THERMO-ELECTRIC DIAGRAM FROM - 200° C. TO 100° C. 787 



Some exception may be taken to the minuteness of the numerical work in the 

 calculations — that it goes far beyond what is warranted by the experiments, that four 

 places or five places of significant digits would have been enough. I will answer this 

 in two ways : First, the solving of a set of linear equations (in the present case generally), 

 three equations for the determination of three unknown quantities, see equations (9, 11), 

 depends on the differences between numbers, and, in the present case, these numbers 

 were not unfrequently very nearly equal. As example, starting from equations (11) 

 with the numerical values inserted, and using 4-place logarithms, the value obtained 

 for y is 89*72. Now the value obtained more accurately is 90-20841 ; this is the value 

 of p sec o>, where p is the parameter of the parabola and w is the angle its axis makes 

 with the axis of E.M.F. The value of p hence deduced is 90'01381, which differs 

 from y by "1946, while the inaccurate y differs from the correct value — the value really 

 contained in the data — by "4884. To attempt the work with 4-place logarithms 

 would therefore ignore the inclination of the axis some two-and-a-half times. My 

 second reply is — it may be granted that I would naturally adopt the process entailing 

 a minimum of labour. In accordance with this postulate, on at least four occasions 

 I began solutions with 5-place logarithms, only to find that (in the language applied 

 to some differences in logarithmic tables) the results became " irregular " ; for, on 

 attempting to verify by substituting these results in the original equations there was no 

 question of agreement. 



A reference to the first, second, and final attempts to determine the curve for copper 

 as shown by C, D, and the final curve on fig. 7, points to the need for great accuracy 

 in order to obtain correct results. 



Again, the working equation for nickel (p. 764) was obtained in the form 



E/200 = -32496-666 -54-4160 + 2702-1507 Jd, 

 with 



= ^ + 853-437. 



One is tempted to take the approximate form, 



E/200 = - 32500 - 54-420 + 2702^/(9. 



The approximation amounts to allowing 



in the absolute term an error of 3 - 5 on 32500 or - l per cent., 

 „ coefficient of „ 3-3 on 54420 „ -006 „ 



„ coefficient of J6 „ 14-0 on 270000 „ "005 „ 



I give these two results calculated by the correct and by the approximate formulae, 



at t = 26-77°, E/200 = -226-4,= -229- approx. difference 2-6, i.e. V2 per cent. 

 aW= -140°, E/200= 855-6,= 847 approx. difference 8-6, i.e. 1-0 „ 



These differences are 5 - 2 and 17*2 micro-volts, while the probable error (p. 765) is only 

 4*45 micro-volts. 



It is enough therefore to note, that on two widely different temperatures, errors in 



