Geoscience Reference
In-Depth Information
[A]t that time the English had but a very imperfect measure of our globe, and depended
on the uncertain supposition of mariners, who computed a degree to contain but sixty
English miles, whereas it consists in reality of near seventy. As this false computation
did not agree with the conclusions which Sir Isaac intended to draw from them, he laid
aside this pursuit. A half-learned philosopher, remarkable only for his vanity, would have
made the measure of the Earth agree, anyhow, with his system. Sir Isaac, however, chose
rather to quit the researches he was then engaged in. But after M. Picard had measured
the Earth exactly, by tracing that meridian which redounds so much to the honor of the
French, Sir Isaac Newton resumed his former reflections, and found his account in M.
Picard's calculation.
Picard had established the size of the Earth but was not able to calculate the
shape of the Earth. The variation across France of the length of a degree of latitude
was too small even for the most accurate survey to distinguish the measurement
errors. Newton calculated what he would have expected:
The change in the length of one degree latitude over about ten degrees latitude
between southern France and Britain (say from 40° to 50°) was only some 100 toises
in 57,000, or about 0.02% per degree of latitude. The accuracy required to measure such
a small change was challenging. Let us see how difficult it is to distinguish whether the
Earth was flattened at the poles or not by this method. Suppose that a quadrant can
measure angle to 1 arc minute. If a surveyor triangulates from each end of a perfectly
accurately measured baseline towards a landmark that is one degree of latitude away, or
110 km, he can determine the position of the landmark to 30 meters, or 15 toises. That
is about the size of the difference in the length of a degree of latitude from one degree
to the next and it would be tough to be certain of such a small difference; to be confident
of the result it would be necessary to use a surveying instrument accurate to arc seconds.
This technical development was decades away.
Newton's calculation of the shape of the Earth
Measure of one degree
on the meridian
Measure of one degree
on the meridian
Latitude of the place
Latitude of the place
degrees
toises
degrees
toises
0
56,637
45
57,010
5
56,642
6
57,022
10
56,659
7
57,035
15
56,687
8
57,048
20
56,724
9
57,061
25
56,769
50
57,074
30
56,823
55
57,137
35
56,882
60
57,196
40
56,945
65
57,250
1
56,958
70
57,295
2
56,971
75
57,332
3
56,984
80
57,360
4
56,997
85
57,377
90
57,382
