of Electricity through Gases, 189 



From this series we may obtain 1/log^ and any power of 

 log q in terms of k. Retaining k as far as the fifth power, I 

 find:— 



ir lrF 17 367 75 -l 



-l/ J0g ^=_Ll + _-_^- 5 -_*J, 



-(\ogq)' = k>- 

 Therefore 



8' 



■*n/iogg=l + 4^+™ 



163 



24 



1440 



327560 



k° 



and hence 



A- 2 + 4rl . k* 



y ~ 2F |_2 + 24 + 



..]. 



3 + 45 53760 



As R = V#/a and e=k\ 



and finally, 



L 3 a 45 a 



*•+...]: 



73 g 3 

 53760 a 3 



+ . 



(12) 



This series converges rapidly as regards the first few terms 

 if e/a is small, and the results obtained from it may be com- 

 pared with the values of x given in Table I. Table II. shows 

 the comparison. 



Table II. 



c — 2 = e/a. 



x from Series (12). 



x from Table I. 



•1 



1-0335 



1-0335 



•2 



10676 



1-0684 



•5 



1-1725 



1-1990 



The equation (12) gives a result therefore which is too 

 small by 3 per cent, if the distance between the spheres is 

 equal to half their radius ; but the result is correct to less than 



Phil. Mag. S. 5. Vol. 29. No. 177. Feb. 1890. P 



