[From the Philosophical Magazine for January and July, I860.] 



XX. Illustrations of the Dynamical Theory of Gases*. 



PART I. 



/ 



ON THE MOTIONS AND COLLISIONS OF PEEFECTLY ELASTIC SPHERES. 



So many of the properties of matter, especially when in the gaseous form, 

 can be deduced from the hypothesis that their minute parts are in rapid motion, 

 the velocity increasing with the temperature, that the precise nature of this 

 motion becomes a subject of rational curiosity. Daniel Bernouilli, Herapath, 

 Joule, Kronig, Clausius, &c. have shewn that the relations between pressure, 

 temperature, and density in a perfect gas can be explained by supposing the 

 particles to move with uniform velocity in straight lines, striking against the 

 sides ef the containing vessel and thus producing pressure. It is not necessary 

 to suppose each particle to travel to any great distance in the same straight 

 line ; for the effect in producing pressure will be the same if the particles 

 strike against each other ; so that the straight line described may be very short. 

 M. Clausius has determined the mean length of path in terms of the average 

 distance of the particles, and the distance between the centres of two particles 

 when collision takes place. We have at present no means of ascertaining either 

 of these distances ; but certain phenomena, such as the internal friction of gases, 

 the conduction of heat through a gas, and the diffusion of one gas through 

 another, seem to indicate the possibility of determining accurately the mean 

 length of path which a particle describes between two successive collisions. In 

 order to lay the foundation of such investigations on strict mechanical principles, 

 I shall demonstrate the laws of motion of an indefinite number of small, hard, 

 and perfectly elastic spheres acting on one another only during impact. 



* Read at the Meeting of the British Association at Aberdeen, September 21, 1859. 

 VOL. I. 48 



