IV. On the Dynamical Theory of Gases. By J. Clerk Maxwell, F.B.S. L.&E 
Received May 16, — Read May 31, 1866. 
Theories of the constitution of bodies suppose them either to be continuous and homo- 
geneous, 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 coordinates, but I am not aware that any theory of this kind 
has been proposed to account for the different properties of bodies. Indeed the pro- 
perties of a body supposed to be a uniform plenum 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 rela- 
tions 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 coordinates when in equi- 
librium. It appears from the mathematical 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. 
Now we know that in fluids the elasticity of form is evanescent, while that of volume 
is considerable. Hence such theories will not apply to fluids. In solid bodies the 
elasticity of form appears in many cases to be smaller in proportion to that of volume 
than the theory gives*, so that we are forced to give up the theory of molecules whose 
displacements are functions of their coordinates when at rest, even in the case of solid 
bodies. 
The theory of moving molecules, on the other hand, is not open to these objections. 
The mathematical difficulties in applying the theory are considerable, and till they are 
surmounted we cannot fully decide on the applicability of the theory. We are able, 
however, to explain a great variety of phenomena by the dynamical theory which have 
not been hitherto explained otherwise. 
The dynamical theory supposes that the molecules of solid bodies oscillate about their 
* [In glass, according to Dr. Everett’s second series of experiments (1866), the ratio of the elasticity of form 
to that of volume is greater than that given by the theory. In brass and steel it is less. — March 7, 1867.] 
MDCCCLXVII. H 
