A View of Sir Isaac Newton's PhilosophyPemberton, Henry
Science
A View of Sir Isaac Newton's Philosophy
Pemberton, Henry
Newton, Isaac, 1642-1727. Principia
35. BUT from this last observation our author is enabled to determine
the proportion between the axis of the earth drawn from pole to pole,
and the diameter of the equator, upon the supposition that all the
parts of the earth are of equal density; which he does by computing in
the first place the proportion of the centrifugal force of the parts
under the equator to the power of gravity; and then by considering
the earth as a spheroid, made by the revolution of an ellipsis about
its lesser axis, that is, supposing the line M I L K to be an exact
ellipsis, from which it can differ but little, by reason that the
difference between the lesser axis M L and the greater I K is but very
small. From this supposition, and what was proved before, that all the
particles which compose the earth have the attracting power explained
in the preceding chapter, he finds at what distance the parts under the
equator ought to be removed from the center, that the force, with which
they shall be attracted to the center, diminished by their centrifugal
force, shall be sufficient to keep those parts in a ballance with those
which lie under the poles. And upon the supposition of all the parts of
the earth having the same degree of density, the earth’s surface at the
equator must be above 17 miles more distant from the center, than at
the poles[275].
36. AFTER this it is shewn, from the proportion of the equatorial
diameter of the earth to its axis, how the same may be determined of
any other planet, whose density in comparison of the density of the
earth, and the time of its revolution about its axis, are known. And
by the rule delivered for this, it is found, that the diameter of the
equator in Jupiter should bear to its axis about the proportion of 10
to 9[276], and accordingly this planet appears of an oval form to the
astronomers. The most considerable effects of this spheroidical figure
our author takes likewise into consideration; one of which is that
bodies are not equally heavy in all distances from the poles; but near
the equator, where the distance from the center is greatest, they are
lighter than towards the poles: and nearly in this proportion, that
the actual power, by which they are drawn to the center, resulting
from the difference between their absolute gravity and centrifugal
force, is reciprocally as the distance from the center. That this may
not appear to contradict what has before been said of the alteration
of the power of gravity, in proportion to the change of the distance
from the center, it is proper carefully to remark, that our author
has demonstrated three things relating hereto: the first is, that
decrease of the power of gravity as we recede from the center, which
has been fully explained in the last chapter, upon supposition that
the earth and planets are perfect spheres, from which their difference
is by many degrees too little to require notice for the purposes there
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