462 



NATURE 



\_March 20, 1879 



II 



would obviously be fallacious if we were to form an esti- 

 mate of the general state of aggregation from that of the 

 few masses we can judge of in our immediate vicinity ; 

 but we should require to know the condition of a region 

 of an extent that we have no chance of overlooking, and 

 under the principles of the kinetic theory, the local varia- 

 tions of the states of aggregation (themselves depending 

 on local variations in the velocities of the masses) would 

 fluctuate within wide limits. In order to have an idea of 

 the actual (mean) state of aggregation, a being would be 

 required that could (on comparative scale) sweep over the 

 universe with the same facility as we sweep through or 

 examine regions in a gas representing a multiple count- 

 less millions of times that of the mean distance of the 

 detached portions of matter composing the gas.^ 



We are led to apply the principles of the kinetic theory 

 to the case of the universe not so much as a speculation, 

 but rather as a necessary deduction following from the 

 known principle that detached masses moving freely in 

 space (as the stellar masses are observed to do) and at 

 such distances apart that gravity between the several 

 masses is incompetent to deflect the path of the masses 

 appreciably, must move in straight lines, and have their 

 motions regulated under the mutual encounters in accord- 

 ance with the principles of the kinetic theory. Only in 

 the relatively near approach of the masses to one another 

 does gravity come sensibly into play and deflect the path, 

 causing under certain conditions rotation about a common 

 centre (double stars), or, perhaps, by almost direct impact, 

 nebulae with but feeble rotation, &c.2 To carry the 

 analogy again to the smaller scale-case of a gas, it is there 

 known that the molecules are in some cases feebly im- 

 pelled towards each other at a near approach, the path of 

 the molecule being thus deflected at its termination, 

 whereby the conditions are given for causing a temporary 

 rotation of the pair of molecules about a common centre, 

 in an analogous way. The relatively vast distances of the 

 stellar masses, compared with their dimensions, would 

 involve, as a rule, an extremely long mean path before 

 the encounters, corresponding to a proportionally long 

 epoch of time adapted to the conditions of life. The 

 apparent extreme simplicity of the means to the end by 

 the application of the kinetic theory to the case would at 

 least seem not to be cut of harmony with its truth. 



Thus the final conclusion to which these considerations 

 lead would be that the universe has attained its final 

 state of temperature equilibrium (if we set no fixed limit 

 to its past existence), in the sense that if we were able to 

 measure the temperature (or contained energy), of a 

 sufficient number of masses through a sufficiently exten- 

 sive region, we should find that in every such ^'^z/rt/ region 

 throughout the universe the temperatiu-e (or contained 

 energy) would be the same ; just as (on a smaller scale) in 

 the case of a gas, if we could measure the temperature of 

 some thousands of millions of molecules in a given region, 

 we should find that though the temperature differed to a 

 practically unlimited extent from molecule to molecule, yet 

 the temperature of every such equal region was the same. 



' JuEt as in the case of a compcund ga?, the T.nifciinUy cf temperature, of 

 states cfaggregaticn, &c., dees net apply to the individual unit lumps of 

 matter (molecules) forming the gas [which may be in vastij' different states 

 from cne to the other] — but to unit volumes containing vast numbers of such 

 un'.ts; so in the case of the universe, the uniformity cf temperature, ttate of 

 aggregation, &c., would not apply to the unit lumps cf matter (stellar masses) 

 hut to unit volumes. In fact the universe may be regarded as a larger scale 

 gas, with the difference that the central force producing the aggregated lumps 

 of matter that move as wholes is not chemical acticn but gravific action. If 

 ■we imagine (merely for illustration) a being en relative scale situated on a 

 .single compound molecule cf a gas in a state of nom:al temperature equi- 

 librium ; this minute being would observe vast differences cf temperature 

 and of states of aggregate n arcur.d him (srme mclecules in scattered parts 

 glowing in a state cf disscciaticn, &c.), and he wxuld form a perfectly wrong 

 judgment of the state tf the gas frcm such a narri.w point of view. So the 

 observer connected with cne unit lump cf matter cf the universe (stellar 

 mass) can form no idea of the state cf the rest frcm his narrow point of view. 

