174 cosmos. 



or that of the star y Ceti. But the duration of its periods is still more 

 irregular: its mean is 33 Id. 20h., while its fluctuations have extended 

 to a month ; for the shortest time that ever elapsed from one maximum 

 to the next was only 306 days, the longest, on the other hand, 367 days. 

 These irregularities become the more remarkable when we compare the 

 several occurrences of greatest brightness with those which would take 



f)lace if we were to calculate these maxima on the hypothesis of a uni- 

 brm period. The difference between calculation and observation then 

 amounts to 50 days, and it appears that, for several years in succession, 

 those differences are nearly the same, and in the same direction. This 

 evidently indicates that the disturbance in the phenomena of light is one 

 of a very long period. More accurate calculations, however, have prov- 

 ed that the supposition of one disturbance is not sufficient, and that sev- 

 eral must be assumed, which may, however, all arise from the same 

 cause; one of these recurs after 11 single periods; a second after 88; 

 a third after 176 ; and a fourth after 264. From hence arises the form- 

 ula of sines (given at p. 169, note *), with which, indeed, the several 

 maxima very nearly accord, although deviations still exist which can 

 not be explained by errors of observation. 



(2) (i Fersei, Algol ; R. A. 44 36', Decl. 4-40 22'. Although Gemi- 

 niano Montanari observed the variability of this star in 1667, and Ma- 

 raldi likewise noticed it, it was Goodricke that first, in 1782, discovered 

 the regularity of the variability. The cause of this is probably that this 

 star does not, like most other variable ones, gradually increase and di- 

 minish in brightness, but for 2d. 13h. shines uniformly as a star of the 

 2-3d magnitude, and only appears less bright for seven or eight hours, 

 when it sinks to the fourth magnitude. The augmentation and dimi- 

 nution of its brightness are not quite regular; but when near to the 

 minimum, they proceed with greater rapidity; whence the time of 

 least brightness may be accurately calculated to within ten to fifteen 

 minutes. It is moreover remarkable that this star, after having increased 

 in light for about an hour, remains for nearly the same period at the 

 same brightness, and then begins once more perceptibly to iucrease 

 Till very recently the duration of the period was held to be perfectly 

 uniform, and Wurm was able to present all observations pretty closely 

 by assuming it to be 2d. 21h. 48m. 58is. However, a more accurate cal- 

 culation, in which was comprehended a space of time nearly twice as 

 Ion" as that at Wurm's command, has shown that the period becomes 

 gradually shorter. In the year 1784 it was 2d. 20h. 48m. 59-4s., and in 

 the year 1842 only 2d. 20h. 48m. 55-2s. Moreover, from the most re- 

 cent observations, it becomes very probable that this diminution of the 

 period is at present proceeding more rapidly than before, so that for this 

 star also a formula of sines for the disturbance of its period will in time 

 be obtained. Besides, this diminution will be accounted for if we as- 

 sume that Algol comes nearer to us by about 2000 miles every year, or 

 recedes from us thus far less each succeeding year ; for in that case his 

 light would reach us ae much sooner every year as the decrease of the 

 period requires; i. e., about the twelve thousandth of a second. If this 

 be the true cause, a formula of sines must eventually be deduced. 



(3) X Cygni, R. A. 296 12', Decl. -J-32 32'. This star also exhibits 

 nearly the same irregularities as Mira. The deviations of the observed 

 maxima from those calculated for a uniform period amount tq forty days, 

 but are considerably diminished by the introduction of a disturbance 

 of %\ single periods, and of another of 100 such periods. In its maxi- 

 mum this star reaches the mean brightness of a faint fifth magnitude, or 



