LAW OF THE ATTRACTIVE FORCE BETWEEN TWO EQUAL SPHERES. 239 



when the opposed surfaces are parallel planes or rings ; but in the case of spheres or 

 bodies of other forms, the experiment assumes a somewhat complicated character. I 

 have succeeded, however, in reducing it to extremely simple conditions, by the aid of 

 some further inquiries into the peculiar mode of action of the attractive force, the re- 

 sults of which merit an attentive examination. 



1°. The attractive force exerted between an electrified and a neutral uninsulated 

 conductor, is not at all influenced by the form or disposition of the unopposed por- 

 tions. The force is precisely the same, whether the opposed bodies are merely circular 

 planes, as represented in fig. 23, or are otherwise backed by hemispheres or cones, &c., 

 as in figs. 24, 25 ; hence two hemispheres were found to attract each other with pre- 

 cisely the same force as the spheres. 



2°. The force is as the number of attracting points in operation directly, and as the 

 squares of the respective distances inversely (67.) ; hence the attractive force between 

 two parallel plane circles being found, the force between any other two similar planes 

 will be given. 



3°. The attractive force between two unequal circular areas, is no greater than that 

 between two similar areas, each equal to the lesser. 



4°. The attractive force also of a mere ring and a circular area on each other, is 

 no greater, than that between two similar rings. 



5°. The force between a sphere and an opposed spherical segment of the same cur- 

 vature, is no greater than that of two similar segments, each equal to the given seg- 

 ment : thus, the attraction between the sphere m and the uninsulated segment w, 

 fig. 26, is the same as that of the similar and equal segments n n\ 



These results have been arrived at by the same methods of research as those above 

 given (19.), figs. 9, 2. The intensity in the diflferent experiments is supposed to be the 

 same, the electrified body being connected with a charged jar of such capacity that 

 trifling differences in the dimensions of the conductors connected with it may be con- 

 sidered as indefinitely small. 



70. A careful induction from the above facts, led me to consider the attractive 

 force exerted between a charged and neutral sphere of equal diameters, as being made 

 up of a system of parallel forces, operating in right lines between the homologous 

 points of the opposed hemispheres, a conclusion quite in accordance with what has 

 been already shown (21.) ; for these being in exactly equal and opposite electrical 

 states, and similarly placed, each two corresponding points should exactly neutralize 

 each other's action in respect of points more distant. The whole force also may be 

 further considered to be as the number of attracting points directly (69.), and as the 

 squares of the distances inversely {^7-), and to be no greater than that arising from 

 the opposed hemispheres (69.). 



71. These simple conditions, enable us to determine a point q q within each hemi- 

 sphere, in which the whole attractive power may be supposed to be condensed, and to 

 exert the same force as if emanating from every point of the hemisphere. The exact 



2 I 2 



