( 486 ) 
(a2 + 22) — 2 (a1 1 + 242) HH HH) = te — 2 ay + Yys 
whilst from the relation 
(@ yo — ta yi)? = (2? +22) (92 + 2)— ign + 2242)?» 
or 
(cy)? = Tr Yy — Ty Yr 
ensues that the covariant (zy) is related to the covariants 2, and #y= yz. 
Now from these three absolute comitants follows immediately the 
invariant character of the symbols 
da ap and (ab). 
According to the above these absolute invariant symbols are con- 
nected by the relation 
2 
. 
(ab)? = aa by — a> 
So for the construction of orthogonal comitants we can dispose of 
the symbols 
Bas b's, ble Aes (at), te By Whey) 
Evidently linear invariants can be generated only by the symbol 
dq and present themselves only in the study of forms of even degree. 
Consequently the form a?" possesses the linear absolute invariant *) 
rn 
an = dong HN a2 n—2,2 H (3) G2n—4,4 +++ + 7 40,2n- 
3. The quadratic form 
a? = gq 24 +242 2 + Gog 23 
furnishes the invariants 
dq = a99 4 Agg » 
EE ef 
as dn dit 02’ 
1) The existence of this invariant was proved by Mr. W. MANrEL by means of an 
infinitesimal transformation (Wiskundige Opgaven, Dl. VII, p. 148). 
