410 Dr. A. D. Fokker on the Electric Current from 



Thus we see that its position at the time # (4) will be given by 



aP + pV, ^ (2) + yo ( ' 2) , x^ + pW, 

 where 



p a — r a — w a r (4) (5) 



For an obvious reason p (4) = 0. 



Next, to obtain the second approximation, consider the 

 nucleus at the instant 



a W _ ? .(4) _ 1 2 / c) OL ? ^ 2 OL ^ Cr (4) | 



when its co-ordinates are 



This line implies the preceding as a special case, for a = 4. 

 Then the displacements o£ the electron will be 



f + i2(V) |^^~2(c) |^W 4 >, 



so that its position will be given by 



#a + r a_ l0 « r (4) + r (4y,4) + V( ( . )\± r c( " — ^a^ ) 





Taking a = 4 it is easily seen that this formula yields the 

 positions just at the instant .u (4) , ?'. <?., the simultaneous posi- 

 tions and displacements ; for w M) =l is a constant, and all 

 terms vanish except the first. 



We can simplify the formula considerably. Writing 



v J d^ dV 



and introducing a notation well known in three-dimensional 

 vector-analysis : 



S(^§j = &».V), 



our expression reduces to 



^ + ^ + i(p.V)p«~i^ 4) |^--( i o.V> a }, 

 and the simultaneous displacements are 



P°+i(p-V)P«-ir {i) {-£-(p-V)w«} . .(a=l,2,3). (6) 



