April 22, 1875] 



NA TURE 



487 



be the energy due to the attraction of those forces multiplied by 

 n - I, and for a given quantity of gas will vary as the density 



raised to the power of "^^. 

 3 



The sum of the virials due to gravitation does not appear suffi- 

 cient to account for the observed effects, and moreover would 

 vary with the quantity of gas in a compound ratio. We must 

 conclude, then, that tlie ratio of the force to the distance is a 

 higher one than that of the inverse squares. 



Upon that law, as already stated, the sum of the virials would 

 increase, for equal quantities of gas, in the ratio of the cube root 

 of the density. Prof. Maxwell has shown that for equal volumes 

 the increase; must be as the square of the density, that is, for 

 equal quantities as the density. In order to obtain the same 

 result directly, supposing the density to vary, the quantity re- 

 maining constant, it is necessary to assume the forces to vary 

 inversely with the fourth power of the distances. On this sup- 

 position the sum of the virials will vary for a given density, as 

 the facts appear to indicate, directly with the volume. 



The formula of Clausius does not elucidate the phenomenon of 

 the increase of/ ?' at low densities with increase of density, 

 e.xperimentally demonstrated in the case of hydrogen gas only, 

 but probably true, as conjectured by Regnault, of other gases 

 also at sufficiently high temperatures. 



The rationale of this I believe I have discovered, but will not 

 now attempt to enter upon this point. 



Prof Maxwell mentions that Clausius had long ago pointed 

 out that the ratio of the increment of the whole energy to that of 

 the energy of translation may be determined if we know by ex- 

 periment the ratio of the specific heat at constant pressure to 

 that at constant volume. 



The same result is obtained by comparing the specific heat at 

 constant volume with the difference in the kinetic energy of 

 translation on increase of temperature indicated by the increase 

 of presaure ; a method by which a small error arising from the 

 variation in the value of / f-'at different densities is eliminated, 

 the sum of the virials remaining constant. 



Taking c-^ to represent the specific heat at constant volume, / 

 the mechanical equivalent of heat, / and V the initial pressure in 

 pounds per square foot and volume in feet of a pound weight of 

 the gas, 7;, and 7"j the energy exclusive of that of translation at 

 zero and i' Centigrade respectively, a the coefficient of expansion 

 for constant volume,* we shall have — 



For atmospheric air r, /may be taken at 233'4I, and/ fat 

 26215, and a, by RegnauU's experiments, is '003665, so that— 



71 - ?« = 233-41 - 144-12 = 89-29- 



This gives the increment of energy due to other motions than 

 that of translation not quite two-thirds of that due to the motion 

 of translation. The exact ratio is I '859 to 3. 



The experiments of Regnault prove that neither / Knor a are 

 absolutely constant at all densities. He found o at '1.444 atmo- 

 sphere to be '0036482 and 4'8l atmosphere '0037091. His 

 experiments do not indicate an appreciable difference in the 

 value of/ Kbetween '1444 and i atmosphere, but between i and 

 481 atmosphere it appears to be diminished about '004 of its 

 amount. "The value of | a/ Kin the former case will therefore 

 be about 143 '46, and in the latter I45'27. 



Supposing the Specific heat to be independent of density, this 

 would inuicate that the ratio of the increment of the energy of 

 translation to that of the remaining energy, and therefore 

 probably that of the energies themselves, increases with tlie 

 density. It is, however, not improbable that Cj may likewise 

 vary, and that the ratio of the two elements may be constant. 



M. RegnauU's experiments to deteimine the specific heat of 

 air were all made at somewhat high pressures, varying at the 

 commencement of the experiments from 4 to 6000 mm., and at 

 the termination from 800 to 3000 mm. They more nearly corre- 

 spond, therefore, to a pressure of 4'8l atmosphere than to i 

 atmosphere. And if S 0/ J' = 145-27, T-j - 7',, = 88'I4, aratio 

 between the elements of the energy of 3 to I '82. 



