124 



SCIENCE. 



[Vol. II., No. 26. 



are formed of ultimate atoms of the same kiud ; 

 so that, on this h3'pothesis, there is but one kind 

 of substance from which all others are com- 

 pounded. Chemical atoms might be compared 

 to a chime of bells all cast from the same ma- 

 terial, but each having its own special series of 

 harmonic vibrations. 



A necessarj- result flowing from this hypoth- 

 esis would be, that the atomic weights should 

 all be exact multiples of some fraction of the 

 atomic weight of hj'drogen, which would in- 

 clude Prout's h3-pothesis as a particular case. 

 The experimental data are, perhaps, not yet 

 sufficiently precise to enable us to obtain a 

 trustworthy result as to the probabilit}' of the 

 truth of Prout's hypothesis ; j-et Clarke's ^ re- 

 sults as to the atomic weights seem to show 

 that the hj-pothesis has a high degree of proba- 

 bilit}'. 



If the chemical atoms of all bodies are as- 

 sumed to be formed of ultimate atoms, which are 

 in all respects equal and alike, this hj'pothesis 

 furnishes a basis for investigation at once defi- 

 nite and simple, some of whose consequences 

 we shall now endeavor to show to be in ac- 

 cordance with experimental facts. 



We wish, in the first place, to show that this 

 hj'pothesis will make the temperature of a gas 

 proportional to its mean kinetic energ}'. A 

 chemical atom maj- be assumed to be a per- 

 fectlj' elastic body, as its deformation is as- 

 sumed to be extremely small. But according 

 to the mathematical theory of elastic impact,^ 

 "when two such bodies come into collision, 

 sometimes with greater and sometimes with 

 less mutual velocity, but with other circum- 

 stances similar, the velocities of all particles 

 of either bod}' at corresponding times of the 

 impacts will alwaj's be in the same propor- 

 tion ; " from which it is clear, that in a mix- 

 ture of two kinds of gas, as hj-drogen and 

 oxj-gen for example, when the mean velocitj' 

 of the molecules is so increased that the vibra- 

 tion of the ultimate atoms of the hydrogen is 

 increased a certain per cent, then that of the 

 ultimate atoms of the ox3'gen is increased by 

 the same per cent. But the circumstances 

 of the encounters and the forces acting be- 

 tween the ulitmate molecules determine what 

 fraction the mean kinetic energy of vibration 

 of the ultimate atoms shall be of that of the 

 molecules whose encounters cause these vibra- 

 tions. Since the circumstances attending the 

 encounters are dependent simply upon the 

 forces acting between the ultimate atoms as- 



1 Constants of nature, part v. A recalculation of the atomic 

 weights. WaBhington, 1882. 



= Thomson and Tait's >fatural philosophy, 1867, art. 302. 



sumed to be in all respects equal, the energj* 

 of their vibration will be the same in an atom 

 of hydrogen as it is in an atom of oxygen ; for 

 each degree of freedom of every ultimate atom 

 of either element is similarl}' circumstanced, 

 both as regards forces between itself and other 

 ultimate atoms of the same chemical atom, and 

 also as regards the impacts of other molecules. 

 The proposition of the kinetic theory which 

 makes the energy of each degree of freedom 

 the same, which has been erroneously applied 

 to the degrees of freedom of molecules, can 

 therefore be correctlj- applied to the ultimate 

 atoms. 



But it might not, at first glance, be apparent 

 whether these vibrations are caused by, and 

 are proportional to, the mean progressive 

 energy of the molecules, or to their rotary 

 energy combined with it. But it is not dif- 

 ficult to show that the vibrations of the chemi- 

 cal atoms with respect to each other are pro- 

 portional to the mean progressive energy alone, 

 and then to show the same for the ultimate 

 atoms. Although, in the paper upon the 

 vibratory motions of atoms within the mole- 

 cule, we have for mathematical purposes con- 

 sidered the centrifugal force as causing vibra- 

 tions of atoms with respect to each other, j'et 

 in fact the vibrations so caused are vanishing 

 quantities, compared with those caused bj' the 

 component of the impulsive force acting during 

 an encounter along the line joining the atoms 

 of a molecule. The magnitude of such a vibra- 

 tion, other things being equal, depends upon 

 the suddenness of the impulse ; and the sud- 

 denness of the force called into play during 

 a change of rotary velocity, by deviation from 

 motion in a tangent to motion in a circle, can 

 bear no comparison to the suddenness of a 

 direct impulse along the radius of the circle. 

 Hence the direct impulse due to the progres- 

 si\'e motion need alone be considered. 



It thus appears that the energy of vibration 

 of chemical atoms with respect to each other 

 in a simple gas is proportional to its mean 

 progressive energy. The same is true of the 

 vibrations, with respect to each other, of the 

 ultimate atoms which form a chemical atom, 

 and for the same reasons ; for the forces which 

 act upon the ultimate atoms are the impulses 

 due to the encounters of other molecules, and 

 those due to the remaining chemical atoms of 

 the same molecule. The energy of the latter 

 of these motions is proportional to the former, 

 as has just beeu shown ; hence their sum is so 

 also : therefore the energy exerted to deform 

 a chemical molecule, and set it in vibration, is 

 proportional to the mean progressive energy. 



