28 PROCEEDINGS OF THE AMERICAN ACADEMY 



atmosphere and consequent greater absorption at the edges. The 

 effect of such an absorption is best determined by the consideration 

 that if, owing to absorption, the average light of the eclipsed portion 

 is less than tliat of the whole disk, the effect of the atmosphere will 

 be to diminish the proportion of the light cutoff; in the opposite 

 case, it will increase it. Now when a small portion only of the star is 

 eclipsed, evidently the average light of this portion, since it lies near 

 the edge, must be less than that of the whole. The atmosphere, 

 although then diminishing the light of the remaining portion, will not 

 reduce it as much as it does that of the entire disk ; the relative 

 light will therefore be increased. On the other hand, when a large 

 part of the eclipsed portion is from the central and brightest portion 

 the opposite effect will be produced. We should therefore expect, 

 when t is large, that the computed light should be increased. When 

 t is small, it may be diminished. In the case of the Sun the effect is 

 so slight, except close to the borders, that the previous ex2:)lauation 

 seems more probable. 



We return now to the consideration of differences in the rate of 

 diminution and increase of the light. The observations ought to give 

 this quantity with much accuracy. An error in estimating the light 

 of the standard stars will not sensibly affect it, since the same stars 

 are used in measuring the increase and diminution. The effect of 

 atmospheric absorption is reduced, since some of the comparison stars 

 are always above and others below the variable, and besides, although, 

 when observed before passing the meridian, the star is brighter when 

 increasing than when diminishing, yet the opposite effect is produced 

 wlien the star is west of the meridian. Nevertheless this difference 

 is doubted by many astronomers, and if it exists it is evident that an 

 important cori-ection should be applied to the observed minima of 

 Algol. If the curve found by Schonfeld is correct, an error of ten 

 minutes in the time of the minimum might be caused by comparing 

 with a star like £ Pejsei, having a brightness of about twelve grades, 

 and taking the mean of the times when the two stars appeared equal. 



Three explanations may be offered for tiiis phenomena. First, that 

 the satellite is not spherical, but egg-shaped, and that the large end is 

 turned forwards ; or that the satellite is of unequal density, and that 

 the heaviest portion is forward. In this case the centre of gravity 

 of the disk would follow that of the satellite, or for a given distance of 

 the centres the interposed area would be greater when the satellite 

 was passing off, than when coming on. So great a deviation from the 

 spherical shape would be needed to produce the observed difference 



