containing 4, 5, 6, 7, and 8 corpuscles, etc. 45 



and & = -=— , where b is the radius of the sphere of positive elec- 

 tricity. Thus p, q, r, which are proportional to the coordinates of 

 the centre of gravity of the six corpuscles, are principal coordinates ; 

 the time of vibration of each of these coordinates is 



2tt 



/m 



\/k' 



if pi = 2(& + &)-(& + & + £. + fc), 



ft = (£. + &) -(£. + &), 



?i = 2(t? 2 + 17b) - (Vi + Vs + Vs + Vt)> 



q2 = vi + Ve- (v* + Vi), 



then we can show that 



d 2 p, 7 d 2 p 2 , 



with similar equations for q 1} q 2 , r^, r z . Hence p x ,p 2 , qi,q 2 > r i> r 2 a,re 

 principal coordinates, the time of vibration corresponding to the 



coordinates with the suffix one is 2tt a/ 77, that corresponding to 



/ 7Yb 



,t.*ose with the suffix two is 2tt a /t-> 



. VV2+1, |V2+1 



tC-i — := rC , K 2 — 7= K. 



4V2 + 1 4V2+1 



I f £l-& = ft, Vl-V6 = <l>i, ?1-?6 = '^ , 1, 



&--|?5=0«, ^2-%=</>2. ^2-^5=^2, 



^3-^4 = ^3, V3~V4=<f>3, £ 3 ~ £4 = ^3, 



then 



^2 ^2 ^2 



wi^(^ 8 -^ a ) = 0, m^ 2 (cf> 1 -e 2 ) = ) m ^(9,-^ = 0, 



d 2 d 2 



m -i- (<f> s +y}r 2 ) = - k 3 (<f) s + yfr 2 ), m -^ (fo + 2 ) = - & 3 (^ + ft), 



W ^2 (^ + ^l) = fc 3 (ft + f l), 



ft— ^— A 



where . 1 



4 H 



