On Systems of Rays. 37 
oT ; 60’ 
S557 Os, (PS ae gt 2 Ws 
ar_ aw 78M BT hy gy BD, 
5 eg peg 2 Pe (Z*) 
ee af e S76 aig 
5 = +(T- wy, | Sas WT ay > 
oF _ or 
1 pr OQ! 
oF eT W)S + Tae 
Differentiating the expressions (Z*), a eliminating 62’, dy’, dz’, by means of the 
differentials of the general equations (G'), we obtain, by ( Y*), the following system, 
analogous to the system ( Y*); 
yy 87 ca’) kW 7.87 79 oQk) 88W 7.87 ON} 
M8042 80' = 8-8) + QO - Hg) te gs F aa 
ala 
aah a7 te ; 
ee ae SPAY 8a’) oe >. BO 
ASQ + 2’, 8Q =waypOx— ¥ 8x) oy? Ge = a) + tear slay Cer 
We, 
ae +67 5 | 
ge OW So’ AYE er sr 80/ 
Ns6Q +N's80' = eos —Ws tae as -wae +e hoe — Woh) 
ow 
—8 +éu ; 
epee 60’ Pe 4 9 62 fen 
ASO +2130 = —— o+(8e5 ~Wa)+ = a as po) tae ee / ws) x 
g og 8 
ie —T )+ Was 5 
ow 8a’ Gi! AWW 00’ 
X82 + po= 2 2 a; Wae)+ se Gx; -W35,) 
ye: a pre ee 
xo N20 (ee ee ee a yee SW oe) 
Suda’ BY oa ov 
ee-T2 », wae | 
ow aa e | 
A,8Q +280’ = Se uf ser mi): : se wh = -; (2 a seo 
ea 8a! 
ae ay, Dean, 
VOL. XVII. 
