62 ELECTRICAL EQUILIBRIUM. 



This ratio shows already that the total charge of electricity is the 

 same on all zones of equal height. On a very elongated ellipsoid, in 

 the form of a double point, we may say that the linear density is 

 constant* 



From this we get for the capacity of the ellipsoid 



i = i ws i r dx 



C qpabcj r 2 a J Jx*+y*' 



If it is an ellipsoid of revolution about the major axis, e being 

 the eccentricity, and Cj the capacity, we have 



i +a dx i _ + a i i+e 



- [ ex+ 



If the ellipsoid is one of revolution about the minor axis, the 

 capacity C 2 is then 



dy i I , ey~\ + & arc sin e 



arc sin 



i i 



_L / 02,2 



2b\ a *- 



J , V ^ 2 



~~D . 



' -- 2ae\ D I . 0* 



Each of these formulae gives 



/- x- 



when the eccentricity is null; that is, when the ellipsoid becomes 

 a sphere. 



* This remark enables us to explain the power oj points. On a very 

 elongated ellipsoid in the form of a double point, it will be seen that the surface 

 density is inversely as the diameter and constantly increases towards the extremity. 

 If the insulating power of the air were itself without limit, the density and the 

 tension, which is proportional to the square of the density, might increase without 

 limit. But, as a matter of fact, when the tension has attained a certain value for a 

 given pressure of air, the electricity passes from the conductor into the masses of 

 air surrounding it, aud these being charged with electricity escape along the lines 

 of force, producing the phenomena known as the electrical aura and of the brush 

 discharge. 



