102 Blake on the Teeth of Cog-WheeU. 



therefore the point of intersection be considered as a de- 

 scribing point, and if in the mean time another circle b« 

 made to revolve about a centre b in such a manner, that its 

 velocity shall be constantly equal at the point p to the velo- 

 city of the other circle at the same point, then the point of 

 intersection will simultaneously trace the curve pe and a- 

 nother curve on the plane of the circle b. These by propo- 

 sition 9 are fellow atripsic curves. 



CoR. — Many curves may have either an atripsic or an isos- 

 agistic fellow; for many of the isosagistic curves recede con- 

 tinually both from the centre and from the radius in which 

 they commence. 



Definition. — The corresponding points 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- 

 ways 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 centres of 

 the circles. Hence it is evident, that a fellow atripsic curve 

 may be described for any curve whatever which is capable 

 of having one, in the following manner. 



Let a, Fig. 12, be the centre of a circle to whose plane 

 is attached a curve 1 4 capable of acting without fri^Jtion. 

 Divide the curve 1 4 into any number of indefinitely small 

 equal parts by the points 1, 2, 3, 4, he. and join those 

 points with the centre a of the circle. 



From & as a centre describe concentric circles whose radii 

 are equal to the successive differences ab — a 1, 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 a circle whose centre is b. 



