100 EQriLII'.KIUM Of 



107. V in Art. D that the 



of the divisibility of matter leads us to tin- supposition that 



body consists of an assemblage of material part id 

 molecules which are held together by their mutual attraction. 

 Now we are totally unacquainted with the nature 

 molecular forces; if, however, w M8Hmfl the two hyji-.t' 



n of any two molecules on each other is the 

 same, and also that its direction is the straight line joining 



then we shall be able to dedi. nditions of < 



librium of a rigid body from those of a single particle. 



To deduce the conditions ofequilH>rium f 

 those of a single particle. 



Let the body be referred to three rectangular axes; and 

 let x^ y,, z l be the co-ordinates of one of its constituent par- 

 ticles; X lt I 7 ,, Z t the resolved parts, parallel to the axes, of 

 the forces which act on this particle exclusive of the mole- 

 cular forces; P lt P 8 , P 8 , ...... the molecular forces acting on 



this particle; 0^,^,7^; a,, y9 2 ,7 a ; ...... the angles their re- 



spective directions make with the three axes of co-ordi: 

 Ihen, since this particle is held in equilibrium by the above 

 forces, we have, by Art. 27, 



=0 ...... (1), 



+ ...... =0 ...... (2), 



= ...... (3). 



We shall have a similar system of equations for each particle 

 in the body; if there be n particles theiv will !>e :;// <-qu.v 

 These 3n equations will be connected one with another. 

 any molecular force which enters into one system of equations 

 must enter into a second system ; this is in consequence of 

 the mutual action of the particles. 



There are two conditions which will enable us to de- 

 duce from these 3;i equations six equations of condition, 

 independent of the molecular forces. These will be t In- 

 equations which the other forces must satisfy, in order that 

 equilibrium may be maintained. 



