﻿the Electrification of Air. 233 



in the drawing was made for the purpose of acting as a trap 

 to prevent the natural dusty air of the locality from entering 

 the vat when the water-dropper ran empty. 



§ 11. The equilibrium of electrified air within a space 

 enclosed by a fixed bounding surface of conducting material 

 presents an interesting illustration of elementary hydrostatic 

 principles. The condition to be fulfilled is simply that the 

 surfaces of equal electric " volume-density " are surfaces of 

 equal potential, if we assume that the material density of the 

 air at given temperature and pressure is not altered by elec- 

 trification. This assumption we temporarily make from want 

 of knowledge; but it is quite possible that experiment may 

 prove that it is not accurately true ; and it is to be hoped that 

 experimental investigation will be made for answering this 

 very interesting question. 



§ J 2. For stable equilibrium it is further necessary that the 

 electric density, if not uniform throughout, diminishes from 

 the bounding surface inwards. Hence if there is a portion of 

 non-electrified air in the enclosure, it must be wholly sur- 

 rounded by electrified air. 



§ 13. We may form some idea of the absolute value of the 

 electric density, and of the electrostatic force in different parts 

 of the enclosure, in the electrifications found in our experi- 

 ments, by considering instead of our vat a spherical enclosure 

 of diameter intermediate between the diameter and depth of 

 the vat which we used. Consider, for example, a spherical 

 space enclosed in metal of 100 centim. diameter, and let the 

 nozzle of the water-dropper be so placed that the stream 

 breaks into drops at the centre of the space. The potential 

 shown by the electrometer connected with it, being the differ- 

 ence between the potentials of the air at the boundary and 

 at the centre, will be the difference of the potentials at the 

 centre due respectively to the total quantity of electricity dis- 

 tributed through the air and the equal and opposite quantity 

 on the inner boundary of the enclosing metal ; and we there- 

 fore have the formula : — 



= H/ (£-?)* 



where Y denotes the potential indicated by the water-dropper, 

 a the radius of the spherical hollow, and p the electric density 

 of the air at distance r from the centre. Supposing now, for 

 example, p to be constant from the surface to the centre 

 (which may be nearly the case after long electrification as 

 performed in our experiments), we find V = #7rpa 2 : whence 

 p = 3V/27ra 2 . 



