Table 5.

Fitting parameters for the thermal expansion of sample S-M (80 Wt% Pt + 20 Wt% Rh)

Equation used in least-squares fitting procedure:

$$\mathrm{\Delta }{N}_{\text{vac}}(t_i,t_{i+1})={\displaystyle \sum _{n=1}^m{A}_n({t^n}_{i+1}-{t^n}_i)}$$ (26)

Determination of number of polynomial terms for “best fit”:

p = 45 data points

m	σ a	F m b	F0.95(1, p-m)
1	2.169 2
2	0.130 7	12073.4	4
3	0.084 7	60.4	4
4	0.066 7	26.6	4
5	0.061 8	7.8	4
6	0.060 4	2.9	4

Coefficients of 4th degree polynomial:
n	An	σ of An
1	0.805 840 5	0.000 897 4
2	0.000 201 509	0.000 005 967
3	−0.000 000 095 958	0.000 000 014 034
4	0.000 000 000 053 023	0.000 000 000 010 233
N(0 °C)=92,548.2 fringes (calc)

^aσ: the estimated standard deviation of the fit.

^b

F_m: an index used to estimate the level of significance of the mth coefficient in the equation fitted to the data.

$$F_m=1+(p-m+1)[{({\sigma }_{m-1}/{\sigma }_m)}^2-1]$$

where p is the number of data points and m is the number of coefficients in the polynomial. The coefficient A_m is considered significant at the desired level of confidence F_m is greater than the corresponding value given in the fourth column. (Entries in column 4 were taken from a standard table for the F-distribution, e.g., table 3 of reference [34].)