170 



SCIENCE. 



[N. S. Vol. XXIII. No. 579. 



energy is directly dissipated into the ether 

 also possess equal amounts of energy, dif- 

 .ferent from the other amounts, and corre- 

 sponding to another function t, whose 

 dimensions are those of temperature, and 

 which conforms to a formula similar to the 

 one just given, with the same constant B. 

 The two temperatures thus introduced 

 Jeans calls the principal and subsidiary 

 temperatures, and the degrees of freedom 

 to which they correspond, the principal 

 and vibratory degrees of freedom. He 

 shows that, provided the product of the 

 time occupied by a collision between two 

 molecules and the frequency of the atomic 

 vibration is large, the transfer of energy 

 from the principal to the vibratory degrees 

 of freedom goes on very slowly, and he 

 shows further, that we may believe that the 

 postulate here made applies to real bodies; 

 so that, when a gas is heated, we may con- 

 sider that practically all the energy which it 

 receives is taken up by the pi'incipal degrees 

 of freedom. If this be granted, we may 

 ignore, for practical purposes, the multi- 

 tudinous vibratory degrees of freedom, and 

 are brought back to the simpler view of the 

 constitution of the molecule as a collection 

 of atomic masses bound together into a 

 system. We have thus set before us the 

 task of making plausible estimates of the 

 number of principal degrees of freedom in 

 the various gases, and of calculating the 

 specific heats of these gases and the values 

 of the ratio of their two specific heats. In 

 doing this we shall follow the procedure of 

 Staigmiiller. 

 In the formula 



2k 



nk + P 



+ 1 



the denominator nk -\- P represents the en- 

 ergy received by the molecule, when its 

 temperature rises one degree. We assume 

 that the potential energy P is entirely that 

 due to the displacements of the atoms in 



the molecule, and that the motions of those 

 atoms are simple harmonic, so that the 

 mean potential energy corresponding to 

 each internal degree of freedom is equal to 

 the mean kinetic energy. Using a to rep- 

 resent the number of degrees of freedom of 

 the molecule as a whole, and i to represent 

 the number of internal degrees of freedom,. 

 we have 



2 

 + 2i 



n^a-\-i, P=ik, and 



. + 1. 



When we use 6 to represent the sum a -\- 2i,. 

 the formula takes the simple form 



_ -» + 2 



Our task is to estimate the values of a and' 

 i in particular cases, and to calculate there- 

 from the values of y. 



Before proceeding to do this we will cal- 

 culate the expression for the specific heat 

 of constant volume in terms of the degrees 

 of freedom. Denoting again by k the en- 

 ergy corresponding to one degree of free- 

 dom, which a gram-molecule of the gas 

 receives when its temperature is raised one 

 degree, and by m the molecular weight, we 

 may write C^m^^kO, and may calculate 

 k as follows: 



We know from Joule's calculation, that 

 the velocity of mean square for hydrogen 

 is 1.842 X 10^ centimeters per second. 

 From this we get the total mean kinetic 

 energy of translation of a gram-molecule 

 of hydrogen, one third of which is the 

 amount of kinetic energy apportioned to 

 one degree of freedom. We then get the 

 change in the energy apportioned to one 

 degree of freedom, which occurs when the 

 temperature rises one degree, by dividing 

 by the absolute temperature 273, and re- 

 ducing the result to gram-degrees, obtain 

 for k the value k = 0.9886. This value is 

 so nearly equal to 1 that for many of our 

 siibsequent cal-culations k will be taken 

 equal to 1. 



