AND OF THE SECOND LAW 17 



a, given constant. (2) Another person, in com- 

 plete ignorance of the velocities so assigned, scatters the spheres 

 at haphazard throughout S. And they start from the initial 

 positions so assigned by (2) with the velocities assigned to them 

 respectively by (i)." 



The system thus synthetically constructed would without 

 doubt, at the start be " molekular-ungeordnet " in fact, it is as 

 near an approach to chaos as is possible in an imperfect world. 

 But there is reason to doubt if it would continue to be thus " molek- 

 ular-ungeordnet." For the distribution of velocities is according 

 to any law consistent with the above-mentioned conditions and 

 some such laws would lead to results hostile to the Second Law, 

 and then we may safely say such laws of velocity distribution 

 would never occur in Nature and would therefore belong to the 

 cases which have been specially excepted. 



Now there are mechanical systems which possess the entropy 

 property and it has been truly said that the Second Law and irre- 

 versibility do not depend on any special peculiarity of heat motion, 

 but only on the statistical property of a system possessing an 

 extraordinary number of degrees of freedom. In this sense 

 Professor J. W. GIBBS treated Mechanics statistically and showed 

 that then the properties of temperature and entropy resulted. 

 This matter has already been touched upon, but as numerous 

 degrees of freedom is a feature of the " elementary chaos " under 

 consideration it deserves repetition here and more than a passing 

 mention. 



Illustration of Degrees of Freedom. Refer a body's motion to 

 three axes, X, Y, Z. If a body has as general a motion as possible, 

 it may be resolved into translations parallel to the X, Y, Z axes 

 and to rotations about these axes. Each of these two sets furnishes 

 three components of motion or a total of six components; then 

 we say that the perfectly unconstrained motion of the body has 

 six degrees of freedom. If a body moves parallel to one of the 

 co-ordinate planes, we say it has two degrees of freedom. When 



