34 , On Electrostatic Theorems. 



So if one confocal is a surface of uniform pressure, so are 

 those close to it. But the confocal at infinity is of course at 

 zero pressure all over ; so all the confocals are surfaces of 

 equal pressure, and amongst them the conductor itself. The 

 surfaces of equal pressure are therefore at right angles to 

 the supposed displacement, and so the medium is in 

 equilibrium. 



I should like to point out here the curious fact that in an 

 ordinary proof of part of the above theorem, viz., that part 

 which asserts the distribution of the charge on the ellipsoid 

 to be represented by the expanding of the ellipsoid " similarly/' 

 the reasoning has to do with attractions inside the ellipsoid, 

 and takes no account of actions outside, whereas the proof just 

 given is exactly the reverse of this. 



It should be noticed that the ordinary proof is exceedingly 

 defective, for it is upset entirely by supposing the presence of 

 non-uniform dielectric in the interior of the conductor, which 

 would make calculation of the attractions impossible ; also it is 

 apparently unaffected by any want of uniformity of the 

 external dielectric. The proof given above has neither of 

 these faults. 



In connexion with the subject it is worth noticing that the 

 method of this paper leads to a most simple proof of the law 

 that a closed conductor perfectly screens its interior from the 

 action of external charges. 



For the only way in which the pressure of the aather in the 

 conducting shell could affect the dielectric (uniform or not) in 

 the interior would be by changing the shape of it, pushing it in 

 in some places, and therefore allowing it to bulge in others. 

 But since the pressure is uniform over the conductor and the 

 interior of the shell is unalterable in volume, no work is done 

 by any such deformation. Hence no energy can be imparted 

 to the interior of the conductor, and consequently no changes 

 can take place ; every forced change would of course require 

 energy to produce it. 



I hope that I have made clear the value of this method of 

 treating electrostatic theorems. It seems to me to possess 

 several advantages. In the first place the student is able to 

 form a mental picture of the physical meaning of every step 

 in the mathematical reasoning, and he therefore finds it easier 

 to understand the step, to remember it, and give it its proper 

 relative importance. Moreover, the mathematical reasoning 

 itself is much simplified in the case of some of the problems 

 dealt with above. Again, the expression for the specific 

 inductive capacity appears in every equation as it should do, 



