13 
Ordinary Meeting, October 30th, 1877. 
Dr. R Angus Smith, F.R.S., Vice-President, in the Chair. 
Professor Osborne Reynolds, F.RS., showed and ex- 
plained some models illustrative of the manner in which 
waves enter upon the undisturbed surface of water. 
Professor W. Boyd Dawkins, F.RS., exhibited and ex- 
plained the results of the Creswell Caves Exploration of 
1876. 
Ordinary Meeting, November 13th, 1877. 
E. W. Binney, F.RS., F.G.S , President, in the Chair. 
“Note on Envelopes and Singular Solutions,” by Sir 
James Cockle, F.R.S., Corresponding Member of the 
Society. 
1. Leibnitz (16.94) showed how to find the curve formed 
by the continuous intersection of an infinity of curves 
included, on making the parameter vary, in one and the 
same equation. This gives rise to a new equation by which 
a value of the parameter is expressed as a function of the 
coordinates. And this value substituted in the proposed 
equation gives at once a finite equation for the required 
curve. Applying this method to the question of finding the 
curve whereof the normals have a given relation to the 
portions of the axis of abscissae intercepted between the 
origin and the normals, Leibnitz considers this curve as 
formed by the continuous intersection of an infinity of 
circles having their centres on the axis. Then the radii of 
Proceedings — Lit. & Phil. Soc. — Vol. XVII. — No. 2 — Session 1877-8. 
