DIFFERENTIAL INVARIANTS OF STACL 
J'l = {rchcY, 
L = {ahu)', 
T. = (aha'Y, 
T, = (aa'vf, 
I. = {r^r/hy, 
ir, = Yri/iy, 
I, = {a'h'cy, 
13 = (aah) {/3ah) 
Ig = (aaa') {/3aa') {a/Siy, 
110 = (a«7>') {/3a'l/) {a/3uy, 
111 = {«^y) Y^/3l() (ayv) {/3yv), 
Ili = (^/ 3 y) (a/ 3 S) (ayS) (/ 3 -y 5 ), 
1 13 = (a/Sy) {rx^a) (aya) {/3yu), 
I’u = (a/ 3 a') (/ 3 yrL) HSyK.), 
1 15 = (^/^y) (a/ 3 S) («ye) ivy'll) (Sen)-, 
In; = («jSy) (o-^S) ('5‘ye) (J3yC) {8el)\ 
Iir = (ySv)- {ftyii) {aht). 
The first seven of these nre tlie set of seven 111 § 17 , 'which lielono- to tlie system of 
twm quadratics. Tlie next three are olitainecl, hv renlacino; n,, n.„ v_. l)v -% I ■ 
" cx.^ 
respectively, inserting these changes in I,„ 1,5 so as to turn them into operators, 
and then operating upon the kno'wn mixed concomitant belonging to the 
cubic. Of the remainder, Ii„, I^., 1^,,, Tj- belong to the system of the cubic ; I13 
and Ti^ are obtained by ojierating on y with the symbolical operators 
o, 
(V, 
+ ^'0 X + 
Of., 
( H., 
and 
a 
ru, 
I / 
+ -2 
(It,, 
respectively, or, what is the same thing, liy the respectivf 
ors 
y n 
I 1 r' 
.1 
f " 
cv 
1 
rc.,~ 
( n.r 
.1 -h 'V 
O- 
c I'., rii„ 
o 2 
O 
+ 2-/ + 21, 
r'o'o r/ 7 , 
-\ o 1 
( III Cll., 
a 
C"' 
0?q 
VOL. cell.-A 
, -f b . , + c 4 - : 2 f + 2g.^-V 
oiiy cuy cu.,cu.y ° c iu,?u 
2 T 
. 01 9 - 
1 d?qd/x 
