<o6& Mr. A. A. Robb on the Conduction of Electricity 



This pressure is roughly 1| atmospheres. It will be well to 

 give a short account o£ the method of calculating these 

 tables. 



The first function to be calculated is 



cosh 



_L p day 

 i-'fl) " 



J cosh 1 " 



J cosh 



This may be expressed as a series in two forms, of which 

 the one possesses the advantage that it converges more 

 rapidly, while the other is better adapted for the second 

 integration. We accordingly give both series. 



df) 



Writing cosh co = we have dco= — , 



Thus 



_L_ r* dco —e T-— r* dQ 



— 6 



— cosh 1 - 6 ^ ~i — iZ^O 



J cosh 1 " 6 g) J <9 l " 



cosh 1 - 6 © J e l -'^/e 2 -i 



• Expanding the expression under the integral sign in 

 descending powers of Q and integrating term by term, we get 



2 2 |2 (h-tey 



The expression inside the brackets { } represents the 

 integral and clearly vanishes when we put # = co . We may 

 thus write 



1 e &)4 j — ~ cosh 1 e ool 



J cosh 1-6 © J cosh r 



~~ e \ 2 (3-2e)cosh*G> _l ~ 2 2 {2 (5-46)cosh 4 w" f + )- (5) 



Tin's series converges for all real values of co including 

 (o = : , and is the one most suitable for calculating the 

 function. We shall next obtain the other series which is 

 adapted for the second integration. For this purpose we 

 make use of the formula 



P deb 1 sinhco m-f IT deo 



J cosh m a> ~ m cosh m+1 o> m J cosh w +^/ 



