1026 Dr. A. C. Crehore on 



effective in this latter force, and hence we possess the com- 

 plete solution. The rigid solution for the electrostatic force 

 between two oblate spheroids of charge in general positions 

 is unknown, hence an approximation has been made to it, 

 as explained in the second paper, by substituting for the 

 negative electron a ring and a point, the solutions for which 

 are known. The charge on the point situated at the centre 

 is E l5 and that on the ring E 2 , their sum being equal to the 

 electron's charge, e. The ratio of the charge E 2 to e is 

 defined as p, which evidently must be less than unity. This 

 ratio is obviously determined by the eccentricity of the 

 oblate spheroid, and it was shown to be equal to the square 

 of this eccentricity in the previous paper. Taking the 

 eccentricity e = "945 as determined in the first paper, the 

 value of \/p is, therefore, about 1*12. 



The process followed has been indicated in detail in the 

 second paper, and it is not practicable to give here more 

 than a bare statement of the results obtained. These are 

 all, however, derived in the manner described by the use 

 of the inverse square law between infinitesimal elements 

 of charge according to the principles of electrodynamics. 

 A starting point may now be said to be the electrostatic- 

 force upon one electron due to a second, and, in the nomen- 

 clature employed before, this is given below as resolved 

 into x- and ^-components. The ^/-component has the same 

 form as that of x, provided the direction cosine X outside 

 the brace is exchanged for Y. The symbol U 2 = X 2 + Y 2 has 

 been employed for brevity, and this may be converted into 

 a function of Z only, since X 2 + Y 2 = l — Z 2 . 



F, = fx{--r-<>+pa%, i (Uy- i + pa% e (lJ)r-° 



electron % 



electron. + P*%, s(U)r~" + pa%, 10 (U>- 10 + p"a% tf (U>"« 



+ /3 V/,, 14 (U)r- 8 + / >V/,, 16 (U>- 10 ...}. . (1) 



The £-force has the same form, but in place of the ^-func- 

 tions of U must be substituted ^-functions, namely, instead 

 of ,/a?,4(U) write f gt JJJ) and so on : also the direction 

 cosine Z takes the place of X outside the brace. These 

 functions have the following values : — 



/ X>4 (U) = 6- |lP, (2) 



/ M (U)=-^ + ^ 5 lP-^US (3) 



