F. H. Bigelow — Further Study of the Solar Corona. 345 



N 

 cos 6, — cos 8. = 1 — cos 6 = — — ,. 



1 2 2ttM 



Now if these masses be brought infinitely near together, the 

 d l and # 2 will differ by an infinitely small amount, h ; we have, 



. +6 .6 —6. 

 cos y, — cos 0„ = 2 sin — ? sm — ■ 



= 2 sin . - ■ = sin . h. 

 2 



. _ la sin 6 2a . .. 



= sm o . = — . sm 0, 



r r 



where a is the distance apart of the particles, and r the mean 

 distance of the point P from M^M^. 



Hence, N — 2tt (2Ma) , 



which is the equation of a line of force. 



Term 2a. M is the moment of the system, and if we choose 

 to deal only with the outside of a large sphere, it is equivalent 

 to the layers of gliding on a polarized sphere, and these again 



4 

 to ua , where u is the volume of the sphere -ttR 3 , and a of 



the surface density at the poles. Therefore, 



3 x o! r 



From this equation we may draw typical lines of force by as- 

 suming 7tW<T equal to unity, and this is the best form for use 

 until we have the means of determining the value of a ; thus 

 we finally get, 



XT 8tt sin 2 



3 r 



The Equation for Fquipotential Surfaces. 



M 



The potential of a mass M x at a distance r x is, Y 2 = — l , and 



i 



M 

 of a Mass M 2 , at a distance r 2 is, Y^-A If these masses are 



equal and of opposite signs, at the point of intersection of i\ 

 and r„ 



r x r 2 \r : rj 



These surfaces are of an ovoidal form, with a single sheet, 

 tending to merge into spheres in proportion as they approach 

 the centers of action. 



