But the directions of the coordinates are perfectly arbitrary, and therefore this number must depend on the distance from the origin alone, that is f(x))f(z)=(x2+y2+z2) Solving this functional equation, we find f(e C d(r2) If we make A positive, the number of particles will increase with the velocity, and we should find the whole number of particles infinite. We therefore make A negative and equal to- 1/, so that the number between x and x+ dx is NCe-la)dx Integrating from x=-oo to x =+oo, we find the whole number of particles, Nvzx=M,∴C≈、l av兀