OF A SURFACE, AND THEIR GEOMETRIC SIGNIFICANCE. 
357 
-j. ¥ 
W = 
10 
d(f) 
01 
¥ 
10 
d(f), 
10 a ; I roi ^rr 
01 ci/zio 
01 
+ 
0F 
op + 
rAx 
^ a’ 
0L 
¥ 
aM 
+ 3 
( P-^- 
V ap 
+ Q^ 
' ^ ^ aQ 
+ iq'| + s 
+ ^' 
i ¥ 
+ lS54 + y^^+8 
¥ 
\ ea 
ep 
'Y 
CO 
+ h| 
¥ 
+ >> 2 + 
c '■t+ 
s/ 
/ 
\ ea 
eh 
( (• 
ea 
+ 8V| 
¥ 
f / 
( r / 
+ 11 (i % + I £f + -HI 1^- + n y- 
\ etc t i ( III ell 
¥_ 
¥ 
+ 11 ( k' J- I' _j_ LL _j_ st 
\ ek el eni c/c 
(li)' 
Association with Binariants. 
20. The expression of these equations at once associates tlie solution with known 
results in tlie theory of the concomitants of a system of simultaneous binary forms. 
The equations (L)', (Ij.)', (L)" are tlie flifferential equations of the invariants of the 
system of binary foiins 
I' «/ 
('A 10^ l'/'io> '^olI^:=)^ 
(E,F, 01=.)^ (L, M,NX#)^ {a,h,(^Y, {a',h\e'M\ 
(P, Q, R, SX#)3, {k, I, m, nX#)A (F, m\ n'X*f, 
(a, y, 8, €X=:^=)b 
or, what is the same thing, they are the differential equations of the invariants and 
covariants of the system of binary forms 
^^1 = ('/'10> 
w. = (E, F, GX</>I,1, - 
''4 = NX4n — 
w", = {a, h, tX<Aon — ^io)% 
w'", = [a', h', c'X<f>oo — 'Aio)'T 
u’-i = (-P> Q, SX<^on “ </>io)b 
3 ~ (^') '‘'X^OO 
w"z = {iX I', to', rdX</>on — </'io)^ 
= (a, /3, y, 8, eX<^on “ 
