270 Remarks on the Central Forces of Bodies 



supposed power of the magnet, and we have shown that the 

 same effects would follow without the use of the magnet. And 

 that the impelling or moving power performs no other part in 

 producing the complex effects attendant upon rotation, than sim- 

 ply to move the particles of a mass of matter in circles about a 

 fixed axis, may be clearly shown by the theory of curvilinear 

 motion, which those experiments were designed to illustrate. 

 But without attempting to prove this at present, by abstract math- 

 ematical reasoning, the nature of deflection and the extent of its 

 operation in exciting the central forces may be explained by a 

 reference to the action of electro-magnetism as shown in Fig. 1. 



The bar A, when attracted by the magnet, being supposed to 

 revolve in a circle of one foot in diameter, at the rate of eight 

 revolutions in a second, or 25.14 feet, to determine the amount of 

 deflection in any unit of time, say one fiftieth of a second, the 

 whole space through which it moves in a second may be divided 

 into fifty parts, which will give six inches for each unit of time. 

 If this space be measured on the tangent from B to a;, and on the 

 circumference of the circle to v, the deflection for the one fiftieth 

 of a second would be equal to the square of By, divided by BD, 

 or the diameter. For by dynamics, " if a body revolve uniformly 

 in a circle, the space through which it would move by the action 

 of the centripetal force alone in any unit of time, such as a se- 

 cond, will be equal to the square of the arch described in the 

 same unit divided by the diameter or twice the radius."* And 



the deflection of the bar in the j\ of a second = a75-=^5- = 3 



inches. That is, the deflection from the tangent B"* during the 

 time that the bar would have passed over six inches in that line, 

 is three inches ; and the deflection corresponding with the space 

 Bg, which is equal to two feet, and through which the bar would 



2^ 

 have passed in the j\ of a second, would be=oT = 4 feet, and so 



of any other space. 



Now to show that the amount of this deflection or centrifugal 

 force depends upon the curve in which the bar is moved in a 

 given time, and not upon the moving power, or projectile force, 

 we will cause the same bar, moving with an equal uniform velo- 

 city, to be attracted in a similar manner by the magnet m, attach- 



* Brewster's New Edinburgh Encyclopedia, Art. Dynamics. 



