198 Mr. J.J. Waterston on some Electrical 



the lateral force at each root respectively in the circles a and b. 

 Multiplying these by the number of roots m and n } we have 



7/1 7t 7YI Cl 7YI 



~Y = p. Hence -3- = p ; and the density at a being -^, and 



n 9 - 

 at b r—> we have the ratio of the density at b to that at a as 1 to 



-2 -«p which by substitution is equal to ( -g ) 3 . 



b. Suppose a continuous metallic envelope to intersect all the 

 lines that radiate from the surface of SB beginning at a certain 

 point P. If P were at an infinite distance from S B, it is evident 

 that the envelope would be spherical : so at intermediate distances 

 such envelopes would graduate between the extremes of such a 

 surface as S B and a perfect sphere, while those close to the pri- 

 mary SB would be less contrasted than it in the curvature of its 

 extremities. The surface would be similar to S B, but less and 

 less pointed as the distance is greater. 



c. The mechanical action of the electric roots on S B being at 

 each perpendicular to the surface, the integral of all these forces, 

 resolved in one direction, ought to be zero, because all the lines 

 being supposed free, and no discharge taking place at the sharper 

 end, the body is at rest ; the static pull at the surface is equal in 

 all directions. 



59. Free electricity of the same kind on two adjacent insu- 

 lated conductors. 



a. While the excited bodies are forced together, the lines are 

 closer packed and have their integral power augmented, me- 

 chanical power being converted into electric tension, and vice 

 versa. When they fly from each other, electric tension is con- 

 verted into mechanical force or work, e. g. the two hemispheres 

 Hj K (fig. 32) ; when separate and equally electrified, their collec- 

 tive surface measures six great circles, when in close contact it 

 measures only four. 



b. The repulsion between H and K is immediately caused by 

 the increased quantity of electricity accumulated on the off sides 

 of the hemispheres (leading to a preponderance of root puttings 

 on these sides), which is effected by the lateral repulsion of the 

 lines that issue from H on those that issue from K bending them 

 round. 



c. The disposition of the electricity on the adjacent sides of the 

 hemispheres as they approximate must be peculiar. The lines 

 belonging to one that lie next to the lines belonging to the 

 other, as ab, cd (fig. 32), while approximating at a and c and ex- 

 ternal to these points lying adjacent, and forming part as it were 

 of one system, must at the lower part b and d diverge to these 



