The twenty-seven lines upon the cubic surface ... by Archibald Henderson.

ANALYTICAL INVESTIGATION

51

45' — 21(+ ) ( ) (- + -2) =0
(i z 2 U2 2- W zl Y12 Z2
46-722X (- + 4 + WI + 1 1) - Yi + Z) =\^ WIl x2 - kxI / 3 W /
51' = 2,3 + ) + ( )
XI 91 XI W2, - k w,,i IV,
53'- 4 ( - ++ - + + k (2 +1 - + = 0
2 \i 1y2 y\ 2 —i/ )+ +i=~
6/_3'-7r26 / y(z-k+) +( Y-2 -w 1 +, =(( ~o
613 =- 7(. + - -kw + i —=
x —~ w'
21' -727 ZlZ2 (Y2- yl) (W2 - kWl) +-ZlZ2 (X2 - kxl) (W2- kwl)
+ (2 - kl) (2 Zl ^2 - kYz2 Wl) Z + Z1 2 (X2 -- 1) (Y2 - ky1) w = 0
23' -- 728 1 W 12 (,2 - Ik1) (Z2 - kzl) X + -1 W2 (X2 X) (- kZx) ( )
-+ 21 W2 (2 - kXl) (Y2 - k1) - + (2 - kyl) (~2 Z2WI - kX1 Z1 2) = -0
41' = 729 Y1/2 (2 - kzl) (W2 - kl) X + (W2 - kwl) (X,2ylZ - kXly Zl) y
+Y2/12 (2 - kXl) (w2 - kwol) z+yl/2 (2 - kxl) (2 -k z) w = 0
43'- 7'30 (Z2 - '1) (X1Y2Jw2 - kx2l2/1 jl) x + XlX2 (z2 - kZl) (W2 - k vl) y
+ xl 2 (Y2 -- k2l) (W2- k21) Z + X 1x2 (Z2 - kzl) (Y2 - kYl) W = 0
12.36.45 y.2zzlW2 (2 - kzl) x+$2zIZ2 (W2 - kw2) y
-1 7r3l + 2 (y21 (t2 - k1 Z2 I'l) 2 +X2z1Z 2 (Y2 - kl) w = 0
12.35.46 y1 Z2wl (2 - kzl) x + X1izIZ2 (W2 - kw1) y
7r32 + X1l (Y2Zl W2- kl Z2 1) Z + X1 Z1 Z2 (Y2 -k1) 'w=0
14.25.36 21:y2/W2 (z2 - kzl) x +w 2 (2Y1 22 - kly2z1) y
-r 33 +X-21y W2 (2 (- kxl) Z + 2yI 21 (Y2- kyl) =-0
14.26.35 yl/Y2 Wl (22 - kZl) +- Wl (22/122 - t'Xly2z1) Y
-7r34 +Yly2w12 (X2 - kxl) z +lXy2Zl (Y2- Ikl) w= 0
15.23.46 Yw1 UW '2 (z2 - kzl) x + Zi Z1 W2 (w2 - kw1) y
-r35 - +Ylq 12 (X2 - kl) Z -+Y1 (X2sZ2Wl - kXl Zl 2) W —=o
15.26.34 z1 (31/2 02 2- ]x2gl/i) X+f 132Z1 (W 2 — kl) 3Y
-.'36 +4- X2Y1'V (X2- kxl) Z +" 15C2Z1 (3/2- khl) O =
16.23.45 y2w1w2 (z2 - kl) x+ X22w1 (w2- kl) y
r37 +Y2 w1 W2 (x2- kXl) Z +y2 (X2 Z2 w - kx12 ziw) w=-0
4-2