62 
ALGEBRAIC INVARIANTS 
the result L 3 , of operating on J with Q and the result Z, 4 of operating on Q 
with U (so that L 3 and L 4 may be derived from L x and L 3 by replacing 
a,d by the corresponding coefficients of J) ; the intermediate 
invariant At+Cr—2Bs of Q and h (§ 11); the resultant of Q and/: 
a 2 C 3 —6abBC 2 +6acC{2B 2 —AC) +ad{QABC-8B 3 ) +9 b 2 AC 2 
-18bcABC+6bdA(2B 2 -AC)+9c 2 A 2 C-6cdBA 2 +d 2 A 3 ; 
the resultant of L x and Z 4 ( = resultant of Z, 2 and L 3 ), obtained at once as a 
determinant of order 2. Salmon, Modern Higher Algebra, § 198, gives geo 
metrical interpretations. Hammond, Amer. Jour. Math., vol. 8, obtains the 
syzygies between the 15 covariants.