{\text{ijk}}{\left(\text{cos}{\theta }_1\right)}^{v_1-h-k}{\theta }_1{\left(\cos {\theta }_2\right)}^{v_2-h-k}{\left(\sin {\theta }_1\sin {\theta }_2\right)}^{h+k}{\left(\cos \left({\Phi }_1+{\Phi }_2\right)\right)}^{h+k}$$

where

$$\begin{gathered} v_1=l+t+2i-2j \\ {v}_2=l+t+2j \end{gathered}$$

and

$$C_{\text{hlst}}^{ijk}=\left(\begin{array}{l}l\hfill \\ h\hfill \end{array}\right)\left(\begin{array}{l}s\hfill \\ i\hfill \end{array}\right)\left(\begin{array}{l}i\hfill \\ j\hfill \end{array}\right)\left(\begin{array}{l}t\hfill \\ k\hfill \end{array}\right)2^{(l-i+3t-2k)}\frac{{(-3)}^i}{l!s!t!}{(-1)}^{l+s+t}.$$

In what follows, we shall use the subscript β to refer to the set of subscripts hlst and γ to refer to the superscripts ijk.

The integration over the azimuthal angles Φ₁ and Φ₂ can be simplified with the help of the transformation

$$\begin{array}{l}{\Phi }_1+{\Phi }_2={\chi }_1\\ {\Phi }_1={\chi }_2.\end{array}$$

There results the easily evaluated double integral

$$\begin{gathered} J_{hk}={\int }_0^{2\pi }d{\chi }_2{\int }_0^{2\pi }d{\chi }_1{\text{cos}}^{h+k}{\chi }_1 \\ =2^{2-h-k}{\pi }^2\frac{(h+k)!}{{\left[\frac{(h+k)!}{2}\right]}^2}\text{ for }h+k\text{ even } \\ {J}_{hk}=0h+k\text{ odd } \end{gathered}$$

$$\begin{gathered} Q_{lst}=\frac{2^{-h}}{16{\pi }^2}\sum _{h=0}^l\sum _{i=0}^s\sum _{j=0}^i\sum _{k=0}^t{C}_{\beta }^{\alpha }{2}^{2-h-2k}{\pi }^2\frac{(h+k)!}{{\left[{\left(\frac{h+k}{2}\right)}^{!}\right]}^2} \\ \times \left[2^{n+k+1}\frac{\left(\frac{v_1}{2}\right)!\left(v_1-h-k\right)!\left(\frac{h+k}{2}\right)!}{\left(v_1+1\right)!\left(\frac{v_1-h-k}{2}\right)!}\right] \end{gathered}$$

or

$$\begin{array}{l}\times \left[2^{h+k+1}\frac{\left(\frac{v_2}{2}\right)!\left(v_2-h-k\right)[\left(\frac{h+k}{2}\right)!}{\left(v_2+1\right)!\frac{\left(v_2-h-k\right)!}{2}]}\right]\\ Q_{lst}=\sum _{h=0}^l\sum _{i=0}^s\sum _{j=0}^i\sum _{k=0}^t{C}_{\beta }^{\alpha }\frac{(h+k)!\left(v_1/2\right)!\left(v_2/2\right)!}{\left(v_1+1\right)!\left(v_2+1\right)!\left(\frac{v_1-h-k}{2}\right)!}\\ \frac{\left(v_1-h-k\right)!\left(v_2-h-k\right)!}{\left(\frac{v_2-h-k}{2}\right)!}\end{array}$$ A-4

Appendix B

SUBROUTINE ALPHA(A,I,J)
COMMON /FCTR/ FF
DOUBLE PRECISION FF(50),F(49),X,A ,Q
EQUIVALENCE (FF(2),F(1))
IP=I+J+1
X=0.D0
DO 10 KK=1,IP
K=KK-1
10 X=X+F(2*K)/(F(K)*F(K))
X=F(2*IP-1)**2/(4.D0**(I+J)*F(IP-10**2*X)
A=0.D0
LS=J+1
DO 30 LT=1,LS
IS=LL-1
DO 30 LT=1,LS
IT=LT-1
IF((IS+2*IT).NE.J) GO TO 30
L=2*I+MOD(IT,2)
A=A+Q(L,IS,IT)
30 CONTINUE
A=A*X
RETURN
END
FUNCTION Q(L,S,T)
INTEGER S,T,V,W,H
COMMON /FCTR/ FF
DOUBLE PRECISION FF(50),Q,F(49),C,A
EQUIVALENCE (FF(2),F(1))
Q=0.D0
LL=L+1
LS=S+1
LT=T+1
DO 80 IH=1,LL
H=IH-1
DO 80 II=1,LS
I=II-1
DO 80 IJ=1,II
J=IJ-1
DO 80 IK=1,LT
K=IK-1
KH=H+K
IF(MOD(KH,2).NE.0) GO TO 80
V=(L+T+2*I-2*J)/2
W=(L+T+2*J)/2
A=C(F,I,J,K,H,L,S,T)*2.D0**K *F(KH)
A=A*F(V)*F(W)/(F(2*V+1)*F(2*W+1))
KV=V-KH/2
KW=W-KH/2
A=A*F(2*KV)*F(2*KW)/(F(KV)*F(KW))
Q=Q+A
80 CONTINUE
WRITE(6,99) L,S,T,Q,I,J,K,H,V,W,A
99 FORMAT(4X,3I5,D25.15,6I5,D25.15)
RETURN
END
FUNCTION C(F,I,J,K,IH,L,M,N)
DOUBLE PRECISION C,F(49)
C=(−3.D0)**I*2.D0**(L -I+3*N-3*K) *(−1.D0)**M
LI=L-IH
MI=M-I
IJ=I-J
NK=N-K
C=C/(F(IH)*F(LI)*F(MI)*F(J)*F(IJ)*F(K)*F(NK))
RETURN
END
SUBROUTINE FAC
COMMON /FCTR/ F
DOUBLE PRECISION F(80)
F(1)=1.D0
DO 10 I=2,80
X=I-1
10 F(I) = F(I-1) * X
RETURN
END
FUNCTION FACT(I)
COMMON /FCTR/ F(60)
DOUBLE PRECISION SUM,F,FACT
SUM = 0.
II=I+1
DO 10 JJ=1,II
J=JJ-1
10 SUM = SUM + F(2*J+1)/F(J+1)**2
FACT = 4.D0**I*SUM*(F(I+1)/F(2*I+2))**2
RETURN
END