23 201 



potential difFerence between the inner systems and either of the outer conductors 

 is constant. 



This can be demonstrated in the following manner. 



In a closed condenser, the charge that the inner system of conductors carries 

 is expressed by 



E = c{v,-~u,), 



where c, the capacity of the condenser, and «, and i'.^ are respectively the potentials 

 of the inner and the outer system of conductors. In the above mentioned apparatus 

 the charge e, held by the inner cylinder (/c), the rod (;/) and the aluminium leaf, 

 can be analogically expressed by the formula: — 



e = Ce{Vi—Ve) + Cb(Vi~Vb), (1) 



Cc and c/, are the respective capacities of the electroscope and the ionisation 

 chamber, and y,, n^ and vt are the potentials of the inner cylinder, the electro- 

 scope vessel and the ionisation chamber respectively. Leakage from the inner 

 cylinder will cause a change in e, i>i, v,. and Vh and we get in the same way as before 



e = Ce{v'. — v'^) + Cbiul — v'^) , (2) 



when the new values of the variable quantities are marked. Subtracting (2) from 

 (1) we have 



e-e' = c^ {(v. - v^) - (v. — «;))+ c^ {iv^ - «,,) - {v'. ~ v'^)). 



Assuming that the potential ditTerence between the electroscope vessel and the rod 

 {g) remains constant, we have 



Hence we get 



e — e 



"h 



{iu^-u,)-{u'-ol)) 



e - e' = c^ {(v-v^)- (v[~ v^ )) , (4) 



which affords the required proof 



Equation (4) shows that the leakage is equal to the product of the capacity 

 of the ionisation chamber and the change in the potential difference between the 

 electroscope vessel and the ionisation chamber. The leakage is, on the other hand, 

 independent of the electroscope capacity and of the absolute potential of the inner 

 cylinder. 



A possible objection to the above demonstration is that the formula (1) is not 

 applicable because the two condensers regarded separately are not entirely closed, 

 but as I have shown in Phys. Zeitschr. ' the formula holds good, provided that 

 the electroscope and the ionisation chamber form a single closed condenser when 

 a conductive connection is established between them. 



' Pliys. Zeitschr. 7, 834, 1906. 



