It is the editor’s intention to pursue the inquiry and should he discover a clear theory and systematic practice in the use of the involute, he shall feel himself bound to give his views to the public in a separate treatise. He thinks he perceives a wide field, but is free to confess that his vision is as yet obscure. What he has given on the involute is more than was due from him, as editor of Camus, who treated only of the epicycloid, but the zeal of a new convert to any doctrine is not easily restrained. So far as the writer knows this is the first _real_ appreciation of the value of the involute curve for tooth outlines, and Hawkins should be given a credit which he has not received,[64] especially as he points the way, for the first time, to the possibility of a set of gears any one of which will gear correctly with any other of the set. It was thought at that time that there should be two diameters of describing circles used in each pair of gears, each equal to the pitch radius of the opposite wheel or pinion. This gave radial flanks for all teeth, but made the faces different for each pair. The use of a single size of describing circle throughout an entire set of cycloidal gears, whereby they could be made to gear together in any combination, was not known until a little later. [64] John Isaac Hawkins was a member of the Institution of Civil Engineers. He was the son of a watch and clock maker and was born at Taunton, Somersetshire, in 1772. At an early age he went to the United States and “entered college at Jersey, Pennsylvania, as a student of medicine,” but did not follow it up. He was a fine musician and had a marked aptitude for mechanics. He returned to England, traveled a great deal on the Continent, and acquired a wide experience. He was consulted frequently on all kinds of engineering activities, one of them being the attempt, in 1808, to drive a tunnel under the Thames. For many years he practiced in London as a patent agent and consulting engineer. He went to the United States again in the prosecution of some of his inventions, and died in Elizabeth, N. J., in 1865. From a Memoir in the “Transactions of the Institution of Civil Engineers,” Vol. XXV, p. 512. 1865.