Dielectric Strength in High Frequency Fields. 247 



Writing 



■Vq-W_ 



m, and -g-y = n, and substituting 



for m in equation (13) the series A(l + k x z + k 2 z 2 + . . .)j w0 

 obtain 



2 + ™ + * { ^ *i + (wi - l)*x-n | 



+ ^{^^ + (m-I+3 + 5)* I »n* 1 } 



+ ...= (18) 



Each term vanishes identically and the first series becomes 



T, = 1- 2mz + || (m - 1) m -V n \ z 2 



- ^- [(m-4) .| j(m-l)m + /i i +2mn~j * 3 + . . . (19) 



In the same manner the second series gives 



^{^•Z 2 + (m-^)+0} 



+ «*»{^. «.+(»- ^)?.-ni,} 



+ . . . = (20) 



In this Z 3 = — 5( ,n — -12) aQ d 



• • • (21) 

 Making the necessary substitutions and finally obtaining 



a series lor -7- , the conditions for breakdown are given by 



equating to zero the denominators of successive terms, each 



of these then making -7- infinite. 



