June 1, 1898.] 



KNOWLEDGE 



115 



1st Type. 2nd Type. 



ju, in hie;b galactic latitude ( ± 40° to ±90°) _ . „f, ,.o(. 

 ju. in low galaccic latitude ( — 30" to +30°) ~ 



7 in high galactic latitude 

 7 m low galactic latitude 



1-42 



1-2U 



The agreement could not fairly be expected to be better. 

 Somewhat less satisfactory is the comparison of the values 

 of q and r, as will be seen from Table 2. 



Even here, however, the disagreement of the first two 

 values of 7 may probably be explained by their probable 

 errors (probable errors of each of these two values 

 roughly -f 0"005). 



~ Tamk 2 ('). 



(3 (galact. latit.). 

 + ■«) to ± 90 



— 30 „ + 30 

 + 40 „ +90 



— 30 „ + 30 



Further investigations on this point must be deemed 

 very desirable. 



The proper motions were originally taiien from Auwers's 

 re-reduction of Bradley. A look at the proper motion r, 

 however, showed at once that a correction of the con- 

 stant of precession (that of 0. Struve) was necessary. 

 This correction has been deduced by L. Struve, so that 

 the proper motion o- and t could be readily corrected. 

 As this was done, however, after the completion of most 

 of the computations, some of the results as given below 

 are still based on the iojcorrected proper motion. Where 

 this is the case it will be explicitly mentioned. 



After this introduction, the speaker discussed the 

 following propositions. 



Prop. I. If stars with very small or insensible proper 

 motions are disregarded, there remains a group of stars 

 showing no longer a condensation towards a plane (no 

 Milky Way). 



Prop. II. Stars with very small or insensible proper 

 motions (-g 0''04) show condensation towards the plane 

 of the Milky Way. This condensation exists as well for the 

 stars of the 2nd as for those of the 1st type, so that in 

 the arrangement of the stars of the 2nd type, too, there 

 may be recognized an incontestable dependence on the 

 position of the Galaxy. The condensation of the stars of 

 the 1st type, however, is more considerable, and begins to 

 be sensible for somewhat greater proper motions. 



Prop. III. This condensation of stars of insensible proper 

 motions is very considerable even for the brighter stars 

 (0"' — 6"'-5). For stars of the 2nd type it is as considerable 

 as for the whole of the stars of the nmth magnitude. For 

 stars of the 1st type it is much more considerable. 



Prop. IV. Either this condensation is at least partly 

 real (i.e. not optically produced by greater depth), or there 

 is real thinning out at the poles of the Milky Way. 



Prop. V. The arrangement of the stars found by W. 

 Struve has no real existence. The cause of the fallacy 

 of his result lies in the fact that the mean distance of 

 stars of determinate brightness in and without the Milky 

 Way is not the same. 



Prop. VI. (Compare communication of 29th April, 

 1892.) The nearest vicinity of the sun contains nearly 

 exclusively stars of the 2nd type ; with increasing distance 

 the proportion (> of the number of stars of the 1st type to 

 that of the 2nd grows gradually. Equality of number is 

 reached at a distance corresponding to a total proper motion 

 of 0"07. At still greater distances the stars of the 1st type 

 begin to predominate very strongly. 



(') In Tables 1 and 2 the values of q furnished by stars whose 

 distance from the apex is less than 40°, and which are necessarily very 

 uncertain, have been omitted. 



Prop. VII. It is exceedingly probable that (at least in the 

 immediate vicinity of the sun) the variation of tlie value 

 of ',' must be attributed mostly to a real thronging of the 

 stars of the 2nd type about a point not far from the sun, 

 while the distribution of the stars of the 1st type is more 

 nearly uniform (cluster of 2nd type stars). 



Prop. VIII. The centre of greatest condensation of the 

 stars of the 2nd type lies near the point of which the 

 co-ordinates are 



a = Oh. 0. 8= + 42°. 



Prop. IX. This centre coincides nearly with the point 

 which, according to the investigations and observations of 

 Struve and Herschel, represents the apparent centre of 

 the Milky Way (considered as a ring). 



