CONTRIBUTIONS TO SCIENCE. 569 



of freedom" the ratio of the kinetic energy of translation 

 to the whole kinetic energy of the system must be equal to 

 the ratio of 3 to n. Now in a rigid body capable of rotating 

 in any manner n is equal to 6, and this makes the total 

 energy equal to twice the energy of translation. This requires 

 that the ratio of the two specific heats should be 1*33 instead 

 of 1'408, and the observed ratio therefore disproves the 

 hypothesis of hard bodies. If we suppose the molecules to be 

 material points, incapable of rotation or vibration n is equal 

 to 3, and the energy of translation is the whole of the kinetic 

 energy possessed by the molecules. This would make the 

 ratio of the specific heats to be 1*66, which is too great for 

 any real gas except mercury vapour, for which the ratio has 

 been shown by Kundt and Warbourg to be nearly 1'66. 



The spectroscope shows that the molecules of a gas are 

 capable of executing vibrations in various periods. They 

 must therefore be material systems, and cannot have less 

 than six degrees of freedom. The ratio of the specific heats 

 cannot therefore be greater than 1/33, and this is too small 

 for most gases. Every additional degree of freedom pos- 

 sessed by the molecules makes the ratio less, and requires 

 that the specific heat of the gas should be greater than is 

 observed to be the case. 



In a paper " On Boltzmann's Theorem on the Average 

 Distribution of Energy in a System of Material Points," read 

 before the Cambridge Philosophical Society on May 6, 1878, 

 Maxwell showed that whatever be the forces acting upon or 

 between the molecules, provided they be subject to the prin- 

 ciple of conservation of energy, the average kinetic energy of 

 any two given portions must be proportional to the number 

 of degrees of freedom of these portions, and hence the total 

 kinetic energy corresponding to an increment of temperature 

 of 1 C is shown to be proportional to the product of the 

 number of degrees of freedom into the absolute temperature. 



The actual dimensions of molecules were first estimated 

 by Loschmidt in 1865, then by Stoney in 1868, and by 

 Thomson in 1 8 7 0. At his lecture " On Molecules," before the 

 British Association at Bradford, Maxwell gave the following 



