MAXWELL: THE DYNAMICAL THEORY OF GASES Phil Mag. 19(1860)19153 Let n be the whole number of particles. Let x, y, z be the com ponents of the velocity of each particle in three rectangular direc- tions, and let the number of particles for which x lies between x and x + dx, be Nf(r)dx, where f(r) is a function of x to be determined The number of particles for which y lies between y and y dy will be Nfdy; and the number for which z lies between z and z dz will be Nf(z)dz, where f always stands for the same function Now the existence of the velocity x does not in any way affect that of the velocities y or z, since these are all at right angles to each other and independent, so that the number of particles whose velocity lies between x and x dx, and also between y and y t dy, and also between z and z dz, is Nf()fo)f(z)dx dy dz If we suppose the N particles to start from the origin at the same instant, then this will be the number in the element of volume (dx dy dz) after unit of time, and the number referred to unit of volume will be Nf(fo)f(z)Phil. Mag. 19 (1860) 19