194 
MR. H. L. CALLENDAR OR THE PRACTICAL 
If we assume as an empirical formula 
R/R 0 = 1 -}- at -{- fit'- + yf\ 
and, taking data from the curve, calculate the values of the constants a, fi, y, we shall 
obtain a more or less unsatisfactory formula of interpolation. To show how much 
the values of a, fi, y, vary for slightly different data, the following Table may be 
interesting: — 
Data. 
Formula. 
Values of constants. 
100 ° 
300 ° 
500 ° 
a 
P 
7 
1-3460 
2-024 
2-640 
(60 
•0034508 
+-00000020 
--00000000108 
1-3460 
2 020 
2-640 
(b) 
•0034675 
0 
--00000000075 
1-3460 
2-010 
2-640 
00 
•003505 
--00000045 
0 
The formula ( b') represents the observations fairly well within the experimental 
range, but is quite inadmissible for extrapolation, for it has a maximum R/R 0 = 3 '52 
at about 1090° C., whereas I have observed values of R/R 0 exceeding o'O. The 
second formula, 
Ry' Rq = 1 -)-at — fit^, .......... (6) 
has only two constants, and represents the curve nearly as well, but is subject to the 
same objection. The third formula (c) is approximately the nearest parabola, but does 
not represent the observations so satisfactorily at low temperatures.* 
Schleiermacher, t who has incidentally investigated the question, unfortunately 
gives no numbers, but represented his results graphically by drawing a series of 
straight lines for each interval of 100 °, using the curve thus obtained to give the 
temperature in terms of the resistance. ITis observations extended to 1000 °, but he 
does not publish the curve. • 
In 1871 Siemens suggested that the true law of change of resistance with tempe¬ 
rature was R= fi0 fi-y ; where a, fi. y, are constants and 0 the absolute tem¬ 
perature. 
The nearest empirical formula of the Siemens type calculated from the above 
data is 
R = •037710*+ •0025200— ’2450. (s) 
This differs radically from the other empirical formulae. It represents the observa¬ 
tions about as well as the parabola (c), but at high temperatures d R, d 0 approaches 
* For correction of this formula, see Appendix, p. 220. 
t Wiedemann, ‘ Annalen,’ vol. 26, p. 287, 1885. 
