OF THE REFLECTION AND REFRACTION OF LIGHT. 
701 
W = —| [ j (V v 9 iy.dxdydz 
+ 
87tKJ J 
While the complete value of T is 
1 
J ch l_ c A\ 
dy dz) \dz dx) \dx dy j 
dxdydz 
T= — 
877 J 
dm 
fidt~ -\-8 ttCS ( —. Vv Ot j j dxdydz 
wW 
1 fffr ^.- 2,^,0 pf^/4 M.dy/dk dt\ dUdn dk 
Working as before, and obtaining our equations as the condition that 
[(T-W)cft 
should be a minimum, we have to satisfy the equations 
/*S&S&+4irCS^. Vv Ot ) + 4irCs(|p Vv 80t)-^S(Vv Ot. Vv 8 Ot) 
dxdydz 
K 
dxdydzdt— 0 
or in Cartesian coordinates 
^(^+77877-K§£) 
, 4 c \dHfdl_dJ)\ ,cl8v(4_dt\,d^(chi_4 
n \ dd \dy dz j dd \fte dx)' dd dy 
IdJ fd$£_d8y\ d8y /d8£_d8£\ d£ fd&q_ d8j 
+ 770 1 dd \ dy dz ) + dd [dz~ dx Pdd \dx ~ dy 
_ I j ^ (A ( (I M _ C M\ l d A _ ( K 
)> dxdydzdt = 0 
dy dy )\dy dy) \ dz dx )\d. 
(dhn _dh£\(dr) _d£ 
\ dx dy J\dx dy 
Now of course the terms depending on C are the only additional ones, and it will 
be necessary to integrate them both relatively to the time and also relatively to 6. 
The integration with respect to the time is easily performed as it merely consists in 
removing the dot from one of the terms under the integral to the other and changing 
the sign, so that, neglecting the terms depending on the limits of the time with which 
we are not concerned, our equation becomes 
/rS(9lS0t)-47rCS Vv St+iirCsf— Vv S0t)+|S(F v Oh Vv SOI) 
MDCCCLXXX. 
dd 
4 x 
i/dzdt =0 
