June 1, 1898.] 



KNOWLEDGE 



117 



as in direction), and which therefore undoubtedly form a 

 system, stars of both types appear to be mixed. 



Provisionally it seems more probable to assume that the 

 two types are different phases of evolution of stars per- 

 taining to one and the same system. We then must 

 assume that the temperature in this system increases from 

 the centre towards the circumference. In harmony with 

 this is the fact, communicated by the speaker at the 

 meeting' of 29th April, 1892, that the light of the stars of 

 the Milky Way (/.c, of stars in general more remote) 

 seems to be richer in violet rays than the light of the 

 rest of the stars. 



It is a remarkable fact that in the group of the Hyades 

 the liriijlitexi stars belong principally to the 2nd type, which 

 for the rest is strongly in the minority in this group. This 

 fact, together with Prop. XI., makes us conclude that these 

 objects are by far the most bulky of the system. In this 

 case, therefore, it is difficult to attribute the lower tempera- 

 ture to a more advanced state of cooling, so that, here at 

 least, it seems more plausible to assume that the 2nd type 

 stars are in a less advanced stage of evolution (rising 

 temperature) than those of the 1st type. Whether this is 

 the rule in the great system of the Milky Way seems very 

 difficult to decide. 



Prop. VII. If it is assumed that the distances are in- 

 versely proportional to the proper motion, it is easy to 

 determine the relative volume of the spherical shells in 

 which the stars with different proper motions are contained. 

 The comparison of these volumes with the corresponding 

 number of stars affords an insight into the real star 

 density at different distances. In the following table the 

 first column gives the limits of proper motion, the second 

 the volume of the corresponding spherical shells. The 

 following columns give the number of stars for unit of 

 volume. As the numbers of the difil'i-ent columns are in 

 no case comparable, they have been severally multiplied 

 by such a number that the number corresponding to the 

 proper motion 0"165 — 0"195 has become 1-0. If the 

 distribution in space of the stars considered were uniform, 

 then the numbers of each of the last four columns 

 separately would be equal. 



The third column was obtained by counting all the stars 

 of the 1st t3rpe and of magnitudes 0-0 — 5-0, common to 

 the catalogues of Stumpe {A.str. Nacli. Nos. 2999—3000) 

 and of Pickering (Draper Catalogue). The numbers of the 

 fourth and sixth columns were furnished by the material 

 Bradley-Draper ; those of the last column but one were 

 taken from Boss's zone catalogue. The number of stars 

 belonging to the 1st type were computed in this case by 

 taking the whole number of stars with proper motion 

 ^ 0"10, and assuming that for these stars, too, the values 

 of Q from Table 7 were valid. At the foot of every 

 column the number of stars is given on which the com- 

 putation rests. 



Table 8. — Number of Stars per unit of volume. 



Type I. Type II. 



volume. 0m0-5m0. OmO— 6m5. OmO— 9m0. OmO— 6m5. 



0"095— 0"l.j.5 898-5 

 01.5.5— 0195 133-6 10 



0-195—0-295 85-9 2-0 



0-295-0-395 328 

 0-395—0-495 

 0-495-0-995 73 1 



0-995 and higher I'OJ 

 Total number of stars 46 



ill i-sj 



0-7 

 1-0 

 1-3 



"I 



200 



0-4 

 10 

 1-2 



11 



(282) 



0-4 

 1-0 

 2-2 

 3-3 



5-8 

 11-9 

 39-2 

 438 



If we confine ourselves to proper motions > 0"155, we 

 see that the distribution of the stars of the 1st type 

 approaches towards uniformity as we include more and 

 more of the fainter stars in the discussion. On the other 



hand, we find the stars of the 2nd type with known proper 

 motions more strongly condensed the more we approach 

 our system. Now it may be that future extension of the 

 available material will increase the number of small proper 

 motions in a somewhat greater proportion than that of the 

 more considerable proper motions ; but it seems highly 

 improbable that this will ensue to such a degree as to 

 change the condensation implied in the last column into a 

 uniform distribution. It can be shown, for instance, that 

 even if all the stars which Horschel could see with his 

 IG-inch reflector in high galactic latitudes furnished proper 

 motions of 0"16 — 0"32 at the same rate as the stars of 

 magnitudes — 9-0 have done (which of course is an 

 absurdly extreme supposition), even then one would not 

 find the stars of this amount of proper motion equally 

 condensed with the stars of proper motion exceeding 3" 

 known at tlic present nidiiient. 



It may be objected that the hypothesis adopted, viz., 

 that the total proper motion is inversely proportional to 

 distance, implies that the linear proper motion of the stars 

 at different distances from the sun are equal, and that 

 the investigations of Mr. Ristenpart (" Veroft' der Grossh. 

 Sternw. zu Karlsruhe," IV., p. 287) seem to point to a 

 contrary conclusion. But it is easy to show that, Risten- 

 part's results being admitted (and those of the present 

 author are confirmatory), our conclusion in respect to stars 

 of the 2nd type is valid a fortiori. In this case, however, 

 we should find the stars of the 1st type, too, somewhat 

 condensed about the sun, though, of course, to an infinitely 

 lesser degree. 



^ Prop. VIII. At the meeting of 29th April, 1892, Prof. 

 Kapteyn stated that the material afforded by the Stumpe- 

 Draper catalogues pointed to the conclusion that the 

 centre of greatest condensation of the stars of the 2nd type 

 does not coincide with the position of the sun, but seems 

 to be situate somewhere in the direction of 28 hours of 

 R.A. This result was derived from a consideration of the 

 quotient Q. 



The Bradley-Draper material has been investigated to 

 the same purpose in two different ways : — 



1st. By the consideration of the quotient Q in different 

 parts of the sky furnished by those stars whose proper 

 motion r > 0"04. 



2nd. By the consideration of the number of stars of the 

 2nd type (for which r g "04) that are foimd per 1000 

 square degrees in various parts of the sky. These numbers, 

 reduced as formerly on the supposition that alt stars of 

 magnitudes 0- 6'5 had been included in the investigation, 

 are given in the last column of Table 9. 



In both cases the sky was divided into thirteen regions, 

 the limits of which are given in the first two columns : — 



Limits in J. 

 -30° to -I- 20" 



Table 9. ' 



Limits in a. 



2'' 36°" — 2'' 53" 



2-53— 6 12 



6-12— 9-46 



9-46 — 1418 



1418 — 16-54 



16-54 — 20-6 



20-6 —23-6 



1-88 48-9 



0-82 461 



0-89 43-7 



0-80 41-0 



0-71 39-0 



1-12 40-6 



093 39-3 



The values of Q, contained in this table, have been 

 corrected for a variation with the galactic latitude, which 

 is not wholly insensible. 



In the column of the ij, as well as in that of the n, the 

 greatest values are found near Oh. of R.A. It is evident, 

 therefore, that there is a certain region in the sky where 

 the density of the 2nd type stars exceeds that of other 



(') In the compiitation of this table the «»correeted proper motions 



were used 



