PROFESSOR CAYLEY’S TENTH MEMOIR ON QUANTICS. G25 
themselves, if one of the covariants 6, c, cl, e vanishes, in particular if b vanishes. 
Suppose 6=0 ; writing also (although this makes but little difference) «= 1, we have 
a = 1, 
6 = 0 , 
c = c, 
d = d, 
e — e, 
f 2 = — cl — 4c 3 , 
9 = e 2 , 
h = &ccl-\-ef, 
i = ce, 
j = 9 d 2 +ce\ 
k = 3 cle, 
l =-3df+2c 2 e, 
m = 9 cd 2 + 3 def — c 2 e 2 , 
n = — 6ccle — e 2 f, 
o = 9 d 2 e-{-ce 3 , 
p =- 9d/+ 1 2 c 2 de+cef 
q = — 54c# — 27# «/+ 1 8c 2 cZe 2 -|-cey, 
r = 9cd 2 e-\-3def — c 2 e 3 , 
.s = — 27df-\- 54c 2 cZ 2 e-t- 9cdeJ- — 2c 3 e 3 , 
t =-81c/y-G#e 3 +216c 2 #c+54cc6V/-24cW-c 2 ey; 
w = — 2 7 d 5 — 18 cd s e 2 — 4 d 2 ef-\- c 2 de 4 ', 
v =-81 ddef— 6 dV-+ 2 1 6c W + 5 ±ccl 2 ef- 2 4c W - 1 (def 
iv (not calculated). 
These values are very convenient for the verification of syzygies, &c. : take, for 
instance, the before-mentioned relation Sv= — 6dt — Qmrfnq, that is, if V=(Y ni V 1 ^.'r, y ), 
then Y \ = — &dt—§mr-\-nq\ calculating the three products on the right hand side, 
observing that/ 2 when it occurs is to be replaced by its value — d— 4c 3 , and taking 
their sum, the figures are as follows : — 
4 l 2 
