742 



therefore loc/ L varies by the amount 0.20 above and below the 

 mean. If the radins clianges as the number /', the density changes 

 as ƒ', the temperature as /Vs <^iitl the radiation as /''^'j; from 

 log L = ± 0.20 it then follows that log f = ± 0.04, hence / 

 fluctuates between J,l and 0,9. hi the expression for V we must 

 tiiei-efore take 0,1 for A/' and the maximum radial velocity becomes 

 8 or 25 kilometers per second. This value has to be somewhat 

 lowered, since spectographically the mean velocity of the entire front 

 surface is measured, of which only the central parts have the velocity 

 whicii we have here calcidated. But even then (lie value found 

 agrees sufficiently with the measured velocities (10 to 20 kilometers 

 per second) to admit the explanation of the light variation and the 

 variation in radial velocity on the ground of contraction and 

 expansion. 



There are some othei- objections to this explanation. The one is 

 the same objection which also holds against the explanation through 

 an orbital movement viz. that the maximum intensity coincides 

 with the highest velocity towards us. The other objection lies in the 

 coefficient 0.48 found by Miss Leavitt. If for these Cepheids eqtiality 

 of spectral class and thus of emissive power and of 7' may be 

 assumed, the brightness becomes proportional to the surface, which gives 



P^ - L. 



or 



log P - Const. — 0,2 .1/. 

 In this case therefore the coefficient should be 0.2, whereas 

 Miss Lkavitt finds a much larger change of (he period or a much 

 smaller change of the brightness. It is therefore difficult to explain 

 the deviation by means of a dependence of the temperature T on 

 the linear dimension R\ for in (hat case 7^ would have to be smaller, 

 the larger the star. Possibly an ex|)lanation may be found, by 

 assuming, that the mass of the Cepheids is actually small, and 

 therefore the density very low, so low, that the rays emitted from 

 one side of the star may penetrate the complete body without being 

 completely absorbed. If a glowing gas-sphere is so rare, that we 

 observe the emission even from the hindmost layers without any 

 diminution, the total light from the sphere will no longer be pro- 

 portional to its surface, but to its mass, therefore be the same for 

 two bodies of equal mass and different dimension. Intermediate 

 conditions are conceivable in which the total light will then be 

 proportional to a lower power of R, say to the first power. In the 

 latter case the coëffiicient of M in the formula for log P would 

 become about 0.40. 



