Note 19 — SECTION A MAXWELL'S LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES

In MAXWELL'S distribution the molecules are assumed to be uniformly scattered throughout the unit volume; it is the velocities only that are variously distributed in the different elementary regions. To realize the haphazard character (necessary in Calculus of Probabilities) of the motions of the molecules, we must bear in mind that each of the molecules in the unit volume has a different velocity and direction; here no direction has preference over another, i.e., one direction of a molecule is as likely as another. Here at first we write expression for the number of molecules whose velocities parallel to the co-ordinate axes are respectively confined between the velocity limits: To find the number of molecules thus limited the procedure given above is essentially as follows: Expressed as a fraction = probability of velocities parallel to axis having values between and expressed as a number = number of molecules having such velocities between the assigned limits; similarly, = probability of velocities parallel to axis having velocities between . As these are two independent sets of velocities, the probability of their concurrence is the product and the number of molecules thus concurring is equal to . Similarly, the number of molecules concurrently possessing velocities parallel to each of the three axes is The problem is simpler in this Maxwellian case than in the more general case of any state of the body in which there is an unequal distribution in space of the molecules.