Mr green, on THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 61 



(n-1 



sin I -— — TT 



(28). 



.p = {]r-r')' .|const. Jp.dcr,- — ^^] 



By supposing w = 2, the preceding investigation will be applicable 

 to the electric fluid, and the value of the density induced upon an 

 infinitely thin conducting plate by the action of a quantity 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 



1 7 , y/a'-b'] 



^ = 7ltptHst--^/^'^<^' 



B' 



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

 simply have to make pi = in the preceding formula; and thus 



,„^, const. 



(29) p = 



Vb'-r"' 



Biot (Traite cle Physique, Tom. ii. p. 277.)> has related the results of 

 some experiments made by Coulomb on the distribution 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 compared with the diameter of the plate, which was 

 imdoubtedly 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 observer as Coulomb 

 must always be interesting, we will here give a table of the values of 

 the density at different points on the surface of the plate, calculated 

 by means of the formula (29), together with the corresponding values 

 found from experiment. 