 ^ The occasional flashing out of stars, as if due to scmic sudden convulsion 

 that might be referred to cclhsicn as a suitable cause, is a nctoritus fact in 

 astronomy; though, frcm the extremely limited view cf the universe that we 

 possess, it would be uiureasonable to expect such phenomena to be of frequent 

 ixxtirrence. 



So in an analogous way as regards the state of aggre- 

 gation of the matter of the universe, since this depends 

 on the temperature, it would follow, assuming an in- 

 definite past time, that the mean state of aggregation of 

 the matter, like the mean temperature (mean energy), is 

 the same throughout, i.e.^ the average size of the separate 

 rnasses, or the number in Unit of volume (taking suffi- 

 ciently large units of volume for comparison) would be 

 equal throughout, though indefinite fluctuations of dimen- 

 sions would occur from one mass to another, in analogy 

 with the fluctuations of velocity from one mass to 

 another. 



It would further follow from the known principle that 

 molecules of different densities (molecular weights) tend 

 forcibly to become uniformly diffused, that by an indefi- 

 nite past duration of the universe all the matter must be 

 uniformly diffused if (as in the case of uniform velocity 

 and uniform state of aggregation) regions of sufficient 

 extent could be taken for relative comparison. This again 

 resembles in principle the smaller scale case of a gaseous 

 mixture, where it is known that the small detached por- 

 tions of matter (molecules) are uniformly mixed, only 

 when appreciable regions containing vast multitudes of 

 molecules are examined, but that there is room for consi- 

 derable local fluctuations of mixture (such as if only a few 

 hundred thousand molecules were examined). 



Thus it appears that the kinetic theory, applied to the 

 universe, would have the peculiar characteristics of allow- 

 ing almost indefinite local fluctuations of temperature, of 

 states of aggregation, and of composition, of the matter 

 forming the universe within regions very extensive, abso- 

 lutely speaking, but infinitesimal, relatively speaking {i.e., 

 in comparison with the boundless universe), these regions 

 being amply extensive enough to allow an amount of 

 activity and variability of energy adapted to the condi- 

 tions of life ; while at the same time the principles of the 

 theory, from their very nature, involve perpetually re- 

 curring and yet indefinitely variable changes within cer- 

 tain localised limits, the constitution of the vast whole 

 (looked at broadly) remaining uniform throughout. 



S. ToLVER Preston 



FRITZ MULLER ON A FROG HA VI NG EGGS 

 ON ITS BACK— ON THE ABORTION OF THE 

 HAIRS ON THE LEGS OF CERTAIN CADDIS- 

 FLIES, &-C. 



CEVERAL of the facts given in the following letter 

 *^ from Fritz Miiller, especially those in the third 

 paragraph, appear to me very interesting. Many persons 

 have felt much perplexed about the steps or means by 

 which structures rendered useless under changed condi- 

 tions of life, at first become reduced, and finally quite 

 disappear. A more striking case of such disappearance 

 has never been published than that here given by Fritz 

 Miiller. Several years ago some valuable letters on this 

 subject by Mr. Romanes (together with one by me) were 

 inserted in the columns of NATURE. Since then various 

 facts have often led me to speculate on the existence of 

 some inherent tendency in every part of every organism 

 to be gradually reduced and to disappear, unless in some 

 manner prevented. But beyond this vague speculation I 

 could never clearly see my way. As far, therefore, as I 

 can judge, the explanation suggested by Fritz Miiller well 

 deserves the careful consideration of all those who are 

 interested on such points, and may prove of widely 

 extended application. Hardly anyone who has con- 

 sidered such cases as those of the stripes which occasion- 

 ally appear on the legs and even bodies of horses and 

 apes — or of the development of certain muscles in man 

 which are not proper to him, but are common in the 

 Quadrumana— or again, of some peloric flowers — will doubt 

 that characters lost for an almost endless number of 

 generations, may suddenly reappear. In the case of 



