400 Note 1 8 : Cavendish's early views on electricity 



be pressed close together, and in all the space within that, the density would 

 be the same as on the outside of the sphere. 



The pressure of a particle adjacent to the inside surface against it is equal 

 to the repulsion of all the redundant matter in the sphere collected in the center, 

 and the force with which a particle is pressed towards the surface of the sphere 

 diminishes in arithmetical progression in going from the inside surface to that 

 point at which its density begins to be the same as without, therefore the whole 

 pressure against the inside of the sphere is equal to that of half the redundant 

 matter in the sphere pressed by the repulsion of all the redundant matter 

 collected in the center of the sphere. 



Therefore, if the quantity of fluid in the sphere is such that its density, if 

 uniform, would be i + A, and the radius of the sphere be called r, the whole 



dr 3 dr 3 

 pressure against the inside surface will be as x ^ , and the pressure against 



a given space of the inside surface will be as d 2 r 2 . 



If this pressure be called P, d is as , and dr 3 is as r-\/P. Consequently, 



supposing the fluid to be pumped into different sized globes, the quantity of 

 fluid pumped in will be as the square root [of the force] with which it is pumped, 

 multiplied by the square of the diameter of the globe. 



If the density within the sphere is less than without, then the density 

 within the sphere will not be uniform, but will be greater towards the middle 

 and less towards the outside, and if the repulsion of the particles is inversely 

 as the square of the distance, there would be a sphere concentric to the hollow 

 globe in which the density would be the same as on the outside of the globe, 

 and all between that and the inside surface of the globe would be a vacuum. 



From these corollaries it follows that if the electric fluid is of the nature 

 here described, and is spread uniformly through bodies, except when they give 

 signs of electricity, that then if two similar bodies of different sizes be equally 

 electrified, the larger body will receive much less additional electricity in pro- 

 portion to its bulk than the smaller one, and moreover when a body is electrified, 

 the additional electricity will be lodged in greater quantity near the surface of 

 the body than near the middle. 



Let us now suppose the fluid within the globe BDE to be denser than without, 

 and let us consider [in what manner] the fluid without will be affected thereby. 



ist. There will be a certain space surrounding the globe, as ftSe, which will 

 be a perfect vacuum, for first let us suppose that the density without the globe 

 is uniform, then any particle would be repelled with more force from the globe 

 than in the contrary direction. 



2ndly. Let us suppose that the space jSSe, BDE is not a vacuum, but rarer 

 than the rest of the fluid ; still a particle placed close to the surface of the globe 

 would be repelled from it with more force than in the contrary direction. 



3rdly. Let us [suppose that] the density in the space between BDE and 

 /38e is greater than without, then according to some hypothesis of the law of 



