30 



SCIENCE 



[N. S. Vol. XXXVII. No. 940 



U Ophiuehi, BZ Centauri and SZ Centauri shows 

 that the periods of these variables are double the 

 values heretofore given, for in each ease two 

 minima of unequal depth alternate. This is also 

 probably true for SS Carinfe and for EX Draconis. 



For more than 80 per cent, of the orbits studied 

 circular elements represent the observations satis- 

 factorily. In no instance has an orbital eccen- 

 tricity been found to exceed 0.1. The fainter 

 component is very generally the larger of the pair. 

 In only one case out of nine is the dark companion 

 definitely smaller. Pairs of equally luminous 

 stars are rare; equal radii are more common. 



The elongations of the component stars through 

 gravitational interaction has affected the shape of 

 the light curves for one third of the number here 

 considered to a degree sufficient to be taken into 

 account in the discussion of the orbits. The square 

 of the eccentricity of a meridian section of the 

 assumed similar prolate spheroids is greater than 

 0.30 for /3 Lyrse, SS Sculptoris, SR Centauri and 

 V Puppis; it is greater than 0.20 and less than 0..30 

 for U Pegasi, U Seuti and u Herculis; and be- 

 tween 0.10 and 0.20 for V. Ophiuehi, V Serpentis, 

 SZ Centauri and SZ Centauri. These data have 

 enabled the comparison of the observed relation 

 between the prolateness and distance of centers 

 with the theoretical relation derived by Darwin 

 for equal masses of homogeneous, incompressible 

 fluid. A remarkable agreement is found. 



The densities of the pairs were computed in 

 terms of the sun's density, on the assumption of 

 equally massive components. An important rela- 

 tion is found connecting density and spectral type. 

 The average density of nine stars of Classes Bl 

 to B8 is 0.16; of 26 stars of Class A it is 0.13; 

 but for eight stars of Classes A5 to F the average 

 is 0.55. No star of the first two groups has a 

 density as great as one half that of the sun; and 

 the solar density is not exceeded by any in the 

 third group. 



A general investigation has been made in con- 

 nection with Professor Russell of the theory of 

 da,rkening at the limb in eclipsing variables and 

 of the relation existing between orbital elements 

 derived on the assumption of uniformly illumi- 

 nated disks and of disks darkened to zero at the 

 limb. Tables analogous to those used in deriving 

 elements on the former assumption have been 

 constructed. 



On the Graphical Representation of Eclipsing 

 Variables: Henry Norms Russell. 

 The computed elements of an eclipsing variable 



are admirably adapted for graphical illustration. 

 A diagram of the system as seen from the earth 

 exhibits at a glance all the geometrical elements. 

 By a proper choice of scale, it may be made to 

 show much more. If we assume that each com- 

 ponent is equal in mass to the sun, their mean dis- 

 tance (in solar radii) will be 5.29 P2/3, where 

 P is the period in days. If platted on this scale, 

 the radius of the orbit will at once indicate the 

 period, and those of the individual stars their 

 probable densities (on the usual assumption of 

 equality of mass). By suitable shadings, the rela- 

 tive surface brightness may also be indicated, and 

 thus practically all the facts for several systems 

 may be displayed on a single sheet. 



Such diagrams also give, in all probability, a 

 very good idea of the actual dimensions of the 

 various systems. No stellar system has yet been 

 reliably investigated whose mass is less than one 

 fourth that of the sun; and masses exceeding 

 sixteen times the sun's are very rare. It follows 

 that the actual dimensions of a given system, com- 

 pared with the sun, are very unlikely to be more 

 than twice, or less than half, those indicated by 

 diagrams prepared as above. Since most eclipsing 

 variables are too faint for direct spectrographic 

 investigation, this is probably the best way at 

 present available of getting an idea of their real 

 size. 

 Relation Between Spectrum and Color-index of 



500 Stars: J. A. Parkhurst. 



The revised data from the writer's forthcoming 

 catalogue of magnitudes and spectra of northern 

 stars- furaishes material for a curve showing the 

 relation between spectrum and color-index. The 

 range in magnitude of the stars used is between 

 4 and 9, the greater number lying between 6 and 

 8.5. The average magnitude is 7.3 visual, corre- 

 sponding to 7.7 photographic since the color-index 

 of the average star is 0.4. The Harvard classifi- 

 cation is used. 



Platting the color-index as abscissffi and the 

 spectral class as ordinates, a straight line is found 

 to fit the points better than any simple curve. 

 The lantern slide accompanying the paper shows 

 a comparison between this ' ' curve ' ' and those 

 published by King in Harvard Annals, 59, 180, 

 and Schwarzschild in his Gottingen Aktinometrie, 

 B, 19. King's stars are mostly brighter than 

 magnitude 4.5, while Schwarzschild 's are about 

 the same brightness as those measured by the 

 writer. The present work differs from the other 



^Ap. J., 36, 169, 1912. 



