XOVEMBEB 6, 1903.] 



SCIENCE. 



595 



Harvard circular No. 33. The same is again 

 published on page 2 of the present volume. 

 In the 23 clusters which had been examined, 

 19,050 stars were compared, and not less than 

 509 variables were found. The distribution 

 among the different clusters is very different. 

 In two of them no variable was found, in 

 three, only one; in four, only two; and so on. 

 The two clusters Messier 3 and <« Centauri 

 show the greatest number of variables. The 

 first has 132 among 900 stars examined, the 

 second, 128 among 3,000 stars compared ; in 

 the first case there is one variable, in every 

 seven stars, and in the second case one in 

 every twenty-three. 



In the present volume only the cluster w 

 Centauri is discussed, for which more material 

 was available than for the others. In regard 

 to number of stars it is the most striking 

 cluster in the sky, and, on account of the 

 brightness of the individual stars, photographs 

 of it can be obtained with shorter exposures 

 than of the other clusters. 



To the naked eye it appears as a hazy star 

 of the fourth magnitude. Its form is ellip- 

 tical. A count of the number of stars, made 

 in the year 1893, gave for the best photo- 

 graphs, 6,389. The diameter was taken as 

 35', but a few variables were found somewhat 

 more distant from the center, and as it ap- 

 peared probable that these really belonged to 

 the system, the borders of the clusters were 

 thus somewhat extended, even to a diameter 

 of 40'. In regard to the niagnitudes of the 

 stars, there is no star brighter than 8 magn., 

 less than 100 stars between 8 magn. and 12 

 magn., and more than 0,000 between 12 

 magn. and 14J magn. A large number of the 

 stars which were counted may perhaps not 

 belong to the system, but are only accidentally 

 projected upon it. 



The photographic plates which furnished 

 the basis for the investigation were nearly all 

 made with the thirteen-ineh Boyden refractor, 

 which for the photographic rays has a focal 

 length of 191.5 inches. On the original 

 plates, therefore, 1 mm. is equivalent to 42.4". 

 The images of the fainter stars have a mean 

 diameter of 2". This quantity, however, 

 varies considerably on different plates. For 



keeping the position of the stars fixed on the 

 plates no finder was used, but an eye-piece, 

 which was inserted near the plate, in the field 

 of the main telescope itself. A few plates were 

 made with the Bruce 24-inch telescope, and 

 with the 11-inch Draper telescope, which are 

 of less focal length than the 13". The time 

 of the exposure which was necessary at 

 Arequipa, in order to show the faintest vari- 

 ables when at minimum, was for u> Centauri 

 30 minutes. For the fainter clusters notably 

 longer exposures are necessary: in the case of 

 Messier 5 about 50 minutes, for Messier 3 

 about 100 minutes, and for others even two 

 hours. In most clusters the central portions 

 are so densely crowded with stars that a de- 

 tailed study is quite impossible. 



The method which was pursued by Bailey 

 in the discovery of variables in clusters was 

 substantially as follows : The particular 

 cluster was divided into a number of parts 

 each of which contained about ten stars. 

 These stars were arranged in a so-called 

 sequence according to their brightness, from 

 the brightest to the faintest. This sequence 

 was then memorized and as large a number 

 as possible of original plates (if possible, at 

 least ten) was tested and comijared as to how 

 and to what extent the particular sequence 

 was changed. In this way the whole cluster 

 was examined piece by piece. This labor is 

 extremely tiresome. It demands a rigorous 

 examination of numberless plates under a 

 microscope of considerable power, in order to 

 separate the thickly crowded portions, and 

 extraordinary care not to confuse the different 

 stars with one another. In all cases where 

 the variation is small, or where the period is 

 about twenty-fovr hours or a fraction thereof, 

 the detection of the variability was difficult. 

 On this accoimt many variables may have re- 

 mained undiscovered. Especially difficult is 

 found the examination of the central portion, 

 where the star images coalesce, and precise 

 comparisons are impossible. On this ac- 

 count it happens that, especially in the 

 densest clusters, relatively few variables are 

 found near the center. The discovery is also 

 rendered difficult from the fact that the dura- 

 tion of the maximum phase is only a com- 



