OF ARTS AND SCIENCES. 23 



disks, one uniformly bright, the other dark, and that the form of orbit 

 is circuhir. Three cases may occur, corresponding to a total, an annu- 

 lar, and a partial eclipse of the star. In the first case, all the light 

 would be cut off for a longer or shorter time ; in the second, the mini- 

 nuHu light would be maintained during the transit of the .satellite 

 across the face of the star ; and in the third case the light would 

 diminish until the minimum was attained and then immediately begin 

 to increase. Algol appears to belong to the last of the classes. We 

 must next determine the relative diameters of the satellite and star. 

 A minimum diameter of the satellite may be computed from the mini- 

 mum light. To reduce the light to 0.416, or to cut off O.o84 of the 

 light, the diameter of the satellite must be at least y 0.584 = 0.764 

 times that of the star. In this case it would just pass completely on 

 to the disk before it began to pass off. No maximum can be deter- 

 mined in this way, so that the diameter is only limited between 0.764 

 and infinity. A change in diameter will, however, produce a change 

 in the law of variation of the light. We may deduce the diameter 

 from the values agreeing most nearly with observation. We must 

 now determine the amount of light remaining when the star is par- 

 tially eclipsed by a satellite of radius r. The radius of the star is 

 taken as the unit. The area of the segment of a circle of radius unity 

 whose versed sine is z, is equal to versin~-^2; — (1 — z) \2z — z^. 

 A table is given in the eighth edition of the Encyclopcedia Britannica, 

 xiv. 525, Art. Ilensnration, which gives this quantity for values of z 

 varying by hundreds from 0.00 to 1.00. The portion of the disk cut 

 off will always be composed of two segments having the radii 1 and r, 

 and having a common chord which may be computed when we know 

 the distance of the centres. The area of each may be taken from 

 the table, multiplied by the square of the radius of its circle, and the 

 two areas added. This will give the required diminution in light. 



If now we assume r the radius of the satellite, several of the ele- 

 ments may be computed. 



The period of revolution of the satellite is given with much pre- 

 cision from the observations of the minima. It appears to undergo 

 slight changes, but may be assumed for the present time to equal 

 2 days 20 hours 48.9 minutes. Calling w the longitude of the satel- 

 lite in its orbit reckoned from its minimum, the mean change in w per 

 hour will equal 5°.023. Since the beginning and ending of the ob- 

 scuration precede and follow the minimum by 4'' 35™, the corre- 

 sponding values of w will be 337°.0 and 23°.0. At these points the 

 centre of the satellite will be at a distance (1 -j- r) from the centre 



