382 
MR. A. CATLET OX THE COXIC OF FIVE-POIXTIC 
so that the term is 
- jr, cia,H, 3.H)' 
+2®(3(m-2)H-«3,H)(®3,H+®3,H) 
- g(3(m-2)H-«3,H)’; 
or reducing 
= C, #, 0, 
+ 6(m-2)H.<aB,H+lB,H+6B,H) 
-9(m-2)mP. 
23. The other terms may be obtained in a similar manner; and it is easy to see that, 
collecting all the terms, the sum will be 
3S, C, S, B,H, 
+ 6 — 2 )H + /Aj/ + V2:) { ( -j- +((§/-+ + C , H 
-9(m-2)^hP(a, c, df, #, IB, i^, vf; 
or, attending to the signification of the symbols O, □ , T, we have 
(m~l)"(DH)"= -9(w-2)^ff (h 
+ 3(m-2)HD^ 
24. Next, 
DTI=((B.-C^)B,+(CX-Av)B,+(Af-(.-Bx)B,)^H, 
or, what is the same thing, 
]3^H={?.(CB,-BB,)+^(AB,-CB,)+<BB,-AB,)}^TI; 
and if we attend first to the term which contains the coefficient is 
(CB,-BBJ^H. 
Now substituting for C^, CB, B^ as before, we have 
(w_l)-^(CB,-BB,)TI= (- ^P+21^'^ 
+ 2( — dfA" + 0.Ty + %Tz — %2)B^B^.H 
C'P+2#.T2: — 9[P)B;H 
= — P(^, df, CJB^, BJ-^H 
+ + #B„,)H 
-^(yB,+.B,)Ti, 
where it is to be observed that the symbols of differentiation affect H only. A^*e have 
(//B^ + 2;B^)T-I = (a’B., + ?/B^ + ^B JT4 
— 2(^B,, +^By + 2B,)a'B,,H 
