MATTER AND ITS STATES 



lines to and fro, striking against each other and against the 

 walls of the cage, ever varying their distances apart, yet 

 always remaining equally distributed throughout the cage, 

 i. e., always keeping their average distance apart the same. 



Thus far nothing has been said of any restraining force to 

 counteract in a measure the motion of the particles and keep 

 them from flying apart indefinitely. Such a force might be 

 roughly compared to the walls of the cage just referred to, 

 for it is these restraining walls which prevent the indefinite 

 enlargement of the swarm of angry insects. More accu- 

 rately, the restraining force in the illustration is the sum of 

 the reactions produced by the several impacts of the moving 

 insects against the rigid walls. There is, indeed, such an 

 active restraining force present in all masses of matter ; it is 

 ordinarily made evident, however, only in liquids and solids. 

 This force is the cohesion of the particles themselves. It is 

 probably akin to gravitation, in exhibited larger bodies, 

 and is an inverse function of the square of the average dis- 

 tance apart of the moving particles. That is, the mutual 

 attraction exerted by two particles decreases at the same rate 

 as the square of their distance apart increases. It will thus 

 be seen that this force becomes negligible at a comparatively 

 small distance from any particle. But the particles of 

 liquid^ and solids are so near to one another that their cohe- 

 sive force is sufficient to overcome, to a certain extent, their 

 energy of motion and to hold most of them within certain 

 fixed limits of space. 



The science of thermo-dynamics rests upon another sup- 

 position of the kinetic theory of matter, namely, that the tem- 

 perature of any body is directly due to the kinetic energy of its 

 vibrating particles. Since the mass of any particle remains 

 constant, and the kinetic energy of any moving body is, at 

 any instant, one-half the product of its mass and the square of 

 its velocity (KE \M F 2 ) , it is seen that the average kinetic 



