322 
A THIRD MEMOIR UPON QUANTIC8. 
Such covariants are called Combinants, and they possess the property of being inva- 
riantive, quoad the system, i. e. the covariant remains unaltered to a factor pres, when 
each quantic is replaced by a linear function of all the quantics. This extremely 
important theory is due to Mr Sylvester. 
Proceeding now to the theory of ternary quadrics and cubics,— 
First for a ternary quadric, we have the following tables:— 
Covariant and other Tables, Nos. 51 to 56 (a ternary quadric). 
No. 51. 
The quadric is represented by 
(a, b, c, f g, hjoc, y, zf, 
which means 
ax 3 + by* + cz : + 2 fyz + 2gzx + 2hxy. 
No. 52. 
The first derived functions (omitting the factor 2) are— 
(a, h, gjx, y, z), 
(h, b, f\x, y, z), 
(9> f c^x, y, z). 
No. 53. 
The operators which reduce a covariant to zero are 
( h, b, 2f#d g , d f , d c ) — zd y , 
(-g, f, c "$d a , d h , d g )-xd z , 
( 2h, g Jd h , d b> d f )-yd x , 
( g> % G ]$ h , d b , dj) — yd z , 
( a, h, 2gjdg, d f , d c ) - zd x , 
(2 h, b, fjd a , d h , dg)-xd y . 
No. 54. 
a> d b , d c , 
The evector is 
(9, 
9/, 9g, d h \%, 7], £)-.