402 Prof. A. P. Chattock on the Velocity and 



infinite earth-connected flat metal plate A ; and x and y two 

 infinite planes parallel to A and distant apart dz. 



da is a small area on x, and the arrow F represents tbe field 

 at da, being the angle between F and the normal to m. 



Fk;. 1. 



B 



dz 



y 



A 



p is the volume -density of the + ions in the element da.dz. 



is the whole current passing from B to A; dC the current 

 through da ; both in electrostatic units. 



V is the velocity of the ions in unit electrostatic field rela- 

 tively to A. 



If it be assumed that the motion of the ions is viscous, and 

 that their velocities are very great compared with any motion 

 of the gas as a whole, 



dC = P YF cos Oda (i.) 



The passage of the ions through the gas is accompanied by 

 a drag on the latter which, if the ions move with uniform 

 velocity, is equal to the product of their charges and the 

 strength of the field : hence if d^p be the component of the 

 drag in element of volume da . dz resolved normal to A, 



d 2 p=pF cos 6 da dz (ii.) 



Combining (i.) with (ii.) 



Y = dCdz/d 2 p (iii.) 



Since V and dz are constant for the planes x and y it follows 

 that dG/d?p is constant, and that we may therefore replace this 

 ratio by G/dp, where dp is the total drag on the gas between 

 x and y normal to A. Then, since is constant for all planes 

 between A and B, dz/dp is constant, and may be replaced by 

 z/p, where p is the total normal drag on the gas between A 

 and B due to electrical forces only. Equation (iii.) thus 

 oe comes 



Y = Gz/p (iv.) 



