TRANSACTIONS OF THE SECTIONS. 389 



This law is immediately apparent when the opposed surfaces 

 are parallel planes or rings ; but in the case of spheres, or 

 bodies of other forms, the experiment is of a somewhat more 

 complicated character. 



With a view of reducing the experiments to a more simple 

 form, the author has been led to some further inquiries into the 

 peculiar mode of action of the force under examination, which 

 merit an attentive consideration. He finds, 



1. The force exerted between an electrified and insulated 

 neutral conductor is not at all influenced by the form and dis- 

 position of the unopposed portions. Thus the force is precisely 

 the same, whether the opposed bodies are merely circular plane 

 areas, or are otherwise backed by hemispheres or cones. 



2. The force is as the attracting surface directly, and as the 

 squares of the distances inversely. Hence the attractive force 

 between 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 exerted between two similar areas each 

 equal to the lesser. 



4. The attractive force between a mere ring on a circular 

 area is no greater than that between two similar rings. 



5. The force between a sphere and an opposed spherical seg- 

 ment of the same curvature is no greater than that of two similar 

 segments each equal to the given segment. 



These results have been arrived at by the instruments already 

 mentioned, the electrical intensity in each series of experiments 

 being supposed the same. 



A careful induction from the above facts has led the author 

 to consider the attractive force between two equal spheres as 

 made up of a system of parallel forces operating between the 

 homologous points of the opposed hemispheres, the total force 

 being as the nvmiber of attracting points directly, and as the 

 squares of the respective distances inversely. 



These simple elements enable us to determine a point q «/ 

 within each hemisphere, in which the whole force may be sup- 

 posed to be concentrated, and to be the same as if emanating 

 from every point of the hemisphere. The locus of this point 

 within the surface will depend on the distance between the near- 

 est points of the spheres, and may be readily found by the ex- 



(f^ + 2 a r*) a 



pression s. = ^ — ■ , a being the distance between the 



nearest points of attraction, and r the radius of the sphere, 

 and z the distance of the point within the hemisphere. 



The points q (/ being thus found, the whole force is observed 



