1897.] Newly Prepared Gases. 353 



with small electromotive forces it is evident that we may disregard 

 the effect of mutual repulsion of the carriers when the gas is 

 carrying a cloud. When the gas is bubbled through sulphuric 

 acid the radius of the carrier is so much reduced, that the effect 

 of the mutual repulsion of the particles carrying the charge is 

 easily detected. 



(9) The following is a general method of investigating the 



motion of a gas in a vessel of any shape, the initial distribution 



being uniform. Let p be the density of electrification in any part 



of the gas, u, v and w the velocities of the carriers along the axes 



of x, y and z. 



m, ,• r. ,- ■, • 1 bp du dv dw _ . 



I he equation of continuity is --£ + — + — + 7 =0 the 



p bt dx dy dz 



notation being the same as that used in Lamb, Motion of Fluids. 



Let <f> be the electric potential ; — =? — / and J- , are the 



T dx dy dz 



forces which act on the charged carriers, and their velocities u, v, 

 and w, are given by the equations : — 



,,. dd> d<b dd> 



(1) ku = — e-r-\ KV = — e-^-\ KW = -e-r-, 

 dx dy dz 



where e is the charge on the carrier and k is a constant to be 

 determined experimentally. 



Substituting these values for u, v, and w, in the equation of 

 continuity and we obtain : — 



- £- eV°~c}> = 0, but V 2 </> = - 4vrp, 



therefore — ■ ~ = - \ire. 



p l bt 



Integrating and we obtain : — 

 . (2) 9 — 



1 + j^Po t 



where p is the initial density, which is uniform throughout the 

 space considered. 



Equation (2) shows that the motion takes place in such a way 

 that the density p is a function of the time only and does not vary 

 from point to point in the gas, on this account no variation in 



the pressure of the charged gas takes place and the terms -£■,-£-. 



dx dy 



