near the former 

 in a state of 

 equilibrium ; 



the coordinates 

 of the same 

 particles re- 

 spectively at 

 any time t 

 during the 

 motion. 



of Luminous Waves in Transparent Bodies. 205 



this difficulty and arrive at exactly the same results as those 

 just mentioned; so that these results arc true in general what- 

 ever be the arra7igement of the luminous pai'ticles in the inter- 

 stices between the particles of matter. 



Formation of the Eqiiations of Vibratory Motion. 



Let us adopt the following notation, viz. let 

 X y z he the coordinates of any particle of^ 



aether, I when in a state 



x,yi Zi be the coordinates of any particle of [of equilibrium ; 



matter, J 



x+^xy + dy z + Sz be the coordinates^ 



of any particle of aether, I 



.r, + 8 x^ yi + $yi z^ + S ;:, be the coordinates j 



of any particle of matter, J 



T + aj/+j3^+7 



'^/ + «/ i// + /3, -;+r/ 



X, + Ui + ^x, + ^u,y, + fi, + ly, + 8^^ 5", + 7; + IZi + 87^ J 



Let us for brevity put 

 8 a?2 + sy + 8 2^ = ,.2 

 tx^ + 8j/2 + l;s^=r^ 



(8^ + 8«)2 + (ly + 8/3)2 + (8^ -f 8y)2 = (,• + p)2 

 (8^, + 8a,)2 + [ly^ + 8/3^V2 + (S^, + 87,)^ = (;• + p^)2 



(X - a^,)2 + (j/- 3/^)2 + (;,_.^)2 = , 72 



(>^ + «-^/-«/)' + (3/ + /3-i/,-/3,)2 + (^ + 7-.^,-y^)2 = (/ + p')2. 



Also let the attraction at the time t of 

 A particle of aether on a particle of asther be m{r + p)f{r + p) 



pether m^{r' + p')<p{r' + p') 

 matter ffi{r' + p')<p[r' + p') 

 matter m,(r, + p,)^ri + p^). 

 Hence we evidently have the following equation for the mo- 

 tion parallel to the axis of x of any particle of gether, viz. 



^ = S ^rnf(r + p){hv + U)-i-m,ip{r' + p'){x,-x + u,-u) I. 



We shall suppose the relative motion of any two particles 

 within the sphere of mutual attraction or repulsion to be very 

 small compared with the distance between them ; hence « 8a 

 a, p p' are very small compared with ^x {Xi — x) r r' : we 

 have therefore approximately, 



matter 

 aether 

 matter 



