?f„ ('OS 



396 



2rr 2rr it„A 2jr 



!/ lol 



(2) 



where naturally ?6, z^^, c, A, t and T' must all be expressed in the 

 same units (km. and sec.) The observed velocities will thus show a 

 spurious excentricitj, of the amount 



e=z a • . 



T c' 



This unites with the true excentricitj and cannot be separated 

 from it by observations. 



Now it is easy to derive an upper limit for x. Take a well 

 known star like /? Aurigae. The observations giv§ 



;; = 0".014 = 0.005 u, = 110 r= 3.96 days. 



As the largest values which are still compatible with the obser- 

 vations we can take 



^;<0".05, or A > 65 lightyears, 

 é< 0.015. 



We find then x < 0.002. 



Quite possibly other stars will give still smaller values of x. The 

 smallest values, of course, are found from the stars having the 

 smallest parallaxes. Unfortunately the parallax of most spectroscopic 

 doubles is still unknown, and it is thus impossible to give numeri- 

 cal values. We can however assume as certain that for the majo- 

 rity of these stars a xsdue would be found which is still smaller 

 than that given above. 



Postscript. During the discussions at the meeting the remark was 

 made (by Prof. Korteweg) that the star /? Aurigae might have a 

 true excentricity of such amount as exactly to cancel the spurious 

 excentricity produced by the motion. This is, of coui'se, entirely 

 correct. If this true excentricity ^) were e = 0.90 we should find 

 H=r0.12, [taking again p = 0".05 and using the same approximate 

 formula as above, though this is not correct for such large excen- 

 tricities]. Thus if we knew only this one star, we should have to 

 adopt as upper limit for x this value 0.12. There are however a 

 considerable number of stars widi large values of ?<„, whose observed 

 excentricity is very small or zero. Several of these certainly have 

 very small parallaxes. It would evidently be absurd to assume that 

 all of these possessed exactly that true excentricity and position of 

 the periastron which would cancel the apparent excentricity for an 

 observer on our earth. 



1) For (3 Aurigae a large excentricity is particularly improbable on account of 

 the presumably large dimensions of both components as compared with their 

 mutual distance. * 



