MOLECULAB, CONSTITUTION OF BODIES. 427 



thorough study of the motions of an immense number of particles, developed 

 the methods and ideas of modern molecular science. 



To him we are indebted for the conception of the mean length of the 

 path of a molecule of a gas between its successive encounters with other 

 molecules. As soon as it was seen how each molecule, after describing an 

 exceedingly short path, encounters another, and then describes a new path in 

 a quite different direction, it became evident that the rate of diffusion of gases 

 depends not merely on the velocity of the molecules, but on the distance they 

 travel between each encounter. 



I shall have more to say about the special contributions of Clausius to 

 molecular science. The main fact, however, is, that he opened up a new field 

 of mathematical physics by shewing how to deal mathematically with moving 

 systems of innumerable molecules. 



Clausius, in his earlier investigations at least, did not attempt to determine 

 whether the velocities of all the molecules of the same gas are equal, or whether, 

 if unequal, there is any law according to which they are distributed. He 

 therefore, as a first hypothesis, seems to have assumed that the velocities are 

 equal. But it is easy to see that if encounters take place among a great 

 number of molecules, their velocities, even if originally equal, will become un- 

 equal, for, except under conditions which can be only rarely satisfied, two 

 molecules having equal velocities before their encounter will acquire unequal 

 velocities after the encounter. By distributing the molecules into groups ac- 

 cording to their velocities, we may substitute for the impossible task of following 

 every individual molecule through all its encounters, that of registering the 

 increase or decrease of the number of molecules in the different groups. 



By following this method, which is the only one available either experi- 

 mentally or mathematically, we pass from the methods of strict dynamics to 

 those of statistics and probability. 



When an encounter takes place between two molecules, they are transferred 

 from one pair of groups to another, but by the time that a great many en- 

 counters have taken place, the number which enter each group is, on an average, 

 neither more nor less than the number which leave it during the same time. 

 When the system has reached this state, the numbers in each group must be 

 distributed according to some definite law. 



As soon as I became acquainted with the investigations of Clausius, I 

 endeavoured to ascertain this law. 



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