Note 25 — XXX COSMOLOGICAL DIFFICULTIES OF NEWTON'S THEORY

Proof—According to the theory of Newton, the number of "lines of force" which come from infinity and terminate in a mass is proportional to the mass . If, on the average, the mass-density is constant throughout the universe, then a sphere of volume will enclose the average mass . Thus the number of lines of force passing through the surface of the sphere into its interior is proportional to . For unit area of the surface of the sphere the number of lines of force which enters the sphere is thus proportional to or to . Hence the intensity of the field at the surface would ultimately become infinite with increasing radius of the sphere, which is impossible.