380 PROCEEDINGS OF THE AMERICAN ACADEMY 



A comparison may now be made with the light-curve given by 

 Schonfeld in the paper cited above. As has been already stated, the 

 great difficulty lies in deciding what brightness shall be assumed 

 for the comparison stars. In a previous article,* the light of these 

 stars in grades assumed by Schonfeld have been reduced by means of 

 the formula L = 8.446 -|- 0.025 g, in which L gives the light and g 

 the number of grades. This formula is derived from a comparison 

 with the measurement of the comparison stars by Seidel and Wolff. 

 These stars have since been measured with the meridian photometer 

 of the Harvard College Observatory. Each star has been observed 

 on the average on ten nights. 



Three methods of reducing the grades of Schonfeld by these stars 

 may be used. We may adopt the formula ^iven above, which was 

 found by. a least square solution of the measures of Seidel and Wolff. 

 Secondly, we may apply the method of least squares to the Harvard 

 College Observatory measures, and deduce the formula most nearly 

 satisfying them. This gives the value of one grade in logarithms 

 equal to 0.029. In both these cases we have assumed that the value 

 of a grade is the same for bright and for faint stars, and that the devi- 

 ations are due to accidental errors, or to variations which have taken 

 place in the light of the stars. As a tliird method, we may draw a 

 curve through the points whose co-ordinates equal the light in grades 

 and the measured brightness, and reduce the grades by means of this 

 curve. We now assume that the errors are unimportant, but that the 

 grade varifes in different j^arts of the scale. 



Table V. gives, in successive columns, the name of the star, its 

 light in grades, the number of nights on which it has been observed 

 at Cambridge, the resulting magnitude, the probable error, and the 

 logarithm of the light, adopting the same unit as that of Seidel. Ob- 

 servations of (3 Persei have been included in this list, excluding those 

 made within a few hours of its minimum. Three columns of residuals 

 exhibit differences between the measures of Seidel, of Wolff, and of 

 the Harvard College Observatory, and the values computed by the 

 formula L = 8.446 -|- 0.025 </. The next column gives the H. C. 

 measures reduced to logarithms, minus those given by the formula 

 8.391 -[- 0.029 g. The last column gives the difference between the 

 measures of the stars and the values of their light derived from tlie 

 smooth curve. 



* Proc. Am. Acad., xvi. 21. 



