Reflexion and Refraction of Light. 419 



where 



^_ dw c?y c?io ,™ 



"" <fo rfy dz 



Using these in (4) we find, as the equations of motion, 

 fS^-B)g + BV^ t£-(A-B)**ByS, 



? 5=(A-B)| + BV^ • (9), 



where 



*__du dv dw nn\ 



eta dy 4-z * V /» 



and 



V 3 =£ + |r + £ • • • • (")• 



10. From (9) we find, by taking J/eta of the first, d/dy of 

 the second, and djdz of the third, and adding, 



?S= A V 28 d2). 



Put now 



eta a?/ az 



which implies 



eft/ rfi/ e?«/ _~ (\a\. 



dx dy dz ~~ 

 and we find, by (9), 



{Jf-llyV, ?5=B V V ; ^=BW . (15). 



Equations (12), (14), and (15) prove the footnote to § 3 : 

 and they prove, further, that any infinitesimal disturbance 

 whatever is composed of specimens of the condensational- 

 rarefactional wave, and specimens of the distortional wave, 

 coexisting : and, lastly, they prove that the displacement in 



