VARIABLE STARS. 173 



right ascension and declination. The frequently-repeated term grada- 

 tion indicates a difference of brightness, which may be distinctly recog- 

 nized even by the naked eye, or, in the case of those stars which are 

 invisible to the unaided sight, by a Frauenhofer's comet-seeker of twen- 

 ty-five and a half inches focal length. For the brighter stars above the 

 sixth magnitude, a gradation indicates about the tenth part of the dif- 

 ference by which the successive orders of magnitude differ from one an- 

 other; for the smaller stars the usual classifications of magnitude are 

 considerably closer. 



(l)o Ceti, R. A. 32 57', Decl. 3 40'; also called Mira, on account 

 of the wonderful change of light which was first observed in this star. 

 As early as the latter half of the seventeenth century, the periodicity of *. 

 this star was recognized, and Bouillaud fixed the duration of its period 

 at 333 days ; it was found, however, at the same time, that this dura- 

 tion was sometimes longer and sometimes shorter, and that the star, at 

 its greatest brilliancy, appeared sometimes brighter and sometimes faint- 

 er. This has been subsequently fully confirmed. Whether the star ever 

 becomes perfectly invisible is as yet undecided; at one time, at the 

 epoch of its minimum, it has been observed of the eleventh or twelfth 

 magnitude ; at another, it could not be seen even with the aid of a three 

 or a four-feet telescope. This much is certain, that for a long period it 

 is fainter than stars of the tenth magnitude. But few observations of 

 the star at this stage have as yet been taken, most having commenced 

 when it had begun to be visible to the naked eye as a star of the sixth 

 magnitude. From this period the star increases in brightness at first 

 with great rapidity, afterward more slowly, and at last with a scarcely 

 perceptible augmentation ; then, again, it diminishes at first slowly, aft- 

 erward rapidly. On a mean, the period of augmentation of light from 

 the sixth magnitude extends to fifty days; that of its decrease down to 

 the same degree of brightness takes sixty-nine days ; so that the star is 

 visible to the naked eye for about four months. However, this is only 

 the mean duration of its visibility; occasionally it has lasted as long as 

 five mouths, whereas at other times it has not been visible for more than 

 three. In the same way, also; the duration both of the augmentation 

 and of the diminution of its light is subject to great fluctuations, and the 

 former is at all times slower than the latter ; as, for instance, in the year 

 1840, when the star took sixty-two days to arrive at its greatest bright- 

 ness, and then in forty-nine days became visible to the naked eye. The 

 shortest period of increase that has as yet been observed took place in 

 1679, and lasted only thirty days; the longest (of sixty-seven days) oc- 

 curred in 1709. The decrease of light lasted the longest in 1839, being 

 then ninety-one days; the shortest in the year 1660, when it was com- 

 pleted in nearly fifty-two days. Occasionally, the star, at the period of 

 its greatest brightness, exhibits for a whole month together scarcely any 

 perceptible variation ; at others, a difference may be observed within a 

 very few days. On some occasions, after the star had decreased in bright- 

 ness for several weeks, there was a period of perfect cessation, or, at 

 least, a scarcely perceptible diminution of light during several days ; this 

 was the case in 1678 and in 1847. 



The maximum brightness, as already remarked, is by no means al- 

 ways the same. If we indicate the brightness of the faintest star that 

 is visible to the naked eye by 0, and that of Aldebaran (a Tauri),'astar 

 of the first magnitude, by fifty, then the maximum of light of Mira fluc- 

 tuates between 20 and 47, i. e., between the brightness of a star of the 

 fourth, and of the first or second magnitude : the mean brightness is 28 



