Table 7.

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

Equation used in least-squares fitting procedure:

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

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

p = 15 data points

m	σ a	F m b	F0.95(1, p-m)
1	2.898 0
2	0.138 9	6081.2	4.67
3	0.075 8	31.7	4.75
4	0.058 1	9.4	4.84
5	0.026 4	43.4	4.96
6	0.020 5	7.6	5.12

Coefficients of 4th degree polynomial:
n	An	σ of An
1	0.789 424 4	0.001 161 2
2	0.000 185 896	0.000 007 379
3	−0.000 000 072 335	0.000 000 016 695
4	0.000 000 000 037 180	0.000 000 000 011 889
N(0 °C)=90,427.2 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 colimin 4 were taken from a standard table for the F-distribution, e.g., table 3 of reference [34].)