MECHANICS. 59 



105. If two heavy bodies be fixed to a plane 

 moveable about a given point, the bodies will be in 

 equilibria if that point divide the distance between 

 them in the inverse ratio of their weights or quanti- 

 ties of matter. 



A demonstration of this proposition may be derived 

 from the composition of motion, as is done by NEW- 

 TON, Principia Mathematica, Cor. 11. to the Laws 

 of Motion ; and by VARIGNON, Nouvelle Mecanique; 

 see also HAMILTON, Philosophical Essays^ p. 145. 

 A demonstration on a different principle was given by 

 ARCHIMEDES; it has been improved by MACLAURIN 

 in his Account of Newton's Discoveries, and by VINCE 

 in the Philosophical Transactions. See also WOOD'S 

 Mechanics, Art. 73. 



106. The effect of any heavy body, to produce 

 in any system of bodies, an angular motion about 

 a given centre, is proportional to the product of 

 the mass of the body into the perpendicular drawn 

 from the centre to a vertical line passing through 

 the body. 



a. The axis of motion of any body is a straight line, 

 which remains fixed while the body is free to revolve 

 round it. 



107. The product of any heavy body into its dis- 

 tance, from a vertical plane passing through the 

 axis of motion, is called the momentum of the bo- 

 dy relatively to that axis; and in general, if, 



through 



