Refraction
In Deutch 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 fatherinlaw, 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 notebook^{1)}, and the only thing left was all the earthbound measurements of the starpositions’ big problem, the refraction. From earlier times, different refractiontables 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: 

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 Sinerelation used in triangle OAB gives: sin^{(180z)}/_{(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 = zz1: true zenith distance = z’+zz1 Refraction = true zenith distancez=z’z1 

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 barometer^{3)}. He also wrote in a remark^{4)} that the refraction is greater in the morning, but it did not give him the idea that the refraction depends on the temperature. 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.


^{1)} Adversaria, the original in Royal Library, Copenhagen; printed 1910 by the Royal Danish Science Society, p. 231234. ^{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. 