Properties of a Molecule in a Substance. 117 



as on the molecular attraction, the average velocity will 

 always be less than Y v . 



The above equation may be written 



V„=^7 6 (V^) 3 0) 



J. Tib 



by means of equation (3), where W 2 is the same for all sub- 

 stances! at corresponding states. This equation shows how 

 \ v varies with the nature of the substance. 



2 lie Velocity of Sound. 



Consider a molecule moving in a given direction in a 

 substance. Suppose that after collision with another molecule 

 the latter moves off in the same direction with the same 

 velocity. Suppose this process is repeated when the second 

 molecule undergoes collision, &c. It will be evident on 

 reflexion that the velocity with which this disturbance travels 

 is equal to the superior limit of the average velocity discussed 

 in the previous section. In practice, however, the disturbance 

 in a liquid will be propagated with a much smaller velocity, 

 since two molecules before and after collision do not, as a 

 rule, move in the same straight line. Let us consider the 

 propagation of a disturbance in a liquid at right angles to abc 

 in fig. 1 in the direction of the hemisphere. Suppose a mole- 

 cule moving below abc collides with a molecule at b which 

 comes from the other side. After the collision the direction 

 of the path of either of the molecules will lie in the hemisphere 

 of radius r. Each direction we will take as equally probable. 

 The mean of the projections of all the paths I lying in the 

 hemisphere on a line at right angles to abc is 



V f * 



2irr cos 6 . sr . dd . I sin 6 = -> 



where s has the same meaning as before. Thus, on the 

 average, the disturbance passes over the distance ~ during the 

 time a molecule passes over the distance /. The velocity of 

 the disturbance is therefore equal to •—-. But this ex- 

 pression can only give a velocity which agrees roughly with 

 the facts. A disturbance in a liquid consists usually of a 

 wave of compression and rarefaction, which produces first a 

 rise and then a fall of temperature in each portion of liquid 



