There are three of the periodic stars plainly visible to the naked eye at maximum, of which the variations are so wide that they may easily be noticed by any one who looks for them at the right times, and knows how to find the stars. These stars are:
Omicron Ceti, called also Mira Ceti.
Beta Persei, or Algol.
Beta Lyræ.
It happens that each of these stars exemplifies a certain type or law of variations.
Omicron Ceti. On August 13, 1596, David Fabricius noticed a star in the constellation Cetus, which was not found in any catalogue. Bayer, in his ‘Uranometria’, of which the first edition was published in 1601, marked the star Omicron, but said nothing about the fact that it was visible only at certain times. Fabricius observed the star from time to time, until 1609, but he does not appear to have fully and accurately recognized its periodicity. But so extraordinary an object could not fail to command the attention of astronomers, and the fact was soon established that the star appeared at intervals of about eleven months, gradually fading out of sight after a few weeks of visibility. Observations of more or less accuracy having been made for more than two centuries, the following facts respecting it have been brought to light:
Its variations are somewhat irregular. Sometimes, when at its brightest, it rises nearly or quite to the second magnitude. This was the case in October, 1898, when it was about as bright as Alpha Ceti. At other times its maximum brightness scarcely exceeds the fifth magnitude. No law has yet been discovered by which it can be predicted whether it shall attain one degree of brightness or another at maximum.
Its minima are also variable. Sometimes it sinks only to the eighth magnitude; at other times to the ninth or lower. In either case it is invisible to the naked eye.
As with other stars of this kind, it brightens up more rapidly than it fades away. It takes a few weeks from the time it becomes visible to reach its greatest brightness, whatever that may be. It generally retains this brightness for two or three weeks, then fades away, gradually at first, afterward more rapidly. The whole time of visibility will, therefore, be two or three months. Of course, it can be seen with a telescope at any time.
The period also is variable in a somewhat irregular way. If we calculate when the star ought to be at its greatest brightness on the supposition that the intervals between the maxima ought to be equal, we shall find that sometimes the maximum will be thirty or forty days early, and at other times thirty or forty days late. These early or late maxima follow each other year after year, with a certain amount of regularity as regards the progression, though no definable law can be laid down to govern them. Thus, during the period from 1782 to 1800 it was from thirteen to twenty-four days late. In 1812 it was thirty-nine days late. From 1845 to 1856 it was on the average about a month too early. Several recent maxima, notably those from 1895 to 1898, again occurred late. Formulæ have been constructed to show these changes, but there is no certainty that they express the actual law of the case. Indeed, the probability seems to be that there is no invariable law that we can discover to govern it.
Argelander fixed the length of the period at 331.9 days. More recently, Chandler fixed it at 331.6 days. It would seem, therefore, to have been somewhat shorter in recent times. It was at its maximum toward the end of October, 1898. We may, therefore, expect that future maxima will occur in July, 1901; June, 1902; May, 1903; April, 1904, and so on, about a month earlier each year. During the few years following 1903 the maxima will probably not be visible, owing to the star being near conjunction with the sun at the times of their occurrence. The most plausible view seems to be that changes of a periodic character, involving the eruption of heated matter from the interior, of the body to its surface, followed by the cooling of this matter by radiation, are going on in the star.
The star Algol, or Beta Persei, as it is commonly called in astronomical language, may, in northern latitudes, be seen on almost any night of the year. In the early summer we should probably see it only after midnight, in the northeast. In late winter it would be seen in the northwest. From August until January one can find it at some time in the evening by becoming acquainted with the constellations. It is nearly of the second magnitude. One might look at it a score of times without seeing that it varied in brilliancy. But at certain stated intervals, somewhat less than three days, it fades away to nearly the fourth magnitude for a few hours, and then slowly recovers its light. This fact was first discovered by Goodrick in 1783, since which time the variations have been carefully followed. The law of variation thus defined is expressed by a curve of the following form: