OF ARTS AND SCIENCES. 



271 



ness of tlie two sides from 1 -j- ?«' to 1 — m'. The brightness of tlie 



\ ^' 



darker side would therefore equal - — ; ; times that of the blighter. 



^ 1 4" m' * 



In like manner, if the surface was uniformly bright, the variation in 



area of the disk, or the length of the shorter axis in terms of the 



1 n' 



longer, would be _, , . These quantities are given in the sixth and 



seventh columns. The last two columns give the average residuals in 

 percentages before and after applying the terms which are functions 

 of 3 V. 



TABLE XII. — CoAiPARisoN of Light Curves. 



From the column 



1 



- we see that in every case the darker side 



1 + m' 



is more than half as bright as the other, and that the difference in the 

 case of y8 Lyrce amounts only to ten per cent. In other words, if this 

 effect is due to spots, we must conclude that they cover only one-tenth 

 of the hemisphere in the case of /3 Lyrce, and about two-fifths in the 

 cases of rj Aquilce and S Cephei. The next column also shows that 

 P LyrcB is much elongated, the ratio of its axes being as five to three, 

 while the two stars following have this ratio about as six to five. 



The dark portion of /? Lyrce is at one of the ends, since a' = 0° for 

 this star ; it appears also to be symmetrically situated as regards the 

 longer axis. The dark portions, both of t] Aq%i}Ice and of 8 Cepher, are 

 placed somewhat preceding an end, that is, they are turned towards 

 the observer before the end has been directed to him. For this reason 

 the time from minimum to maximum is greater than that from maxi- 

 mum to minimum. This is probably a general law of stars of this ' 

 class, as it has been noticed in several other instances. 



One source of systematic error has been disregarded in the above 

 comparison of observation with theory. In the value of L' the term 

 m' sin (y' -\- a') may be regarded as the measure of the effect of the 

 difference in brightness of the two sides, and n' cos 2 v' as due to the 

 form of the body. Their combined effect, however, would not strictly 

 equal their sum, but would be found by adding each to unity and 



