Conductivity of Metals with Temperature. 203 



where the constants for the best of his two bars, when reduced 

 to the C.Gr.S. system, are 



A=-2331, B=--00755, C = -00000189. 

 6. Forbes's formula may therefore be written 



(-) = -2331(1 - '00324 1 + -0000081 t 2 ) ; 

 and this may be very accurately expressed by a form more 



A 



suitable for our present purpose, j-—-> For this last may be 



U "T" t 



regarded as the sum of an infinite geometrical progression with 

 ratio — yj and may be written, without approximation,- 



_A— Vi_' + £_ , g \ 



b+t~b\ b^b 2 '"^ (b+t)b n - i J J 



stopping at any term one likes, and multiplying it by -j— ■ 



instead of writing the remaining terms. 



Now if T be the highest temperature to which the formula 

 is required to apply, the average temperature -^T may be in- 

 troduced into the denominator of the last term instead of the 

 variable t, without making much difference ; and the above 

 may be written approximately, stopping at the third term, 



b + t b \ b + b(b + ±T)J ' 

 This expression agrees very well with Forbes's formula for a 

 range of 200° ; for taking 6 = 308, 1T=100, and j ='2331, 

 it becomes 



9A f , , = -2331(1 - -00325 * + -000008 1 2 ). 



Hence I shall assume that the results of Forbes may be 

 summed up in the equation 



A 308 h ,, A 



. . (40 



(-) = 



,cp/ F e 308 + £ 308 + £ c p Q * 



The numbers in the last column of the preceding Table give 

 the values of the " constant " A, for the temperatures consi- 

 dered most trustworthy by Forbes. 



7. The variations of conductivity with temperature have 

 also been investigated, by a method depending on fluctuating 



* The symbol £b is used merely to signify approximate equality. 



