Shape of the Earth - Full Meridian of Glory - page 48

NEWTON'S WORK ON GRAVITY was published in the first edition of the
Principia in 1687 and by 1701 Cassini I had finished the survey from Paris to
Bourges. Through his reckoning, the scale of a degree was 57,097 toise, compared to
the value of 56,996 toise that he quotes as measured by Picard from Paris to Amiens.
His conclusion was that each degree was 1/800 (0.1%) shorter as you approached the
pole. This was five-times bigger than Newton had calculated and in the opposite
direction implying that the Earth was prolate, or pointed at the poles. His son, Cassini
II, confirmed his father's conclusion that the Earth was pointed at the poles in 1718
when he had finished the measurement of the Paris Meridian from Perpignan to
Dunkerque: “The success of this work gave us room to conjecture that the degrees of
the meridian increase as they approach the equator,” wrote Jacques Cassini in 1718,
and declared in a presentation to the Academy that the Earth was a prolate spheroid,
the shape, as some had likened, of a pot-bellied man wearing a belt. This most cer-
tainly brought chuckles from the well-fed Academicians in the audience.
This observational result was theoretically backed in 1720-22 by a mathemati-
cian, Jean-Jacques D'Ortous de Mairan. Accepting the pointy Earth as a fact, Mairan
concluded that Newton had obtained the wrong answer from an incorrect theory of
gravity. What ought to be done, argued Mairan, was to use the geodetic observa-
tions showing the shape of the Earth to derive the law of gravity. Mairan suggested
that the force of gravity at the Earth's surface depended on the radius of the sur-
face's curvature. If you fitted a sphere inside the pointy poles of the prolate shape
of the Earth that Cassini had measured, then the sphere would have to have a radius
smaller than the Earth does on average. But the force of gravity was bigger.
Conversely, if you fitted a sphere to the equator of the Cassini shape, you could fit
a sphere the size of the Earth in one direction, around the equator, but the sphere
would have a larger radius to be able to fit along the meridian and here the force of
gravity would be weaker. Mairan conjectured that the force of gravity at the Earth's
surface depends on the inverse of the product of the two radii of curvature at the
surface. It was a logical possibility, but it was an arbitrary theory of gravity that
fitted some results at the Earth's surface, and had nothing to do with any other
property of gravity (for example the motion of the planets).
People Jean-Jacques D'Ortous de Mairan (1678-1771)
A physicist, Mairan worked in a Cartesian framework on theories of heat, light, the aurora,
and gravity. He came from a noble family and had a wide interest in cultural activities -
Chinese culture and the piano, for example.
In his essay, Mairan linked the nature of the force of gravity with the theory of
gravity due to René Descartes, and this established a popular belief of the time that
the pointy shape of the Earth was the result of the Cartesian theory of gravity.
In the Principia , by now well known in France, Newton had clearly linked his
theory of gravity with the prediction that the Earth was oblate rather than prolate.
The shape of the Earth came to be seen as a test for one theory of gravity or the
other. The two theories have been thought, at that time and recently as well, to differ
in this practical way - if you measured the shape of the Earth you could determine