Dynamical Theory of Di fraction. 227 



and convection (electronic) current, w, v, to being the 

 velocity of electrons, we must take 



aj = 2w(h+prt) ; (11) 



while, under statical conditions, 



«»*' = 2,r/+JK|| (12) 



From (9) and (12) we get 



Kv 2 <£ + 4ttp = 0, (13) 



when the electrons are at rest ; while from (9) and (11) 



we have, since - x + . . . + • • . = 0, 



QX 



'dp.'diH . _ 



ot OX 



which is the equation of continuity of a fluid of density p, 

 and is also the condition postulated in the electron theory of 

 Lorentz. 



Now (7) gives, if we introduce the vector-potentials 

 F, G, H, given as usual by 



-*-ihl r (X-.=g + g + f} 



<x (0) x ), 



where (o x is the free molecular displacement. 



This may be interpreted by saying that the force tending 

 to produce free rotational displacement of the sether is 



— F— ^-, &c. ; while (12) shows that the force producing 



K TSch 

 the total effect is proportional iof+j- ^~, &c. (a conclusion 



otherwise arrived at by Larmor, loc. cii.). 

 6. From (7) and (10) we have 



—■[I -i] 



Q2 



flCt = ^ &C. 



