ON STELLAR AND NEBULAR DLSTANCES. 



By PROFESSOR I'RAXR W. \ IIRV. 

 Westwood Astrophysical Observatory, Wcstxc'ood. Massacliiisctts, U.S.A. 



At the meeting of the British Astronomical 

 Association, Wednesday, November 29th, 1911, 

 my paper — " Are the White Nebulae Galaxies ? ""' 

 was introduced for discussion by Mr. Lvnn. In 

 the remarks which followed, some favourable, others 

 adverse, Dr. Crommelin said that " sensible proper 

 motions did not show any perceptible increase in the 

 direction of the Milky Wa}," and that this was fatal 

 to the distance which I have assigned to the Galaxv. 

 He also cited Newcomb's distance as being fifty 

 times mine. 



It is quite true that there are no evidences of a 

 marked increase of proper motion among the 

 galactic stars ; but since, in my view, the galactic 

 velocities are small, because the)' have been 

 annulled to a great extent b}' internal collisions 

 among the component parts out of which the 

 central condensation has developed (and this is 

 why there is such a great accumulation of material 

 in this region), it follows that sensible proper 

 motions are not to be anticipated among the 

 galactic stars. A velocity of one astronomical 

 unit (1-5 X 10"^ kilometres per annum) would give 

 to a galactic star at six hundred billion kilo- 

 metres (6 X 10" kilometres) a proper motion of 

 200,000 X 150,000,000 



= 0"-05 per annum. 

 3f th 



This 

 der of 



600,000,000.000,000 

 gives a preliminary conception 

 magnitude to be expected. 



The size which I assumed, namely, 1-2 X (10)'" 

 kilometres for " the diameter of the galactic spiral 

 in its more condensed discoidal dimension,"* was 

 not intended to include "a wider encompassing 

 shell of sparsely-distributed stars of approximately 

 spherical shape." The latter, reasoning from the 

 analog}' of the extreme outer boundary of a star 

 cluster, compared with its condensed nucleus, may 

 be ten times as distant. This gi\'es an outer boundary- 

 at a distance 6X(10)''' kilometres from the centre. + 

 Lord Kelvin gave a number five times as large as this 

 for his star-sphere t, in which, however, he assumed 

 a uniform distribution of the stars, whereas there 

 is undoubtedly a great central condensation and 

 smaller average distance from the centre. It 

 seems to me probable that the real dimensions lie 

 somewhere between these limits. 



The immense number of the stars may suggest 



distances greater than these, but recognizing the 

 great stellar condensation of clusters and galactic 

 streams, the mere numbers, great as they are, do not 

 constitute an insuperable barrier to the sup[)osition 

 that the galactic distances are of the order named. 



If the absence of sensible proper motion in many 

 small galactic stars cannot be taken as a sure proof 

 of their great distance, what shall we say of the 

 large proper motions which have been found for 

 considerable numbers of faint stars ? Does it not 

 imply that some, at least, of these faint objects are 

 not as far away as the enormous distances which 

 have sometimes been assigned to them ? Professor 

 Eastman, classifying a list of five hundred and fifty 

 stars for proper motion, could find no consistent 

 connection between brightness and apparent speed. 

 Twenty-nine stars of the ninth magnitude had an 

 average proper motion three times as great as the 

 average for an equal number of second magnitude 

 stars. Professor Eastman notes that " assumption, 

 which has developed into a quasi-theorj' and gained 

 general acceptance, asserts that the largest stars are 

 nearest the solar system. Observation [ilainly shows 

 this theory is untenable."!) 



If the star-ratio per successive magnitude were 

 purely a space-ratio, it should continue to increase 

 iiidefiniteh- for the smaller magnitudes (given 

 sufficient telescopic power). Existing telescopes 

 mav not have quite power enough to fix a limit for 

 the galactic stars. Although there is an apparent 

 falling off in the star-ratio beyond the sixteenth 

 magnitude, there may be some doubt whether the 

 photograph registers these very faint stars correctly. 



The case is different for extra-galactic regions. 

 Here there is abundant telescopic power, and it is 

 certain that the curve of the star-ratio per magnitude 

 is not a space-ratio, but more nearly resembles the 

 probability curve for distribution of real variation 

 of brightness. This has been recognized, in a way, 

 for some time. 



Miss Gierke says : " Somewhere, if the stellar 

 system be — as we have reason to think it is — of 

 finite dimensions, .... distance becoming at 

 length eliminated as a factor of magnitude, the 

 differences of the faintest stars represent, chiefly or 

 solely, real inequalities in shining. There may 

 possibh'. for instance, he no 'mean distance' 



Astroiiomischc Nachrichten. No. 4536, Bd. 189, November, 1911. Op. cit., column 450. 

 1 Compare F. W. Very. "Stellar Revolutions within the Galaxy," Atii. Joiirii. of Sci.. Ser. 4, Vol. XVI, page 132, 



Aug. 1903. 

 ; Philosophical Mag. (6), Vol. II, page 161, 1901 ; also Vol. Ill, page 1, 1902. 

 S Bulletin Philosophical Society of Washington, Vol. XI, page 166. 



