CORRECTIONS of the RUDOLPHINE NUMBERS Since

CHAPTER FIFTEEN1

CORRECTIONS OF THE RUDOLPHINE NUMBERS

Since that error which I have found in the Rudolphine Tables is far too great, I think it will not be unappreciated if I show here how the calculation may be corrected so as to agree with this and other observations. I believe in the form of Kepler’s hypotheses, wholly agreeing with them. I earnestly embrace both the annual and diurnal motion of the Earth. The causes of the motions, I am sure, are not intricate arrange- ments of deformed circles, but natural and magnetic,2 to be attributed to the Sun’s rotation about its own axis. He does not understand true astronomy who does not know the shape of an orbit to be elliptical; and the center of it to be the body of the Sun itself and not some fĳicti- tious point near it, that the motion of the planet is truly unequal in its course; and that its whole apparent inequality arises not from its eccentricity alone. Finally, that the inclination of all the planets to the eclip- tic is not a libration in an annual motion, but fĳixed and constant; who denies these, has not carefully examined astronomical observations. For Kepler has sufffĳiciently demonstrated them all, and I have also found them by subsequent examination to be completely true. But to labor toward greater perfection in the structure raised on these principles, for instance in the quantity of the mean motions, orbits and eccentricities, would this not please Kepler himself, for as he ingeniously confesses, these have not yet been deeply investigated. [In margin: Tab. Rudolp., p. 7]3 These emendations, therefore, of the Sun and Venus are those I have now arrived at.

1 Chapter 14 of the second draft. 2 Elsewhere, Horrocks expresses dissatisfaction with Kepler’s magnetic hypothesis and proposes instead a mechanical analogy. Applebaum, Wilbur, “Between Kepler and Newton: The Celestial Dynamics of Jeremiah Horrocks,” Proceedings of the XIIIth International Con- gress of the History of Science, Moscow, August 18–24, 1972 (Moscow, 1974), vol. 4, 292–99. 3 Tabulae Rudolphinae, GW X, p. 44. corrections of the rudolphine numbers 55

1. Of the Sun

1. The mean motion of the Sun, as far as its quantity, is established with sufffĳicient correctness by Kepler,4 but one arcminute needs to be subtracted from its roots. But not on this account should the places of the fĳixed stars be diminished, as Longomontanus wrongly supposes. 2. He has the apogee completely correct. 3. The eccentricity, which he makes 1800 with a radius of 100,000, I make for many reasons no more than 1735. Therefore the greatest equation according to me will be 1o 59′ 18″, which, according to him is 2o 3′ 46″5. And this is Kepler’s principal error, which leads him into many others, as I will show in another work.6 4. Concerning the three ways of equating the natural days,7 namely, the astronomical [as given by Ptolemy], or the demonstrative empirical way of Tycho, and the physical rule of Kepler. I accept the last-named, for this postulates a correction of the lunar motion, and with the diminished solar eccentricity undoes that knot which so wretchedly entwined Kepler [In margin: Tab. Rud. pag. 34]. But more of this in due time, God willing.

2. Of Venus

1. I fĳind the mean motion of Venus much slower than in Kepler, by an amount without a doubt of 8′8 in a hundred years. At the beginning of this year, 1640, however, 9′ 20″ should be subtracted. And thence arises the chief cause of the considerable deviation in this observation from the Rudolphine calculation. 2. The aphelion in this century stays in 5o of Aquarius. And from the observations of the ancients, it is seen that either no motion or a very slow motion is to be assigned to it. Whence it is clear why those who refer the eccentricities of the planets to the center of the great orb of the Earth, [In margin: Astr. Dan. pag. 292] fĳind the eccentricity of Venus less at the present day than the value Ptolemy assigned to it. For

4 The mean motions for given years and centuries as given in the table. Ibid. 5 GW X, pp. 89–90. 6 Astronomia Kepleriana Defensa @ Promota in Opera posthuma, pp. 80–93. 7 The 3 ways of calculating the equation of time. 8 The Hevelius text has 18′, an apparent typographical error.