of the Hall Eject and Allied Phenomena. 531 



where x is the only positive root of the equation 



Thus if we now write 



=V£ 



f =Ae-i»\ 



we find that the solution for the fundamental function f is 

 of the form 



where 



=/o-\ e '^~\ K dt * 



A Bf ov of *o# o# d? ot' 



and the suffix 1 denotes that the functions affected are to be 

 taken for the time t = t v To effect this interpretation it is 

 first necessary to integrate the six differential relations 



dj~ i _ dr) x _ dX\ _ dx x _ dy x _ d% { _ dt^ 



expressed generally as function of the time t u introducing 

 as the necessary constants of integration the values of the 

 variables at the time t l = t. Substituting these values in ^ 

 we obtain its explicit expression as a function of t Y . 

 On substituting the value for / we find 



x = [-2g(fX+,T+fZ) 



The formula for / is thus obtained directly under the most 

 general circumstances, and it is in a form which is directly 

 suitable for application in any special case. If we are pre- 

 pared to put a very general interpretation on r m the generality 

 of the formula will transcend that for the particular cases 

 to be investigated. 



We now proceed to the reduction of this formula in the 

 particular case when the accelerations (X, Y, Z) are produced 

 by the combined action of an electric and magnetic field ; 

 both fields will for the present purposes be assumed to be 



2M2 



