70 



Sven Wicksell 



(H\ 00 = 1.12 1.13 (H\ 2() =lA2 



(H\ u = 1.08 (17%, = 1.08 (ff 2 ) 002 = 0.95 



Now each of the second characteristics fl^ 2 2VW shall be multiplied by the factor 



-y^- — to be corrected for the probable variation of & r 

 (■" 



It will be seen that the ratio of the shortest axis to the two galactic axes will 

 be greatened by a factor equal to ]/ 1.17. As the ratio of the two smaller axes 

 amounts to about 0.83 we will have a corrected ratio of about 0.90. It will be of 

 interest to see what may be the mean error of this ratio. We have approxi- 

 matively 



\ 0 2 0/ \ 1V 0 2 0/ \ lv 0 2 0/ 



and as we shall in the next chapter find that 



^ e{N® t ) = 0.04 = v e W.Ji 



we see that 



W 



-- 0.066. 



Calling the ratio of the two smaller axes for p we find 

 p = 0.90 ± 0.028 



Accordingly we conclude that even after correcting for the probable value of 

 the variation of with galactic latitude we cannot regard the ellipsoid as an ellip- 

 soid of revolution, though the excentricité in sections transverse to the major axis 

 is small. 



A question of some interest in this connection is, what is the value of H 

 required to make the ellipsoid of the same form as found from the radial veloci- 

 ties? Now the answer to this question depends on what value we adopt for q. 

 It is true that a unique solution giving H and q is possible to obtain, but the 

 solution of q is very unsharp. The points will be seen clearly in the following 

 treatment. We have from § 21, dividing by & t a 



(ff 2 )20ü-^2oo = 1380.6 9' -169.0 

 (# 2 )o2o^ 2 o= 749.6 g' -174.1 

 (tf 2 )oo2^o2= 429.0 3'- Ö4.3 

 As by a pure galactic variation of we have (H 2 ) 200 = (H 2 ) 020 we might solve 

 for the three unknowns (ZT 2 ) 200 , (# 2 ) 002 and q\ inserting for the N^ k the values found 

 by Gyllenberg from the radial velocities. Referred to a system of coordinates 

 very close to our system III Gyllenberg has found values that, when means are 

 taken for the spectral types A, F and G, give 



N 200 = 449.4 JV 020 = 176.9 N w2 = 306.3 



We now find 



