TO THE THEORY OF ELECTRICITY. 63 



B for instance, is connected with the ground, Q' will be equal 

 to zero, and consequently Q immediately given. If, on the con- 

 trary, the whole system were insulated and retained its natural 

 quantity of electricity, we should have, neglecting that on the 

 wire, 



and hence Q and Q' would be known. 



If it were required to determine the electrical state of the 

 sphere A, when in communication with a wire, of which one 

 extremity is elevated into the atmosphere, and terminates in 

 a fine point p, we should only have to make the radius of B> 

 and consequently, Q', vanish in the expression before given. 

 Hence in this case 



Q _ f pdxdydz f pdxdydz ^ 



Q _ f 



"^J 



r being the distance between p and the element dxdydz. Since 

 the object of the present article is merely to indicate the cause 

 of some phenomena of atmospherical electricity, it is useless to 

 extend it to a greater length, more particularly as the extreme 

 difficulty of determining correctly the electrical state of the 

 atmosphere at any given time, precludes the possibility of put- 

 ting this part of the theory to the test of accurate experiment. 



(12.) Supposing the form of a conducting body to be given, 

 it is in general impossible to assign, rigorously, the law of the 

 density of the electric fluid on its surface in a state of equilibrium, 

 when not acted upon by any exterior bodies, and, at present, there 

 has not even been found any convenient mode of approximation 

 applicable to this problem. It is, however, extremely easy to 

 give such forms to conducting bodies, that this law shall be 

 rigorously assignable by the most simple means. The following 

 method, depending upon art. 4 and 5, seems to give to these 

 forms the greatest degree of generality of which they are sus- 

 ceptible, as, by a tentative process, any form whatever might be 

 approximated indefinitely. 



