March 20, 1879] 



NATURE 



%ftX 



this matter to be raised to such a degree that the whole 

 forms a gas, consisting of separate or dissociated mole- 

 cules, filling space uniformly. This would evidently be 

 the result of applying sufficient heat, just as for example 

 a gas consisting of compound molecules breaks up into 

 its elementary molecules when sufficient heat is applied, 

 the molecules being unable to aggregate into groups on 

 account of the expansive action of the high temperature. 

 When the temperature of the gas is lowered the molecules 

 (as is known) commence again to aggregate into groups, 

 i.e.., to cluster about common centres in chemical union. 

 So in the case of the universe, in the imaginary instance 

 of an (adequately) extremely high temperature, we should 

 have the entire universe consisting of separate molecules 

 or forming a very rarefied gas, the molecules being unable 

 to aggregate into distinct groups under the action of 

 gra\'ity, owing to the enormous velocities of the mole- 

 cules.' The molecules would simply rebound from each 

 other in straight lines, according to the principles of the 

 kinetic theory of gases.^ Let us suppose, now, the ex- 

 cessive temperature to fall, or in other words the total 

 energy to diminish. Then the molecules would com- 

 mence to cluster into groups (forming masses) under the 

 action of gravity, the mean size of such aggregated groups 

 of molecules becoming greater as the temperature is less, 

 and the number of such groups diminishing in the same 

 proportion. At first, by a slight fall of temperature we 

 should have a large number of small groups (or clusters) 

 of molecules ; by a further faU of temperature a further 

 clustering of molecules under the action of gravity would 

 occur, i.e., the size of the separate masses would increase 

 and their number diminish. The case is, in broad 

 principle, exactly parallel to that of a compound gas when 

 subjected to extreme variations of temperature, indeed 

 as far as the purely mechanical considerations are con- 

 cerned, it is only a question of scale.^ We know that 

 when a compound gas whose molecules possess a high 

 complexity has been heated up to the temperature of dis- 

 sociation, and the temperature is gradually lowered, then 

 at first only a clustering of elementary molecules takes 

 place ; but as the temperature is further lowered, these 

 compound molecules may cluster together to form com- 

 pound molecules of a secondary order or higher degree 

 of complexity (/.^., molecular clusters of a larger mass). 

 Thus the mean mass of the clusters of molecules in the 

 gas increases as the temperature is lowered, and the 

 number of such clusters (or centres of aggregation) dimi- 

 nishes correspondingly. 



We will therefore suppose that the universe has attained 

 a final state analogous to this, i.e., such that the mean 

 mass of a cluster of molecules (a stellar mass) and the 

 number of such clusters (stellar masses) is such as exactly 

 to represent that which must exist by the actual mean 

 temperature of the universe. But it may be said, as far 

 as we are able to appreciate and judge of the universe, it 

 certainly appears as if the entire universe were losing its 

 heat in the ether of space, and that this final state of 

 things (equilibrium) were not yet attained. But it may 

 be urged, in reply, we are judging of the entire universe 

 from the point of view of a single stellar sun to which we 

 belong. It is as if we were to judge of the temperature 

 equilibrium of a gas from the point of view of a single mole- 

 cule (or of a few others surrounding it), in which case it is 

 certain we should be unable to form an idea of the state 

 of temperature equilibrium of the gas. It is known to be 

 a demonstrated consequence of the kinetic theory that 

 the utmost diversity exists among the velocities of the 

 molecules of a gas, or the temperature from molecule to 



^ ' The deflection from a straight line owing to the feeble action of gravity 

 in rte case of single molecules, would evidently be inappreciable. 

 _ - There is, of course, this detail of diflference, viz., that while the aggrega- 

 tion of molecules about a centre in chemical action is limited, the aggrega- 

 tion in the case of gravity is unlimited. We merely apply in principle the 

 same general considerations t j molecules aggregated into clusters (lumps) 

 under chemical action, as to molecules aggregated into lumps under gravific 

 action (stellar masses). 



molecule. In order to have a true idea of the state 

 of temperature of the gas, we must investigate ths 

 conditions of a region containing some thousands of 

 millions of molecules (any appreciable region or space 

 actually containing this number). So in order to have 

 an adequate idea of the state of temperature equilibrium 

 of the universe, we should require the mean temperature 

 (state of energ)') of a region containing some thousands 

 of millions of stellar masses, not the narrow view we have 

 from one of these, and the velocities of the few we have 

 measured — not to speak of the countless dark suns that 

 may exist in space, and about whose velocities we know 

 nothing. Mr. CroU has pointed out ^ how it is probable that 

 such dark suns may possess exceptionaUyhigh velocities, as 

 the bright (visible) suns would naturally have lost in the col- 

 lisions which developed their heat part of their normal 

 velocity of translation, the tr an slatory motion having been 

 partly lost by conversion into heat. In the parallel case of a 

 gas, it is a known fact that even if the mean temperature 

 of the gas be low (less than normal temperature), some 

 molecules in certain parts must acquire in the accidents 

 of collision enormous velocities, and are thrown into very 

 forcible vibration at the encounters, such that they would 

 become luminous if we were able to visualise single 

 molecules. In other words, if all the molecules of the 

 gas possessed the velocities of these single molecules 

 (relatively few in number), the entire gas would appear 

 like a flame. So in like manner, though single stars in 

 the universe may be luminous, it (by analogy) by no 

 means follows that this at all approximately represents 

 the mean condition of the entire universe. This lumi- 

 nous state might be quite exceptional, and the mean 

 temperature of the universe might be exceedingly low for 

 aught we may know. We may happen to be in a part 

 where the mean temperature of the component matter is 

 exceptionally high, as, of course, from the fact of our 

 being in existence, we must be in a part which is suited to 

 the conditions of life. What is there, then, to oppose the 

 inference that the mean temperature of the universe may 

 be such that each stellar mass (or detached portion of 

 matter, glowing or not) on an average receives as much 

 heat from others as it emits itself, in analogy to the mole- 

 cules of a gas in equilibrium of temperature ; and this 

 does not prevent single stellar masses (in analog)' single 

 molecules of the gas) from acquiring exceedingly high 

 temperatures, indeed, they would naturally acquire this 

 from the encounters in certain instances, according to the 

 accepted principles of the kinetic theory. 



As regards the state of aggregation of the matter of the 

 universe as dependent on the energy, it would clearly in 

 the same way be misleading if we were to attempt to 

 judge of the mean state of aggregation from the point of 

 view of the few masses in our immediate neighbourhood 

 (or the narrow range of the universe overlooked by us). 

 Thus, to recur to the smaller scale illustration of a gas. 

 In the case of the molecules of a compound gas in a state 

 of temperature-equilibrium, it is known that some of these 

 compound molecules (representing a cluster of molecules 

 aggregated about a common centre) must acquire now 

 and then, in the accidents of collision, velocities corre- 

 sponding to dissociation temperature. The compoimd 

 molecule is thus broken up into its components at the 

 collision, these components clustering together againin 

 some other part of the gas, the mean state of aggregation 

 remaining unchanged. Thus it would evidently be mis- 

 leading to judge of the state of aggregation of the mole- 

 cules of a compound gas from the point of view of an 

 inappreciable region, containing a few hundred thousand 

 molecules, which might in the accidents of collision have 

 become exceptionally heated. In order to judge of the 

 state of aggregation ' of the gas, we must investigate that 

 of an appreciable region, containing some thousands of 

 millions of molecules. So in the case of the universe, it 



^J-^Quarteyly Journal of Sciettce, Ju'.y, 1877. 



