273 Remarks on the Central Forces of Bodies 



acid upon two contiguous plates of zinc and copper. Centrifugal 

 force may therefore with propriety he considered a physical agent, 

 which is called into action^ by an inscrutable law of nature, lohen- 

 ever matter is made to Tnove in a curve ; — which ought to be no 

 more a subject of surprise than that magnetic force should be ex- 

 cited in a bar of iron by certain chemical operations, the precise 

 nature of which is as little understood as that of inertia. 



The centrifugal principle has been employed as a projectile 

 force from the earliest ages. It would be interesting to notice 

 the extent to which it was used in ancient wars ; and particular- 

 ly to point out, as might be done even with the feeble lights af- 

 forded us, how much Archimedes was indebted to the central 

 forces for the destructive effects of his engines, which I believe 

 to have been no fabled nor imaginary productions of genius. 



As I shall here come in conflict with some generally received 

 opinions, I will give a short extract from Professor Renwick's 

 Elements of Mechanics. Not that he differs from other writers 

 on this subject, but I find that the extract will be useful in ex- 

 plaining what is to follow. " The simplest case of central force 

 is where a body connected with a fixed point by an inflexible 

 straight line is impelled by a projectile force, at right angles to 

 that line. The latter force would have impressed upon the body 

 a motion with a uniform velocity. The body, then, in conse- 

 quence of its connection with a fixed point, describes a circle of 

 which that point is the centre. If the connection were to cease 

 at any point in the curve, the deflecting force would cease to act, 

 and the body would go in a straight line whose direction would 

 be a tangent to the curve. The force acting at any point in the 

 curve must therefore be decomposed into two, one of which is in 

 the direction of the curve, the other in that of the radius."* 



If a ball at A, Fig. 4, weighing one pound, and attached to 

 an inflexible rod AC, two feet long, be impelled by a projec- 

 tile force or moving power at the rate of two entire revolutions 

 in a second, or 25}-^% feet per second, it will have a centrifugal 

 velocity equal to 157.76 feet per second.f Those two velocities 

 then, equivalent to the forces 1.58 lbs. and 9.87 lbs. respectively, 

 constitute the aggregate amount of force acting on the body at 

 any point of the curve or circle ; the former acting in the direc- 

 tion of the curve, and the latter in that of the radius — one caused 



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