On Systems of Rays. 39 
eT =(T- W) 80+ Ws +(W—T) 80" 
+ (8T'—8,w') 82 +(8, W= Wao) ae +°W 
= 3 OF ABCs 3 = eh 
- (2, =e) (8-- Wee) 
-(3,F 0) (2 _ wey, 
8 still referring only to the variations of o, 7, v, x; and the three first equations 
(4°) give, by elimination, 
st wee £0" (3, W— W30) + $720 
] , OW , OW OW ‘a = 
nf Om fate 47 Gears de aay —* 5 
1 Os 4 5 sw 
ee (4 y* = ae (8 Sr) — o¢ Hay 
awe Cae OF) CF Oh, 
38f Lee 0 
sah (¢ Bw 0 (4 av) —u (a S| 
oe a J Oe Av (3 -e) 6 (8 = wy | 
se (eRh EE) (OR 1-102), 
a ~ W333 w— Wie) +2730 ut 
ae e a ay Ve (3203) eee $4! 
tape («Sponge )fv (ag) - 6 (85s 3 
1 , OoW ,o2WV ; ow . ‘ ow 
ape Fangs say fe (ax —&)-7 (85> oe) -J 
in which 
oW SW Sew \? WW SW OCW \? SW ew OoW 2 ; 
“= — (——_— — x’) 
ou’? byt Gay) z' (Se ) F 3c? Sa ae ) ellen 
and 
