438 



mulse, masses are represented by weights ; so that any effective 

 accelerating force/ is supposed to be due to a pressure P acting on 



a mass W, and their relation expressed thus, /= ~. 



The mass of any arc of the circle is denoted by -7- ; being the 



angle at the centre, and c the mass of a given length / of the cir- 

 cumference. The terms of all the formulae are thus made homo- 

 geneous. 



The centre of gravity of the disc, axle, and the ring which carries 

 the pivots of the axle is fixed, and the whole is moveable about that 

 centre in any manner, subject to the condition that the line of the 

 pivots of the ring is always horizontal, unless when detached from 

 the stand. Let this straight line of the pivots be denoted by AB, 

 the common centre of the disc and ring by O, the extremities of the 

 axle by N and S ; and ON=o. 



Let M denote the place of a particle of the disc, its position being 

 determined by the angle AOM (0), and let M' be another point in 

 the disc indefinitely near to M, but more remote from A, the direc- 

 tion in which the disc will presently be supposed to revolve being 

 AMM'B. 



A given force F is applied at N perpendicular to the plane 

 ANBS, so that the disc may describe an angle ^ round AB in the 

 time t ; whereby the points Mand M' describe the two arcs MP=y 

 and M'P > =y' simultaneously. Suppose the circumference of the 

 circle AMB to be divided into four quadrants, commencing at A, 

 where y=O, and corresponding with the four ranges of value of 

 through each of four right angles ; suppose M and M' to be in the 

 first quadrant, so that y' is greater than y ; then if the disc be sup- 

 posed to revolve, a particle at M is carried from the line MP to the 

 line M'P', so as to acquire an increase of velocity from the plane 

 AMM' independently of the force F, and consequently (by the first 

 of the two verbal formulae) all the momentum so acquired by the 

 particle is lost to the disc, ring, &c., which are thus impelled as by 

 a force in the direction PM or P'M', so as to oppose the rotation 

 imparted by F, but to impart another round O in the direction 

 ANB in the plane of the ring ; i. e. in a plane perpendicular to that 

 in which F acts. A force having the same tendency is found, by 



