1813.] 



Imperial Institute of France, 



153 



the surface of conductors; to compare his calculations with 

 accurate observations, to find, if possible, a confirmation of the 

 hypothesis which he adopts. 



' If all parts of a body contain equal quantities of both fluids, 

 no sign of electricity appears. The body is then said to be in its 

 natural state : in that case, if we introduce a given quantity of 

 either fluid, this fluid added will distribute itself on the surface 

 of the body where it will be retained by the surrounding air. 

 This is what Coulomb demonstrated. There will be formed, 

 therefore, at the surface of the body a very thin coating, the 

 thickness of which at each point will depend upon the form of 

 the body, it ought to assum^e the figure proper to produce 

 equilibrium. 



M. Poisson proves that the problem may be reduced to find 

 what ought to be the thickness of the coat of fluid in each point 

 of the surface, in order that the action may be nothing in the 

 interior of the excited body. This thickness will be greatest at 

 the summit of the longest of the three axes, and smallest at the 

 summit of the shortest of them ; and these thicknesses will be 

 to each other as the length of the axes. If we suppose the 

 thickness of this coat to become very small, we shall then have 

 the distribution of electricity on the surface of a spheroid little 

 different from a sphere. This case, and that of an elipsoid, are 

 the only ones in which it is possible, in the present state of the 

 science, to assign the various thickness of the coating of fluid. 



By making use of the formulas of the attraction of spheroids, 

 we may calculate the attraction of the coating for a point placed 

 within or without the excited body. By this means M. Poisson 

 has found that, at the surface of a spheroid, little different from 

 a sphere, the repulsive force of the fluid is proportional to its 

 thickness in each point. The same holds at the surface of an 

 elipsoid of revolution, whatever be the ratio of its axes to each 

 other. Thus in these two kinds of body, the electrical repulsion 

 is greatest in those places where the electricity is accumulated in 

 the greatest quantity. It is natural to think that this result is 

 general ; but it is very difficult to demonstrate that it is so. M. 

 le Comte Laplace has demonstrated it in a manner purely syn- 

 thetical. His demonstration will be found in the memoir. It 

 results from it, that in every case the repulsive force is propor- 

 tional to the thickness. We cannot conclude that the pressure 

 varies at the surface of excited bodies, and that it is proportional 

 to the square of the thickness. In the places where that pres- 

 sure surpasses the resistance which the air opposes, the air gives 

 way and the fluid flows as through an opening, this is what hap- 

 pens at the extremity of pointed bodies, and at the sharp edges of 

 angular ones. 



The principle which constitutes the basis of all this theory 



