The question of the distance of the stars has already been treated in the section on Parallax. In employing our knowledge of star distances for the purpose of comparing their luminosity with that of the sun, we must first ascertain, as accurately as possible, the actual amount of light that the star sends to the earth as compared with the actual amount of light that the sun sends. The star Arcturus gives to our eyes about one forty-billionth as much light as the sun does. Knowing this, we must remember that the intensity of light varies, like gravitation, inversely as the square of the distance. Thus, if the sun were twice as far away as it is, the amount of its light received on the earth would be reduced to one fourth, and if its distance were increased three times, the amount would be reduced to one ninth. If the sun were 200,000 times as far away, its light would be reduced to one forty-billionth, or the same as that of Arcturus. At this point the actual distance of Arcturus enters into the calculation. If that distance were 200,000 times the sun's distance, we should have to conclude that Arcturus was exactly equal to the sun in luminosity, since the sun, if removed to the same distance, would give us the same amount of light. But, in fact, we find that the distance of Arcturus, instead of being 200,000 times that of the sun, is about 10,000,000 times. In other words, it is fifty times as far away as the sun would have to be in order that it should appear to our eyes no brighter than Arcturus. From this it follows that the real luminosity of Arcturus must be the square of 50, or 2500, times that of the sun. In the same manner we find that Sirius, which to the eye appears to be the brightest star in the sky (much brighter than Arcturus because much nearer), is about thirty times as luminous as the sun. Many of the stars are changeable in brightness, and those in which the changes occur to a notable extent, and periodically, are known as variable stars. It is probable that all the stars, including the sun, are variable to a slight degree. Among the most remarkable variables are Mira, or Omicron Ceti, in the constellation Cetus, which in the course of about 331 days rises from the ninth to the third magnitude and then falls back again (the maxima of brightness are irregular); and Algol, or Beta Persei, in the constellation Perseus, which, in a period of 2 days, 20 hours, 49 minutes, changes from the third to the second magnitude and back again. In the case of Mira the cause of the changes is believed to lie in the star itself, and they may be connected with its gradual extinction. The majority of the variable stars belong to this class. As to Algol, the variability is apparently due to a huge dark body circling close around the star with great speed, and periodically producing partial eclipses of its light. There are a few other stars with short periods of variability which belong to the class of Algol.