Prop. X. The stars of the first two spectral types are at 

 equal distances if their mean total proper motion, or proper 

 motion t, is equal. 



Prop. XL The magnitude being equal, stars of the 

 1st type are in the mean 2-7 times more distant than those 

 of the 2nd type. Or put in another way : The stars of the 

 1st type are in the mean seven times intrinsically brighter 

 than those of the 2nd type. 



The demonstration of Propositions I. to IV. was effected 

 as follows : — 



By parallels drawn for every 10 degrees of declination 

 and by hour circles at different distances, the whole sky 

 north of — 30° of declination was divided into portions in 

 such a way that every one of these contained only stars 

 ditfering scarcely more than 10 degrees in galactic latitude. 

 In every one of these portions the number of stars of 

 determinate spectral type and determinate amount of 

 proper motion was counted. Besides this the number of 

 square degrees contained m every portion was computed, 

 and the number of Bradley-Draper stars of magnitudes 

 — 6'5 contained in each such area was determined.* 



After this, and after having united all the areas of equal 

 galactic latitude, it was easy not only to determine the 

 number of stars of different type and amount of proper 

 motion at different distances from the Milky Way, but 

 from these numbers could be further derived the values 

 they would have assumed for 1000 square degrees and for 

 the case that the material had embraced all stars of 

 magnitudes — G'5. 



The results of these countings and computations have 

 been embodied in the two following tables : — 



Table 3. — Arranged according to total pi'opcr motion. (/*■). 



I = 1st Type. II = 2nd Type. ^ = Galactic Latitude. 



/3 /*=0»00— 0»03 0»01— 0»05 0»06— 0»07 0»08-0'/15 0" 16 and 



higher. 



Limits. Me D. I. It. \. U. I. II. I. II. 1. !'■ 



-I- 60° to +90" 69 lg-6 U-9 9-6 13-? S'S U-3 17-0 13-8 6-4 28-7 



+ 50 „ +60 55 19-3 18-6 10-6 11-8 75 6-3 U-9 26-1 6-2 19-3 



H-^+O „ + 50 45 24-6 15-ci 8-4 9-9 7-9 6-4 15-3 23-7 6-4 22-7 



+_30 „ +40 35 3i-3 195 15-7 100 11-4 86 19-5 195 3-3 lS-1 



+ 20 „ +30 25 481 27-8 26-3 144 80 6-9 19-8 20-3 4-8 20-8 



+ 10 ,, +-20 15 76-2 34-6 .30-6 12-1 8-7 7-5 162 18-5 4-0 21-3 



— 10 „ + 10 5 85-8 48-6 27-6 10-8 13-0 6-0 13-2 15-0 7-2 18-6 



Table 4.f — Arranged according to the component T of the 

 proper motion. 



a T=0'/00— 0"03 0»0i— 0»5 0»06— 0*07 0"08— 0//14 0"15and 



higher. 



Limit.. Mean. I. II. L II. I. II. I. II. I H- 



+ 60° 10^*^90° 69 Wi 31-9 159 90 5-3 85 S'S 15-4 3-7 196 



+ 50 „ +60 55 34-2 35-4 8-7 12-4 6-8 62 5-6 155 3-1 12-4 



+ 40 „ -TSO 15 36-5 33-5 U-3 US 39 69 69 10-4 39 15-8 



+"30 „ +"40 35 52-4 333 13-8 10-9 7-6 7-6 9-5 14 3 I'O 9-5 



+ 20 „ +30 25 651 46-S 18-7 14-4 ISO 6-9 8 11-7 1-1 10 7 



H^IO „ +20 15 98-1 46-7 331 14-4 81 104 4-0 U'O 2-3 11-5 



— 10 " +"10 5 112-2 63-4 192 10-2 4-8 5-4 72 138 3-4 7-3 



* This determination was made by aid of Seeliger's Tables, 

 t For this table tlie proper motions have been used wncorrected 

 for L. Struve's alteration of the constant precession. 



