On Systems of Rays. 
115 
eS. ss BOS | oS Best, 
OF 54) tise ebindabe! ads Deer? 
25 2,8) 
Lee aes yg 7 So + oe or’, 
Sadr or? Orda Orér (U") 
os O28 SS. nce OS 4, 
OS Sit oak Oa Dear 
es . | 8S sal a) gigs 
OF ya Oo tas Or t+ arate + oe OT 3 
which give, by eliminating between the two first, 
2 2 2 325 
NE gaan te Jerk ew nay aL 
dada’ Srér’  dadr’ brdo’ Sadr dcdr’ da" Or or’ Ore Oadr Oadr orér v") 
(ee &S oS n= Ce es Laie ee eS 8S BS). ( 
Oooo oror’ oabr’ broa’ ck da* Ordo’ dedr Sado" Ooor Se 32) =) 2 
and therefore, by substituting these values of 80’, dr’ 
, in the two last, 
ona {28 (25.88, BS 9S), BS (ATES _ BS BS) 
30°? \Sa8r daédr’ O02 Srér’ + 3y8r' 60% Srda’ dadr ae 
os oS Fs es omy 
"Sado" \Sado’ Srdr’ Sadr’ Srdo" 
gc ee es &S &S &S es 28 8S _ &s ee 
S02 \ Or? Badr’ Sadr Srdr’ adr’ \daér Sréc’ = Sr? Sarda’ 
Ses (S&S &S Ss os 
tay Geoas Bae naa ae) 
onan f PS (88 BS ESBS) BS (BS ES BS BS) 
oor \dcdr Sadr 8a brér’ 8r% \8c2 Sr8a" Sadr Sada’ 
Ses (2S S&S 8&8 &s 
me as ba ae oa 
eer os (= es &s ay tiie (eee a) 
30’Sr’ \Sr2 Sadr’ Sadr Srdr’ Or’? \8cdr Srdc’ br? Sado’ 
O28 / & Ss es & 3 
Ted pee 
so that by a new elimination we obtain, between the 
final and initial ordinates 2, 2’, 
the following equation, which, by the form of S, is quadratic with respect to each 
ordinate separately, and involves the product of their squares : 
= (55 5 - (ES) ) (Ee ge (Se) ) + 
328 es BS SS Sg Ss 
2 
-orle Ge) - 2 ee? 
6r 
5.2 
2 
Oadr’ orda 
be Bs 
dae’ Stor’ 
828 yt ; 
6067’ 
( 
( 
) 
