S3 



LECTURE IX. 



ON THE MOTIONS OF CONNECTED BODIES. 



The motions of single bodies, acting in any manner on each other, which 

 we have been considering, as far as they belong to the effects of coUision, are 

 of less importance to practical mechanics, than the affections of such bodies 

 as are united, so as either to revolve round a common centre, or to participate 

 in each other's motions, by any kind of machinery. 



It is only within half a century, that the phenomena and effects of rotatory 

 motion have been sufficiently investigated. Newton committed a mistake, 

 which is now universally acknowledged, in his computation of the precession 

 of the equinoxes, for want of attending sufficiently to the subject; and it is of 

 importance in the calculation of many of the effects of mechanical arrange^ 

 ments, that it should be treated in an accurate manner. 



• 



The effect of a moving body, in producing motion in any other bodies, so 

 connected as to be capable of turning freely round a given centre, is jointly 

 proportional to its distance from that centre, and to its momentum in the 

 direction of the motion to be produced. Thus a body, of one pound weight, 

 moving with a velocity of one foot in a second, Avill have three times as great 

 an effect on a system of bodies, to which its whole force is communicated, at 

 the distance of one yard from the centre of their motion, as if it acted only 

 at the distance of a foot, on the same system of bodies : a double weight, or 

 a double velocity, would also produce a double effect. For, supposing two 

 unequal bodies to be connected by an inflexible line, and to move with 

 equal velocities, in a direction perpendicular to that of the line, it is demon- 

 strable, from the principles of the composition of motion, that they may be 

 wholly stopped by an obstacle applied to the centre of gravity, consequently 

 their effects, in turning the line round this point, are equal; here the mo- 



