741 



pressure. Tliey are all nearly of (lie same spectral type, hence (heir 

 temperature cannot differ much. The relation which has been found 

 to hold for them between period antl intensity may therefore be 

 explained in a sim[)le manner by assuming (hat the variation 

 of light arises from a [)ulsa(ion of the gaseous sphere; not, 

 as is often assumed, a pulsating deformation, but a pulsating 

 expansion and contraction. Hereby (he absorbing layers at the front 

 of the star will alternately move away from us and towards 

 us, hence in the s[)ectrum a pei-iodical displacement will take 

 place. This dis[)hicen]ent has usually been taken as indicating an 

 orbital movement and for this lea^on the Cepheids are admitted 

 amongst the spectroscopic double stars. Still an)ongs( (hese they 

 occupy a very excepdonal position. Calculating the mass from the 

 elements of the orbit, very much smaller values are found for the 

 Cepheids than for other spectroscopic double stars, although their 

 volume is much larger (han that of the sun. Although an extre- 

 mely small density is not altogether impossible a priori, still in 

 tiie relatively small radial velocity an indication may be seen for 

 the assumption, that a different explanation must be given here than 

 for ordinary spectroscopic double s(ars. 



But the question arises: is it possible that from an expansion and 

 contraction a radial velocity arises of such a value as the expei-i- 

 mejïts give — of several times ten kilometers per second? 



The luminosity of é Cephei and r^ Aquilae was found by Adams 

 from the spectrum to be 60 times that of the sun; for a mean 

 Cepheid with a period of Q.i) days Hertzsprung derived from the 

 proper motions 600 times the luminosity of the sun. Assuming on 

 the ground of the accordance as to spectral type and colour an 

 equal radiating power per unit surface, these results give a i-adius 

 equal to 8 and 24 times respectively that of the sun. Representing 

 the maximum expansion and contraction by the factor/ = 1 -)- Lf, 

 the maximum radial velocity will be 



V=z ^ — 



86400P, 



where P is the period in days and R the radius. In kilometres R 

 is 8 or 24 x 7 10'. Taking for P 6 days, this gives 



6,3A/X 8 (of 24) X 7.10' 



V = ~ — :^^— -^ Ai^^- = 82 resp. 246 A /' KM. 



4,3 X 10' 



Since these Cepheids fluctuate rather less than 1 magnitude visu- 

 ally and ratliei' over 1 magnitiuie in photographic intensity, we shall 

 assume one magnitude for the variation in complete radiation; 



