141] 
A SECOND MEMOIR UPON QUANTICS. 
257 
the difference in question is equal to the number of the asyzygetie covariants i e the 
number of the asyzygetie covariants of the order /a and the degree 6 is equd to the 
number of terms of the degree 6 and weight less the number of terms of 
the degree 6 and weight \(m6 — /¿) — 1. 
43. I shall now give some instances of the calculation of covariants by the method 
just explained. It is very convenient for this purpose to commence by forming the 
literal parts by Arbogast’s Method of Derivations: we thus form tables such as the 
following:— 
abc 
a 2 
ab 
ac 
be 
b 2 
b 2 
o 2 
ab 
ac 
ad 
bd 
cd 
b 2 
be 
c 2 
a 3 
a 2 b 
a 2 c 
a 2 d 
abd 
acd 
ad 2 
bd 2 
cd 2 
d 3 
ab 2 
abc 
ac 2 
b 2 d 
bed 
c 2 d 
b 3 
b 2 c 
be 2 
c 3 
a 4 
a 3 b 
a 3 c 
a 3 d 
a 2 bd 
a 2 cd 
a 2 d 2 
abd 2 
acd 2 
ad 3 
bd 3 
cd 3 
d* 
a 2 b 2 
a 2 bc 
a 2 c 2 
ab 2 d 
abed 
ac 2 d 
b 2 d 2 
bed 2 
c 2 d 2 
ab 3 
ab 2 c 
abc 2 
ac 3 
b 2 cd 
bc 3 d 
c s d 
6 4 
b 3 c 
b 3 d 
be 3 
c 4 
b 2 c 2 
a 
b 
c 
d 
e 
cd 
ab 
ac 
ad 
ae 
be 
bd 
cd 
cl 2 
b 2 
be 
bd 
cd 
c 2 
c 2