A system of physical chemistry - Index of

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A system of physical chemistry - Index of

APPENDIX I.

Maxwell's Distribution Law and the Principle of Equipartition

OF Energy.

By James Rice, M.A.

The aim of mechanics is the description of motion. We seek to

specify the position of every part of a system of bodies at every instant.

The most direct way of doing this would be to express all the necessary

geometrical co-ordinates of the system as known functions of the time.

To this end the laws of motion are applied to the special features and

environment of each system, and a series of differential equations are

obtained which, among other quantities, involve the first and second

differential coefficients of each co-ordinate with respect to the time,

i.e. the velocities and accelerations. If the mathematician can solve

for us the particular differential equations arrived at, v/e have attained

our object for that system.

have proved amenable to

Many special cases of considerable interest

mathematical treatment, but, at present, no

solution for the general case exists.

In the phrase, "system of bodies," we must be definite as to the

meaning to be attached to the word " body ". In physics and chemistry,

a is

single body a i.e. system, a collection of molecules, which are in

themselves discrete, if minute bodies. Indeed the molecule itself is a

system of atoms and, on present views, the atom is a system of nuclei

and electrons. Even if we regard a body of fluid or solid material as

a system of molecules alone, without concerning ourselves about its

internal structure, the complexity of description involved in a complete

account of molecular motion is so great that it becomes necessary to

introduce the mathematical theory of probability. We are no longer

concerned with an exact solution of the dynamical problem, by which one

could predict with certainty the position and motion of each molecule

at a given instant ; instead we endeavour to find the law of distribution

of the co-ordinates and velocities of the molecules, so as to be able

to state, with but small possibility of error, that at a given instant such

and such a fraction of the molecules will occupy such and such a portion

of the space filled by the body, and have velocities lying between such

and such limits. It is this feature which characterises a problem as one

of statistical mechanics.

In dealing with a system of molecules, the co-ordinates referred to

above are naturally the Cartesian co-ordinates of the centres of each

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