The motion of stars in the line of sight, as shown by the spectroscope--should theoretically alter their brightness in the course of time; those approaching the earth becoming gradually brighter, while those receding should become fainter. But the distance of the stars is so enormous that even with very high velocities the change would not become perceptible for ages. Prof. Oudemans found that to change the brightness of a star by only one-tenth of a magnitude--a quantity barely perceptible to the eye-a number of years would be necessary, which is represented by the formula 5916 years ----------------- parallax × motion for a star approaching the earth, and for a receding star 6195 years ---------- p × m This is in geographical miles, 1 geographical mile being equal to 4·61 English miles. Reducing the above to English miles, and taking an average for both approaching and receding stars, we have 27,660 years ------------ p × m 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.