222 



Memoirs of the American Academy of Arts and Sciences. N.S. 

 Vol. III. 4to. — By the Academy. 



The Ethnological Journal. No. 8. 8vo. — By the Editor. 



Remarks on the Impx'ovement of Tidal Rivers, illustrated by refer- 

 ence to works executed on the Tay and other rivers. By 

 David Stevenson, F.R.S.E. 8vo. — By the Author. 



Annates des Sciences Physiques et Naturelles, d' Agriculture et 

 d' Industrie, publiees par la Societe Royale d'Agriculture, &c., 

 de Lyon. Tom. X. 8vo. — By the Society. 



Annales de la Societe Linneenne de Lyon. Annees 1845—6. 8vo. 

 — By the Society. 



Proceedings of the Royal Astronomical Society. Vol. IX., No. 2. 

 8vo. — By the Society. 



Monday, February 19, 1849. 

 Mr CADELL in the Chair. 



The following Communications were read : — 

 1. Abstract of a Communication on Rolling Curves. 



This paper commenced with an outline of the nature and history 

 of the problem of rolling curves, and it was shewn that the subject 

 had been discussed previously, by several geometers, amongst whom 

 were De la Hire and Nicole in the Memoires de I' Academic, Euler, 

 Professor Willis, in his Principles of 3Iechanism, and the Rev. H. 

 Holditch in the Cambridge Philosophical Transactions. 



None of these authors, however, except the two last, had made 

 any application of their methods ; and the principal object of the 

 present communication was to find how far the general equations 

 could be simplified in particular cases, and to apply the results to 

 practice. 



Several problems were then worked out, of which some were ap- 

 plicable to the generation of curves, and some to wheelwork ; while 

 others were interesting as shewing the relations which exist between 

 different curves ; and, finally, a collection of examples was added, as 

 an illustration of the fertility of the methods employed. 



