102 Blake on the Teeth of Cog-Wheels. 
therefore the point of intersection be considered as a de~ 
scribing point, and if in the mean time another circle be 
‘made to revolve about a centre 6 in such a manner, that its 
welocity shall be constantly equal at the point p to the velo- 
wity of the other circle at the same aoe then the point of 
wntersection will simultaneously trace the curve pe and a- 
nother aint on the plane of the circle 6. These b y propo- 
si'tion 9 are fellow atripsic curves. 
Cor.—Many curves may have eitheran atripsic or an isos- 
apie: — Ae Aaa of the isosagistic curves recede con- 
from the centre and from the radius” in which 
th sascha 
i on.The CoRRESPONDING Ponts of fellow a- 
tripsic curves are those points which come in contact with 
each other. 
Cor.—Since the contact of fellow atripsic curves is al- 
whys in the line of centres, the sum of the radii drawn from 
the centres of the circles to any two corresponding points of 
the curves, is equal to the distance between the 2 ta of 
the cireles. Hence itis evident, thata fellow atripsic cu 
be described for any curve whatever which is apatite 
prs sete one, in the following manner. 
» Let a, Fig. 12, be the centre of a circle to so Sono 
is attached a curve 1 4 capable of acting without 
Divide the curve 1 4 into any number of iadefinitely roa 
equal parts by the points 1, 2, 3,4, &c. and join those 
points with the centre @ of the circle. 
‘rom 6 as a nt cles whose radii 
ave equal to the successive differences ab—a a; ‘ab—a 2, 
ab—a 3, &c. From any point in the first concentric circle 
with a radius equal to one of the divisions of the curve, in- 
tersect the next concentric circle ; and from the point of 
intersection with the same radius intersect the next, and so 
on till all be intersected. Then a curve traced through the 
several points of intersection will be a fellow atripsic curve 
for acircle whose centre is 
