( 434 ) 



Dividing this by (3), we get 



Pï_ a 

 V ' VT' 



an extremely small quantity, because the diameter of the ions is a 

 very small fraction of the wave-length. This is the reason why 

 we may omit the last term in (Ic). 



As to the equations (Vc), it must be remarked that, if the displa- 

 cements are infinitely small, the same will be true of the velocities 

 and, in general, of all quantities which do not exist as long as the 

 system is at rest and are entirely produced by the motion. Such 

 are -^'x, •')'«/' •^'^- ^^^ '"'^y therefore omit the last terms in (¥<■), 

 as being of the second order. 



The same reasoning would apply to the terms containing — , if 



we could be sure that in the state of equilibriunr there are no 

 electric forces at all. If. however, in the absence of any vibrations, 

 the vector S' has already a certain value Sf,\ '^ will only be the 

 difference %' — Sq', that may be called infinitely small ; it will then 

 be permitted to replace %)/ and 5'- by S''».'/ and 5'»- 



Another restriction consists in supposing that an ion is incapable 

 of any motion but a translation as a whole, and that, in the posi- 

 tion of equilibrium, though its parts may be acted on by electric 

 forces, as has just been said, yet the whole ion does not experience 

 a resultant electric force. Then, if ^ 7- is an element of volume, 

 and tlie integrations are extended all over the ion, 



I (>, ?i'o)/ (It = j a^ '^\^, (/ r = . . 



(5) 



Again, in the case of vibrations, the equations (V^) will only 

 serve to calculate the resultant force acting on iin ion. In the 

 direction of the axis of ;/ e. g. this force will be 



pS.'/ 



'S.d.T 



Its value may be found, if we begin by applying the second of 

 the three equations to each point of the ion, always for the same 

 universal time t, and then integrate. From the second term on the 

 rio'ht-hand side we find 



