Purser — Applications of Bessei^s Fniictiona to P/i>/.sic-s. 39 

 The former term vanishes for I - qp \ the hitter 



a charge negati\'e and small of order — • 



We can now solve the problem where two equal circular disks at 

 potentials V, V stand opposite one another at a distance small com- 

 pared with their common radius. For, consider two cases : (1) The 



disks have equal potential ^ ( F' + V). Here it is manifest that we 



have a solution by supposing each disk equally charged, the 

 charge at front and back being the same for each plate, the 

 medial plane being one of zero normal attraction. The law of 

 distribution of charge will be that of an isolated circular plate at 



constant potential. (2) One plate is at potential ^^^{V -V)\ the 



other at potential - \{V - V). This is the case just investigated, 



the medial plane being now of potential zero. 



Combining these, we obtain the solution required. 



F. — Condenser formed of Circular Disk at Potential midway between 

 Infinite Plates at Potential Zero. 



Let h be the semi-interval between planes mR = a„„ where 



Ji{(^,u) = 0, n = s s having all positive odd values. 



Then the potential being evidently symmetrical on either side of 

 the disk, we may assume for it the expression 



a{h - z) + ^„B„Ko{nr) cos7iz + l,,„A„JJ^mr) i a-^mz) y 



for interior of cylinder standing on circular base ; while for exterior 

 space to 00 we have as usual cos 



On evaluation the Fourier term corresponding to A,„ becomes 

 2 m c-mh , 



