of Electrical Conductivities. 87 



a (iirt\ 2a 1 a /4:a 2 i\ 



(iirt\_ % i . /m\ 



we can put 



+ abk^rr} K V~t ^) *W) °\rt)' 



where X, is a positive quantity which can be disposed of at 

 pleasure. The first of these two parts of p can be written 



_8 



JC7T 



,j>(^)<«?)<0 



or, since 



3 (t) = 2^ 2 ™ 

 2 (t)=2^> 2 ™ 

 o (t) = 2(--1)^ 



^ J 1 





where the sum is to be taken thus : for each of the symbols 

 I, m, n all the whole numbers from — oo to + oc are to be put, 

 Now let us suppose 



I 



dte-#=TJ(x); 



and consequently, if a denotes a positive quantity, 



j: 



'<&«-«*« -TT(««)j 



for these functions U(#), and for the interval from #=0 to 

 ^'=3, Kramp, as is known, has calculated a table ; for higher 

 values of the argument their values are found with the aid of 

 the semiconvergent series 



UW ~ 2 \x 2x 3 + 2 2 x s •) 



