20 PROCEEDINGS OF THE AMERICAN ACADEMY 



revolution of the star, this part had been turned around so as to dis- 

 appear on the other side. The short minimum observed could only 

 be caused, according to this theory, by supposing a large dark star 

 with a small bright spot near its polar regions, and that the pole was 

 directed at such an angle from the observer that a large part of the 

 spot would disappear for a short time during each revolution. Even 

 then we have still the apparently insurmountable ditficulty that the 

 bright spot would change its a2i[)arent size and the angle at which it 

 emitted its light to tlie observer, and therefore vary iu brightness dur- 

 ing the whole period of revolution. No such variation has been estab- 

 lished in the light of Algol. 



Before showing how far the theory of an eclipsing body will account 

 for the observed phenomena, we must see what knowledge we have of 

 these variations in light. 



Only five stars are at present known to belong to the Algol class of 

 variables. These are ^ Persei, S Cancri, X Tauri, 8 Libra, and U Co- 

 ronce. Of these, the first is the only one whose variations are known 

 with sufficient precision to justify a discussion in the present article. 

 The variations of fi Persei, or Algol, have been carefully studied by three 

 observers, Argelander, Schmidt, and Schonfeld. Argelander's observa- 

 tions extend from 1840 to 1866, and are nearly two thousand in number. 

 He compared Algol from time to time with the adjacent stars of nearly 

 equal brightness, and noted the apparent difference in steps or grades 

 {Stufen). Arranging his comparison stars in the order of brightness, 

 and determining the number of grades between each from all his meas- 

 ures, he was then able to denote them all in grades. Thus, suppose at a 

 given time he observed that Algol was sligiitly, if at all, brigliter than 

 star A, or that the difference was one grade ; again, that it was per- 

 ceptibly fainter than B, or differed from it by two grades ; if then he 

 found in his final discussion that A = 12.0 grades and B= 14.9, the 

 first observation would make Algol lo.o grades, and the second 12.9. 

 These comparisons are all given in tl:e Buiin Obsercalions, vii. 31.5, 

 but, unfortunately, they have not been reduced, so that at present no 

 use can be made of tiiem. I undertook their reduction, but was in- 

 formed that this had been done at Bonn. No answer has, however, 

 been received to letters of inquiry on this point. 



The observations of Dr. Schmidt extend from 1846 to the present 

 time, and the results up to 1875 are published in i\\Q Astronomische 

 Nachrichten, Ixxxvii. 193. His object was only to determine the 

 time of the minima, and accordingly these only are given, without the 

 comparisons. He also generally used a single comparison star, which 



