80 Mr. J. H. Jeans [March 30, 



from what we imagined it in the past. In the meantime, the attitude 

 of the relativity theory to the ether is that it has no need for that 

 hypothesis. 



The second cloud, over the dynamical theory of heat, is in effect 

 the theorem of Equipartition of Energy, discovered as a mathematical 

 theorem by Maxwell in 1857. The dynamical theory of heat asserts 

 that heat is a mode of motion. Every body has a certain number of 

 capacities of internal motion, or to use the technical term, degrees of 

 freedom, the energy of motion of these degrees of freedom forming 

 what we call the heat of the body. The theorem in question begins 

 by assuming that the motion is determined by laws of the type of 

 Newton's laws of motion, and on this hypothesis it shows that, when 

 any temporary disturbances have passed away, the energy is, so to 

 speak, fairly rationed out amongst the different degrees of freedom. 

 It is not proved that one degree of freedom will have just one ration, 

 but if we take any large group, no matter how selected, their average 

 amount of energy will always be exactly one ration. We can state 

 the matter in a different way l)y saying that the energy is distributed 

 at random amongst the different degrees of freedom : none of them 

 gets any preferential treatment. The simplest instance of the truth 

 of the theorem is, perhaps, found in the law that the atomic heats of 

 all elements is the same. On the average an atom of silver has just 

 the same energy as an atom of aluminium at the same temperature. 

 The atom of silver is four times as massive as the atom of aluminium, 

 but the energies are made the same by the velocities in silver being 

 just half of those in aluminium. 



Another aspect of the meaning of the theorem of equipartition 

 deserves attention. A column of air, say an open organ-pipe of 16 ft. 

 length, can sound not only its own note, but a number of harmonics 

 as well — one in the first octave above the fundamental note, two in 

 the octave above, four, eight, sixteen, and so on, in the succeeding 

 octaves. The degrees of freedom of the air inside the pipe may be 

 thought of as arising from the possibility of motion in spaca of the 

 molecules of the gas, but they may alternatively be thought of as 

 the possibility of the pipe sounding its fundamental note and all the 

 harmonics, down to those of the very shortest wave-length, com- 

 parable with the distances apart of the molecules in the gas. The 

 principle of equipartition now requires that when any exciting agency 

 has died away, and only pure heat-motion remains, the energy shall 

 be distributed equally among all its notes. It can in point of fact 

 be shown by mathematical demonstration that the random heat- 

 motion of the molecules inside the pipe can be resolved into a system 

 of wave-motions such that the fundamental note and all the harmonics 

 have, on the average, exactly the same amount of energy. Thus, so 

 long as the theorem of equipartition remains true, we may regard 

 heat-motion as a musical effect, produced by sounding all the notes 

 which the system is capable of sounding, with equal energy. 



