PROFESSOR CAYLEY ON POLYZOMAL CURVES. 



23 



1m II 



/ /d /rad /?id 



^abc' ^abc' 'Vabc' 



'md 



abc 



Ind 



'Vflhr 



the last of which is the original equation ^777 + */mP + JnW = 0- It may be 

 added that if the first equation be represented by Jrn^V + JnJV + Jp^T = 0, 

 — that is, if we have 



J™* -Sl&> ^ = - /s/p» -/Pi = Vaj^ ' 



and therefore, 



b+c^d-bcVa^b+c 



),=0j 



or if the second equation be represented by *JlU + Jn 2 W + »Jp 2 T = 0, — that 

 is, if we have 



j^=-J%> j**=J1m' ^»=n/^' 



and therefore 



a + c + d 



or if the third equation be represented by Jljj + Jm z V + *Jp z T= 0, — that 

 is, if we have 



Jh — sjtf' J™>z— sj^2> JPz — SjQh c > 



and therefore 



L m. p, 

 i-+b 3 + d= ' 



then the equation of the trizomal may also be expressed in the forms — 



( • , Jm x , Jn x , Jf^ )(JV, JV, JW, Jl)=0 



ac 



/— fobc /m,cd 



