VARIABLE STARS. 169 



periods of the maximum of Mira (iucludin*^ the maximum of 

 brightness observed by Fabricius iu 159G), a formula* has 

 been established by Argelander, from which all the maxima 

 can be so deduced that the 'probable error in a long period of 

 variability, extending to 33 Id. 8h., does not in the mean ex- 

 ceed 7 days, while, on the hypothesis of a uniform period, it 

 would be 15 days. 



The double maximum and minimum of j9 Lyra), in each 

 of its periods of nearly 13 days, was from the first correctly 

 ascertained by its discoverer, Goodricke (1784) ; but it has 

 been placed still more beyond doubtf by very recent observ- 

 ations. It is remarkable that this star attains to the same 

 brightness in both its maxima, but in its principal minimum 

 it is about half a magnitude fainter than in the other. Since 

 the discovery of the variability of j3 Lyra?, the 'period in a 

 period has probably been on the increase. At first the vari- 

 ability was more rapid, then it became gradually slower ; and 

 this decrease in the length of time reached its limit between 

 the years 1840 and 1844. During that time its period was 

 nearly invariable ; at present it is again decidedly on the de- 

 crease. Something similar to the double maximum of /3 Lyra3 

 occm's in 6 Cephei. There is a tendency to a second maxi- 



would be 2d. 20h. 48m. 55s.-182; the former applies to the year 1784, 

 the latter to the year 1842. 



"The mimbers which follow the signs -^ai-e the probable errors. 

 That the diminution becomes more and more rapid is shown as well by 

 the last number as by all my observations since 1847." 



* Argelander's formula for representing all observations of the maxiir.a 

 of Mira Ceti is, as communicated by himself, as follows : 



1751, Sep., 9-7G -|-331d.-3363 E. 

 -l-10d.-5, sin. (Vt'o E. 4-86° 23') -fl8d.-2, sin. (ffo E. -|-23lo 42') 

 -i-33d.-9, sin. (11° E. +170^ 19') 4-65d.-3, sin. (|fo E. -f 6° 37') 



where E. represents the number of maxima which have occurred sinct- 

 Sept. 9, 1751, and the co-efficients are given iu days. Therefore, for 

 the current year (E. being =109), the following is the maximum: 



1751, Sep., 9-764-36115il.-n5-f8cl.-44— 12c]. -24. 

 4-18d.-594-27d.-34=1850, Sep., 8d.-54. 



" The strongest evidence in favor of this formula is, that it represents 

 even the maximum of 1596 {Cosmos, vol. ii., p. 330), which, on the 

 supposition of a uniform period, would deviate more than 100 days. 

 However, the laws of the variation of the light of tliis star appear so 

 complicated, that in particular cases — e. g., for the accurately observed 

 maximum of 1840 — tlie formula was wi'ons: by many days (nearly twen- 

 ty-five)." 



t Compare Argelander's essay, written on the occasion of the cen- 

 tenary jubilee of the KSnigsberg University, and entitled De Stella 

 3 Lyres Variahili, 1844. 



Vor.. III._H 



