The motion of tlie stars 



101 



SO that the expression for the excess now takes the form 

 (104) . 



We have found above that the frequency surface of the hnear velocities has 

 a, rather large, negative excess. We are thus led to the conclusion, that the law 

 of Maxwell, regarding the relation between the mean velocities and the masses, 

 applied to the stars does not alone suffice to explain the observed values of the 

 excess. Possibly such a relation does exist, but there must then also be found 

 some other dynamical law, through which not only the positive excess is counter- 

 balanced but even a negative excess is introduced. 



37. That such a relation between the mean velocity and the masses as that 

 claimed by the law of Maxwell in reality exists, is made probable by the discovery 

 of Frost and Adams regarding the slow peculiar velocities of the Orion stars, as 

 well as by the subsequent extension of this discovery by Kaptetn, Campbell and 

 others to other spectral classes. For comparing the results from the radial velo- 

 cities with the law of Maxwell, it is necessary to have the values of the masses 

 of the -stars ;of different spectral types. 



In order to obtain them Kand. Sven Wicksell at my request deduced the 

 absolute magnitudes (M) of the stars for different spectral types from a list of parall- 

 axes given by Kaptetn in the «Publications of the astronomical laboratory in 

 Groningen» N:o 8. The values obtained by him are given in col. 2 of tab. XL 



TABLE XL Relation between mean velocity (a) and mass ([x) of the stars. 



Sp. 



M 



V- 





a 



a in km 



B 



m 



— -2.31 



5.21 



0.44 



0.44 



6.4 



A 



+ 1,47 



1.63 



0.78 



0.78 



10.5 



F 



+ 3.07 



1.00 



1.00 



1.00 



14.4 



G 



+ 3.85 



0.79 



1.13 



1.10 



15.9 



K 



+ 4.10 



0.73 



1.17 



1.17 



16.8 



M 



+ 8.17 



0.21 



(2.19) 



1.19 



17.1 



The systematic variation of the absolute magnitude with the spectral type 

 comes out very well pronounced. For deducing the values of the masses from M 

 I now postulate the relation (101) and find with the value c = 3 the values of the 

 masses — the mass of a star of type F being taken as unity — given in the third 

 column of the same table. In the fourth column I give the values of the inverse 

 square-root of [x. In the last column are given the values — in kilometres — of 

 the mean radial velocities of the stars of different spectraltypes according to Camp- 

 bell (Lick Observatory BuUetion N:o 196 (1911)), and in the 5*'^ column these velo- 

 cities are reduced to the velocity of stars of type F as unit. 



