450 
ON THE TRIPLE TANGENT PLANES OP 
[76 
= w 11, + kyzx, 
= wmm / 4- kzxy, 
= w nn / + kxyz, 
— w 1,1 + kyzæ, 
= wm ; m + kzxy, 
= w n/ri 4- kxyz, 
= w pp, 4- kgyz, 
= w qq / 4- ^zx, 
= w rr / + kÇxy, 
= w pp, 4- k%yz, 
= w qq / 4- krfix, 
= w rr / 4- &£xy, 
(being the forms containing 
w, out 
of 
a complete 
system 
of one hundred and 
twenty 
different forms). 
The forty-five 
planes pass five 
and five through the twenty-seven lines 
in the 
following manner : 
(«i) (w, 0C, f, X, Ï) 
...12, 
( a i) {oc, 
g> 
h , 1,1 ).. 
.34, 
(a 7 ) (x, m,, n, q,, r) 
... 46, 
(&i) (w, y, V, y,y) 
2', 
Q>i) {y> 
h, 
f , m, m,) . 
• 24, 
(6 7 ) (y, n,, 1 , b, p) 
... 5, 
(Cj) (w, z, Ç, z, z ) 
... 1, 
(C4) (z, 
f , 
cr n TI Ì 
Ö > 11 ? AA / / • 
• 14, 
(c 7 ) (z, 1, , m, p„ q) 
... 5', 
(<h) (f, f, 6, p, p,) 
... 2, 
(<h) (x, 
g> 
h , 1 , 1/ ) . 
. 56, 
(<h) (x, m„ 5 , q„ r ) 
... 36, 
(&s) (V, g, Q, q, q,) 
... 23, 
(M (y> 
h, 
f , m, m,) . 
• 4, 
(6 8 ) (ÿ, fi, , I , b, p) 
...26, 
(c 2 ) (f, h, 0, r, r,) 
... 3', 
(c 5 ) 
f , 
g-n-b).. 
• 4', 
(Cg) (z, I, , m, p,, q) 
...16, 
(«3) (1, f, p, p,) 
... V, 
(««) (x, 
m, 
n / » q> b ) •• 
. 35, 
(a 9 ) (x, m , n,, q , r, ) 
... 45, 
(&s) 0/, g, ^ q> q,) 
.. 3, 
(&g) (y, 
n, 
\ > r , P/) •• 
.25, 
(M (ÿ, n , 1, , r , p,) 
... 6, 
(Cg) (f, h, 0, r, b) 
..13, 
(Cg) (z, 
1 , 
m,, p , q,) .. 
. 15, 
(c 9 ) (z, 1 , m,, p, q,) 
... 6', 
where each line may be represented by the letter placed oppositive to the system 
of planes passing through it. The twenty-seven lines lie three and three upon the 
forty-five planes in the following manner : 
O) 
(hbiCi) 
(f) 
(Zaffili 
O) 
(p) 
a 3 b 7 c 6 , 
(0) 
U2&2^2 > 
(g) 
b 3 c 5 a 4 , 
(m) 
b 5 CyCtÿ, 
(q) 
b 3 c 7 a 6 , 
(0) 
(13^3^3 > 
(h) 
C3®5^4 > 
(n) 
c 5 ci 7 b â , 
(r) 
c 3 ci 7 b e ,