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



approximation used is 



a 9 -l±0\oga{l + ±J\oga + \(9\oga)X\ + \%\oga)}. (7') 



Introducing this into [12], after writing y for the small cor- 

 rection factor £®logtf, and a for the perpetually occurring 



constant loga= log e 1*0077= j-kk, it becomes 



2Ra 



{<-<}'- 



=icc0XA + B6 + C6 2 ), [13] 



where 



A= - ( ounn + m + n — - 1, 



B-^(«+») + i+2(«wi+?), (35) 



1 @ 



(Remember that - = 1 30, and that y = -J a® = =-^ practically.) 



The coefficient C, therefore, is not quite constant, but depends 

 upon 6. The dependence, however, is very slight, since m + n 

 is usually a large number, and a a small fraction; and it will be 

 quite sufficient to write the average value ^® instead of in 

 the brackets of C, and thus to make it a constant. The usual 

 relative sizes of the three constants are, A numerically much 

 larger than B, and B numerically much larger than C. 



For metals whose conductivity increases with temperature 

 all three constants are positive ; but for metals like iron, whose 

 conductivity decreases with temperature and for which there- 

 fore m is negative, A and B are certain to be negative, while 

 C is very likely to be positive but small. We can avoid this 

 change of sign by noticing that when m is negative k is also 

 negative ; hence, if we bring k over to the right-hand side of 



A B 



[13], we shall get new constants, — and -, which will be 



always positive, and — , which is positive for all metals which 



K 



have k positive, but which is generally negative for those 

 which, like iron, have k negative. In all the following equa- 

 tions, where A and B appear alone, they may be always reck- 

 oned positive, because the k has merely been cancelled out. In 



