512 
ON A SPECIAL SEXTIC DEVELOPABLE. 
[373 
which is 
or, what is the same thing, 
(AP-Ba)(- 
+ (A8 -Da)(- 3* 4 ) 
+ (Ae — Ea ) (— t 3 ) 
+ (B8 - D{3)(-8t 3 ) 
+ (Be -E/3)(-3t 2 ) 
+ (De — E8)(—l ), 
= 0, 
a ( Bt 6 + WP + Et 3 ) ' 
+ /3(- At 6 + 8Bt 3 + 3Et 2 ) 
+ 8 (- SAP - 8Bt 3 + E ) 
+ e (— At 3 — 3Bt 2 - D ) J 
and by equating to zero the coefficients a, ¡3, 8, e, we have four equations which are 
easily seen to reduce themselves to two equations only, and which are in fact the 
equations of the tangent line, the equations of this line may therefore be taken to be 
At 3 + SB? + D = 
3At 4 + 8Bt 3 - E=0j 
The coordinates of a point in the nodal curve may be taken to be 
a = V2, b = t, d = — t 3 , e = V2 t 4 , 
and substituting these values in the place of A, B, D, E in the equations of the 
tangent line, we have 
V21 3 + 3t 2 r -r 3 =0, 
3 V2 P + 8t 3 T - V2 t 4 = 0, 
or, what is the same thing, 
r 3 — 3t 2 r + V2 t 3 = 0, i.e. {t + V2 t } {t 2 — V2 ¿t — t 2 } = 0, 
t 4 - 4 V2 ¿ 3 t - 3t 3 =0, {t 2 + V2 tr -1 2 } {t 2 - V2 i-r - i 2 } = 0, 
so that the equations are satisfied by the values of r given by the equation 
t 2 -V2 tr-t 2 = 0, 
that is, by the values 
1±V3 
T ~ V2 
which belong to the points where the tangent line meets the nodal curve. Call these 
values t x and t 2 ; then considering a, b as current coordinates, the values of a : b