On Systems of Rays. 33 
in which 8” refers to 2, y, Zz, and in which V” may be deduced from JV by the 
relation 
2 SV _ 80, sw Pare) ew eQ \? 
<== a ( oo” Wid a = us Poe) (sar ¥ VS) 
& ow & O° & 
(Ge 40 ae) (ae + ae) ~ (Gant Y ie) 
oe ow Or ow SO \? 
Cs ay) (set? sé) ~ (5st =) (N’) 
and the more extensive formula (Z*) has an inverse also, namely, 
pas (8V + V9'04+ BV 3049 IP) = 
(SF+7 22) 20 (3,— 9% _ py) Oy — 9 vee) 
} 0 } OW vo 
(et V ar) {a (et 785) 3 (85 eR) Le 
(Get ae) fa (w- 8er Pay) ele 8 Pe) Y 
6 OW ce x9) ow 6 
oe ae a Ege iar pepe aid 
sie Tate) U2 gH py y®D)G Y_20(0, _ gM _p-g 2D) 
Pye) OW 3 3 37 vo 
coe 2) = (a —&5—--V8 ay ees s) 
Se ee Be heey gk) —2 (ar 9-3 2) 
5 ow x0) 5 ow 6a 
ec: ee ee eM Ee 
Se eee a tee, rs. 
é retaining its recent meaning, so that, as Q does not contain 2’, 7’, 2’, we have, in the 
last formula, 
(P*) 
2 _ FQ. 6Q_ 0 , 02 _ 8&0 
is ~ Sad Be es ~ brdx OG ~ 8udx 8x: 
If we do not choose to suppose //” homogeneous of the first dimension with 
respect to o, 7, v, and if we put for abridgment 
VOL. XVII. K 
