OF ARTS AND SCIENCES. 27 



we see that while a lirge value of r would give an average residual of 

 over one tenth of a magnitude, the value of r = 0.7 G4 would make 

 this quantity less than two hundredths of a magnitude. In all of 

 them, however, there is a distinct systematic variation, the computed 

 light being too small when t is large, and sometimes becoming too large 

 when t is small. It appeared that this error might be reduced by 

 assuming that the eclipse was annular, or that the light retained its 

 minimum value for a short time. The corresponding residuals are 

 given in the last column. They reduce the positive residuals wliea 

 the star is faint, but do not sensibly affect the others, although the 

 time between the internal contacts is assumed to be twenty-four minutes. 

 The observations scarcely admit so great an interval, and certainly 

 would not justify its increase. As the average residual is not dimin- 

 ished by the assumption of an annular eclipse, and as the observations 

 do not indicate that the light remains constant during the minimum, we 

 cannot do better tlian to assume the value of r = 0.764, and adopt the 

 values of the second column of the table. 



Several explanations may be offered of the small systematic error 

 that remains. The most plausible seems to be that derived from the 

 residuals given in the last column of Table VII. They show that, from 

 a comparison of the estimated grades of Schonfeld with the measures 

 of Wolff, that Schonfeld estimated the liglit too faint when the star 

 was funt, and too bright when the star was bright. In other words, 

 that a grade did not have the same values when expressed in logarithms 

 for a faint as for a bright star. Assuming the photometric measures 

 of TVolff to be free from systematic error, we should therefore increase 

 tiie estimates of Schonfeld when the star was faint, and diminish them 

 when it was bright, without affecting the actual maximum and mini- 

 mum values. Such a correction would make the systematic error 

 noted above disappear, or even give it an opposite sign. This view 

 receives a slight confirmation from the measures of Seidel, but the 

 accidental discrepancies far exceed this small systematic error. We 

 may therefore conclude that the computed light agrees with observa- 

 tion as closely as the brightness of the fundamental stars is at present 

 known, and there is no evidence of a real systematic difference between 

 the two. 



Another explanation of the residuals in Table X. has suggested 

 itself. The presence of lines in stellar spectra leads to the belief that 

 the stars, like our Sun, are surrounded by an absorbing atmosphere. 

 They also, therefore, probably resemble it in presenting a disk brighter 

 in the centre than at the edges, owing to the greater thickness of the 



