IS Professor Leslie on 'Electrical "Theories. 
the two spheres, will be equal * ; and, therefore, since the dis- 
tance is the same, they will exert equal forces at P. But a 
force GP will, on account of its obliquity, produce only a mo- 
tion PD in the direction PC ; and an equal force FP, will pro- 
duce a motion PE, in the same direction. Whence the effect 
of the zone GOI log, is to that of the zone TOK Jc of \ as PD to 
PE, or ultimately as AD to AE. And since, AG 2 = AC x AD 
and AF 2 — AC x AE ; therefore AD is to AE as AB to AC ; 
that is, the absolute effects of the corresponding zones upon the 
particle P, are inversely proportional to the diameters of their 
spheres ; and, therefore, the total actions of the anterior surfaces 
will observe the same ratio. Again, the nearer the particle P is 
brought to the balls, the greater will be the disproportion be- 
tween the distances of the anterior and posterior surfaces, and, 
consequently, the greater will be the disparity of their separate 
effects ; and, ultimately, the forces exerted by the posterior sur- 
faces, may be totally neglected, as not sensibly affecting the ge- 
neral result. It appears, therefore, that the final attraction of 
an electrified body of any shape, or its initial repulsion, is in- 
versely as the radius of curvature. But it has been already 
shewn, that the velocity and magnitude of the aerial current is 
proportioned to this maximum force ; and hence the more acute 
the form is, the greater will be the effect produced. In the 
case of an exceedingly small metallic body, other circumstances 
conspire ; the air plays more freely around it, and as the diver- 
gency of the rays is greater, the affluent and refluent streams in- 
terfere less with each other’s motions. When a large ball is used, 
the directions of the attracted and repelled particles of air 
will be nearly parallel, and their opposite forces will occasion 
them to stagnate about the surface, and considerably to obstruct 
the farther egress and ingress -f*. 
* Hence it may be stated , as a simple and elegant proposition , That the space in- 
cluded in a circle described with the same extent of a pair of compasses on any sphere 
or a plane , is always the same. 
-j- I must confess, that I am not satisfied with these investigations ; yet I can- 
not at present discover others which I would chuse to substitute. The various 
considerations involved in the problem are so undefined and complicated, as to 
gender the solution extremely difficult. 
