84 Prof. Clausius on Molecular Motion, 



p, tlescribecl around a molecule and having its centre of gravity 

 for a centre, by the term sphere of action of the molecule. 



I again call attention to the fact that the special hypotheses 

 here made, concerning the nature of the molecular forces, are 

 not to be viewed as a necessary condition for the developments 

 which follow ; their only purpose is to facilitate the comprehen- 

 sion by giving something definite to the imagination. It is of 

 no import how we consider the forces by reason of which the 

 molecules change the directions of their motions ; if we but ad- 

 mit that their effects are only sensible at very small distances, 

 we may assume some distance as limiting value for the purpose 

 of being able to neglect the actions from greater distances, and 

 only regard those for smaller ones. A sphere described at this 

 distance may be called a sphere of action. 



(4.) If, now, in a given space, we imagine a great number of 

 molecules moving irregularly about amongst one another, and if 

 we select one of them to watch, such a one would ever and anon 

 impinge upon one of the other molecules, and bound off from 

 it. We have now, therefore, to solve the question as to how 

 great is the mean length of the path between two such impacts; 

 or more exactly expressed, hotufar on an averacje can the molecule 

 move, before its centre of gravity comes into the sphere of action of 

 another molecule. 



We will not discuss this question, however, immediately in the 

 form just given : we will propose instead a somewhat simpler 

 one, which is related to the other in such a manner that the 

 solution of the one may be derived from that of the other. 



If we assume that not all the molecules present in the space 

 are in motion, but that the one chosen for observation is the 

 only one which moves, and all the rest remain fixed in position, 

 the moving molecule in these circumstances also would strike 

 here and there upon one of the others, and the number of blows 

 which it suffers in this case during one unit of time may be com- 

 pared with the numbers which it would experience in event of 

 universal movement. On considering the matter more atten- 

 tively, we are soon convinced that the number of blows amongst 

 moving molecules must be greater than amongst stationary ones, 

 or, which comes to the same thing, that the mean length of the 

 paths which the molecule watched passes over between two con- 

 secutive impacts, must be less in the first case than in the second. 

 The relation between the lengths of the two paths may be defi- 

 nitely found as soon as the velocity of the remaining molecules, 

 in comparison with that of the one watched, is known. For our 

 mvestigations, that case only is of special interest where the 

 velocities of all the molecules are on an average equally great. 

 In this case, if we only consider the mean velocities, we may 



