520 Dr. 0. J. Lodge on the Variation of 



where the coefficients a, b, c, d are all known. This gives us 



a^o— OqCi +r(l> l c —b c i y 



40. Now looking at equation (41), we see that the value of 



r is - , multiplied by a fraction which contains m indeed, but 



does not depend very much upon it ; for, neglecting the small 

 quantity y, the fraction is 



2 

 amn + m + n 



2 



umn -\-2(m + ii)-\ — 

 a 



and since ra and n are both pretty large, the first term, which 

 is the same in both numerator and denominator, is much the 

 biggest, and accordingly the fraction is not very different from 

 unity. It is likely to be greater than 1 when to is negative, 

 and less than 1 when m is positive. Hence a first approxima- 



tion to r is -, or 780. The fact that r does not depend much 



upon to is apparent in the Table, § 34. 



Making, then, a guess at r as 800 or so, we obtain from (43) 

 a first approximation to to ; and we can afterwards improve it 



by trial and error, so that the quantity 6 „ in equation (40) 



really does go in geometrical progression down the whole 

 length of the rod — for instance, so that 



And then, having obtained the mean value of this constant //,, 

 it is easy to calculate the absolute conductivity of the rod from 

 [21] if one has determined R by experiments on cooling (see 

 § 27). The relative thermometric conductivities of different 

 metals at the temperature of the enclosure are simply inversely 

 as fi 2 (see [21]). 



41. The only experimental results already published which 

 are even apparently at all suitable for applying the method to 

 are those of Wiedemann and Franz ; but it is impossible to 

 get any results from these for reasons stated in § 28. It may, 

 however, be interesting to see how far their numbers for an 

 iron rod in a vacuum will lend themselves to the equations 

 now obtained, if m is assumed to be —700 and r to be 850, as 

 in § 34. 



