404 



NA TURE 



[FEBRUARY 22, I906 



into this development, an element which seems destined 

 t<i affect very radically, not only our interpretation of 

 physical phenomena, but also our general views about the 

 principles of theoretical mechanics. 



There seem to be two things underlying all the pheno- 

 mena in the physical world — the ether and matter. To 

 attain the unification of physical science, shall we consider 

 the ether as a particular kind of matter? Or shall matter 

 be interpreted electromagnetically? The older mechanics 

 dealt exclusively with matter; and when it first became 

 necessary to introduce the ether, this new medium was 

 often endowed with properties very much like those of 

 matter. The hydrodynamic analogy by which the apparent 

 mass of the moving charge was interpreted illustrates 

 this tendency. The physics of the ether has, however, 

 reached so full a development that the properties of the 

 ether are now known far more definitely than those of 

 matter. These properties are contained implicitly in the 

 fundamental equations of Maxwell and Hertz which in 

 their essential features are adopted in the electron theory 

 of Lorentz. 



It is now pretty generally recognised that Newton's 

 "laws of motion," including his definition of "force," 

 are not unalterable laws of thought, but merely arbitrary 

 postulates assumed for the purpose of interpreting natural 

 phenomena in the most simple and adequate manner. 

 I nfortunately, nature is not very simple. " As the eye 

 of the night-owl is to the light of the sun, so is our mind 

 to tin most common phenomena of nature," says Aristotle. 

 And if since Newton's time we have made some progress 

 in the knowledge of physics, it is but reasonable to con- 

 clude that the postulates which appeared most simple and 

 adequate two hundred years ago cannot be regarded as 

 -in li at the present time. 



This does not mean, of course, that the mechanics of 

 Newton has lost its value. The case is somewhat parallel 

 to that of the postulates of geometry. Just as the abandon- 

 ment of one or the other of the postulates of Euclidean 

 geometry leads to a more generai geometry which contains 

 the old geometry as a particular, or limiting, case, so the 

 abandonment or generalisation of some of the postulates 

 of the older mechanics must lead to a more general 

 mechanics. The creation of such a generalised mechanics 

 is .1 task for the immediate future. It is perhaps too early 

 in say at present what form this new non-Newtonian 

 mechanics will ultimately assume. Generalisation is always 

 possible in a variety of ways. In the present case, the 

 object should be to arrive at a mechanics, on the one hand 

 sufficiently general for the electron theory, on the other 

 such as to include the Newtonian mechanics as a special 



1 ,lsr. 



After the searching criticism to which Poincare, especially 

 in his St. Louis address, 1 in 1904, has subjected the 

 foundations of mechanics and mathematical physics, almost 

 the only one of the fundamental principles that appears in 

 remain intact is the principle of least action. It seems, 

 therefore, natural to take this principle as the starting 

 point for a common foundation of mathematical physics 

 and of a generalised mechanics, but with a broader defini- 

 tion of "action," or what amounts to the same, with a 

 generalised conception of " mass " so as to make the 

 latter a function of the velocity. 



The Partition of Energy.' 

 The general theorem which I wish to discuss may lie 

 stated by saying that the kimtic energy of the body is 

 so distributed among the degrees of freedom, bv which 

 the state of the body as a dynamical system is described, 

 that an equal share is, on the average, allotted to each 

 degree of freedom of each tvpe of molecule. 



The questions which have always been raised about 

 this important theorem of the kinetic theory at once come 

 in our minds. First, is the theorem true, or rather, does 

 it si, id- what would be true for an ideal system of particles 

 moving freely within a containing vessel? s.-, ond, is the 

 proof of the theorem impeccable? third, is there any ex- 

 perimental evidence that it applies to real bodies? 



1 "Bulletin des sciences mathematiques" (2). 20, pp. 102-324; English 

 translation in the Bulletin of lite American Mathematical Society, vol. 

 xiii., February, 1906. 



: From the address of Prof. VV. F. Magie, president of Section B, Physics. 



