86 LECTURE IX. 



flexible line, and to be moving with equal velocities in parallel directions; if 

 an immoveable obstacle be applied, so as to form a fulcrum, at the common 

 centre of gravity, they will, as we have already seen, be wholly stopped: but 

 if the fulcrum be applied to any othcf part of the line, one of the bodies 

 will move forwards, and the other backwards, with a velocity which may 

 easily be determined by calculating their rotatory power with respect to the 

 fulcrum. If the fulcrum be applied at a point of the line continued beyond 

 the bodies, the one will lose and tlie other gain velocity, since the quantity 

 of rotatory power will always remain unaltered: that point only which "is de- 

 nominated the centre of oscillation retaining its original velocity. Now the 

 same inequality in the motion of the bodies, and consequently the same an- 

 ;giilar velocity of rotation will be produced, if the connected bodies be ini- 

 tially at rest, and tlie fulcrum be applied to them with the same relative velo- 

 city. For example, if a straight rod or wire receive an impulse at one end in 

 a transverse direction, the centre of oscillation, Avhich is at the distance of 

 two thirds of the length from the end struck, will at the first instant remain 

 at rest, conseciuently the centre will move with on^ fourth of the velocity of 

 the impulse, and this must be the velocity of the progressive motion of the 

 rod, since the centre of gravity of any body, which is at liberty, moves al- 

 ways with an equable velocity in a right line, while the whole rod Avill also 

 revolve equably roimd its centre, except such retardations as may arise from 

 foreign causes. In a similar manner the computation may be extended to 

 bodies of a more complicated form. Thus it has been calculated at what , 

 point of each planet an impulse must have operated, in order to communicate 

 to it at one bloM' its rotation and its progressive motion in its orbit. 



Those who have asserted that the motion of the centre of gravity of a body 

 can only be produced by an impulse, which is either wholly or partly.directcd 

 towards it, have obviously been mistaken. The centre of oscillation is the 

 only point which remains at rest with regard to the first eflPcct of the stroke, 

 and the centre of gravity, which nev^r coincides with the centre of oscilla- 

 tion, moves in the direction of the impulse, while the parts beyond the cen- 

 tre of oscillation begin to move in a contrary direction. Hence it is, that 

 a thin stick may be broken, by a blow on the middle, without injuring the 

 glasses on which it is supported: for the ends of the stick, instead of being 

 depressed by the stroke, would rise Avith half the velocity of the body wtich 



