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| Rømer and the
refraction. Erling Poulsen
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 Around
the year 1690 Ole Rømer constructed his first
transitinstrument at his home in St. Kannikestræde. The
reason why he did not place it in the Round Tower
Observatory was that this was shaking too much, ex. when
a carriage passed by in the street, it was impossible to
pinpoint the stars.
In the following ten years he used this instrument and
it was improved. However, some errors in his
construction demanded a new construction; apart from
some distortions the temperatureinfluens
on his graduated arc was a problem. Furthermore the many
nonastronomical duties he had in Copenhagen kept him
from stargazing.
In the summer of 1704, he constructed a small
observatory near the country house of his father-in-law,
Erasmus
Bartholin, app. 17 km from Copenhagen, near the
place where you today find the Ole Rømer Museum. The
disorders were corrected and his temperature problem was
solved using a full circle as a graduated arc. This
would expand radially so the graduations did not move
away from the proper position when the temperature
changed. This was the Meridian Circle.
He took care of the distortions still remaining in his
notebook1), and the only thing left was all
the earthbound measurements of the star-positions' big
problem, the refraction.
From earlier times, different refraction-tables had been
used but around 1700 a new way of thinking arose, in
which a model or theory of refraction had to be made.
The physical model he used can be found in
"Adversaria"2) and is:
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 The
true zenith distance is z'+v.
The observed zenith distance is z.
Rj is the radius of the earth
h is the thickness of the atmosphere.
The law for refraction: sin z'=n*sin z1
here n is the index of refraction for air.
The Sine-relation used in triangle OAB gives:
sin(180-z)/(Rj+h) = sin z1/Rj
sin z1 = (Rj/(Rj+h))*sin z
From this we get z1
z' is found from the law of refraction
v = z-z1: true zenith distance = z'+z-z1
Refraction = true zenith distance-z=z'-z1
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A theory about the decreasing density and
therefore decreasing refraction when you move up in the
atmosphere was not known. He thought that there was a
sharp line between the air and the ether (what today is
known as empty space).
There are two variables in the calculations, the index
of refraction for air and the relative thickness of the
atmosphere (compared with the radius of the earth).
He tried with different indexes and different
thicknesses to find a combination that was in accordance
with his observations. This led to a measurement of the
thickness of the atsmosphere, which is compared to
another way of measuring the same, with a barometer3).
He also wrote in a remark4) that the
refraction is greater in the morning, but it did not
give him the idea that the refraction depends on the
temperature.
The calculations. These start
with a reference to calculations made in Paris, here
they used 1,000285 as index the of refraction of air,
and 6/10000 as the relative
thickness of the atmosphere (compared with the earth
radius). Then, from observed refraction, he found that
the index is 1,00027; this index is used to calculate
the refraction of a star with observed latitude 1° at
two different thicknesses (6/10000
and 18/10000). Now, by comparing
with observations made by Cassini and la'Hire, he found
that the thickness must be close to 6/10000.
By comparing with observations of a star at 32°, he
found that the values, which could best be compared with,
the observations must use an index of 1,00032 and a
thickness of 7/10000.
He then tried with a thickness of 9/10000
and the same index. The result is compared with an
observation of la'Hire. Calculations with different
thicknesses followed and he found that 18/10000
was too much, maybe he was thinking of barometric
readings.
He then calculated a table for stars with latitudes 0°,
4° and 20°, and from this he concluded that above 20°
the thickness of the atmosphere had no influence. He
then compared the thickness 6/10000
with barometric readings and found that they were in
agreement. Furthermore, he wrote a remark that the ether
between the atmosphere and the moon must be light (weight
air:ether=200000:1) and have a very small refraction.
He finished his calculations on refraction with a recipe
for calculating refraction. We can compare the method of
Rømer with F. W. Bessel's observed average values of
refraction. Rømers values are calculated with 1,000276
as the index of refraction and 6/10000
as the relative thickness of the atmosphere, those were
the values he prefered in the end. The Bessel values
come from "Norton Star Atlas", 17 ed., p. 35;
and they are for 10°C and 752 mmHg.
| Latitude 90 -z |
0° |
1° |
5° |
10° |
20° |
30° |
40° |
50° |
80° |
| Rømer |
31'37" |
27'16" |
10'15" |
5'18" |
2'36" |
1'39" |
1'08" |
0'48" |
0'10" |
| Bessel |
34'54" |
24'25" |
9'47" |
5'16" |
2'37" |
1'40" |
1'09" |
0'48" |
0'10" |
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1) Adversaria,
the original in Royal Library, Copenhagen; printed 1910
by the Royal Danish Science Society, p. 231-234.
2) p. 94 - 103, on fol. 50 in
the original are a small drawing, you don't find it in
the printed version.
3) p. 101.
4) p. 100. |
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