Pagina 164 van 212

[24] Proof-According to the theory of Newton, the number of

"lines of force" which come from infinity and terminate in a mass

m is proportional to the mass m. If, on the average, the mass

density ρ0 is constant throughout the universe, then a sphere of

volume V will enclose the average mass ρ0V. Thus the number of

lines of force passing through the surface F of the sphere into

its interior is proportional to ρ0V. For unit area of the surface

of the sphere the number of lines of force which enters the

sphere is thus proportional to ρ0V/F or to ρ0R. Hence the

intensity of the field at the surface would ultimately become

infinite with increasing radius R of the sphere, which is

impossible.