Blake on the Teeth of Cog-Wheels. 89 



mark here that it is by no means intended that all the 

 curves which are included under this name are adapted to 

 practical purposes, for even the epicycloidal curves are not 

 all so. — But it is not improbable that further investigations 

 may show that some of them are better adapted to mechan- 

 ical purposes than any of the epicycloidal curves. 



It is another great desideratum in wheel work that the 

 teeth should act without friction. — But this point, though 

 it hardly deserves less attention than the other, has been 

 but little noticed by men of science. Some of the mathe- 

 maticians before mentioned seem to have supposed that the 

 epicycloidal curves act without friction. And the writers 

 of practical treatises on the teeth of wheels, who have de- 

 rived their ideas chiefly or wholly from the writings of these 

 mathematicians, have, 1 believe, all of them, either taken 

 the same for granted, or asserted it in unequivocal lan- 

 guage.* I propose to shovi^ in a iew remarks, under the 

 head " Epicycloids," not only that these curves do not pos- 

 sess this property, but that it is impossible even in theory 

 that any action between the teeth of wheels, whatever may 

 be their form, should be uniform in force and velocity, and 

 at the same time without friction.f 



But dispensing with the desirable property of uniform ac- 

 tion, it is possible to give to the teeth of wheels such a form 

 that they will act without friction ; and when practical means 

 shall have been devised of forming them with facility, they 

 may probably be adopted with advantage in many mechan- 

 ical operations where small variations in force and velocity 

 are unimportant. The curves which possess this property, 

 like the Isosagistic curves, are infinitely numerous, and to 

 avoid circumlocution I have assigned to these also a name 

 significant of their common property. They will therefore 

 be treated of under the head Atripsic curves, where the 

 general principle which embraces all possible curves of this 

 sort, will be given ; together with the means of determining 



* See Smith's Eanorama of Arts and Sciences, — Rees' Encyclopedia; ar- 

 ticles, Mill Work and Clock Movement, — Imison's School of Arts, — Grego- 

 ry's Treatise on Mechanics, &c. 



t This remark is intended to be applied to all teeth whose acting faces are 

 m'lde np of straight lines parallel to the axis of the wheel. It is not true of 

 the spiral or Helicoid teeth, invented a few years since in France, and now 

 used with °:raat success in some branches of mechanics in this country. 



Vot.. VIT.— No. 1 . 12 



