PROFESSOR CAYLEY ON POLYZOMAL CURVES. 97 



205. V- *JT= s/m= Jn = Jp\ order of tetrazomal is = 5 ; orders of tri- 

 zomals = 3, 2 ; same as V. supra. 



VI.JT+ Jp = 0, Jm + s/n = 0, aJJ + b s /m + cjn + djp = 0; order 

 of tetrazomal = 5 ; orders of trizomals are i3, 2. 

 We have here 



it a + d /7 



v 'l 



d v " 



Jm x = 



Jm + J^-^Jm, 



Jn x = 



J™ + J\k c ^ 1 ' 



or writing the values of Jm x , s/n x in the form 



s/mi= Jm+ijy-- j Jm, 

 Jn x = ~ Jm+ J^- | Jm, 



then observing that as before I = ^- m, if to fix the ideas we assume 



be 

 m,. 



. /™ . the eauations are 



Jl x = ^-3— x/z and similarly JT 2 = — ? — V/ 



V/ = s/^ Jm , the equations are 



x/w^ = Vm + t >/Z, Jm 2 = Vto — d V Z , 



Vt^ = — Jm + - Jit Jn 2 = Jm — - Jl , 



whence 



V^ + Jm~ x + J^h ~ ° » V% _ ^ m 2 - J n i — ° • 



We have moreover 



._ «a + ad ,- 

 a A= — g — Jl, 



_ bb + cc i - 



bjm x + cjn x = (b — c) Jm + — d — Jl, 



and thence 



aj\ + h J~m x + c Jn x ~= (a — d) Jl + (b — c) Jm = , 



so that 



JT['- Jm x ■ Jn x = b — c:c — a :a — 6 ; 

 VOL. XXV. PART I. 2 B 



