32 PROCEEDINGS OP THE AMERICAN ACADEMY 



touch, yet they would come so near that the least disturbance would at 

 once produce a catastrophe. This, therefore, gives the limiting value 

 to the eccentricity. A computation with a smaller eccentricity gave 

 less satisfactory residuals. The question now arises, will it not be 

 possible to satisfy the observations by returning to the circular ele- 

 ments, since we have permitted a change iu the times of contact and 

 of minimum. Columns D give the residuals for a circular orbit with 

 a diminution of 0.1 hour in the time of minimum, and assuming that 

 the periods of ingress and egress are each equal to 4.45 hours instead 

 of 4.6 hours. In other words the ingress occurs about fourteen min- 

 utes later, and the egress two minutes earlier, than was assumed by 

 Schonfeld. 



The errors which remain, even in the last orbit, are not wholly acci- 

 dental ; but their values are so small, and the changes of sign so fre- 

 quent, that it is not safe to base important conclusions upon them. 

 Their average value is only .012, or expressed in logarithms .009, and 

 in magnitudes .02. Accordingly, we may compute the variation in the 

 liglit of Algol, which shall not differ from observation on an average 

 more than a fiftieth of a magnitude. If then this is not the true 

 cause of the variation of the liglit, it at least satisfies it well within 

 the errors of observation. The orbit D may therefore be adopted as 

 repre.senting the law of variation as well as it is at present known. 



The stellar magnitude of Algol is about 2.0, so that by Table 11., 

 if its brightness equals that of the Sun, its diameter will equal 0".006. 

 The diameter of the orbit of the satellite will be about 0".028. The 

 motion of the bright star, if its density is the same as that of its sat- 

 ellite, will equal 0".009, since its mass in this case will be to that of 

 its satellite as 1.000 is to 0.446. It would therefore be useless to 

 attempt to observe the motion micrometrically. For the same reason, 

 there seems to be no means by which we can determine the position 

 angle of the satellite, or the direction of tlie axes of the ellipse into 

 which the orbit is projected. Even if future observations should ren- 

 der a larger value of the radius probable, the motion would be scarcely 

 perceptible micrometrically. If r = 2.000, the diameter of the orbit 

 becomes 0".08 and the motion of Algol about 0".07. It would be 

 difficult to measure so small a quantit}^ although, as it is traversed in 

 less than a day and a half, many sources of systematic error would be 

 eliminated. 



Below are given, in successive columns, the corresponding values of 

 several elements of the orbits A^ B, C, and D. The diameter of Algol 

 is assumed to be 0".006. The times are given in minutes from the 



