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the Jews still use them in some countries for the purpose of 
circumcision. This might account for the rude mode of con- 
struction; it may be conventional and archaic, perhaps pre- 
scribed by the ritual of Druidism. However, in this instance, 
the number found would appear to negative the supposition. 
They were probably intended for daily use, and the moss 
would serve to steady the hand and prevent its slipping.” 
Rey. Joseph A. Galbraith read a communication on the 
Apsidal Motion of a freely suspended Pendulum. 
Sir William Rowan Hamilton entered into some explana- 
tory details respecting the nature and properties of that 
Aconic Function of six vectors, of which he had spoken in a 
recent communication with reference to a certain generali- 
zation or extension of Pascal’s theorem, conducting to a rela- 
tion between ten points on a surface of the second order. 
In the Proceedings of the Royal Irish Academy for July 
20, 1846, it was remarked by Sir W. Rowan Hamilton, that 
the theorem of Pascal might, in the calculus of quaternions, 
be expressed by the following general equation of cones of the 
second degree : 
Ss. BP P= 0, 
B=V(V.aa’.V.a™a"), 
B=V(V.a'a".V. aa"), 
B’=V (V. a"a™. V. aa); 
where 
a, a', a", a", a’, a’ being any six homoconic vectors, and the 
letters S and V being the characteristics of the operations of 
taking respectively the scalar and vector parts ofa quaternion. 
Now it is precisely that function of six vectors a . . a‘, which 
was thus denoted in that communication of 1846, by S. BB’, 
to which it has since appeared to Sir W. Rowan Hamilton 
VOL. Y. N 
