30 Walter Gyllenberg 



TABLE X. 



The mean velocity and its variation with spectral classes. 





Num- 















Results of Campbell 



Type 



ber of 



Mean 



Velocity 





■9- 







Number of 







stars 















stars 



Average velocity 



ß 



247 



1.854 



+ 0.083 



1.479 



+ 0.066 



2.958 



+ 0.132 



225 



1.366 — 1.410 



A 



283 



3 102 



+ 0.149 



2 475 



+ 0.119 



4.950 



+ 0.238 



177 



2.215 — 2.312 



F 



237 



3.816 



+ 0.175 



3.045 



+ 0.140 



G 030 



+ 0.280 



185 



3.034 



G 



208 



4.173 



+ 0.204 



3.330 



+ 0163 



6.660 



+ 0.S26 



123-128 



2.723 — 3.160 



K 



85 



4.517 



+ 0.348 



3.628 



+ 0.278 



7.256 



+ 0.556 



70-73 



3.251 — 3 618 



M 



48(3 



4.200 



+ 0.135 



3351 



+ 0.108 



6.702 



± 0.216 



369-382 



3.18S — 3.547 



magn 4.9 



1069 



3.527 



+ 0.076 



2.814 



+ 0.061 



5 624 



+ 0.122 







magn _> 5.0 



4G2 



-1.094 



+ 0.135 



3.267 



+ 0.108 



6.534 



+ 0.216 







ail stars 



1531 



3.C23 



+ 0.066 



2.891 



+ 0.053 



5.782 



+ 0.106 



























The average velocities are the values determined by Campbell and in the last 

 column I have for a comparison reprinted his results and expressed them in the 

 units used here. The remaining column gives the value of il that is the mean 

 absolute velocity defined through 



Concerning the mean velocities of brighter and fainter stars the latter give a 

 much higher value than the former, this fact may however exclusively be due to 

 the large number of stars of so called later types that enter the group magn > 5.0. 



The ellipsoidal hypothesis in its generalized form. 



27 Returning to the table IX, these values may be used for a closer exami- 

 nation of the velocity distribution. To this end the ellipsoidal hypothesis was adopted 

 n its generalized form. In another paper I have given a short description of the 

 solution and preliminary derived the numerical results 1 . 



As to the developement of the formulas and the expressions I have used the 

 same signification as Charlier in his memoir. It was however necessary when 

 studying the three axial distribution of the velocities to introduce three variables. 



I give here only the expressions for the moments about the origin and about 

 the mean. 



The former is denoted by: 



+ » 



( 1 3) N m = fff d U d V d W <p( U, V, W ) U 1 V-' W\ 



1 Meddelande fr. Lunds Astr. Obs. N:o 59. 



