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RE: Bulges



S. Chandrasekhar in his beautiful commentary "Newton's Principia for the
Common Reader" says that Newton did explicitly describe the tidal action of
one gravitating body on another such that it effects equal bulges at
antipodal points of the attracting body.

The specific passage cited by Dave Hamilton is in Book 3, Prop. 24, Theorem
10. On p. 258 of Motte's 1729 translation Newton refers to Plate 10, Fig 2.
Here we see an ellipse representing "...the Earth covered with deep
waters". The following discussion clearly indicates that the sphereoid
resulting from rotating the ellipse about an axis connecting the center of
the Earth and the Moon represents the surface of the water and that one
bulge is under the moon and the other is on the opposite side of the Earth.
Chandrasekhar notes that the figure is not always an ellipse. Newton does
not explain in Book 3 why the bulges should occur.

The results of this section in Book 3 are based on Prop. 56, Cor. 18 - 22
in Book 1. Specifically Cor. 19 supports the elliptical figure in Book 3.
Chandrasekhar helps us through the quagmire of Newton's prose and notation
to see the beauty of his insight. Even though Newton was not entirely
correct in his explanation, his results were remarkable.

Paul Middents
Olympic College
Bremerton, WA

----------
From: Dave Hamilton
Sent: Saturday, March 01, 1997 9:59 AM
To: Phys - L
Subject: Re: Bulges

In the System of the World (Book III of Principia), Newton clearly
indicates that there are two tides per day and draws an ellipse that
represents a cross section of the Earth (showing bulges on both sides).
He goes so far as to explain some unusual occurrences that had been noted
by sailors in Batshaw and the kingdom of Tunquin that, on the day
following the moon's transition from one side of the equator to the
other, there is only one tide per day.

In my quick perusal of this passage, however, I cannot find where he
explains why there must be bulges on opposite sides of the Earth.

Am I wrong in thinking that the usual attribution of TWO tidal bulges is
to
Newton? And he did this by recognizing that the Moon/Earth system
revolves
about the mutual center of mass. This is certainly the presentation in
various physics texts. But I don't find these thoughts in the Principia.

Can the list help?


Jim Green
JMGreen@sisna.com


It has been my impression that Newton did not understand that his theory
predicts two tides. I have not read the Principia.

Leigh


David J. Hamilton, Ed.D. "And gladly wolde he lerne,
Franklin HS, Portland, OR and gladly teche."
djhamil@teleport.com Geoffrey Chaucer

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