TAIT'i " THBK1IODYNAMIC8." 



^ mfrh^u,, by supposing the relative frequency of different kinds of 

 enotmntan to be distributed according to the laws of probability. 



The troth of the second law is therefore a statistical, not a mathematical, 

 troth, for it depends on the feet that the bodies we deal with consist of 

 million* of molecules, and that we never can get hold of single molecules. 



Sir Will** 1 " Thomson* has shewn how to calculate the probability of the 

 ooourreace within a given time of a given amount of deviation from the most 

 probable distribution of a finite number of molecules of two different kinds 

 in a vessel, and has given a numerical example of a particular case of the 

 diffusion of gases. 



The same method might be extended to the diffusion of heat by conduction, 

 and the diffusion of motion by internal friction, which are also processes by 

 which energy is dissipated in consequence of the motions and encounters of 

 the molecules of the system. 



The tendency of these motions and encounters is in general towards a 

 definite state, in which there is an equilibrium of exchanges of the molecules 

 and their momenta and energies between the different parts of the system. 



If we restrict our attention to any one molecule of the system, we shall 

 find its motion changing at every encounter in a most irregular manner. 



If we go on to consider a finite number of molecules, even if the system 

 to which they belong contains an infinite number, the average properties of this 

 group, though subject to smaller variations than those of a single molecule, are 

 rtill every now and then deviating very considerably from the theoretical mean 

 of the whole system, because the molecules which form the group do not submit 

 their procedure as individuals to the laws which prescribe the behaviour of 

 the average or mean molecule. 



Hence the second law of thermodynamics is continually being violated, and 

 that to a considerable extent, in any sufficiently small group of molecules 

 belonging to a real body. As the number of molecules in the group is increased, 

 the deviations from the mean of the whole become smaller and less frequent; 

 and when the number is increased till the group includes a sensible portion 

 of the body, the probability of a measurable variation from the mean occurring 

 in a finite number of years becomes so small that it may be regarded as 

 practically an impossibility. 



"On the Kinetic Theory of the Dissipation of Energy," Proe. K.S. Edin., February 16, 1874, 

 Vol. via p. 323, ako iu Tafcwe, Vol. UL p. 441. 



