DIAMETERS OF THE STARS DANJOKT. 



169 



The same thing is yet more apparent in the case of type M which 

 includes a part of the red stars. The appearance of a banded spec- 

 trum belonging to titanium oxide confirms a considerable lowering of 

 temperature in the case of class M. The temperature of these stars, 

 indeed, cannot exceed that of the electric arc. At higher tempera- 

 tures, these bands characteristic of composite molecules, vanish be- 

 cause of atomic separation of the molecules. 



We come finally to the stars of class N which are especially 

 characterized by bands due to carbon. This group contains only very 

 red and at the same time faint stars. 



The essential features of the Harvard classification are given in 

 the following table. It also contains the probable values of the 

 effective temperatures of each spectrum class as indicated from a 

 consideration of all the values published. 



If we now assume Stefan's law applicable, at least as a first ap- 

 proximation, we can, based upon these temperatures, make calcula- 

 tions of the relative amounts of energy emitted per unit surface by 

 the various stars. For example, let us calculate the diameter of 

 Sirius. Taking its temperature as 8,500° and that of the Sun as 

 6,000°, we obtain from the fourth powers of these temperatures a 

 ratio of about 4 to 1. Therefore, for equal surfaces, Sirius radiates 

 four times more energy than does the Sun. Accordingly we have 

 assigned to it a surface four times too great. We should divide the 

 equivalent diameter by 2 in order to obtain a more probable value for 

 its true diameter. Thus we finally get 0".009. 



A number of writers have applied the preceding considerations 

 to the determination of stellar diameters. They have utilized the 

 best possible observational data, searching to reduce to a minimum 

 the share taken by hypotheses. 



The angular diameters' calculated for Betelgeuse by Eddington, 

 Nordmann, and Kussell are respectively 0".051, 0".059, and 0".031. 

 We must fix our ideas only on the " orders " of magnitude and not 

 regard these as precise determinations. With this reservation, the 

 accordance is satisfactory. It will appear even more so when we see 



