In order to escape this dilemma, Seeliger suggested a modification of
Newton's law, in which he assumes that for great distances the force
of attraction between two masses diminishes more rapidly than would
result from the inverse square law. In this way it is possible for the
mean density of matter to be constant everywhere, even to infinity,
without infinitely large gravitational fields being produced. We thus
free ourselves from the distasteful conception that the material
universe ought to possess something of the nature of a centre. Of
course we purchase our emancipation from the fundamental difficulties
mentioned, at the cost of a modification and complication of Newton's
law which has neither empirical nor theoretical foundation. We can
imagine innumerable laws which would serve the same purpose, without
our being able to state a reason why one of them is to be preferred to
the others ; for any one of these laws would be founded just as little
on more general theoretical principles as is the law of Newton.
Notes
*) 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.
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