5 to &EMARK6 ON PROP. WOOD's THEORY. 



The centrifugal Tliat the point of the circle generating an epicycloid, 

 creased in any ^^^''^'^ ^^ farthest from the centre of the circle round which 

 point of an it revolves, moves fat^ter through space, and consequently 

 epicyc«i j^g^ ^ greater absolute velocity, than the opposite point, % 



am not inclined to dispute. But I presume the motion, 

 that produces centrifugal force, is the rotary motion round 

 that centre, from which the particles of matter have a ten- 

 dency to fly off: and it appears to me, that, the rotary mo- 

 tion of every point in the circumference of the generating 

 circle round the centre of that circle being the same, its 

 velocity with respect to that centre is uniform, and of 

 course there is no alternate increase and diminution of this 

 velocity, vyhich produces the centrifugal force. 

 i^arther il'as. This is perhaps the simplest mode of considering the 

 tration of this subject : but we might take it in another point of view. If 

 we suppose the circle A D ]B E, in prof. Wood's diagram, 

 vol. XXVI, pi. V, fig. 7, to be moving through space in 

 the direction C C, while revolving in the direction A D B ; 

 and put a for the velocity with which A revolves round C, 

 b for the velocity with which B revolves round C, and c for 

 the velocity >yith which the centre, C, is parried iu the 

 direction C C: then, as the motions of A and C are in thp 

 same direction, the absolute velocity of A through space 

 will be a-^-c; and, as the motions of B and C are iu op- 

 posite directions, the absolute velocity of B will be b — c. 

 But the relative velocity of A with respect to C will be sim- 

 ply «; because from its absolute velocity, a -{• c, we must 

 deduct the velocity of C, moving in the same direction, 

 anda-f-c — c obvipusly zza: and again, the relative velo- 

 city of B with respect to the centre C must continue — b; 

 because, if to its absolute velocity, b — c, we add that of 

 C, moving in the opposite difection, >ve shall have b- — c + 

 c z:zb. Now IX and b are clearly equal, because they merely 

 express the velocity, with which two different points iu the 

 circumference of the same circle revolve round its centre: 

 and therefore the centrifugal force is not in any way affected 

 by the epicycloidal motion. 



I am. Sir, 

 Your very obedient humble servant, 

 ^ov, 12, 1810. T. NOQT. 



Remarks, 



