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 Nicolè in the Mémoires de l'Academie, Euler, Professor Willis, in his Principles of Mechanism, 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.