367 
1898—99.] Lord Kelvin on Reflexion and Refraction, 
y 2 to denote the Lap! 
the equations of motion 
^2 ^2 ^2 
y 2 to denote the Laplacian operator —— + + — , we find as 
ax (Xy ciz“ 
pg=(*+l»)|+»v 2 ft 
/©-<* + «!+•*** i- 
P g=(^ + i»)| + »V 2 4 
( 1 ), 
//denoting the density of the medium, £, rj, £ its displacement from 
the position of equilibrium (x, y, z), and 8 the dilatation of bulk at 
fa y , z) as expressed by the equation 
8 = ^1 + ^ + ^! ( 9 .\ 
dx dy dz\ - ■ ■ ■ \ 
§ 3. Taking d/dx, d/dy, dfdz of (1), we find 
pjf=(fc + !»)v 2 8 
■ (3). 
From this we find 
■ ■ ■ 
• (4). 
Put now 
V=VI + ^ V -H; C=Ci + |v-*' 
S; (5). 
These give 
• (6), 
d£i _j_ ^Vi _j_ _ q 
dx dy dz 
and, therefore, eliminating by them £, 97 , £ from (1), we 
find by 
aid of (4) 
_ 2 e . nn 2 n • o^^ —nv? 2 1 * (7) 
P W v P W v Vl> p lP~ n v Cl ’ (7 ' 
§ 4. By Poisson’s theorem in the elementary mathematics of 
force varying inversely as the square of the distance, we have 
00 
V - 2 S = - 1 J f fd (volume) . ~ ; ( 8 ) , 
where 8 , 8 ' denote the dilatations at any two points P and P'; 
d (volume) denotes an infinitesimal element of volume around 
the point P' ; and PP' denotes the distance between the points 
