2G6 



PROCEEDINGS OF THE AMERICAN ACADEMY 



The mean value of Z or a is 81.1. When v z= 0°, Z = a — m — n; 

 when V ^ 180°, L = or-|-?« — «; v = 90° or 270°, gives L = a 

 -\- tn — n. Were there no accidental errors, either two of these three 

 equations would determine ?« and «. After various trials the equation 

 Z = 81.1 + 4.1 sin (v — 90°) + 20.0 sin (2 v — 90°) was found 

 to give the most satisfactory results. The brightness computed by 

 this formula, and the residuals found by subtracting them from the 

 mean of the observed values, are given in the last two columns. 



TABLE VI. — Variation in Light of fi Lyr^. 



These residuals are much larger than in the case of ^ Geminorum ; 

 hut this is to be expected, since the variations in light are greater. 

 Evidently, if the changes were small, any two smooth curves would 

 agree closely-. Their average value amounts to about .04 of a magni- 

 tiide, and their greatest value does not exceed the greatest diflference 

 of each of the observed curves from the others. The greatest errors 

 of observation are those of the light of the comparison stars. The 

 residuals near the princiijal mininuim may be greatly reduced if the 

 fainter compari.son stars are assumed too faint, with a corresponding 

 change in the value of the fainter grades. The rejection of e LyrcB in 

 Table v., while its effect on Table VI. cannot be eliminated, may 

 account for this apparent error. An increase in the logarithm of the 



