THE EQUILIBRIUM OF FLUIDS. 181 



pose that b is the measure of the same radius, in this case we 

 shall only have to write r > r > -TT and j- in the place of a, /, 



da^ and R respectively, recollecting that is a quantity of the 



dimension with regard to space, by so doing the resulting 

 value of p is 



n-3 ( 



= ft- - ,/ . 



Sinl --7T 



const. -- - - ..... (28). 



By supposing w = 2, the preceding investigation will be ap- 

 plicable to the electric fluid, and the value of the density induced 

 upon an infinitely thin conducting plate by the action of a quan- 

 tity of this fluid, distributed in any way at will in the plane of 

 the plate itself will be immediately given. In fact, when n = 2, 

 the foregoing value of p becomes 



p= w=7*\ 



If we suppose the plate free from all extraneous action, we 

 shall simply have to make /o t = in the preceding formula; 

 and thus 



,(29). 



Biot (Traiti de Physique, Tom. II. p. 277), has related the 

 results of some experiments made by Coulomb on the distribu- 

 tion of the electric fluid when in equilibrium upon a plate of 

 copper 10 inches in diameter, but of which the thickness is not 

 specified. If we conceive this thickness to be very small com- 

 pared with the diameter of the plate, which was undoubtedly 

 the case, the formula just found ought to be applicable to it, 

 provided we except those parts of the plate which are in the 

 immediate vicinity of its exterior edge. As the comparison of 

 any results mathematically deduced from the received theory of 

 electricity with those of the experiments of so accurate an ob- 

 server as Coulomb must always be interesting, we will here give 