NO. 1895, V °L. 7 3] 



I would remark about the first question that the theorem 

 is so distinguished by its simplicity, and by its aspect as a 

 sort of unifying principle in nature, that few men can set 

 it fairly before their minds without at least desiring to 

 believe it true. Most of those who have recognised that 

 Maxwell's original demonstration was not flawless are still 

 convinced of the truth of his conclusion, or at least believe 

 his conclusion to be so probable as to make it worth 

 while to try for a more accurate demonstration. Their 

 state of mind is like that of Clausius and of Lord Kelvin, 

 when they perceived that Carnot's theorem respecting the 

 efficiency of a reversible engine could not be proved in the 

 way in which Carnot tried to prove it. 



With respect to the second question, it was ver) soon 

 pointed out that Maxwell had made in his proof an 

 assumption that could not be justified by immediate in- 

 spection, and which was itself in need of demonstration 

 or of avoidance. The later demonstrations of Maxwell and 

 Boltzmann have been likewise subjected to criticism, and 

 can be shown to involve assumptions that will not be 

 granted on inspection. The difficulties that arise in these 

 proofs come from the necessity of applying in them the 

 calculus of probabilities, and centre around the question 

 of the legitimacy of the application of that calculus. It 

 is commonly agreed that Maxwell and Boltzmann have 

 assumed a condition of the system of moving particles, as 

 a requisite for the application of the calculus of prob- 

 abilities, which is contradicted by many systems ol which 

 we have certain knowledge, and cannot without proof be 

 admitted as likely to obtain in other systems, about which 

 less is known. In the method emploved bv Jeans tin- 

 application of the calculus of probabilities is made in a 

 different manner, and does not necessitate the introduction 

 of the hypothesis of Maxwell and Boltzmann. It seems li> 

 me that, in this last form of the theory, the difficulties 

 which have environed the subject have tit lasl been 

 mastered. 



In respect to the third question, that concerning the 

 experimental evidence for the truth of the theorem, it is 

 well known that, in general, Boyle's law follows as a 

 consequence of the general principles of the kinetic theory, 

 that Gay-Lussac's law is an immediate consequence of a 

 relation plausibly assumed between temperature and the 

 kinetic energy of the molecule, that the motion of the radio- 

 meter and the laws of transpiration and many other 

 properties of gases can be deduced from the general theory, 

 and, in particular, that Avogadro's law follows from the 

 simplest form of the theorem of equipartition. But further 

 proof of this theorem in its general form is still needed. 

 Such proof as we have will be discussed in this address. 



Considering the bearing of the relations that have been 

 adduced upon the general question of the equipartition of 

 energy, it seems to me that their general consistency with 

 that principle, especially the wa\ in which the heat 

 capacities of the organic compounds can be portioned out 

 among the atoms by means of simple assumptions about 

 their degrees of freedom, does afford some confirmation of 

 the principle. Mere chance can hardly account for so 

 large a number of successful coincidences. 



The Sanitary Value of a Water Analysis.' 

 Though much valuable information can be obtained from 

 the careful study of the nitrogen content of a water, the 

 water analyst does not depend alone upon these factors 

 in forming an opinion as to the source of the organic 

 matter, and turns to other chemical as well as to bacterial 

 data to substantiate or modify the opinion thus formed. 

 From the chemical point of view the most important of 

 these data is the combined chlorine that a water contains. 

 This is due to the fact that though chloride of sodium 

 occurs in rain-water, especially near the sea, and in small 

 amounts is found in all soils, it is a characteristic con- 

 stituent of sewage, the animal body expelling the same 

 amount of salt as it absorbs. 



A careful study of the amount of combined chlorine in 

 normal waters, made by Prof. Thomas M. Drown, showed 

 that in Massachusetts, where salt-bearing strata do not 

 occur, the amount of chlorine in a surface water depended 

 on its distance from the sea, and that for Massachusetts 



1 From the address of Prof. Leonhard P. Kinnicutt, president of Sectior 

 C, Chemistry. 



