Purser — Applications of Bessei^s FiDidions to FJiyfiic^. 4'i 

 Now, TT^ 1 (\ 2\ 4 ah 



'^^"32 "8' ^^2 TT^ 

 8ah 



Or, 



Now, total charge on plate 



the term in e indicating the correction to be made for not indefinitely 



small. A further approximation will be found by taking note of the 

 terms cjs, €15, . . . hitherto omitted. Their values will be found to be 



1 7 

 ei3 - - j^, - - • • • 



This problem is discussed by Maxwell Electricity and Magnetism," 

 vol. i.). I have given the investigation above as proceeding on definite 

 lines of approximation, the degree of accuracy of which can be readily 

 estimated, which can hardlv be said to be the case in his method. 



G. — Theory of Guard-ring. 



Two large circular plates front one another at a distance h ; the 

 upper has the ring between two circles jR, R' (where R' - R = B is 

 small compared with R) cut out. The upper plate is at potential zero, 

 the lower at potential F, to find the effect of the cutting out of the 

 groove on the charge on the upper circular disk. Taking z from the 

 upper plate, we have now three forms of potential : — 



I. For cylinder on circular base, radius R, extcudiug from upper 

 to lower cylinder, 



2 



V = V ^ + ^/i',,/!"^ sin nz. 



J) 2 



