489 
414] ON POLYZOMAL CURVES. 
The meaning is, that, taking the trizomal curve fl-JJ + fm 1 V+fn 1 W = 0, this regarded as a 
tetrazomal curve, U+ Vm x V + fn x W + V0T = 0, satisfies the condition -^ + -^ + -^ + ^ = 0; 
and the like as to the trizomal curve f LU + f m. 2 V + fn 2 W = 0. 
45. The equation by which the decomposition was effected is, it is clear, one of 
twelve equivalent equations; four of these are 
№ 
Vm , 
fn ,0 j 
[fu, Vv, \fw, VtJ = 
(° 
hi 
v m -1 , 
a wm 
fn , fp ^ 
( . )•■ 
-1- -(cfpW-dfnTX, 
cda m\ ) 
(Vi 
0 
Vre + bV,r ^ ) 
( - )■ 
(w 
fm , 
o , vp+4.) 
c yp/ 
( - T = 
and the others may be deduced from these by a cyclical permutation of (U, V, W), 
(a, b, c), (l, m, n), leaving T, d, p unaltered. 
Article Nos. 46 to 51. Application to the Trizomal; the Theorem of the Variable Zomal. 
46. I take the last equation written under the form 
(a fmU - b fl V)'- = (fjpU+ f^pV+ (p + ^ Vf J, 
which, putting therein p = 0, is 
(afmU-bflVy=~nT, 
which is in fact the trizomal curve, 
a fmU- b flV + nT = 0, 
C. VI. 
62