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Fig. 2. 

 si. 



of lim(. He imist therefore exert liis strength at A in the direction of 

 the rcsultiint of the two forces with an effort which is equal in amount 

 to their mechanical equivalent. If we make A:; t>nd Ac in length pro- 

 portionate to the forces 3 and 10 resjiectivelv, then the diagonal Ay" 

 of the parallelogram AtJ'c, will show the dirtetion in which lie draws 

 at the string, and j/ 10- + 3- := 10-44 lb. will be the amount of force 

 necessary to give the required velocity; of which, as shown above, 

 two-thirds are expended in retaining the stone in the circle. Xow it 

 would be about as easy to show that a man can draw at a flexible cord 

 secured to a stationary object with a force equal to 10 pounds, and at 

 the same time press against that oh^ec\, by means of the cord, ■f;\i\\'.x 

 force equal to six pounds, as to prove that the centrifugal force in this 

 case is the immediate efl'cct of the moving power. The man moves 

 liis hand in a small circle and jnills at a stone, nearly in the direction 

 of the string to whicli it is attached, with a force equal to six times 

 the weight of the stone, and yet, according to the popular belief, he 

 not only imparts directly to it all the force with which it is projected, 

 but dashes it off at right angles to the thong, as if it were moved at 

 the end of a lever. 



The thong of the sling, from what is said above, may be considered 

 as in the place of an inflexible rod, the hand resisting tlie pressure that 

 would act as a strain upon an axle at c ; and if such a rod had a handle 

 ut A, the same effect might be produced. But it would cause great 

 friction and strain npon the axle, and to obviate those difficuhies, we 

 will consider the circle ST as jjassing through the centre of the rim of 

 A fly-wheel connected by arms with the small circle AB, representing 

 a nave working on an axle at c. If the rim be supposed to weigh I JO 

 lb. it might easily be revolved at the rate of two entire revolutions in 

 a second by a handle at A, which is four inches from the centre, or so 

 considered for illustration. M'hen the winch A is moved about the 

 axis, the force may be considered as acting by repeated slight impulses, 

 as if it were applied at right angles to the radius of the circle, at each 

 instant of time along the side of a polygon with an infinite number of 

 ^ides, drawn within the circle. If the sides of the polygon be one 

 hundred in number, they would be one fourth of an inch long, and then 

 one and a half inches in the larger circle ST, will be the length of each 

 side of a polygon along which the centre [larticles of the rim may be 

 supi>osed to move. As the proportion of the circle ST is to A B as 

 six is to unit, amoving power acting on the latter at the winch A, with 

 a given force, through g-, //, one fourth of an inch, will move the rim 

 through /, /•, equal to six times that sjiace, with one sixth of the force 

 applied; hai -as ilic niomevl of rolalion is tquul /u force mulliplied by 

 l(Vtragc,i\\Q whole amount of force upon the rim through that space 

 must be exactly equal to the power applied through the fourth of an 

 inch upon A. And so of each side of the two polygons rcspe< lively. 

 15ut they are considered infinitely small and ultimately become parts 

 of tlie two circles ; Ihe power therefore must be applied in a circle, 

 luid the parlicles of the rim must be propelled in circles with a force 

 exactly equal to thai power. Consequently, the moving power, ap- 

 plied to a fly-wheel or to any other revolving body, cannot be expended 

 in pressing tlic particles of such bodies from the centres nor in the 

 direction of tangents to the circles in which they revolve. And this 

 is evident from the fact, that such moving bodies cannot give out nor 



impart, in any manner whatever, more force than is applied to revolve 

 them. And that force is not only (rjual to the power applied, but it is 

 always returned in the circle in which the body moves, a7iij in a direc- 

 tion contrary to thai in which it teas received. "If a wheel spinning on 

 its axis with a certain velocity be stopped by a hand seizing one of the 

 spokes, the effort whicli accomplishes this is exactly the same, as,' had 

 the wheel been pre\ iously at rest, would have put it in motion in the 

 ojiposite direction with the same velocity."* The force applied to 

 the winch, in the case above, was wholly expended in giving velocity 

 to the rim, with the slight exceptions mentioned. Consequently, 

 whatever other forces ra.iy have operated on the rim whilst revolving 

 must have originated in some other way. And yet those extraneous 

 forces would amount to 14bO lb., as shown by the above formula, the 

 rim weighing 1501b. and being revolved at the rate of two entire re- 

 volutions in a second. Xo part of this force could be communicated 

 to the arm of a man who would stop such a wheel by seizing one of 

 the spokes, because each partiiit of the rim is acted upon by the cen- 

 tral forces, which are always opposite and equal, in the direction of 

 the radius of the circle a/ that jjoint ; and it has just been shown that 

 the moment of rotation of each particle is equal to the moment of ro- 

 tation of the power that impels it, but " as the direction of the centra! 

 forces is in that of the radius, their moment of rotation is equal to uo- 

 thing."-'- Consequently the centrifugal force cannot act upon the hand 

 that stops the wheel. If, indeed, the centrifugal force were increased 

 to sixteen times the above amount, the result would be the same. By 

 giving the wheel eight revolutions in a second we would have the 

 central force = 14b0 X hi = 23,GsO lb. and the force in the circle 



would be := 



1-2-57 X 8 X 130 



= 92.jlb. Here the centrifugal force is 



16 



twenty times greater than the force in the circle, and yet as the cen- 

 tral force would act in the direction of the radii, its moment of rotation 

 would be =r 0. Or, what is more strictly the fact, the central force 

 acts by pressure, and a resultant from that pressure and the force in 

 the circle is the consequence, but so long as resistance from cohesion 

 continues, neither motion nor pressure can be imparted to another body 

 by the central force. These are the obvious reasons why no greater 

 force could be communicated by the rim than the 925 lb., which it only 

 possesses as a mass of matter moving in a circle. 



The following experiment may be considered as a practical illustra- 

 tion of the theoretical views given above. A whirling table may be 

 made of any convenient size, we will say, for the present occasion, 

 rather more than four feet in diameter, to revolve horizontally on fric- 

 tion rollers placed near the centre ; the axle being a hollow cylinder, 

 through which four cords pass to the floor to be connected with a tin 

 tube for containing shot or some other weight. The cords are brought 

 over the pulleys p, p, p, p, fig- 3, at the centre, and secured to the 

 dishes d, d, d, d, weighing one pound each, and moving, with very 



Fi3- 3. 



little friction, on little wheels adapted to the strips or rails r, r, r, r. 

 By connecting this table with wheel-work, having bands or teeth act- 

 ing on the lioUow cylinder as a spindle, by means of a weight or power 



*" Kater and l^ardner on Mechanics, p. 24. 

 Kcnwick's Matliematics. Art. C'omposiiion of Forces. 



