144 ON THE MECHANICAL DESCRIPTION OF CERTAIN SEXTIC CURVES. [504 
2°. Here A = 0, B = 0, G = 46 (b — a), D = 46 (b + a) ; the equation contains the 
factor v, and throwing out this and also the constant factor 4b, the equation is 
v [(6 — a) + (b + a) w 2 ] 4- 2au = 0, 
viz. v is given as a rational function of u. 
3°. Here A = 4a (a — c), B = 0, (7 = 0, D = 4<a (a + c); or, dividing by 4a, the 
equation is 
(a — c) + 2 a uv + (a + c) wV = 0; 
viz. this is 
(uv + 1) [(a + c) uv + a — c] = 0, 
which may be reduced to 
(a + c)uv + a — c =0, 
giving u or v each a rational function of the other. 
I do not discuss the theory in detail, but only remark that in each case there is 
a conic thrown off, and that in place of the sextic we have a unicursal (or trinodal) 
quartic curve.