118 MR. A. R. FORSYTH ON A CLASS OF FUNCTIONAL INVARIANTS. 
Similarly for others of the simultaneous concomitants of Aq and A^. And it is not 
difficult to show that all functional invariants within the rank 4, or, what is the equi¬ 
valent, all the simultaneous concomitants of Aq, A^, A 3 , considered as three binary 
forms, can be expressed in terms of the foregoing six quantities Aq, Hq, A^^, Jqj, H^, Q, 
and the succeeding five, viz.:— 
— -^ 2 > 
“h ^^3^13) ^ ~ ^ 02 ’ 
^13^) '^i ^ H2, 
—— 4:1^2q'?/'22 “I” ^ - 13* 
Inferences can also be deduced as to the expressibility of the simultaneous concomi¬ 
tants of Aq and A 3 alone as simultaneous quantics, and of the simultaneous concomi¬ 
tants of Aj^ and Ag alone, as simultaneous concomitants ; but all such results are 
chiefly interesting from the point of view of the theory of binary forms, and are more 
useful in that theory than in the theory of functional invariants. 
