OF ARTS AND SCIENCES. 279 



motion was direct or retrograde. It mijiht also lielp to determine the 

 amount of the inclination when the latter is not lar-xe enouirh to 

 be determined precisely by niicrouictric measurements. Such a law 

 would render an important aid to the study of the orbits of the dark 

 companions of stars of the fifth class. Tlicy would afford a check on 

 the observed inclination, and would define the position angle of the 

 major axis of the orbit, which is now wholly indeterminate. An 

 inspection of the orbits of the binaries fails to show any law, but 

 it is possible that this might be brought out by a more careful exami- 

 nation, as has been done with the pro[)er motion of the stars. The 

 conclusion regarding the motion of the Sun in space is liable to lar<>-e 

 error, in case systematic errors exist iu the catalogues on which 

 the positions of the stars depend. Such an error in Bradley mi^ht 

 greatly change the conclusion generally accepted. The orbits of the 

 binaries, on the other hand, are wholly independent of each other, and 

 there is little danger of a systematic error aflPecting all. 



The elegant method of Argelander for determining the light curve 

 of the variable stars leaves little to be desired as a means of determin- 

 ing their periods and the times of their minima. Its sirai)licity, and tlie 

 need of no instrument but a telescope powerful enougli to show the 

 variable, are strong arguments in its favor when comparing it with 

 the best [)hotometric methods. If, however, we wish to determine the 

 true light curve, the following sources of error become perceptible. As 

 the comparison stars are selected from the immediate neighborhood of the 

 variable, they are few iu number ; aud if any one of them proves to be 

 itself variable, the errors introduced are large. It is ditiicult to obtain 

 independent estimates, since there is but little range of clioice in the star 

 to be selected at any given time. Much skill is required on the part 

 of the observer to make a grade the same when the variable is bright 

 as when faint, to make it the same on different nights, and to make the 

 interval of two. grades double that of one. In reducing the light to 

 logarithms, it appears to be impossible to render the errors of the 

 measures of the comparison stars as small as those of the light curves. 

 The comparisons given above show that the errors of the measure- 

 ments of the comparison stars probably exceed those from all other 

 sources combined. 



Three methods may be used for determining the brightness of the 

 stars without a photometer. First, the observer may keep a certain 

 scale in mind, and by it estimate the light of the stars in tenths of a 

 magnitude. He should first estimate several known stars, and compare 

 his result with their true brightness, so as to apply mentally to his 



