Notes on alpha and beta

1) In Bayer's Uranometria two stars -alpha (Rukbat Alrami) and beta(Arkab, a double star visible to the naked eye) are in the right foreleg of Sagittarius. Ptolemy says instead that the first one is in the left fore-hoof ; and the second inside the knee of the same leg. The positions given by Ptolemy seem therefore inverted with reference to the Bayer's figure as if the position of the stars was described from the outside of a solid sphere (as for example in the Hevelius' atlas of 1690 in which, in fact, alpha and beta are in the left leg).

2) As far as the horse-part and the head are concerned, we have changed Bayer's image in order to keep to the real positions of the stars. Bayer, in fact, moves alpha and beta towards the Scorpion and he gets a more elegant image since two forelegs are less distant and more proportionate, but it does not correspond to the sky. Hevelius corrects Bayer's error since he draws two forelegs opened very wide, as in our figure, but his figure does not keep to the position of the stars set inside the head since they are too low (nu1 and nu2 have to be inside the eye).

3) For Ptolemy alpha and beta are the brightest of the constellation, they have the second magnitude. Bayer (1603) follows Ptolemy and indicates them as the stars of second magnitude and he attributes the first two letters of the alphabet to them; however, Hevelius (1690) reduces their magnitude of as much as two degrees and he marks them as stars having the fourth magnitude as they actually appear to the observer. Sûfîle catalogued them as stars having 4.5 magnitude already in the X century and in 1430 they appear as stars having the fourth magnitude in Ulugh-Beigh's catalogue. These two stars are not variable in modern catalogues, therefore it seems to be Ptolemy's mistake repeated by Bayer. On the other hand, Sagittarius' legs are quite well visible only in the most southern zones of Europe and Bayer is likely to have followed the Almagest without attaching much importance to the direct observation. However, Ptolemy's mistake seems too serious, as it was already pointed out by Camille Flammarion at the beginning of the XX century: "On the other hand, Ptolemy is not likely to have made such a blunder, since he compiled his Catalogue based on his and on Hipparchus observations with the greatest care and attention and, after all, all the copies of the Almagest are completely in agreement on this matter. However, if we could find other ancient observations of these two stars, our appraisal and judgement would be certainly more sure. Therefore, Arato's help arrives to us at the right moment. It seems that in the following passage Arato refers just to the stars in question : "Under the Sagittarius, he writes, we discern a circle which is not bright at all (the main stars of Corona Australis, in fact, have only the fourth magnitude), while under the fore-hoofs much more shining stars can be seen." Flammarion ends by saying that hence it must be the matter of alpha and beta of Sagittarius (since there are not any other stars in the mentioned region of the sky) and that it is necessary to admit that they have fallen from second to fourth magnitude".