1921 - 22 .] Concomitants of Quadratic Differential Forms. 
From the coefficients of ij^.22 > V122 > S122 > ^122 similarly have 
0^4. ^=,0 = o = 
^^22 ’ ^^12 ^^^22 ’ ^/l2 ^.'9'22 ’ ^^22 ^ 
but, because ^~ = Q , the second of these leads to 
SI) 22 
dcf) 
db -^2 
From the coefficients of ^^33, 77^33, $1335 ^133 similarly have 
BcKgg 0f/,3 S/igg 0/j3 -^^33 «^o,3 
but, because ^- = 0 , the third of these leads to 
eS'as 
dfj) 
^ 4 -‘>^ = C) ^+M_=o- 
Sc,, ai 33 '" 0«,3 ' 
0Ci 
= 0 . 
From the coefficients of ^^44, rj^, $444, ^444 we similarly have 
M.4.^ = o ^ 4 > ,s<I> a 
’ e </44 a «,4 
^+2^=0; 
d/44 d(ij4 
but, because — 0 , the last of these leads to 
^=0 
dd,, • 
From the coefficients of ^223’ '^223 > ^223 ^223 similarly have 
^ +M =0 2M + M = 0 -i+2®^=0 S<j> d<f> ^ . 
9^'-23 ^^22 ’ "^^23 ^/22 ’ "^^22 ’ """ 
07/123 ^^22 
but, because ^^ — 0 , the second of these leads to 
%2 
M = 0. 
0*23 
From the coefficients of ^^234 , ')j224 , C224 > ^224 '"^6 similarly have 
^■^+^ = 0, - 2 ^+^ = 0 , ^+^ = 0 , --'^+2-^-=0; 
” ’ 0/24 0«22 ^ ' 
0/^24 ^le)o 
0024 0»^22 
0/>^24 0G?22 
but, because ^-^ = 0 , the second of these leads to 
dm22 
From the coefficients of ^233 ? '^233 ’ ^233 ? ^233 similarly have 
^+2^=0 2 ^ 4 .^ = 0 ^+M=0- 
^^/23 ^^33 ^^23 ^*^33 ^*^23 ^33 
^/23 ^*^33 
but, because ^^ = 0 , the third of these leads to 
07/23 ^^33 
