THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



MARCH 1888. 



XVIII. On a Law of Distribution of Molecular Velocities 

 amongst the Molecules of a Fluid. By John Buchanan, 

 B.Sc* 



IT is knownf that if a mechanical system at rest be set in 

 motion by impulses, the kinetic energy of the system is 

 a maximum or a minimum. 



The kinetic energy is always a maximum when the impulses 

 are given, and when different motions possible under the 

 conditions of the system, and fulfilling the law of energy, are 

 considered. It is a minimum if the system be started from 

 rest by impulses applied only at places where the velocities to 

 be produced are specified. 



The present paper has for its object the introduction of 

 these theorems into the Kinetic Theory of Gases, and into 

 questions whose mathematical treatment may be of a similar 

 nature. 



Many years ago Clerk-Maxwell discovered his law relating 

 to the most probable manner of distribution of the molecular 

 velocities amongst the molecules of a quantity of gas whose 

 centre of gravity is at rest, or is moving uniformly in a 

 straight line. I propose to show that a law of the same form 

 holds for the distribution of the molecular velocities in a fluid 

 whose molar kinetic energy fulfils a maximum, or a minimum, 



* Communicated, by the Author. 



t See Thomson and Tait's 'Natural Philosophy,' vol. i. part 1. §§ 311 

 and 312. 



Phil. Mag. S. 5. Vol. 25. No. 154. March 1888. N 



