116 



KNOWLEDGE 



[June 1, 1898. 



From Table 8 it is evident that a condensation towards 

 the plane of the Milky Way begins to show itself for stars 

 of the 1st type with proper motions 0"04 - 0"05 ; for 

 stars of the 2nd type only in the stars of quite insensible 

 proper motion (^0"03). For these, however, the con- 

 densation IS not in the least dubious ; it is as strong as 

 the condensation of the whole of the stars of the ninth 

 magnitude, and this proves conclusively that stars of 

 this type are not arranged independently of the Milky 

 Way, as might have been thought probable from the 

 results obtained by Prof. Pickering ("Ann. of the Obs. of 

 Harv. Coll.," Vol. 26, p. 462). 



It is very easy to show that a systematic error in the 

 estimation of the magnitudes of the stars in the JNlilky 

 Way cannot change this result. It certainly is not im- 

 probable that such an error exists, and that this will 

 prove sufficient to annul the slight thiniiuiff of the stars 

 of the 2nd t}'pe with sensible proper motions in the 

 vicinity of and in the MUky Way, but the condensation 

 of the stars with insensible proper motions would then 

 come out all the stronger. 



Table 4 proves that these conclusions are independent 

 of the motion of the solar system in space. 



An attempt has been made to prove the truth of Prop. I. 

 for fainter stars. The only fit material for such an investi- 

 gation accessible to Prof. Kapteyn is furnished by the 

 catalogue of stars of magnitudes 0—9-0 of L. Boss. 

 The proper motions given in this catalogue, derived 

 mainly from comparisons of the modern observations with 

 those of Lalande and Bessel, were counted. If we assume 

 that the number of these proper motions is incomplete to 

 nearly the same extent as the zones of Bessel, we can 

 derive the probable total number of the really existing 

 proper motions. These have been given in the last two 

 columns of the following table. 



Table 5. 



Distance 



Xuniber of 



Number of Probable total 

 , proper motions in number of 



from galaxy, square degrees, 'boss Catalogue. proper motions. 

 0"10-0"20 ^0"20 O"10-O"2O g0"20 

 5.1° to 65° 390 46 .39 76 65 



39 „ 55 390 45 32 71 50 



90 „ 39 390 41 29 73 53 



-20 „ -H20 390 35 15 72 31 



For the proper motions 0"10— 0"20, the imiformity 

 leaves nothing to be desired. For the more considerable 

 proper motions there appears to be a thinning out in the 

 Milky Way. Prof. Kapteyn thinks that this thinning out 

 is not to be considered as accidental, but that probably it 

 is still only apparent. For if we assume a systematic error, 

 of which the sensf as well as the amount (0-2 mag.) is 

 equal to that which Prof. Pickering really finds for the 

 estimations of the Bradley-Draper stars in the Milky Way, 

 this thinning out wiU be found to disappear. 



Prop. IV. — The truth of this proposition, too, is proved 

 by Table 3 ; for, as mentioned already, an unmistakable 

 increase in the number of stars of the 1st type is visible 

 for proper motions of 0"04 — 0"05, i.e., within what pro- 

 bably is a spherical shell we find a smaller number of 

 stars near the poles of the Milky Way than near that zone 

 itself. This evidently implies a real difference in the star 

 density. 



Prop. V. — The incorrectness of Struve's views appears 

 from Prop. I. Struve assumes, and in his time any other 

 assumption would have been hardly reasonable, that the 

 stars of different magnitudes are included between spherical 

 surfaces, or, in other words, he assumed that in all 

 directions the mean distance of stars of a determinate 

 magnitude is equal. This appears to be incorrect, for 



Table 1 proves that, in the direction of the Milky Way a 

 far greater number of stars of magnitudes — 6-5 lie 

 at the exterior of the sphere, the radius of which corre- 

 sponds to a pi'oper motion of 0"035, than in the direction of 

 the pole of the Milky Way ; from which it follows that the 

 mean distance of such stars is considerably greater in the 

 Galaxy than elsewhere. It may, however, be objected 

 against most of what has been said, that one cannot as yet 

 consider it as absolutely demonstrated that equal dis- 

 tances correspond to equality of m, or r in the Milky Way 

 and outside it, and that if this proves ultimately not to 

 be the case, the results drawn from Tables 3 and 4 

 cease to be correct. It will be well, therefore, to prove the 

 truth of Prop. V. dircrtli/. For this purpose the values of 

 (/ ( solar motion as seen at right angles from star) in high 

 and low galactic latitudes have been compared. Values 

 of r above 0"50 have been excluded because they have an 

 undue and excessive influence on the results. 



Table 6. — Values of q. 

 fi Type I. Type II. 



± 40° to ±90 + 0"0355 (336) -i- 00583 (449) 



— 30 „ -I- 30 + 0-0250 (4<;i5) + 0-0451 (285) 



As the stars compared in both regions are of equal 

 magnitude, it appears that for both types of stars there 

 really exists a difference of distance at different galactic 

 latitudes. 



Prop. VI. was already discussed at the meeting of April, 

 1892. Then, however, the demonstration was almost 

 exclusively based on the proper motions stars brought 

 together by Mr. Stumpe. The stars now investigated 

 confirm the conclusions of the preceding year in a most 

 striking manner, as will be seen when the following table 

 is compared with the one then given : — 



Table 7. 



1189 



1106 



The values of ',' are nearly represented, with the excep- 

 tion of the first, by the formula : — 



(J = 14 /A 



especially if we exclude the Hyades, whereby the value of 

 ',' for the proper motions 0"10— 0"15 becomes considerably 

 larger. 



It may be asked whether this variation of Q may be 

 explained by the hypothesis that the stars of the 2nd type 

 form a group of stars independent of that formed by the 

 stars of the 1st type. 



A definitive settling of this question seems difficult, but 

 in the opinion of the speaker the following arguments seem 

 to militate against such an hypothesis : — 



1st. Both types of stars show the same sort of arrange- 

 ment in respect to the plane of the Milky Way (Prop. II.). 



2nd. The centre of condensation of the stars of the 2nd 

 type seems to coincide with the centre of the Milky Way, 

 which consists, in great part at least, of stars of the 1st 

 type (Prop. IX.). 



3rd. In groups of stars like that of the Hyades, which 

 show a common proper motions (equal in amount as well 