It is also probable that c^ varies to some extent at different 

 temperatures, but I am not aware that any experiments have 



* The coefficient ot the increase of pressure, the volun 

 stant, as well as the coefficient of expansion properly so called, is term 

 the coefficient of expansion by Regnault. in vie-.v, however, of the vari 

 tion which exists from the law of Boyle and Marriulte. it is necessary' 

 observe the distinction. 



been made to ascertain this. Regnault throughout assumes the 

 specific heat to be constant for all temperatures. 



Prof. Maxwell states that a consequence of Dr. Boltzmann's 

 theorem is that the temperature tends to become equal through- 

 oiit a vertical column of gas at rest. He also confirms this doc- 

 trine as an independent conclusion of his own. 



It is with great diffidence that I advance a different view from 

 that which has the sanction of such high authority. 



It seems obvious, however, that the mean energy of the 

 molecules moving downwards must be increased, and tliat of 

 those moving upwards diminished, by the amount of the work of 

 gravitation. And there is nothing to counteract this tendency 

 unless there is repulsion between the particles ; attraction would 

 increase it. At all parts of the system there is exchange of 

 energy between the particles ; but, supposing equilibrium to 

 have been attained, the mean amounts of energy transmitted in 

 opposite directions at any given point must be equal. Equili- 

 brium, therefore, can only exist when the difference of the actual 

 energy at different distances from the centre of attraction is the 

 same as the difference due to the transfer of particles from one 

 distance to the other. 



I think that the equality of temperature must be involved, 

 either explicitly or implicitly, in the data from which the theorem 

 of Boltzmann is deduced. 



If this reasoning is correct (supposing the gas at rest), the fol- 

 lowing equation will represent the relation of the temperatures 

 at different elevations : — 



U=h-- 



c,J 



where x-^ x^ are the heights, t^ /j the corresponding temperatures' 



The difference of temperature which would exist in the atmo- 

 sphere at different heights in consequence of this law (one degree 

 Centigrade for every 233 feet) is partly counteracted by the action 

 of the currents ; the rate of cooling by expansion being less for 

 the same difference of height. But in a long-continued calm the 

 increase of heat in the lower region of the atmosphere is well 

 known to be intense. 



If the condition of equal temperature at all heights were one of 

 atmospheric equilibrium, it would be one ot stable equilibrium. 

 It would sooner or later be attained, and would be subject to little 

 disturbance. But the equilibrium which the law above stated tends 

 to induce in still air is extremely unstable, inasmuch as a body 

 of air which has risen in consequence of being warmer and 

 lighter than the surrounding portions of the same stratum has a 

 still greater difference of temperature from the higher strata, 

 having suffered less refrigeration from expansion than that due 

 to the difference of elevation in still air. Slight affections of 

 temperature are therefore capable of causing great atmospheric 

 disturbances, and the tropical calms before alluded to are com- 

 monly followed by the most violent tempests. 



Prof Maxwell observes that a molecular a;ther would be 

 neither more nor less than a gas. This statement requires one 

 qualification, as the theory does not necessarily imply the exist- 

 ence of either attraction or repulsion between the particles, and 

 from the universal diffusion of the Eether it must be inferred that 

 no such forces exist. This constitutes a difference of some impor- 

 tance from the condition of a gas. It is true that an equilibrium of 

 temperature would /c«(/to establish itself between the agitation of 

 the ordinary molecules and those of the rether. But the esta- 

 blishment of such an equilibrium would be constantly counter- 

 acted by the rapid transmission of the energy communicated to 

 them, through space, by the molecules of the lether ; in other 

 words, by radiation. There are doubtless difficulties in this 

 hypothesis, but its rejection involves the conception of the trans- 

 mission of energy by other means than the motion of material 

 particles, and we have no sufficient ground for supposing any 

 other mode of transmission to be possible. 



It has been suggested that the alternative to the conception of 

 a molecular tether is a continuous material substance, not made 

 up of parts, and that such a substance might be capable of motion 

 and of transmitting energy. But a continuous material substance, 

 not made up of separate parts, capable of internal motion, and 

 permeable throughout by ordinary matter, can hardly be called 

 material in an ordinary sense. I find it as difficult to conceive 

 such a substance as an immaterial substance capable of trans- 

 mitting energy. But I am profoundly conscious of the difference 

 between the limits of our powers of conception and the limits of 

 possibility. 



AthenjEum Club, April 9 R. C. Nichols 



