VARIABLE STARS. 235 



The maximum brightness, as already remarked, is by no 

 means always 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,) a star of the 1st magnitude, by 50, 

 then the maximum of light of Mira fluctuates between 20 

 and 47, i. e. between the brightness of a star of the 4th, and 

 of the 1st or 2nd magnitude: the mean brightness is 28, 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 fluc- 

 tuations 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 place if we were to calculate these maxima on 

 the hypothesis of an uniform period. The difference between 

 calculation and observation then amounts to 50 days, and 

 it appears, that for several years in succession those differ- 

 ences 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 cal- 

 culations, however, have proved that the supposition of one 

 disturbance is not sufficient, and that several 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 1 76 ; and a fourth, after 264. From hence arises 

 the formula of sines (given at p. 228, note 12), with which, 

 indeed, the several maxima very nearly accord, although 

 deviations still exist which cannot be explained by errors of 

 observation. 



(2) Persei, Algol; R. A. 44 36', Decl. + 40 22'. 

 Although Geminiano Montanari observed the variability of 

 this star in 1667, and Maraldi 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 

 diminish in brightness, but for 2d. 13h. shines uniformly as a 

 star of the 2 '3rd magnitude, and only appears less bright for 

 7 or 8 hours, when it sinks to the 4th magnitude. The 

 augmentation and diminution 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 



