SELECTED READINGS IN PHYSICS: KINETIC THPORY E DYNAMICAL THEOR f()is therefore e-(/a there be n particles of the first system, and Nof the second Whence we may draw the following conclusions: then NN is the whole number of such pairs. Let us consider the Ist. The number of particles whose velocity, resolved in a certain velocities in the direction of x only; then by Prop. IV. the number of the first kind, whose velocities are between x and x + dx, is direction, lies between x and x +dx is la)dx 2nd. The number whose actual velocity lies between u and D The number of the second kind, whose velocity is between x +y and x+y+dy,is (2) 1。(x+》P rd. To find the mean value of v, add the velocities of all the where B is the value of a for the second system articles together and divide by the number of particles; the result is The number of pairs which fulfil both conditions is mean velocity =2a NN Br e-t/e*at?"8)dx dy 4th. To find the mean value of u2, add all the values together and ivide by N Now x may have any value from -oo to ao consistently with the mean value of u2=影2 difierence of velocities being between y and y +dy; therefore itegrating between these limits, we find This is greater than the square of the mean velocity, as it ought It appears from this proposition that the velocities are distributed NNa+I among the particles according to the same law as the errors are distributed among the observations in the theory of the"method of for the whole number of pairs whose difference of velocity lies be- least squares. "The velocities range from 0 to oo, but the number of tween y and y+小 those having great velocities is comparatively small. In addition to This expression, which is of the same form with(1)if we put NN these velocities, which are in all directions equally, there may be a for N, 2+B2 for a2, and y for x, shews that the distribution of general motion of translation of the entire system of particles which relative velocities is regulated by the same law as that of the velocities must be compounded with the motion of the particles relatively to themselves, and that that the mean relative velocity is the square root of one another. We may call the one the motion of translation, and the sum of the squares of the mean velocities of the two systems. the other the motion of agitation Since the direction of motion of every particle in one of the systems Prop. V. Two systems of particle may be reversed without changing the distribution of velocities, it iw stated in Prop. IV. to find the number of pairs of particles, one that the velocities compounded of the velocities of two of each system, whose relative velocity lies between given limits es, one in each system, are distributed according to the same ula(5)as the rel