144] 
A THIRD MEMOIR UPON QUANTICS. 
321 
ad a + bdp + ..., 
ocd a + fid b + .... 
C. II. 
41 
The coefficients of this quantic are termed Emanants, viz., excluding the first coefficient, 
which is the quantic itself (but which might be termed the 0-th emanant), the 
other coefficients are the first, second, and last or ultimate emanants. The ultimate 
emanant is, it is clear, nothing else than the quantic itself, with (X, F, ...) instead of 
(x, y, ...) for facients: the penultimate emanant is, in like manner, obtained from the 
first emanant by interchanging (x, y,...) with (X, F, ...), and similarly for the other 
emanants. The facients (X, F, ...) may be termed the facients. of emanation, or simply 
the new facients. The theory of emanation might be presented in a more general 
form by employing two or more sets of emanating facients; we might, for example, 
write Xx+fiX + vX', \y + /juY + vY', ... for x, y, ..., but it is not necessary to dwell 
upon this at present. 
The invariants, in respect to the new facients, of any emanant or emanants of a 
quantic (i.e. the invariants of the emanant or emanants, considered as a function or 
functions of the new facients), are, it is easy to see, covariants of the original quantic, 
and it is in many cases convenient to define a covariant in this manner; thus the 
Hessian is the discriminant of the second or quadric emanant of the quantic. 
60. If we consider a quantic 
and an adjoint linear form, the operative quantic 
(9«, d b ,...\%, 
(which is, so to speak, a coutravariant operator) is termed the Evector. The proper 
ties of the evector have been considered in the introductory memoir, and it has been 
in effect shown that the evector operating upon an invariant, or more generally upon 
a contravariant, gives rise to a contravariant. Any such contravariant, or rather such 
contravariant considered as so generated, is termed an Evectant. In the case of a 
binary quantic, 
(a,b,...Jx, y) m , 
(d a , d b ,...fy, - x) m 
the covariant operator 
may, if not with perfect accuracy, yet without risk of ambiguity, be termed the Evector, 
and a covariant obtained by operating with it upon an invariant or covariant, or 
rather such covariant considered as so generated, may in like manner be termed an 
Evectant. 
61. Imagine two or more quantics of the same order, 
(a, b, ...fix, y) m , 
(a, ¡3,...fx, y) m , 
we may have covariants such that for the coefficients of each pair of quantics the 
covariant is reduced to zero by the operators