(cS) 
~ 
On Systems of Rays. 
Let us therefore resume the equations 
aw * Spd weak SOAR» Sea Se) SM, ae) 7 
Go + Vee sae! Sao cw) 
which were deduced in the sixth number from the homogeneous form that we now 
assign to JV’, and which are to be combined with the following 
Rei, Be 6a r3 
(0) = By Tr = + V ax ’ (W ) 
and with the general equations of the fourth number, 
Sa 3, (S3w) 4.80 , 
ee al =? v S“ineet (G’) 
and let us eliminate 
Qu, Sy, 32, 80’, &', Sv’, 32, 
Ce) 
by (4°), from the differentials of these seven equations, (J/”*) (G') (JV’*), that is 
from the seven following,” 
soe: Fe po er. 
oo oa oo 
sw 8a oad 
85 + V8 =~ BP, 
ee V7 322 5, 25 V, (X°) 
ou ou ou 
ae te Seay OE 
da = 60, 8 Ma Mae” 
ow 6Q SV 8a 
This elimination gives 
OU Yel ow 6a OV ow eQ 
X® BQ = — es + 8 yom (° - SBME sa COnass Yee) 
: 
ox* ardy | 
eee vss), 
wm aas ere 4 (ai 4 vat) + (a + ae) | 
2 (2 4 78), | 
A 3Q= —4F + (38 4 vas) +o = yee) 
7 7%, | 
