of Electricity through Gases. 197 



is spherical, will be 47r/3, as already given by John Hop- 

 kinson*. Combining the equations (14) and (13) we find 



B = G+(47r-n)I, 



I=-*G, (15) 



B = G(l + (47r-w)£)=\Gr, . . . (16) 



and if 



it follows that 



which gives the relation between the force G on which the 

 magnetization depends and the magnetic induction. 



Let now B stand for the electric induction, and Gr for the 

 electric force tending to separate the ions. The ions will 

 separate when G, and therefore B/A, has reached a certain 

 value, which value may, however, be different according as 

 the molecule is near the surface of the body, or within the 

 space occupied by the gas. In the case of electrolytes no 

 finite force is required to separate the ions ; and it is at any 

 rate possible to imagine that if there is a condensed layer of 

 gas on the surface of the electrode, the critical value of B/A 

 may not be as great as if the particles were altogether inde- 

 pendent of each other. 



The most remarkable fact connected with the disruptive 

 discharge seems to me to be the apparent diminution of 

 dielectric strength with a diminution of pressure. Imagine 

 the state of a molecule in the gas just before the spark passes 

 at atmospheric pressure ; next imagine half the number of 

 molecules to be suddenly removed. Why should the discharge 

 now pass ? What difference can the removal of some mole- 

 cules make in the state of those which are still left ? None, 

 as far as I can see, unless a great change in the inductive 

 capacity has taken place. But no sufficient diminution of 

 inductive capacity is observed within the bulk of the gas ) and 

 unless our present ideas are altogether wrong, I can see no 

 way out of the difficulty except by assuming a surface-layer 

 of gas in contact with the solid having a large inductive 

 capacity. If the layer is thin the electric displacements will 

 not be materially changed by its presence; and if the discharge 

 begins within the layer we have to substitute in B/A, for X the 

 inductive capacity not of the gas itself, but that of the con- 

 densed layer. If k is large in equation (16) above, A will be 

 nearly proportional to the density of the layer, and will there- 

 fore diminish with the pressure. There seems to me to be no 

 difficulty in imagining the value of k in a gas to be large 



* Phil. Trans, clxxvi. p. 4G8 (18S6). 



