MOLECULAR MOTIONS AND TEMPERATURE 165 



other words, we have obtained an expression which 

 states the facts of Boyle's Law. 



The molecules, considering their motions of trans- 

 lation only, have what is called three " degrees of 

 freedom. " A railroad train has only one degree of 

 freedom. It may move back and forth along only 

 one direction, namely that of its track. A pedestrian 

 has two degrees, for he may move along a north and 

 south direction and also along an east and west direc- 

 tion. Having these two degrees of freedom he may, 

 of course, move anywhere in the plane of the earth's 

 surface at his locality. Thus, if he moves northeast, 

 we may think of each small displacement in that 

 direction as the result of small displacements to the 

 north and to the east. An aviator, on the other hand, 

 has three degrees of freedom. He is not restricted to 

 motion hi a line or in a plane, but may move through 

 space. So far as concerns his motion to any point 

 we may think of it as the result of component motions 

 along three directions, as N-S, E-W, and Up-Down. 



In the same way we may think of the total kinetic 

 energy of the molecules of a gas as energy of motion 

 in each of three rectangular directions. The kinetic 

 energy due to motions along any one of these directions 

 or axes, is on the average just as much as that due to 

 motions along any other. In other words, if the total 

 kinetic energy of translation is thought of in terms of 

 the degrees of freedom, it is evident that it should be 

 equally divided among them. That is, there is an 

 equipartition of energy, each of the degrees of freedom 

 having one third of the energy. 



As is evident from the equation (1), if we keep the 



