4 Br 0. Taylor, On Newton's description of Orbits. [Oct. 28, 



John Reynolds Vaizey, M.A., Peterhouse. 



Besides these, we have lost one honorary member: 



James Prescott Joule, F.R.S. 



It had been my intention to attempt a short biography of 

 each of these; but I found that I had neither time nor materials 

 to perform such a task efficiently. Moreover, they are for the 

 most part too well known, and too intimately connected with 

 this University, to need such commendation. It would, however, 

 be a personal satisfaction to myself to remind you that in Mr 

 Vaizey — who died from the results of an accident at the beginning 

 of this year — the Biological School has lost an energetic worker, 

 whose usefulness as a teacher had been already recognised, and 

 who, had he lived, would probably have risen to eminence in his 

 own special science, Botany. 



The following Communications were made to the Society: 



(1) On Newton s description of orbits. By Charles Taylor, 

 D.D., Master of St John's College. 



The Master drew attention to the fact that the problem of 

 constructing a Conic Section to satisfy given conditions has been 

 treated incidentally with great power and considerable complete- 

 ness in the Principia. A comparison was made between the 

 methods of Newton and the more modern methods: and some 

 improvements were suggested. The way in which Newton passes 

 from cases of real intersection of lines with conies to cases in 

 which real points of intersection do not exist, strongly suggests 

 the question whether he had possession of the idea of imaginary 

 points, which is usually ascribed to a much later period. 



(2) On impulsive stress in shafting, and on repeated loading. 

 By Prof. Karl Pearson, University College, London. 



(3) On Liquid Jets and the Vena Contracta. By H. J. Sharpe, 

 M.A., St John's College. 



1. When liquid flows out of a vessel through an orifice, a 

 liquid particle in contact with the vessel describes an ordinary 

 stream-line as long as the particle is within the vessel, but the 

 moment it escapes through the orifice, this stream-line suddenly 

 becomes also a line of constant velocity, if no force acts on the 

 liquid. In the solutions presently to be given, which are capable 

 of infinite variety, the coincidence between the outer stream-line 

 of the jet and a line of constant velocity is not (as in Kirchhoff's 

 solutions) mathematically perfect, but (even near the orifice, 

 where it is most imperfect) can be made, as will be seen from 

 examples, very close, and as we pass along the jet. becomes very 



