2 



C. V. L. Chailier 



In dealing with these passages we must have recourse to the theory of pro- 

 bability. We are thus led to the same problem as is met with in the theory of the 

 gases, which has resulted in the bold theories of Clausius and Maxwell. Unfor- 

 tunately the kinetic theory of the gases is not directly applicable to the motions of 

 the stars. This theory supposes, indeed, — as far as quantitative results are con- 

 cerned — either that the molecules behave as elastic balls (Clausius), or that they 

 repel each other inversely as the fifth power of the distance (Maxwell). Neither 

 of these assumptions is valid for the stars, which we know attract each other in- 

 versely as the square of the distance. It is thus necessary to work out a kinetic 

 theory (I prefer to use the term of Gibbs »Statistical mechanics*) based on the law 

 of Newton. This iis the object of this memoir. 



For the objections that may be made against the application of statistical 

 mechanics to the motions of the stars I refer to Meddel. N:o 81. 



Such parts of the kinetic theory of the gases as are not dependent on the law 

 of attraction are naturally applicable here also. I have, however, preferred to give 

 a condensed exposition of these parts also, since in so doing I have had opportunity 

 to elucidate some points in the current literature of the subject which to me at any 

 rate, and possibly to other readers, have seemed obscure, I have given in Meddel. 

 N:ris 69, 70 some introductory remarks of this kind; these remarks will be found 

 further developed in the first two chapters of this memoir. 



Where stars are concerned it is necessary to distinguish between real collisions 

 and passages. Consequently I have devoted a chapter to the consideration of the 

 collisions of the stars. It may be that such collisions perform some important func- 

 tion in the history of the molecules. 



In the fourth chapter 1 consider the jff-theorem. 



The integration of the fundamental differential equation of Boltzmann is 

 performed with the help of the frequency series of type A. 



The development of the passagefunction, given in chapter VI, is not so easily 

 worked out by Newton's law as it is by Maxwells. There are, however, no serious 

 mathematical obstacles in the way. 



In the last chapter I compute the time of relaxation for stars, which is found 

 to amount to the considerable value of^lO^^ years. 



Applying the law of Newton to the kinetic theory of the gases, I find that 

 such an application is only possible if we use for the molecules a constant of 

 attraction 10^^ times^as great as|that valid for the attraction of the heavenly bodies. 



