The general Characteristics of the frequencyfunction of stellar movements 



7 7 



As a conclusion we may say that the two-stream hypothesis seems to be in- 

 adequate as a physical explanation of the properties of distribution of stellar move- 

 ments. As a working hypothesis it is as good as the assumption of an ellipsoid of 

 revolution, besides giving a pretty good description of the slcewness. As regards 

 the excess the two-stream hypothesis cannot be thought to give even its main features. 

 If it should be necessary to adopt another value of q the two-stream distribution 

 will give a still poorer fit. 



31. In figures 2, 3 and 4 we have plotted out the frequency curves of the 

 motion as projected on the [7W- the V {s) - and the T^-axes ; the dotted curve is the 

 normal frequency curve and the unity is the respective dispersions. 



In a similar way fig. 5, 6 and 7 illustrate the distribution of the apparent 

 motions as projected on the same axes. It is seen by the form of those curves that 

 in the case of the apparent motions the characteristics of orders higher than the 

 fourth cannot be neglected. 



On the whole the fig. 2 — 7 and the other results of this chapter and chapter VII 

 show the remarkable and very interesting fact, that in spite of the distribution of 

 the apparent motions being so excessively unnormal as to make its representation 

 by a frequency function of the A-type almost illusory, or at least requiring the 

 computations of characteristics of the fifth and sixth orders, the distribution of the 

 linear motions may well be thought to be a nearly normal three axial distribution. 



On speaking with Mr. Gyllenbkrg of this Observatory on the above subjects 

 he has told me that the information to be gathered from the radial velocities in all 

 essentials is in consistence with the conclusions here drawn. Taking together stars 

 surrounding each vertex he has computed frequency curves that may be regarded 

 as giving the essentials of the distribution along our axes of coordinates. The only 

 deviation from our results were found to lie in the excess' along the and F (s) 

 axes. In the f7 (8) axis he found the excess to be zero and in the F (s) axis to be 

 about 10°/o positive (ß 040 = -(- 0.04); the main feature of the higher characteristics 

 of the radial velocities is, however, that they are all small. Knowing what would 

 become of our characteristics if another value of q should be adopted, we may 

 assert, that the value q = 0.75 gives the best agreement possible to obtain between the 

 higher characteristics as derived from the proper motions and those indicated by the 

 radial velocities. 



As is well known Prof. Charlier has in his here often cited work concluded 

 that the skewness of the linear motions is not small and that the excess is »tho- 

 roughly negative». Evidently this opinion is due to his having used a value of q 

 so low as 0.62. As seen from our tables XIV and XV of chapter VII q = 0.62 

 gives most thoroughly negative values of the higher characteristics. To the same 

 cause we also "may attribute the circumstance that his attemps at dissecting the corre- 

 lation function of the linear motions into two components, viz. the two star-streams, 

 gave so altogether negative results. Evidently an attempt to reconcile the charac- 



