262 



PROCEEDINGS OF THE AMERICAN ACADEMY 



Table II. gives the data for converting the grades into light ratios by 

 means of the comparison stars. The successive columns give the name 

 of the star, its light in logarithms as measured by Wolff, its liglit 

 in grades assumed by Argelander, the corresponding ordinate of the 

 curve, and the second column minus the fourth, or the assumed ei'rors. 



TABLE II. — Comparison Stars for ( Gemixorum. 



The curve here agrees very well with the measurements, but its 

 inclination is much greater for the brighter than for the fainter stars. 

 In other words, a grade represents a much larger difference in magni- 

 tude when the star is bright tlian when faint. The change is, however, 

 slight between the limits within which the curve is used. 



Table III. gives a comparison of the light curve with theory. The 

 successive columns give the angle v, the corresponding time from the 

 minimum, and the observed light in grades, in logarithms, and in 

 percentages. The next column gives the light computed by the 

 formula, L = 89.6 -{- 10.0 sin v ; this is followed by the residuals found 

 by subtracting the computed from the observed brightness. As they 

 show a perceptible systematic error, two more columns are given 

 corresponding to the formula L = 89.6 -}- 10.2 sin {v — 11°. 3). This 

 gives an entirely satisfactory agreement with observation, the average 

 deviation amounting to less than one per cent. It cannot be reduced 

 directly to magnitudes, since, when the light equals 100, one per cent 

 equals .011 magnitudes, when 80, .014 magnitudes, and M-hen 50, .022 

 magnitudes. The average deviation is accordingly only about one hun- 

 dredth of a magnitude. Since two smooth curves are compared, the 

 small irregular variations in the residuals are principally due to the 

 neglected thousandths in the logarithm of the light. They are, how- 

 ever, probably far less than the real errors of the curves. The mean 

 of the residuals is given in the last line of the table. 



