10 CLAUSIUS ON THE MECHANICAL EQUIVALENT 



On the surface both expressions give the same value, and 

 hence both propositions in this case hold good simultaneously. 

 In the instance before us the tinfoil coatings form two con- 

 centric spherical surfaces, whose radii may be called a and a + c, 

 c being the thickness of the glass. Let us first consider a point 

 on the interior coating ; in this case we can apply the first pro- 

 position to both the spherical surfaces ; connecting the potential 

 functions of both quantities of electricity Q and Q! together, we 

 obtain 



V=-5_-«L (5) 



a a-{-c 



For a point on the outer coating, on the contrary, the second 

 proposition is to be applied, and if in this case we call the po- 

 tential function V, we have 



(6) 



a + c a-\-c 



Through the condition that the exterior surface is in commu- 

 nication with the earth, we possess a means of estimating the 

 quantity of electricity Of. It is known that when several con- 

 ducting bodies are connected together, that the equilibrium of 

 the electricity is so established that the potential function in the 

 interior of the entire system possesses the same value. Hence, 

 as in the earth, where in general equal quantities of positive and 

 negative electricity are present, the potential function is zero; 

 this must also be the case for the exterior covering. We have 

 therefore 



V' = 0; 

 and hence, according to (6), 



and thus (5) becomes 



V=-Q_£_; (7) 



a{a-i-c) 



when the fraction is developed according to C, the superficial 

 content of the inner coating, that is 4aV, being denoted by S, 

 we have 





(i-£+l,-&c.). . . . (7«) 



We are now in a condition easily to determine the potential 



