40G Dr. A. D. Fokker on the Electric Current from 



quantity dt/dt, we shall for symmetry denote by w w , w (2 \ 

 w {3 \ iv {i \ respectively. In the same way we shall often for 

 convenience' sake write a ](1) , x {2 \ x^\ x^\ for a; y, z, t. The 

 components tv {a) are assumed to be continuous functions of 

 the co-ordinates and the time. 



The stream-components are seen to be Nw {l \ ~Nio {2 \ and 

 Nw (3) , to which we add a fourth Nw (4) = N. They will be 

 altered when the particles suffer displacements as defined in 

 the following. 



We take 6 as a variational parameter and suppose a 

 quaternary vector given with components r {1 \ r (2 \ r (3) , ?* (4) . 

 If the parameter increases by dO, the particles shall shift 

 from the positions (#, y, z) occupied by them at the instant 

 t to the positions 



x + iV>d0, y + r™d0, zW %) dO, 



to be occupied at the instants 



t + r^dd. 



The components r il \ r {2 \ r { ' A \ r (4) are assumed to be con- 

 tinuous functions of the co-ordinates and time. For- each 

 particle the values of r a must be taken which are actually 

 found in the place and at the instant from where the 

 infinitesimal shift begins. 



It will be seen that the total displacements and shift in 

 time of the particles from the point-instants of their un- 

 disturbed motions (0 = 0) will be 



r (1) 0, r^0, rW0, r^d, 



in a first approximation, and, taking account of terms with 

 6 2 in a second approximation : 



**"=£"( 



V/A^' 



rP.+ SCc)^— r c S 



= r-e + i X(c)^d 2 , (a=l,2,3,4) . . (1) 



where r a and ~dr a /~dx° have values corresponding to the 

 point-instants of the undisturbed motion. In this and sub- 

 sequent formulae the summations are to be extended over all 

 values from 1 to 4 of the index put in brackets. 



In consequence of these displacements the stream-com- 

 ponents will change to 



Nw a + SNio a + ±S 2 Niv a + . . . . 



