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 [Greek: ê] 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]