A. MATHEMATICS AND ASTRONOMY. 39 



that the principal one of the stars observed by Mayer was 

 itself double; which observation was again confirmed, in 

 1825, by Sir James South. The three stars are nearly equal 

 in brightness, and are ranked as between the fifth and sixth 

 magnitudes; but whether the masses of the three bodies are 

 really nearly the same can only be determined by their own 

 movements, as deduced from such observations as have been 

 made by William and Otto Struve. The former astronomer 

 observed them first in 1826, since which time thev have been 

 closely followed by himself and son. The remarkably accu- 

 rate observations of Baron Dembowski at Gallarate, near 

 Milan, in Italy, together with those made by Dawes in En- 

 gland, have been by Otto Struve combined with his own ; 

 and from the entire assemblage of all the appropriate obser- 

 vations he finds that the apparent orbit of the star B about 

 the star A is completed in about 62.4 years, under the as- 

 sumption that the apparent orbit is circular, which appears 

 to be very nearly the case (the real orbit has an eccentricity 

 of 0.35). The third star of the group, indicated by the let- 

 ter C, is apparently about ten times as far from A as is the 

 star B. Its angular movement relative to the former star is 

 therefore correspondingly slow, it having described only 47 

 in ninety years, while the star B has entirely completed its 

 revolution and described a portion of its second orbit. An 

 interesting peculiarity of the motions of the star C consists, 

 however, in this, that its movements are by no means regular. 

 It is in fact subject to repeated alternations within periods 

 of about ten years, within which time it moves sometimes 

 forward rapidly, and at other times backward, and at other 

 times it is stationary. Its apparent orbit around the star A 

 is therefore essentially an epicycloid ; but unhappily the pres- 

 ent state of mathematical analysis does not enable us to say 

 whether these irregularities in its movement are due to the 

 perturbing attractions of the stars A and B, or w r hether we 

 must assume that the star C describes an elliptical orbit 

 about an invisible point central between it and a fourth 

 invisible star, D, while the central point itself describes a 

 much larger orbit about the stars A and B. Otto Struve 

 states that if we refer the positions of the star C to a point 

 h^f-way between the stars A and B, we can closely repre- 

 sent all our observations by assuming C to move in a small 



