496 Proceedings of the Royal Society 
which is general enough to represent the experimental results for 
small distances. 
Next let s he greater than a, where a is the distance from a 
conductor at which K ceases sensibly to vary, then, 
Here the first and last integrals are equal and constant, say each = 
— l9 where K' is intermediate between K 0 and K r In the second 
integral K is constant throughout, and equal to K p we thus get 
' s dx 2a s— 2a 
Whence 
r*ax _ za 
Jo K“K' 
K: 
This gives a straight line for distances greater than a, and accords 
with the interpretation which I am inclined to put upon the results 
of experiment. 
This theory then would allow us to retain the notion of a definite 
dielectric strength for air, and at the same time to reproduce the 
results of experiment. The only question to he settled is whether 
the assumed variation of the specific inductive capacity actually 
exists. Equation (5) would of course allow us to find the nature of 
the variation, if any such existed. Since, in the case of air, by the 
unanimous testimony of experimenters, the intercept on the axis of V 
is positive, we must have > K' , and hence, since K' is inter- 
mediate to and K 0 , K x > K 0 , i.e., the specific inductive capacity 
of air in the neighbourhood of a conductor is less than in free air. 
This seems at first sight a somewhat startling conclusion ; but on 
reflection I see nothing against it except perhaps prejudice. At all 
events it will scarcely be said that the kinetic theory of gases settles 
it immediately either way. 
The above theory may at once be subjected to a very interesting 
