where p = parallax in seconds of arc, and m = radial velocity in English miles per second.
Prof. Oudemans found that the only star which could have changed in brightness by one-tenth of a magnitude since the time of Hipparchus is Aldebaran. This is taking its parallax as 0″·52. But assuming the more reliable parallax 0″·12 found by Dr. Elkin, this period is 4⅓ times longer. For Procyon, the period would be 5500 years.[282] The above calculation shows how absurd it is to suppose that any star could have gained or lost in brightness by motion in the line of sight during historical times. The “secular variation” of stars is quite another thing. This is due to physical changes in the stars themselves.
The famous astronomer Halley, the second Astronomer Royal at Greenwich, says (Phil. Trans., 1796), “Supposing the number of 1st magnitude stars to be 13, at twice the distance from the sun there may be placed four times as many, or 52; which with the same allowance would nearly represent the star we find to be of the 2nd magnitude. So 9 × 13, or 117, for those at three times the distance; and at ten times the distance 100 × 13, or 1300 stars; of which distance may probably diminish the light of any of the stars of the 1st magnitude to that of the 6th, it being but the hundredth part of what, at their present distance, they appear with.” This agrees with the now generally accepted “light ratio” of 2·512 for each magnitude, which makes a first magnitude star 100 times the light of a 6th magnitude.
On the 4th of March, 1796,[283] the famous French astronomer Lalande observed on the meridian a star of small 6th magnitude, the exact position of which he determined. On the 15th of the same month he again observed the star, and the places found for 1800 refer to numbers 16292-3 of the reduced catalogue. In the observation of March 4 he attached the curious remark, “Étoile singulière” (the observation of March 15 is without note). This remark of Lalande has puzzled observers who failed to find any peculiarity about the star. Indeed, “the remark is a strange one for the observer of so many thousands of stars to attach unless there was really something singular in the star’s aspect at the time.” On the evening of April 18, 1887, the star was examined by the present writer, and the following is the record in his observing book, “Lalande’s étoile singulière (16292-3) about half a magnitude less than η Cancri. With the binocular I see two streams of small stars branching out from it, north preceding like the tails of comet.” This may perhaps have something to do with Lalande’s curious remark.
The star numbered 1647 in Baily’s Flamsteed Catalogue is now known to have been an observation of the planet Uranus.[284]
Prof. Pickering states that the fainter stars photographed with the 8-inch telescope at Cambridge (U.S.A.) are invisible to the eye in the 15-inch telescope.[285]
Sir Norman Lockyer finds that the lines of sulphur are present in the spectrum of the bright star Rigel (β Orionis).[286]
About 8½° south of the bright star Regulus (α Leonis) is a faint nebula (H I, 4 Sextantis). On or near this spot the Capuchin monk De Rheita fancied he saw, in the year 1643, a group of stars representing the napkin of S. Veronica—“sudarium Veronicæ sive faciem Domini maxima similitudina in astris expressum.” And he gave a picture of the napkin and star group. But all subsequent observers have failed to find any trace of the star group referred to by De Rheita![287]
The Bible story of the star of the Magi is also told in connection with the birth of the sun-gods Osiris, Horus, Mithra, Serapis, etc.[288] The present writer has also heard it suggested that the phenomenon may have been an apparition of Halley’s comet! But as this famous comet is known to have appeared in the year B.C. 11, and as the date of the Nativity was probably not earlier than B.C. 5, the hypothesis seems for this (and other reasons) to be inadmissible. It has also been suggested that the phenomenon might have been an appearance of Tycho Brahé’s temporary star of 1572, known as the “Pilgrim star”; but there seems to be no real foundation for such an hypothesis. There is no reason to think that “temporary” or new stars ever appear a second time.
Admiral Smyth has well said, “It checks one’s pride to recollect that if our sun with the whole system of planets, asteroids, and moons, and comets were to be removed from the spectator to the distance of the nearest fixed star, not one of them would be visible, except the sun, which would then appear but as a star of perhaps the 2nd magnitude. Nay, more, were the whole system of which our globe forms an insignificant member, with its central luminary, suddenly annihilated, no effect would be produced on those unconnected and remote bodies; and the only annunciation of such a catastrophe in the Sidereal “Times” would be that a small star once seen in a distant quarter of the sky had ceased to shine.”[289]