1 86 On the Optical Laws of Rock-Crystals. 



then depends only on the relative displacements of the molecules. 

 But when this is not the case when, as in quartz, each mole- 

 cule is supposed to vibrate in a curve then it is natural to con- 

 ceive that the function V may depend, not only on the relative 

 displacements, but also on the relative areas which each mole- 

 cule describes about every other more or less advanced in its 

 vibration. This idea, analytically expressed, introduces a new 

 term v into the value of the function 2Y ; and, if the plane of 

 the wave be taken for the plane of xy, it is easy to show that 



\dz dz* dz dz z j 

 Now if we integrate by parts the expression 



JJJ dxdydzSv, 



so as to get rid of the variations of differential co-efficients, the 

 reduced form of the triple integral will be 



from which it appears that the quantities 



are to be added to the usual expressions for the force in the 

 directions of x and y respectively. These are the very terms 

 in the addition of which the hypothesis before alluded to 

 consists. 



