22 



PROCEEDINGS OF THE AMERICAN ACADEMY 



Schonfeld has given on page 84 of his memoir a table of his mean 

 results, arranged in seventy-nine groups, seventy-two of them occur- 

 ring within about four hours and a half of the minimum, and sixty-two 

 within three hours of tiie minimum. He then drew an empirical curve 

 tlirough these points, and gives their residuals, which vary from 

 -|-0.73 to — 0.58 grades, and have an average value of 0.17 grades. 

 Reducing this to logarithms, by multiplying by 0.02o, gives 0.004, or 

 only one hundredth of a magnitude. There are thirty-five changes of 

 sign in the residuals, out of a possible seventy-one. Thei-e is, there- 

 fore, no reason to doubt that the curve repi'esents the observations as 

 nearly as possible. 



The light in grades for intervals of every half-hour before and after 

 the minimum is given in Table VIII. The successive columns give 

 the time in hours, the corresponding light in grades before and after 

 the minimum, the difference between these two, their mean, and the 

 corresponding light expressed in logarithms. This is found by sub- 

 tracting the light in grades from 20.8, which is assumed by Schonfeld 

 as the full brightness of Algol, multiplying the result by 0.025 to re- 

 duce to logarithms, and taking the arithmetical complement. The 

 number corresponding to this logarithm is given in the last column. 

 It gives the light of Algol, its maximum light being assumed as 1.000. 



TABLE VIIL — Light Curve of fi Tersei. 



From this table it appears that the law respecting the increase of 

 light is not the same as that of its diminutiou. At a given interval 

 of time from the minimum, the light is greater when decreasing than 

 ■when increasing. The mean value will first be considered, and the 

 cause of this dillurence then discussed. 



We shall first assume that the star and satellite present circular 



