Pebbuaky 2, 1906.] 



SCIENCE. 



169 



the molecule, added to an unknown amount, 

 P, of potential energy. We thus get 



2k 



nk+P 



If we assume that the molecules of the 

 gas do not take up potential energy, so that 

 P =^0, and then assume that the molecules 

 are practically points, so that n^^3, cor- 

 responding to the three translational de- 

 grees of freedom, we have y = 5/3. This 

 is the number found for this ratio in cer- 

 tain cases, in one of which, at least, that 

 of mercury vapor, we have independent 

 reasons to believe that the molecule is 

 monatomic. If we set w = 5, as would be 

 the case if the molecules were solids of 

 revolution, we get y = 7/5, which is the 

 value found for several diatomic gases. If 

 n = 6, as would be the case if the molecules 

 were irregnilar solids, we get y = 4/3, a 

 number not often found as the value of the 

 ratio, the numbers obtained for gases not 

 belonging to the other two classes being 

 generally less than this. So far we seem 

 to have an imperfect agreement with the 

 theory, but the conditions assumed are evi- 

 dently not those of real molecules. Staig- 

 miiller has shown a way, to which I shall 

 direct particular attention, to modify the 

 formula so that it can be applied to real 

 gases; but before doing so, I wish to con- 

 sider the general question, which will not 

 be settled by our being able to find that 

 certain assumed values of n will give ob- 

 served values of y. Have we a right to 

 believe that the number of degrees of free- 

 dom of a molecule, other than the three 

 degrees of translational freedom, are ever, 

 in any case, so few as we must suppose to 

 get the results referred to? Are we not 

 rather bound to believe, from the evidence 

 of internal vibration afforded us by the 

 spectroscope, that the molecules or the 

 atoms of all gases are vibrating in many 

 modes, or are compound bodies whose parts 



are executing vibrations? And should we 

 not therefore set our number n of degrees 

 of freedom very large, and so obtain a 

 value of y practically equal to unity for all 

 gases, in entire disagreement with the ex- 

 perimental results? The view of the con- 

 stitution of the atom which prevails at 

 present, that it consists, at least in part, of 

 an assemblage of electrons having the essen- 

 tial properties of mass and moving in orbits 

 with enormous velocities, supports the evi- 

 dence of the spectroscope, and makes it all 

 the more necessary for us to admit that the 

 molecule of gas will have a great number 

 of degrees of freedom. 



A reconciliation of these views with a 

 modified doctrine of equipartition has been 

 made by Jeans. The proofs of the theorem 

 of equipartition apply to a conservative 

 system, and fail as soon as they are applied 

 to a system in which the energy is not con- 

 , stant. Now we know that, as a matter of 

 fact, every material system is transferring 

 energy to the ether— indeed, as Jeans i-e- 

 marks, our seeing it at all depends upon 

 that operation— and it appears therefore 

 that we ought not to expect the theorem of 

 equipartition to apply to real systems with- 

 out further examination. To carry on this 

 examination we conceive of a system so " 

 constituted that the energy which corre- 

 sponds to certain of its degrees of freedom 

 can and does pass rapidly into the ether, 

 while that corresponding to the remaining 

 degrees of freedom is dissipated by transfer 

 to the degrees of freedom of the first class. 

 On this supposition Jeans shows that the 

 energy resident in the system may be di- 

 vided among the degrees of freedom ac- 

 cording to a modified' mode of equiparti- 

 tion ; those coordinates whose energy is not 

 transferred directly to the ether possessing 

 equal amounts of energy, corresponding 

 to the temperature of the body indicated 

 by the thermometer and to the formula 

 mi'- = 3RT, while those coordinates whose 



