AND OF THE SECOND LAW 23 



first likely to share these views with said man in the street, and 

 at best feels that its introduction is of remote interest, far fetched, 

 and tends to hide and dissipate the kernel of the matter. The 

 student must disabuse himself of these false notions by reflecting, 

 how much there is in Nature that is spontaneous, in other words, 

 how many events there are in which there is a passage from a 

 less probable to a more probable condition and that he cannot 

 afford to despise or ignore a Calculus which measures these 

 changes as exactly as possible. 



In this Connection BOLTZMANN says: (W. S. B. d. Akad. d. 

 Wiss.,. Vol. LXVI, B 1872, p. 275). 



"The mechanical theory of heat assumes that the molecules 

 of gases are in no way at rest but possess the liveliest sort of motion, 

 therefore, even when a body does not change its state, every one 

 of its molecules is constantly altering its condition of motion and 

 the different molecules likewise simultaneously exist side by side 

 in most different conditions. It is solely due to the fact that we 

 always get the same average values, even when the most irregular 

 occurences take place under the same circumstances, that we can 

 explain why we recognize perfectly definite laws in warm bodies. 

 For the molecules of the body are so numerous and their motions 

 so swift that indeed we do not perceive aught but these average 

 values. We might compare the regularity of these average values 

 with those furnished by general statistics which, to be sure, are 

 likewise derived from occurrences which are also conditioned by 

 the wholly incalculable co-operation of the most manifold external 

 circumstances. The molecules are as it were like so many indi- 

 viduals having the most different kinds of motion, and it is only 

 because the number of those which on the average possess the 

 same sort of motion is a constant one that the properties of the 

 gas remain unchanged. The determination of the average values 

 is the task of the Calculus of Probabilities. The problems of 

 the mechanical theory of heat are therefore problems in this 

 calculus. It would, however, be a mistake to think any uncertainty 



