Purser — Applications of BesscVs Ffoictions to P/n/sics. 38 



It is further apparent that, if we take a cylinder of height C 

 standing on the circular face, its radial attraction on any point r of 

 either terminal face will be proportional to 



D. — Circular Disk at Constant Potential Tin centre of Cylinder of 

 large dinmisions at Potential Zero. 



We now assume for the inner cylinder 



Potential = a{l - %) + ^B^KJiiir) cos nz + ^p^JJ^mr^e-"'% 

 and for the outer 



SIT 



Potential = "^A^YQiiir) coswz, 7i = 



s having all odd values. 



Expressing the terms in K^ijir) in a series of ^^{nir) terms, where 

 the m are given by Ji{mR) = ; and expressing that Potential = V 

 for 2 = 0, we find for w?-, different from 0, 



= - fT-rr. ^.B„K,{nR) ^ ; (30) 



jQ^mR) uE m- + 71- 



while, corresponding to m = 0, we have 



V=al+ 2X,B„ . ^K,{nR). (31) 



The Fourier expression for the a (/ - z) term is then, as before, 



2a 1 

 — . Z,^ — cos 71Z. 

 t 71' 



That for the is easily seen by calculation of 



J e~*"- cos 7izdz, 



= - y cos nZ^„ ./'^ ., XjB„,K,{7i'R)^ ./^ = P„ COS 7iZ. 



i 71- + in- n R m- -r n - 



