KnobelBall Edward, Ulugh Beg's catalogue of stars (Washington, 1917). For the most complete list yet published of works that contain all or part of Ulugh Beg's Zij (star catalogue) see KrisciunasK., “The legacy of Ulugh Beg”, in Central Asian monuments, ed. by PaksoyH. B. (Istanbul, 1992), 95–103.
2.
EvansJames, “The origin of the Ptolemaic star catalogue: Part 1”, Journal for the history of astronomy, xviii (1987), 155–72, in particular pp. 162–5.
3.
ShevchenkoM., “An analysis of errors in the star catalogues of Ptolemy and Ulugh Beg”, ibid., xxi (1990), 187–201.
4.
Evans, op. cit., 171 (ref. 28).
5.
For the non-statistician reader let me give the following simplified definitions. Say for a given constellation a particular parameter of interest (x) were measured for each star. The arithmetic average of this parameter is the mean (x). Approximately 68% of the values will lie within one standard deviation (“σx,”) of that mean. 95% of the measures will lie within two standard deviations of the mean. The standard deviation of the mean is equal to σx / √N, where N is the number of observations in the sample. Thus if x = 20 and σx = ±15, 68% of the measures are within 5 and 35, and if this is based on 25 data points, the standard deviation of the mean is ±15 / √25 = ±3.
6.
Shevchenko, op. cit., 199. He does not say exactly what he did, but we have done the following. Consider the columns labelled “σ” and “N” in Tables 1 and 2. For some random variable x let the function S(x) be S(x) = (N-1) σx2. This is just another way of saying that the standard deviation of the distribution is the square root of the estimate of the variance of the distribution, and that the variance is estimated by a sum of squares of deviations, S(x), about the mean of a set of measures, divided by N-1. The square root of <mu> gives the random error for a group (or the catalogue), where Ntot is the total number of stars, and the sum over i simply means adding up the respective sums of squares for all the constellations.
7.
ThorenVictor E., The Lord of Uraniborg (Cambridge, 1990), 297, note 130. For Tycho's brighter stars the average absolute errors were 1.9′ for ecliptic longitude and 1.2′ for ecliptic latitude. For the fainter stars the errors increased to 2.8′ and 2.6′, respectively.
8.
Shevchenko, op. cit., 190.
9.
KremerR., “Bernard Walther's astronomical observations”, Journal for the history of astronomy, xi (1980), 174–91, p. 180.
