110 Mr. G. H. Livens on the JS umber of 



each integral in powers of - and retain the first few terms 



only. We have, for instance, 



f£!^ = if,,( 1 _i + f!_...W 



J S + * aj \ a ^ a 2 J 



whilst 



f^ = . i r4_f + ...) r ., 



J s + * aJ Q \ a / 



Vtt/3 15 105 \ 



~ a U"8a + 16a 2 *••/' 



so'that we have with sufficient approximation 



2tt/jucc <r 1A 3 12\ 



A, 1 — aA 



and 



2_ 2 97rmq- 2 1/ J> 35^ \ 



For metals of good conductivity, for which, therefore, 



- is very small, we should have 

 a. 



2-7rfiKC an 1 



\ ~ 1 — ttA'a' 



whence inserting the value of a 

 27rfifcc 16NV 



so that 



or since 



X ~9p 2 m 2 a (l-aA)' 



2ttc 

 2 _ 97r¥WV<ro n . 



This result differs from Nicholson's formula by the factor 



|(1-«A). 



