134 



SCIENCE 



[N. S. Vol. XLIX. No. 1258 



liminary General Catalogne it appears that 

 these stars, which have a mean period of about 

 seven days, have a mean absolute magnitude 

 of — 2.3 on Kapteyn's scale. Eoug-hly speak- 

 ing, they average at maximum about 1,000 

 times as bright as the sun and at maximum 

 about 500 times the sim's brightness. 



By combining these data, Shapley, in a re- 

 markable series of papers, has derived an em- 

 pirical curve which gives the absolute magni- 

 tude of any Cepheid whose period is known. 

 The cluster variables are of median absolute 

 magnitude — 0.2 and average about 100 times 

 as bright as the sun. The Cepheids of longest 

 periods, forty days and over, appear to be fully 

 ten thousand times as bright as the sxm. With 

 the aid of these data he has shown that the 

 Cepheids proper lie in a region only a few 

 hundred parsecs thick, which extends along 

 the galactic plane for several thousand parsecs 

 in all directions, while the isolated variables 

 of the cluster type spread out into space far 

 on each side of this region. The same data 

 have been fundamental in his determination 

 of the distances and distribution in space of 

 the globular clusters — which has revolutionized 

 our conceptions of the extent of the imiverse, 

 and of the relation of the naked eye stars to 

 it, but would lead us too far from the theme 

 of the present hour. 



Our empirical knowledge of Cepheid va- 

 riables is therefore both extensive and ac- 

 curate, and has already led to astrophysical 

 conclusions of far-reaching importance. But 

 our understanding of the nature of the phys- 

 ical process which lies behind the variation of 

 these stars lags far behind in the rear. 



Some things seem fairly clear. The con- 

 comitant variations in brightness, color and 

 spectrum indicate very strongly that the 

 proximate cause of all three is a variation in 

 the surface temperature of the star. The 

 enormous magnitude and great rapidity of the 

 changes (a cluster variable may increase its 

 brightness by fifty times the sun's whole light 

 in two hours, and lose all this again in six 

 hours) make it probable that the changes in 

 temperature must arise from some process by 



which heat energy is transformed jjeriodicaUy 

 back and forth into some form of ]x>tential 

 energy — ^the loss by radiation during one 

 period being relatively insignificant. Finally, 

 the regularity of the process indicates that the 

 regulative force behind it is gravitational — 

 the potential energy taking some from such as 

 an expansion of the mass against gravity — 

 and that the physical process involved is some 

 form of gravitational oscillation of " pulsa- 

 tion" of the mass, probably involving the com- 

 pressibility of the material as an essential 

 factor. 



There are various alternative hypotheses, 

 some of them attractive, for example, that 

 which assumes that we have to do with a 

 rotating body, hotter and brighter on one side 

 than the other. This explains the general 

 character of the changes in light and spec- 

 trum, and their regularity; but a detailed 

 analytical study of the problem shows that it 

 is impossible for the rotation of a convex 

 body, brighter in some parts than others, but 

 with each portion of invariable brightness, 

 to give rise to a light curve in which the rise 

 is as rapid, compared with the fall, as in the 

 case of many typical Cepheids, and aU the 

 cluster variables. Hence it appears certain 

 that actual changes in the temperature and 

 brightness of the surface of these stars must 

 take place during each period. The variations 

 in radial velocity are also very hard to ex- 

 plain on the rotation theory, which would 

 give the wrong phase. 



Another attractive hypothesis, which meets 

 the difficulty about the radial velocities, as- 

 sumes that the face of the star which precedes 

 in the orbital motion is brighter than the 

 hinder side, as would be very probable if the 

 motion took place in a resisting medium. But 

 this idea appears less alluring when it is 

 realized that these stars, which are very sim- 

 ilar to the sun in spectrum and color, and 

 presumably in surface brightness, must in 

 that case have radii of the order of 20 million 

 kilometers, while the average radius of one of 

 the spectroscopic orbits is less than two million 

 kilometers. Hence the stars themselves are 

 in all probability much larger than their orbits 



