228 COSMOS. 



Periods within periods have been distinctly observed in 

 the case of Algol, of Mira Ceti, of Lyrse, and with great 

 probability also in % Cygni. The decrease of the period of 

 Algol is now unquestioned. Goodricke was unable to per- 

 ceive it, but Argelander has since done so ; in the year 1 842 

 he was enabled to compare more than 100 trustworthy 

 observations (comprising 7600 periods), of which the ex- 

 tremes differed from each other more than 58 years. (Schu- 

 macher's Astron. Nachr., nos. 472 and 624.) The decrease 

 in the period is becoming more and more observable. 11 For 

 the periods of *he maximum of Mira (including the maximum 

 of brightness ; observed by Fabricius in 1596), a formula" 



11 " If," says Argelander, * I take for the epoch the 

 minimum brightness of Algol, in 1800, on the 1st of January, 

 at 18 h l m mean Paris time, I obtain the duration of the 

 periods for : 



1987 . . 2 d 20 h 48 m , or 59-416 8 '316 



1406 .. 58-737 O s -094 

 - 825 .. 58-393 O s -175 

 + 751 .. 58-154 O s -039 

 4-2328 .. 58 S -193 O s '096 

 + 3885 .. 57 S -971 0*'045 

 + 5441 .. 55"-182 Os.348 



" In this table the numbers have the following signification : 

 if we designate the minimum epoch of the 1st of Jan. 1800, 

 by 0, that immediately preceding by 1, and that immediately 

 following by + 1, and so on, then the duration between 1987 

 and 1986 would be exactly 2 d 20 h 48 m 59 S> 416, but the 

 duration between + 5441 and + 5442 would be 2 d 20 h 48 m 

 55-182; the former applies to the year 1784, the latter to 

 the year 1842. 



" The numbers which follow the signs are 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." 



18 Argelander' s formula for representing all observations 

 of the maxima of Mira Ceti is, as communicated by himself, 

 as follows : 



