The three dark lanes discovered by Lord Rosse, as well as several others around the most compressed part of the cluster, are easily seen on this photograph. Professor Holden1 speaks of these lanes as being regions which contain no stars, and bounded by one or two lines of bright stars. He counted thirteen points at which two or three of these lanes intersected, and suggested that they might be considered as centers of force. In all but two of these lanes - one, the largest of the three discovered by Lord Rosse, and the other, at quite a distance from the center of the cluster-from five to fifteen faint stars could

be counted. A photograph which would not show a star of the fourteenth magnitude would probably show these lanes entirely empty of stars, but when the faint stars become visible the effect is that of gaps between the bright stars only. It is within these lanes that the faint stars can be seen nearest the center, showing that they probably exist in the center but are concealed by the bright stars.

The distribution of the bright stars is marked by the existence of these dark lanes and by the rays, while the arrangement of the faint stars is much more nearly globular.

LICK OBSERVATORY.

September 1899.

1 Pub. A. S. P., 3, 375.

THE PERIODS OF THE VARIABLE STARS IN THE CLUSTER MESSIER 5.*

By S. I. BAILEY.

THE cluster Messier 5 (N. G. C. 5904) contains about 900 stars on the photographs made with the 13-inch Boyden refractor. Of these about eighty-five, or one in eleven, are variable. The period and light-curve of No. 18 were determined in 1896 by Professor E. C. Pickering. (See A. N., 140, 285.) The periods of Nos. 1, 42, and 84 were determined in 1898 by Professor E. E. Barnard, from visual observations with the great Yerkes refractor. These periods are confirined by the Harvard photographs. (See A. N., 147, 243.)

Measures of sixty-three of these variables had been made on nearly one hundred plates, by Miss E. F. Leland and myself, when I left Cambridge in March of the present year. From a study of these measures the periods of about forty stars have been determined. The results are given in the following table, which gives in successive columns the star number, the period, the residual obtained by subtracting the mean period from each, the maximum and minimum magnitudes, the range, and the distance, to the nearest minute of arc, from the center of the cluster.

The star numbers were assigned in order of discovery and bear no relation to the positions of the variables. The periods are here given to the nearest thousandth of a day. It is believed that few, if any, of them are in error more than five ten thousandths of a day (seven tenths of a minute). minute). A few of them

No. 42,

have been determined to within one or two seconds. which is the brightest star in the cluster, and which has a period of 25.75, has not been included in this discussion. In length of period it appears to belong to a different class, though the form of light-curve is similar to that of the others. No. 50 also

Read at the Third Conference of Astronomers and Astrophysicists, Sept. 6, 1899.

appears from the photographs to have a period of a month or more, as was observed visually by Professor Barnard. No other variable, whose period has been found, is omitted from the table. Although the present study is provisional and includes only about half the variables, the general results should not be materially altered by later more elaborate investigations.

A brief examination of the above table will disclose a striking similarity among all these variables, not only in regard to length of period, but in magnitude and range of variation. The same is true of the form of the light-curve, as may be seen by reference to the figures, where are given drawings of the curves of the first eight variables in the group.

Of the forty variables given in the table, No. 9 has the long

est period, 0.699d=16h 46.6m. This is an exceptional case however, for, aside from this star, the maximum period is that of No. 26, 0.62414h 58.6m. The minimum period is that of No. 4, 0.450d 10 48.0m. Omitting No. 9, the extreme range is only 0.174d4h 10.6m. The mean period is 0.526d 12h 37.4", and the mean residual, 0.0471h 7.7m. The greatest deviation. from the mean (after No. 9, which is 4h 9.2m) is No. 26, 0.098d =2h 21.1m.

This remarkable tendency to equality in the length of the periods is matched by the similarity of the magnitudes. At maximum they range between 13.4 and 13.9, and at minimum between 14.5 and 14.9. The range of variation is between 0.7 and 1.4 magnitudes. Even these differences may be partially accounted for by the difficulties of measurement and the proximity of very close companions.

This uniformity of period, magnitude, and light-curve, among so many variables associated in the same cluster, points unmistakably to a common origin and, cause of variability. Perhaps at one time the periods were precisely equal, but if so, the perturbations which have caused the present divergence have, apparently, no relation to the star's distance from the center of the cluster. If we group the stars according to the residuals. given in the third column of the table, placing in the first group those stars whose residuals are between 0 and ±0.025a, in the second, those from 0.026 to 0.050d, in the third, from ±0.051 to ±0.075a, and in the fourth all greater, the mean distances of the groups from the center are respectively 2.7', 3.4', 3.0', and 3.6'. Grouped by positive and negative residuals the result is much the same.

In the great cluster @ Centauri, in which I have determined the periods and light-curves of over 100 variables, no such uniformity was found. (See H. C. O. Circular No. 33.)

For the more exact determination of the form of light-curve a few of these variables in Messier 5 have been studied with special care. Two of these are represented on page 259. These periods are correct within 25. The black dots represent the individual measures, and a smooth curve has been drawn through these which probably well represents the photographic lightcurve. A few of the residuals, from measures on poor plates, are rather large, but these could be much reduced by repeating the measures once or twice. These stars well represent what may be called the Cluster Type of variables. A large number of variables in @ Centauri are of this type and, so far as known at present, all the variables in Messier 5. The most striking feature