838 
Proceedings of the Royal Society 
on the co-ordinate planes of ZX and XY respectively by the planes 
1, 2, 3 produced, we shall get 
and 
6 vol. SA 2 CoB, ,, I'yAl 3 
I a 2 c i II a A II a \ c i II <Ws I 
6 vol. SA 3 B 3 C, = — — n — I "iMs I 8 — 
II H a f >e l II a i^2 C 3 I 
with corresponding expressions for the tetrahedra similarly formed, 
and having their vertices at P, Q, and E respectively. 
S 
But, from the geometry of the figure, we have 
PQBS = PDFC + EEBF - QADE - SABC, 
where EABCD is the figure formed on any co-ordinate plane by the 
planes 1, 2, 3, 4 produced. 
Hence, denoting by (1 2 3) any one of the above three expressions 
obtained for volumes, we have 
6 vol. PQRS = (234) - (1 34) + (1 24) - (1 23) 
^2 ^ 3^4 I I ^ 3^4 I I ^ 1 ^ 2^4 I I 
*y (II). 
