( 731 ) 



tlierefore confine ourselves to considering only tiie lirst; in dt)ing 

 so we shall write V instead of I'^,- . We shall have to remember 

 however that after having found tiie result that is due to the A^'-com- 

 ponents of the E. M. F. we have still to add to this a second amount 

 given by the F'-component ; this amount can be written down at 

 once by analogy with the first. 



^ 4. The general solution of the equation 



ds" ï'^F'^ a ^ U 



is given by 



. 2;tj' ;' .2;r:' .2-nz' z' . 2^z' 



g;^ = — e J €v e dz — -^e J S^.' e dz . . (6) 



The lower limit of these integrals is arbitrary, so that, as could 

 be expected, two arbitrary constants occur in the solution. It is 

 easily understood, that in the final result tliere will likewise be a 

 certain indefiniteness. Indeed botli a propagation towards and one from 

 will be contained in it. It is sufficient for our present pur[)ose to 

 consider only the first solution and in order to leave aside tlie second 

 we have to give completely definite values to the constants, as will 

 appear in the following manner. We consider the two planes perpen- 

 dicular to OZ', tangent to the boundary surface of the space r; let 

 these planes be determined by the equations 



z' := — h^ aud z' z= h.^ . 



Then, since <S« stands for 



1 d'® 



— ^— - dio , 



8ji' Ös" 



it will differ from zero between tiie planes and will be zero in tlie 

 space outside them. The first integral of (6) must vanish for 



z'>K 



and the second for 



z' <-/>,. 

 This is only possible, if 



9i< — 'h and 



.9, > /'.• 

 For tiie rest g^ and g,^ may have any value satisfying these une- 

 qualities ; it is evident that the result of the integrations will always 

 be the same, if we take into account what has been said about the 



51 

 Proceedings Royal Acad. Amsterdam. Vol. VIII. 



