598 



SCIENCE. 



[N. S. Vol. XVIII. No. 462. 



without great difficulty by the use of several 

 groups of plates which in greater number 

 were made on closely associated dates, as, for 

 example, those of 1895, from May 31 to June 

 30, and of 1897, May 13 to June 17. So by 

 degrees the period can be continually im- 

 proved, until eventually a use of the widely 

 separated observations is possible, with the 

 use provisionally of a derived light curve, 

 which then gives the final sure value of the 

 period. When this value is once found, and 

 an initial epoch determined, one can at length 

 for each individual measure find the differ- 

 ence in time from the preceding maximum 

 or minimum, arrange the magnitudes accord- 

 ing to these differences, unite the several 

 adjacent ones to means and by the help of 

 these normal magnitudes construct graphic- 

 ally the mean light curve. 



The light curves obtained by the author for 

 the reasonably sure variables are reproduced 

 in Plates II. to VII. at the end of the 

 volume, and give a glimpse at the peculiari- 

 ties of the light changes for the individual 

 objects. The scale of these curves is chosen 

 somewhat small. By a somewhat larger repre- 

 sentation clearness would have been gained. 

 The residuals of the individual observations 

 from these curves have already been given 

 in the table of observations in Chapter IH. 

 Also in Chapter IV., in a special table ap- 

 proximate values are found for the duration 

 of the maximum and the minimum phases, as 

 well as for the increase and the decrease of 

 the light, and for the rate of increase and 

 decrease in magnitudes per hour, and finally 

 the mean residual, that is, the mean of the 

 residuals from the curves without regard to 

 sign. The last value varies between 0.07 and 

 0.25 magnitude, the mean being 0.128. 



In order to obtain an idea as to the cer- 

 tainty with which the elements of the light 

 changes may be derived from the available 

 materials, the writer selected at random 

 several stars, and without knowing before- 

 hand the results obtained by the author, in- 

 dependently determined the elements. The 

 results agreed closely in all cases with those 

 in the present volume. One may, therefore, 

 put full confidence in them. One who has 



himself carried out such computations and 

 knows thereby how many attempts and ap- 

 proximations must be made before a satisfac- 

 tory arrangement of all the materials of ob- 

 servation is reached, will at best be able to 

 appreciate what enormous labor is involved 

 in his table of elements. 



A glance over this table shows that for 

 nearly all the stars the length of period is 

 only a fractional part of a day. Only 5 stars 

 make an exception, which have periods of 

 1.35, 14.75, 29.34, 297 and 484 days, respec- 

 tively. For 26 stars the periods are less than 

 10 hours; ISTo. 19 has the shortest period, 7.2 

 hours. 



The range of light variation is noticeably 

 different for the different variables. The 

 difference between the maximum and mini- 

 mum brightness varies between 0.45 and 4.58 

 magnitudes, and in general also, as with 

 variables not situated in clusters, the longer 

 the period the greater is the amplitude. A 

 range of less than 1 magnitude for the deter- 

 mined difference is found in the case of 56 

 stars. Where the amplitude is less than 0.6, 

 or perhaps 0.5 magnitude, the determination 

 of the light curve is naturally somewhat un- 

 certain, and one must look upon these objects 

 with some doubt. It ought not to be over- 

 looked, however, that frequently the real 

 changes in brightness will be somewhat 

 greater than those given in the table, since 

 for many stars the brightness changes with 

 great rapidity at maximum, and on this ac- 

 count the photographs, especially when the 

 exposure is very long, do not record the true 

 maximum brightness, but one something less. 

 Especially is the relatively long duration of 

 the exposure, which for these swiftly chang- 

 ing objects may be a considerable part of the 

 whole period, a provoking hindrance to the 

 determination of the genuine light phe- 

 nomena. 



Of great interest is the study of the light 

 curves. These are by no means alike for all 

 the variables in the cluster. They are, how- 

 ever, always of certain types. The author has 

 distinguished three different classes of light 

 curves. The first class, in which 37 stars may 

 be reckoned, is characterized by the fact that 



