366 Note 3: canals of incompressible jtuid 



But we have seen that p l = p 2 = o. Hence dividing by p we find for the 

 condition of equilibrium v v 



or the electric potential of the two bodies must be equal. 



We arrive at precisely the same condition if we suppose the bodies con- 

 nected by a fine wire which is made of a conducting substance. 



Let V as before be the potential at any given point due to the electrified 

 bodies, and let V 1 be its value in A lt and F 2 its value in A 2 , and let V be the 

 potential due to the electrification of the wire at the given point, then the 

 condition of equilibrium of the electricity in the wire is that V + V must be 

 constant for all points within the substance of the wire. Hence at the two ends 

 of the wire F, + F.'-^* F.'. 



Hence the actual potential due to the bodies and the wire together is the same 

 in A 1 and A 2 . 



The only difference, then, between the actual case of the wire and the 

 hypothetical case of the canal is that the surface of the wire is charged with 

 electricity in such a way as to make its potential everywhere constant, whereas 

 the canal is exactly saturated, and the effect of variation of potential is counter- 

 acted by variation of pressure. 



Hence the canal produces no effect in altering the electrical state of the other 

 bodies, whereas the wire acts like any other body charged with electricity. 



The charge of the wire, however, may be diminished without limit by 

 diminishing its diameter. It is approximately inversely proportional to the 

 logarithm of the ratio of a certain length to the diameter of the wire. Hence 

 by making the wire fine enough, the disturbance of the distribution of electricity 

 on the bodies may be made as small as we please. 



[GREEN ON CAVENDISH'S THEORY.] 



From the [beginning of the"] Preface [1828] to Green's "Essay on the Application 

 of Mathematical Analysis to the Theories of Electricity and Magnetism." 



"After I had composed the following Essay, I naturally felt anxious to 

 become acquainted with what had been effected by former writers on the same 

 subject, and, had it been practicable, I should have been glad to have given, in 

 this place, an historical sketch of its progress ; my limited sources of informa- 

 tion, however, will by no means permit me to do so; but probably I may here 

 be allowed to make one or two observations on the few works which have fallen 

 in my way, more particularly as an opportunity will thus offer itself, of noticing 

 an excellent paper, presented to the Royal Society by one of the most illus- 

 trious members of that learned body, which appears to have attracted little 

 attention, but which, on examination, will be found not unworthy the man who 

 was able to lay the foundations of pneumatic chymistry, and to discover that 

 water, far from being according to the opinions then received, an elementary 

 substance, was a compound of two of the most important gases in nature. 



