74 
MR. A. R. FORSYTH OH A CLASS OF FUHCTIOHAL INVARIANTS. 
exposed in which the dependent variable does not enter into the equations of trans¬ 
formation, and the transformations above indicated in which the occurrence of the 
dependent variable in the equations of transformation is essential, that different 
results will be obtained. Two examples will suffice. First, a comparison of the 
'characteristic equations of Elliott’s reciprocants and of those characteristic of the 
present functional invariants may be made from the forms expressed in the notations 
of this memoir :— 
Annihilators of Elliott’s reciprocants. 
fli = ,-®+2s| + a| + 2(.| + 3c|^+.. 
- * 0s + I + a, + I + 3'' S + 
- El _ - ^ + 3i- g® + 2s I + ( g® 
+ 4a£ + 36| + 2o|- + cZ^^ + 
-Eij--fs + rg^^+2s| + 3<| 
+“ s+1+a;.+S+ 
Y = S + (’■* + 2s=) I + Sst I 
Annihilators of Invariants in this memoir. 
0 
0 
a 
dt 
A3-2a^,+«S+2^a,. 
no=-3X+22>| + jg| 
+ 6a£H-56g®j + 4c|+3c«|-^ + .. 
0 0 
ni=-3X + pg-+2gg-^ 
+ 2'-|.+ 3s|+«| 
+ 3n£ + 46|+5c|+6(i|^+.. 
/ 0 ^ 0 ^ 
Ai=l(2 3-+2i>g-] 
+"l*a^+2®a^+®’’s;)+ 
^s=i(r|+‘2j| 
+ 21’-al+2‘a + 3qj+.. 
