168 



SCIENCE. 



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



it is not true in fact. To demonstrate the 

 latter statement, in default of any direct 

 experimental method, he has resorted to 

 the calculation of the paths and velocities 

 of a moving body within an envelope of 

 some assumed form, and a comparison of 

 the kinetic energies associated with each 

 degree of freedom. To introduce the ele- 

 ment of chance, the courses of the body 

 were mapped out by the help of numbers 

 obtained by drawing numbered cards from 

 a pack. The results obtained differed con- 

 siderably from the exact equalities deduced 

 from the Maxwell-Boltzmann theorem. I 

 do not pretend to be able to show that these 

 results of Lord Kelvin are of no value as 

 evidence against the truth of the theorem, 

 but I would remark that we can at least 

 .justify a doubt about them by noticing 

 how small a deviation in the experiments 

 from perfect impartiality of conditions will 

 suffice to produce a large deviation from 

 the expectation of the theory of probabili- 

 ties. To test this, and remembering that 

 when I used to play whist we noticed that 

 a black card turned up as trump oftener 

 than a red one, I procured a new pack of 

 cards, which ought to be impartial and 

 unbiased, if anything is, and cut it a num- 

 ber of times, noting the suit of the card 

 exposed by the cut. In 312 cuts the black 

 suits were recorded 196 times, the red suits 

 116 times. Spades were recorded 111 

 times, clubs 85 times, diamonds 68 times, 

 hearts 48 times. Practically the same ratio 

 (184^121) between the black and red suits 

 was obtained with an old pack, though the 

 order of suits was different. Such a per- 

 sistent departure from the expectation of 

 an equal number of each color and of each 

 suit indicates that for some reason the 

 cards are not impartial; and a scrutiny of 

 a new pack .shows, I think, the reason for 

 this. When the pack is examined, the bot- 

 tom card is usually the ace of spades, and 

 then the spade suit follows in order. The 



uppermost suit is generally. the hearts. I 

 believe that, when the pack is trimmed, the 

 knife is pressed out as it goes down, so 

 that the upper cards are cut a little smaller 

 than the lower ones. The difference in 

 size can be seen if the pack is evened up on 

 a smooth surface. Some cards will then 

 appear a little wider than the others, and 

 if they are picked out, they will generally 

 be found to be black cards. Now I do not 

 know how Lord Kelvin's pack of cards was 

 made, or how the cards were drawn, but I 

 think we may fairly suppose that the dis- 

 crepancies of 15 per cent, or so, which ap- 

 peared in his experiments, may have been 

 due, not to a failure of the theorem of 

 equipartition, but to trifling departures 

 from impartiality in his method of experi- 

 mentation. 



We are now ready for the examination 

 of the experimental evidence for the appli- 

 cability of the theorem of equipartition to 

 real bodies. The most important evidence 

 that bears on the question is found in the 

 observed values of the specific heats of 

 gases, and of the ratios of their specific 

 heats of constant pressure and of constant 

 volume. If we consider the distribution of 

 the energy which enters a gas at constant 

 volume when its temperature rises one 

 degree, designating its specific heat of con- 

 stant volume by C^, the increase in the 

 energy of translation of the molecules by 

 (7q, and the ratio of the two specific heats 

 by y, it is easy to show that 



, 2 Co 



Now if each degree of freedom acquires 

 an equal share of kinetic energy, say k, 

 the energy of translation increases by 2k, 

 so that 



2k 



'-' = c:,- 



Furthermore, C^ will equal k times the 

 total number, n, of degrees of freedom of 



