OF ARTS AND SCIENCES. 261 



corresponding to v = 0°, 15°, 30°, 45°, etc. The period is divided 

 into twenty-lour equal parts, and the number of grades corresponding 

 to each is taken from the light curves. Argelander and Schoufeld 

 give the number of grades for each hour, and the number of grades 

 was found from their tables by interpolation. Oudemans represents his 

 results graphically, and the grades were taken from his curves by 

 inspection. These curves were used rather than the original observa- 

 tions, in order to reduce the accidental errors. The results are free 

 from prejudice, since they were drawn by the observers themselves with- 

 out regard to any theoi-y. They are, however, open to the objection 

 that small systematic errors may be present which are not easily 

 detected. 



We must next pass from grades to the actual intensities of light. 

 For this purpose we cannot rely on an assumed value of a grade, since 

 we have no certainty that this will be the same for lights of different 

 intensity. Accordingly, the comparison stars used by each observer 

 are compared with the measures of Wolff.* Points were constructed 

 whose abscissas equal the assumed light of each comparison star in 

 grades, and their ordinates, the logarithms of the light as measured by 

 Wolff. A smooth curve was then drawn through these points, and 

 served to convert the grades into logarithms. The readings are only 

 made to hundredths, since one unit in this place corresponds to one- 

 fortieth of a magnitude, and all the curves are uncertain by much more 

 than this amount. The largest logarithm is then subtracted from all 

 the others, and the number corresponding to the difference gives the 

 intensity of the light. This is multiplied by one hundred, so that the 

 results are given in percentages. 



In the equation, L^a -\- m sin (v -\- a) -\- n sin {2 v -\- /3). a is 

 found from the mean of all the observed values of L. The other con- 

 stants might be found from a solution by least squares, forming twenty- 

 four equations of condition with the twenty-four deduced values of L. 

 Sufficient accuracy is, however, obtained by approximate graphical 

 methods. By adding together the values of L, corresponding to values 

 of V differing 180°, we eliminate the term m sin (y -j- «). Their dif- 

 ferences, in like manner, eliminate n sin (2 v -\- /3). Each then may 

 thus be found independently of the others. 



^ Geminorum. In 1848, Argelander gave a light curve of this star.f 



* Photometrische Beobaclitungen an Fixsternen, Leipzig, 1877. 

 t Astron. Nacli., xxviii. 33. 



