740 



cosmic gas-splieres the (listi'ihntioii ol' ,? along llie radius is (he same, 

 llie expression 



L (r t 



/ VV 'K 



must be tl)e same function tor tiiem, provided B i.e. «(i*^ for them 



is the same number. If for each of tiiem a suitable tinje- and distance- 

 scale is assumed, the motions and variations expressed on this scale 

 are for all these bodies identical. 



Assuming thai a periodical solution of the equations (IJ) exists in 

 which the panicles move radially to and fro and the density perio- 

 dically becomes adiabalically larger and smaller, this condition ot 

 motion will be valid for all such bodies provided the periods of the 

 variations are expressed in d as unit and the dimensions of the 

 bodies in terms of y. We must then have the relation 



'^ d/ y -■-'=: ^VV y-^ 

 Now <(^ Hl\„ (at the centre), therefore proportional to llie tempe- 

 rature at the ceidre. Calling /' the period of I he variations and H 

 the radius of the gas-sphere, this gives-. 



1. ■ t - ./. • .^.^ • 



If we may assume, that similar bodies of this kind have the same 

 temperature, the brightness becomes proportional lo R- , i.e. to /^'. 

 Otherwise the temperature will still depend on .some power of R 

 and we have the more general relation 



F' ^ L" 



or 



2 log P = Const. + » hf/ L 



or 



2 lop P z= Coi^t. — 0,4 n X M 

 if M represents the absolute magrdtude. A relation of that kind was 

 found by Miss Leavitt for the variable stars of the d Cephei-type 

 in the small Magelhanic-cloud '). For 25 stars with periods from 

 1.25 to 127 days she fonnd, that the period increased with the 

 magnitude in such a manner that the logarithm of the period 

 changed by 0.48 per magnitude-class. 



The Cepheids are giant-stars, to which our suppositions are in so 

 far applicable, that gravity, small in itself by the small density, 

 must moreover for the greater part be neutralized by the radiation- 



) Harvard Circular Nr. 173. 



