38 



Froceedinys of the Royal Irish Academy. 



Now 



QOSX = 



Je ^ Jl 



dx 



QO^X — + 

 X 



' dx 

 cos^ — . 



6 



x 



The former part is a finite number K] the latter = JT' -logc, where 

 K' is another finite number, giving finally 



(37) 



Charge on Dish. 



The total charge on disk = fff A. rdrdO . A ^r^, being' the 



47rJJV d% ) dz 



dV 



discontinuity of — in passing from the hither side of the disk to 



the further. In considering this now, we may neglect the terms 

 in as involving no discontinuity. The p terms may also be 

 neglected as involving, when integrated, the factors J^{mR)^ which 

 vanish. There remain only the terms in a. I^ow for hither side 



this term = a, for further - - — -, giving discontinuity r — -, or 



^ — ^ ^ ~ s 



So. 



q. p. a. Hence total charge = — , S being area of disk. Now, 



retaining only principal terms in equation for V, we have F=a^; 

 SV 



.'. total charge = • 



47r4 



Charge on Bach of Dish. 

 Neglecting the P,, terms, we have 



B., = - 2a.RY,{nR) - 2a^F.(«i?) . ■ 



^ ^ nc; nl 



Now, total charge on back of disk 



= — • f (- a I a>S') + ^ ' [rdrdO nB,, . Kfnr) . cos ni 



= - aC — - - - sin 2nt, . RK,{nR) Y,{nR). 



