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T is a curious fact that the ancient astronomers, notwithstanding the care with which they observed the heavens, never noticed that any of the stars changed in brightness. The earliest record of such an observation dates from 1596, when the periodical disappearance of Omicron Ceti was noticed. After this, nearly two centuries elapsed before another case of variability in a star was recorded. During the first half of the nineteenth century Argelander so systematized the study of variable stars as to make it a new branch of astronomy. In recent years it has become of capital interest and importance through the application of the spectroscope.

Students who are interested in the subject will find the most complete information attainable in the catalogues of variable stars, published from time to time by Chandler in the 'Astronomical Journal.' His third catalogue, which appeared in 1896, comprises more than 300 stars whose variability has been well established, while there is always a long list of 'suspected variables'—whose cases are still to be tried. The number to be included in the established list is continually increasing at such a rate that it is impossible to state it with any approximation to exactness. The possibility of such a statement has been yet further curtailed by the recent discovery at the Harvard Observatory that certain clusters of stars contain an extraordinary proportion of variables. Altogether at the time of the latest publication, 509 such stars were found in twenty-three clusters. The total number of these objects in clusters, therefore, exceeds the number known in the rest of the sky. They will be described more fully in a subsequent chapter. For the present we are obliged to leave this rich field out of consideration and confine our study to the isolated variable stars which are found in every region of the heavens.

Variable stars are of several classes, which, however, run into each other by gradations so slight that a sharp separation cannot always be made between them. Yet there are distinguishing features, each of which marks so considerable a number of these stars as to show some radical difference in the causes on which the variations depend.

We have first to distinguish the two great classes of irregular and periodic stars. The irregular ones increase and diminish in so fitful a way that no law of their change can be laid down. To this class belong