Blake on the Teeth of Cog-Wheels. 97 
Cor.—Since (prop. 4. Cor. 3.) the point of action and 
describing point constantly coincide, the point of action or 
t of the acting curves does not rena ad remain in 
the line of centr 
Pror. 9.—No Isosagistic curves act apon: each other 
without friction. 
gi, gh Fig. 6. be two isosagistic curves in action at 
the point gand attached to the circles a and 6 in contact at-e: 
Now (by prop. 2. Cor.) during the action of the isosagistic 
curves the velocities of the circles at e are equal. -Conse- 
quently the circles may be considered as rolling together at 
the point e. ‘Then(by prop. 3.) the point a considered asa 
describing point traces a curve ad on the extended plane of 
the circle 4 which is constantly perpendicular to the line ae 
>that is, to the line of centres. "Now let it wea sg that 
: i plese : 
curve which is constantly perpendicular to the line ag. But 
the line Aa does not constantly coincide with the line ae, ior 
(prop. Cor.) the point g is not consiantly in the line ad. 
ook te the — ad is constantly perpendicular, at the 
Same point of it, to two. different lines which do not constantly 
Therefore the 
&' do not roll upon = other aa si friction. The same 
eer be proved of any other fellow argue curve se! oo 
Enierctoms.. 
Sa Whanth aa e 
describing tis in the. mi er a ‘the curve genera- 
ted on one a fellow. circles is an exterior epicycloid and 
thaton the other is an interior epicycloid. When the diame- 
ter of the generating circle is half that of the circle on which 
the interior epicycloid is described, the interior epicy- 
me aw a straight line tending to the centre of the circle ; 
and the forms traced on the planes of the circles are those 
which are recommended in the practical. treatises, for fellow 
teeth which are designed to act sihes-a wholly before or 
~ r-the line of centres. the interior epicy- 
neds curve the action is before the line of cen- 
Aa Me fF 13 
