739 



120 times the radius of the siin, therefore again a \alue of the 

 same order of magnitude. 



The Novae in the first stage of their brightness thus possess the 

 characteristics of the giant-stars ; in order that their mass may not 

 become too exceptionally large, theii- density must be small even 

 before the expansion. The relation found here between T, R, and A 

 cannot teach us anything on this point, as it does not contain the 

 density. A further indication for a small density may be found, 

 however, in the fact that after a decrease of 4 magnitudes the 

 spectrum at the minima of the light-variations luore and more 

 approached the character of a nebula-spectrum, and after another 

 few months the star had become a nebula. At this stage the density 

 has become so small that the visible emission is derived from the 

 whole body including even the hindmost layers and still gives but 

 a feeble surface-brightness ; the fact that this condition sets in, when 

 the expansion factor has become something like 10 or 20, proves 

 that the original density must also have been far below nnitj'. 



111. 



The original equation of motion (1) may also be written in such 

 a form that it does not contain any dimensions. 



Let us put 



r = ys A = y,i- t ^=z (fz .... (10) 



where y is a linear measure, ff a length of time and s, x, and z 

 are numerical values. The equations then become 



d^iv 7 d' dy dy \ 



d^~~~2 y^ds~~' ds 



J- • • • (11) 



s \^ ds 



where (3 is a function of the coordinate .s,,. The function ^ and 

 the constants a, y, (f which determine the special constitution 

 and size of the star are united in the one coefficient B. The 

 law of change of a; with z is solely dependent on this coefficient, 

 and is the same for all bodies with the same B. Equations (11) 

 detei'mine all possible movenients — progressive, irregular or periodical, 

 which may occur in a cosmic gaseous mass, in so far as they are 

 a function of /• only and as gravitation may be left out of account. 

 Without calculating these movements themselves, a relation of 

 similarity may be derived from the formulae which establishes a 

 connection between the changes in different stars. If for diffeient 



48* 



