Blake on the Teeth of Coz-Wheels. 87 
that they may act with a constant and equable force, and 
produce a uniform velocity. Several of the most eminent 
mathematicians of the last century gave their attention to 
this branch of mechanical science. ‘I'he first who came to 
any practical result was Olaus Roemer, sae celebrated as- 
tronomer and mechanist of Denmark. He discovered that 
wheels possess the property of sastveiiieg a uniform force 
and velocity, when sections of the acting faces of the teeth 
one of them are the incipient portions 0: extertor Epicy- 
same generating circ 
M. De \a Hire soon wialieneed took up the stibjeee ov" 
proved that it is not necessary, as Roemer had supposed, 
that the diameter of the generating circle’ should be half 
that of the circle on which the interior epicycloid is ‘déscri- 
bed, since the same result will follow if the generating cir~ 
cle be of any other diameter whatever. He also 
that it is not necessary in order that the teeth’ may possess 
the property of transmitting a uniform force and’ velocity, 
“that they should be exact epicycloids in the sense to 
ich geometers usually restrict that term, since they will 
ute, and of an epicycloid.” 
The subject was afterward ——— by Camus, fio 
ler, Varignon, and others on the Continent. But their la- 
bours, though they afforded some ara ‘elucidations “of 
ae contributed nothing to extend it beyond the dis* 
cmevineok De la Hire. Nor has any abit iat oe. been’ 
since made in the science, except by Professor’ 
of Edinburgh, who pointed out a single spetieu on tot 
Possessing this property, which are not embraced in” the 
sfieyelcidat principle of De la Hire. These teeth’ are in 
the form of the involutes of circles, smaller than the pitch 
circles, and concentric with them, whose diameters are to 
each other as the diameters of the pitch circles. Mr. 
Brewster has erroneously remarked that “the principle of 
these teeth is not new;” and classed them among the’epi# 
