368 Note 4: charges on two adjacent disks 



forming thus a closed circuit, it is evident from the principles of hydrostatics, 

 and may be proved from our author's 23rd proposition [Art. 84], that the whole 

 of the hypothetical canal will be in equilibrium, and as every particle of the 

 portion contained within the system is necessarily so, the rectilinear portion aA 

 must therefore be in equilibrium. 



"This simple consideration serves to complete Cavendish's demonstration, 

 whatever may be the form or thickness of the real canal, provided the quantity 

 of electricity in it is very small compared with that contained in the bodies. 



"An analogous application of it will render the demonstration of the 22nd 

 proposition [Art. 74] complete, when the two coatings of the glass plate com- 

 municate with their respective conducting bodies by fine metallic wires of any 

 form." 



NOTE 4, ART. 83. 



On the charges of two equal parallel disks, the distance between them being 

 small compared with the radius. 



The theory of two parallel disks, charged in any wa.y, may be deduced from 

 the consideration of two principal cases. 



The first case is when the potentials of the two disks are equal. If the 

 distance between the disks is very small compared with their diameter, we may 

 consider the whole system as a single disk, the charge of which is approximately 

 the same as if it were infinitely thin. Hence if V be the potential, and if we 

 write A for the capacity of the first disk, and B for the coefficient of induction 

 between the two disks, the charge of the first disk is 



and that of the second is 



If we make V 1 = V 2 = V, 



Q 1 + Q,= 2(A-B) V. 

 Hence, by Note 2, 



The second case is when the charges of the disks are equal and opposite. 

 The surface-density in this case is approximately uniform except near the 

 edges of the disks. I have not attempted to ascertain the amount of accumu- 

 lation near the edge except when n = 2. If we suppose the density uniform, 

 then for a charge of the first disk equal to na 2 , its potential, when b the distance 

 between the disks is small compared with a the radius, will be approximately 



27r - 



