OF ARTS AND SCIENCKS. 281 



instrument, and this should be repeated on several eveuin;^s. The rela- 

 tive liglit will thus be obtained with great accuracy, as the same errors 

 will be likely to affect them all. If this cannot be done, the Uranome- 

 tria Argentina, with the measures now in progress at the Harvard Col- 

 lege Observatory, will give the brightness of all the naked-eye stars, 

 with an error probably less than a tenth of a magnitude. 



The light of the variable would be found by selecting two compari- 

 son stars, one a little brighter, the other a little fainter than it, and 

 comparing the interval between the variable and the brighter, with 

 that between the two comparison stars, which may be assumed equal 

 to 10. Thus, a 4: b will denote that the interval between the bright 

 com])arison star a and the variable is estimated at only four-tenths of 

 that between the two comparison stars. Of course the time of each 

 comparison must be recorded. This measure should be repeated with 

 different pairs of comparison stars. Thus, if a and b are brighter 

 and c and d fainter than the variable, we may compare the latter with 

 aCj ad, be, and bd. In like manner, with six. comparison stars we may 

 obtain nine independent measures. The reduction is very simple, since 

 it is useless to carry the estimates beyond tenths of a magnitude. 



The above paper has suggested several researches of importance, 

 and which are accordingly placed together below : — 



1. Determination of the light curves of any of the variables of short 

 period, except f] Persei, t, Geminorum, /3 Lyrce, -q Aquilcs, and 8 Cephei, 

 for which satisfactory curves have already been obtain.ed. The method 

 of Argelander, or that proposed above, may be used with advantage. 



It must be remembered that the observations will have little value, 

 unless they are reduced and the light curve found. A vast number of 

 excellent observations of these stars already exist, including the larger 

 part of those of Argelander, which will have no value until they are 

 reduced. 



2. Determination of the light curve of the stars of the fourth class 

 photometrically. This may be done w^ith great accuracy by an instru- 

 ment similar to that described in the Annals of the Harvard College 

 Observatory, xi. 4, Figs. 1 and 2. The proximity of the companions 

 render these objects especially suitable for photometric measurement. 



3. Photometric measures of the comjjarison stars used in (1), of 

 those used by previous observers, and the reduction of the observations 

 by these measures to light intensities. 



4. Search for variables of the fourth class, selecting from the Durch- 

 musterung those fulfilling the conditions named above. They may be 

 readily identified by their companions, and observed very rapidly by a 



