[From the Philosophical Transactions, Vol. CLVH.] 



XXVIII. On the Dynamical Theory of Gases. 

 (Received May 16, Read May 31, 1866.) 



THEORIES of the constitution of bodies suppose them either to be continuous 

 and homogeneous, or to be composed of a finite number of distinct particles or 

 molecules. 



In certain applications of mathematics to physical questions, it is convenient 

 to suppose bodies homogeneous in order to make the quantity of matter in each 

 differential element a function of the co-ordinates, but I am not aware that any 

 theory of this kind has been proposed to account for the different properties 

 of bodies. Indeed the properties of a body supposed to be a uniform ^/e/iwm 

 may be affirmed dogmatically, but cannot be explained mathematically. 



Molecular theories suppose that all bodies, even when they appear to our 

 senses homogeneous, consist of a multitude of particles, or small parts the 

 mechanical relations of which constitute the properties of the bodies. Those 

 theories which suppose that the molecules are at rest relative to the body may 

 be called statical theories, and those which suppose the molecules to be in 

 motion, even while the body is apparently at rest, may be called dynamical 

 theories. 



If we adopt a statical theory, and suppose the molecules of a body kept at 

 rest in their positions of equilibrium by the action of forces in the directions 

 of the lines joining their centres, we may determine the mechanical properties 

 of a body so constructed, if distorted so that the displacement of each molecule 

 is a function of its co-ordinates when in equilibrium. It appears from the mathe- 

 matical theory of bodies of this kind, that the forces called into play by a 

 small change of form must always bear a fixed proportion to those excited by 

 a small change of volume. 



