Febkuaey 2, 1906.] 



SCIENCE. 



173 



between pi-ineipal and vibratory degrees 

 of freedom. We may suppose that the 

 forces between the atoms of a molecule 

 vary with exceeding rapidity for relative 

 motions in certain directions, while they 

 do not vary nearly so rapidly for motions 

 in other directions. If this is so, the period 

 of the vibration due to the rapidly varying 

 force will be very small, and the vibration 

 will be of the type which communicates 

 energy rapidly to the ether, so that motion 

 in that sense will correspond to a vibratory 

 degree of freedom. The other motions, of 

 longer period, will correspond to principal 

 degrees of freedom, and will alone be op- 

 erative in taking up energy when the gas 

 is heated. 



It does not seem possible to extend 

 Staigmiiller's method directly to other 

 more complicated molecules, for which it 

 would be impossible to assume the atomic 

 arrangement. But if we accept it as veri- 

 fied by its success in describing the specific 

 heats of gases, we may use it to calculate 

 the degrees of freedom in more complicated 

 molecules from their known specific heats, 

 and can then see if the numbers thus ob- 

 tained appear to have any relation to the 

 numbers and kinds of atoms in the mole- 

 cules. ' 



To exemplify this mode of procedure let 

 us take the case of methyl alcohol. Its 

 molecular formula is CH^O ; its molecular 

 weight is 32; its specific heat between 5° 

 and 10° is given by Regnault as 0.59; its 

 molecular heat is therefore 19. If we may 

 neglect the potential energy of the mole- 

 cules with respect to each other in com- 

 parison with their kinetic energies, this 

 molecular heat is distributed among 6 de- 

 grees of freedom of the molecule and the 

 unknown number of internal degrees of 

 freedom which is to be determined. From 

 Staigmiiller 's formula, C^m ==k{a -\-2i), 

 we get for i, 6.5 +• Of course this is an 

 impossible value for i, which should be 



integral, but the specific heat of Regnault 's 

 specimen of methyl alcohol is almost cer- 

 tainly too high, on account of the presence 

 of water. We may take 6 as the most 

 probable integral value for i. We might 

 speculate about the possible assignment of 

 these degrees of freedom to the different 

 parts of the molecule of methyl alcohol 

 according to its structural formula, but 

 such a procedure would be too arbitrary 

 to carry conviction. What is immediately 

 noticeable is that the number of degrees of 

 freedom thus obtained is equal to the num- 

 ber of atoms in the molecule; so that if we 

 assign one degree of freedom to each atom 

 we can reproduce the molecular heat of 

 methyl alcohol. This would be nothing 

 more than a coincidence if it were not the 

 case that the same relation holds for the 

 other alcohols, whose specific heats are 

 given in Landolt and Bernstein's tables for 

 about 0°. 



Methyl alcohol... 



Ethyl alcohol 



Propyl alcohol.... 

 Isobutyl alcohol . 

 Isoamvl alcohol.. 



CH^O 

 CsHgO 



No of Atoms. 



6.5 

 9.5 



12.5 



15 



19 



The general tendency of the values of i 

 is to run above the sum of the atoms. This 

 may be taken account of by a special as- 

 sumption, as, for example, by assigning 

 two degrees of freedom to the hydrogen 

 atom in the hydroxyl group ; but it is very 

 likely that the specific heats given in the 

 tables are. too high, on account of the diffi- 



Ethyl ether i C^HioO 



Benzol CjHg 



Oil of turpentine i CioH,6 



Hexan | CgHu 



Heptan : CjHjj 



Octan ! CgHjg 



Decan , C,|,H.22 



Dpdecan i CjjHjj 



Tetradecan j CJ4H30 



Hexadecan ' Cj^Hsj 



Tolnol ■ C,Ha 



