Laws of Molecular Force, 293 



pressions and putting M/p = u and aZ=U, v/v n =n n , v/V=N 

 we get . 



tt(^-l)=u(N-l-?-NVl-?n"): 



as k is equal to 1, seeing that if 8 = andU = ?i, then N must 

 be equal to n. This equation is the companion to that for 

 still matter, namely, 



i»(n-l) = U(N-l). 



But to allow for deformation of the wave-front in passing- 

 through molecules it was shown (Phil. Mag. Feb. 1889, 

 p. 150) that this first approximation might be altered to the 

 form 



u(n-l) = U(N-l)+cp, 



where c is a constant, and this form was verified, so that we 

 may write 



tt(n tf -l)=U(N-l-|N)(l-|n"j +cp 



= u ^- 1 )( 1 -~. S ?T-^' / ) + ^ 



neglecting the term in 8 2 ; 



n"-n _ S U(N-l) n-l( N" „\ 



n v u{n — 1) 



Now 



IU III V V >AJ\J IAJ\J m . -I 



—^- = -rf- = " v = ~ 7 a PP roxlmatel y- 



where x is the fraction of the water's velocity imparted to the 

 velocity v r to change it to v". Fizeau (Ann. de Ch. et de Phys. 

 ser. 3, t. lvii. ) found a value '5 for x, while Michelson and Morley 

 (Amer. Journ. 8c. ser. 3, vol. cxxxi.), in a more extended and 

 accurate series of experiments, found a value ^=*43±*02, 

 which we will adopt. U(N — 1) is equal to u(n — 1) measured 

 in the vapour of water, for which Lorenz (Wied. Ann, xi.) 

 gives the value 5*6 ; the value for water at 20° C, according 

 to his data is 6, and n is 1*333, which may also be taken as the 

 value for n" where it occurs ; all these values being substituted 

 in the equation 



N n 2 u(n-l) „ 



N-1"*m-1'U(N-1) 



