TO THE THEORY OF ELECTRICITY. 47 



the densities, at any point on either of the surfaces A and B, 

 next the glass, when that on the spherical conductor is known. 



The theory of the condenser, electrophorous, &c. depends 

 upon what has been proved in this article ; but these are details 

 into which the limits of this Essay will not permit me to enter ; 

 there is, however, one result, relative to charging a number of 

 jars ~by cascade, that appears worthy of notice, and which flows 

 so readily from the equations (8), that I cannot refrain from in- 

 troducing it here. 



Conceive any number of equal and similar insulated Leyden 

 phials, of uniform thickness, so disposed, that the exterior coat- 

 ing of the first may communicate with the interior one of the 

 second ; the exterior one of the second, with the interior one of 

 the third; and so on throughout the whole series, to the ex- 

 terior surface of the last, which we will suppose in communica- 

 tion with the earth. Then, if the interior of the first phial be 

 made to communicate with the prime conductor of an electrical 

 machine, in a state of action, all the phials will receive a certain 

 charge, and this mode of operating is called charging by cascade. 

 Permitting ourselves to neglect the small quantities of free fluid 

 on the exterior surfaces of the metallic coatings, and other quan- 

 tities of the same order, we may readily determine the electrical 

 state of each phial in the series: for thus, the equations (8) 

 become 



_ 

 p= 



Designating now, by an index at the foot of any letter, the 

 number of the phial to which it belongs, so that, p^ may belong 

 to the first, p 2 to the second phial, and so on ; we shall have, by 

 supposing their whole number to be n, since 6 is the same for 

 every one, 



"-""fe" 1 

 &c. 



