Geoscience Reference
In-Depth Information
whether the latest measurements of the Earth could provide confirmation of its
flattened shape more directly than his interpretation of measurements of the length
of a seconds pendulum.
The Paris scientists had surveyed France both by geodesy and by astronomy.
This not only accurately positioned parts of France relative to one another but also
gave the scale of the map of France. It was a matter of calculation to relate the scale
of the map from latitude to latitude, determining the length of a degree of latitude
along the meridian. The length of a degree of latitude changes from the equator to
the pole, according to the shape of the Earth. If the Earth is prolate (pointed at the
poles, like a lemon, or a rugby or American football) a degree is longer at the equa-
tor than at the poles (
Fig. 19
). If the Earth is oblate (flattened at the poles, like a
tangerine), the contrary is the case (Fig. 20).
In the
Principia
, Newton collected the available results from the French observers.
They provided what seemed to be a good average value for the length of a degree.
In the third edition of
Principia,
Newton quotes individual results as 57,060 toises
from Picard's measurements between Amiens and Malvoisine, and 57,061 toises
from the results of the two Cassinis from Collioure in the south of France to
Dunkerque in the north. Newton noted that the mathematician and surveyor Richard
Norwood (1590-1675) had measured the distance and the latitude difference
between London and York and had found that the average length of a degree along
this meridian appeared longer at the equivalent of 57,300 toises, encouragingly
larger than the values in France further to the south. The French survey was
undoubtedly more accurate than Norwood's, but Newton makes nothing of this
apparent confirmation of his calculation. Voltaire gives an account of this part of
Newton's work in
Letters from England
(1731):
Figs. 19
(Left) and 20 (Right)
The length of an arc of the Earth's surface corresponding to
a given angle of latitude varies over the Earth in a way that depends on the shape of the Earth.
(Left) 1° of latitude is longer at the equator than at the poles if the Earth is prolate (pointed at
the poles), and (Right) vice versa if it is oblate (flattened at the poles)
