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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