of Light and Heat in wicrystallized Media. 339 



zero, and increasing from that value until Ix becomes equal to 

 -T- or — -, then diminishing till 8 x becomes X, afterwards in- 

 creasing and diminishing in the same manner. 



And further, if the force vary according to an inverse power 

 of the distance, or to a function which can be expanded in 

 inverse powers, the terms introduced by the successive half- 

 waves will diminish rapidly; the whole value of the square of 

 the velocity will then depend essentially on that term which 

 depends on the first halt-wave. 



For this term let us expand the sine and omit the other 

 terms; or rather suppose this one to represent truly the Jbrm 

 7, and we obtain the following expression : 



and similar expressions for v'^ and t/'^ 



Now suppose <^ {?') = -fnji or that the force varies as the 



inverse wth power of the distance : then , = — — . ^ and 

 if g be the distance between two consecutive particles, and 



we shall have 



iH 



s-H-l ,yi , ..a . »^^'Hll 



n+ie 



»±.}{^^^-S?*^^} 





»i-f-3 



P L. i_ 



}^{^-S*^} 



As we are not able to integrate or sum the above series di- 

 rectly, we are obliged to make some hypothesis respecting it ; 

 the most obvious appears to be that which we have adopted, 

 p and q being numerical factors. 



The velocity with which light is transmitted is greater in 

 vacuo than in refracting media, whilst no perceptible variation 

 of velocity is occasioned by the different lengths of waves. 



2X2 



