Geoscience Reference
In-Depth Information
stand how he applied these things [to the explanation in Book III of the
Principia
].
In a word, all I found was gibberish and obscurity.”
Ideas
The Principia
The seeds of Newton's masterpiece, the
Principia
, were planted in 1684 at the Royal
Society. Two astronomers, Edmund Halley and Sir Christopher Wren, suspected from
Kepler's Third Law that there was an inverse square force governing planetary motions but
could not prove it. During a discussion of this point Robert Hooke claimed that he could
prove all of Kepler's laws. When Wren cast doubt on the claim and offered a topic as a
prize for a public proof, Hooke failed to deliver.
Halley put the question next to Newton. Newton had already solved the problem years
before but could not find the proof among his papers. Later he sent Halley a nine page
proof,
De Motu Corporum
, or
On the Motions of Bodies in Orbit
. Halley suggested pub-
lication, but Newton was reluctant to expose his work to public scrutiny, having no
appetite for the cut-and-thrust of debate. Halley persisted and Newton worked for 18
months on the paper, expanding it to three topics where the mathematical theories of
gravity and motion are set out like a topic of geometry with theorems and propositions.
The work was published at Halley's expense as
Philosophiæ Naturalis Principia
Mathematica.
It was written in Latin to make it accessible to scientists throughout the
world. Its English title is
The Mathematical Principles of Natural Philosophy
, but it is
always known by its short title of
The Principia
, pronounced “
Prinsipia”
or “
Prinkipia
.” It
was first published in 1687, followed by a second and a third edition in 1713 and 1726
respectively; copies of the successive Latin editions were immediately available in France.
It was first translated into English by Andrew Motte (1729). A French translation was
prepared by the Marquise de Châtelet with explanations and reworkings of the theorems by
Alexis-Claude Clairaut (1756).
For the purposes of his explanation of Richer's results, which Bernouilli found
obscure, Newton envisaged that the Earth was bored through with a tube that ran
from its pole along a radius to its center, and then from its center along a radius at
right angles to the first, to its equator (Cohen and Whitmore 1999). The tube was
filled with water, and the weight of the water along the polar axis was equal to the
weight of the water to the equator because the water tube was connected at the
Earth's center and the pressures of the two columns must match at the central point
(
Fig. 18
). But the weight of the tube of water at the equator was reduced by centrifu-
gal force because of the rotation of the Earth; for the weights to be equal, the tube
to the equator had to be filled with more water than the tube to the pole. Newton
calculated that the equatorial radius of the Earth was longer than the polar radius
by about 17 miles, and the ratio of the diameter of the Earth at its equator to its
diameter at the poles is 230 to 229 miles.
There is much in this proof that is unstated and others besides Bernouilli have
found it subtle to understand, including the Nobel prize-winner Subramanyan
Chandrasekhar (1910-1995) in his reworking of the
Principia
in modern mathemat-
ics (1995).
To Newton the result that the Earth was flattened at the poles was perfectly
plausible- Jupiter was so flattened at the poles that its elliptical shape was plain to
see in a telescope. Newton knew that in 1691 Cassini I had measured Jupiter's
diameter and its diameter at its equator was about 7% longer than its diameter at
the poles; this was confirmed by James Pound's observations in 1717.
