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PROFESSOR A. R. FORSYTH OX THE HIFFEREXTIAL IXVARIAXTS 
when _/ involves and it must be iiomogeneous in them, sav of degree ; 
when / involves i/ij,, and it must be liomogeneous in them, sav of degree m .; 
when / involves K, F, G, it must be homogeneous in them, sav of degree m ..; 
likewise for L, M, N, say of degree ; likewise for P, Q, P, S, say of degree nu: 
for a, 13, y, 8 , e, say of degree ; for o, h, c, say of degree m ~; for a', h', c’, say of 
degree ; for k, I, m, n, say of degree for //, 1', m\ n', say of degree and 
for V, of degree ; provided the value of p, the index of the invariant, is given liy 
•2jx = »?, -f m., + 2 (w„ + r,ii) + .Si??, -j- 4m,; 
+ Hm- -(- Hm, d- 11 (m^ -)- -f- 8 m 
11 - 
e Avhrile svstem. as follows ; 
Index = 1 , 
Index = 
Index = 
Index = 
Index = 
Index = 
Index = 
2, J(^r2, W.2), 11(4/',,). iv'2. H(a’b) and I (an, v:'.-,) 
2, J (ir.,, U''2). w .; 
4 , V, I (a-., ';Fb), I(?m, w"V), H {?e3), J {w., 
5, J (m., w".), J (i'J., w'".), d ; 
G, H(mG), H(^r'G), (^r.) and A (w,), H(ir,). J(a 
, W.), 214 , I ( 224 ) ; 
k); 
m no 
Index = 8 , J (i(\ J (ir.,, ?r'V); 
Index = 12 , H (mb), H (iF'g); 
Index =18, di(m''p,), ‘h(a-'b); 
Index = 22, A (irb), A(m-"g). 
F 
28. All these are relative invariants, that is to say, when the same function 
of now variables is formed as the function f is of the old variables, then 
irF =/; 
wliere p is the index ofg’, and H = 
In order to have the absolute invariants. 
it IS sufhcient to divide each of them liy a proper power of any one of them. F’or 
this jmrpose, Ave choose 
= H = EG - F-; 
AAe can legaid \ as of index unity, and therefore it aa '111 be sufficient to diA'lde the 
1 elatiA e iiiAariants by a poAA^er of A eipial to its index. AVe therefore haA^e the set 
of 80 absolute invariants, glA’en bA’ 
