177 



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." 



Rev. 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 : 



S./30'j3"=O, 

 where 



/3 = V (V.aaW.aV), 



j3"=V(V.a n a m .V.a v a); 



a, a 1 , a n , a ra , a w , a v 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 of a quaternion. 

 Now it is precisely that function of six vectors a . . a v , which 

 was thus denoted in that communication of 1846, by S. /3/3'j3", 

 to which it has since appeared to Sir W. Rowan Hamilton 

 vol. v. N 



