18 



♦ KNO\VLEDGE 



[Not. 1, 1885. 



afiect tliat zone less markedly, the irregular nebulas 

 (gaseous) are all on or close to that zone, the planetary 

 (also gaseous) affect its neighbourhood. I need not point 

 out the separate significance of these facts, or their yet 

 gre;itt;r significance when taken in combination with the 

 fact that irresolvable nebute withdraw from the neigh- 

 bourhood of the galaxy. 



3°. Wherever there is a large extra-galactic space singu- 

 larly clear of lucid stars there also irresolvable nebulse 

 are .singularly few in number. 



i'. But where amidst a number of small stars there is 

 a small space singularly clear of stars, there nebuLi; are 

 abundant (as both your father and yourself testify). 



[These are not contradictory as they seem at first 

 sight. If we suppose irresolvable nebulre to be 

 sim])l3' aggregations of small stars and star mate- 

 rial in place of single (relatively) large stars, we 

 can understand that nebulw and lucid stars should 

 be wanting together, or that in small-star neigh- 

 bourhoods the formation of nebula? should drain 

 the district. Both facts require to be accounted 

 for as not accidental, and no other explanation 

 seems possible, while this one seems at once 

 natural and satisfactory.] 

 5°. There are in places well-marked star-streams — 

 such as the River Eridanus which the moderns have 

 carried farther towards the South Pole, and the stream 

 from the water-can of Aquarius, which the moderns 

 have carried over the back of Grus towards the south. 



6°. The two last-named streams of stars lead up to 

 the two Magellanic Clouds. 



7°. There are well-marked nebular streams in both 

 hemispheres ; btit two singularly distinct streams in the 

 southern. 



8^. The two last-named streams of nebula' lead up to 

 the Magellanic Clouds. 



9°. One of these streams agrees with one of the star- 

 streams named above, the other with the other ! 



10°. In the Magellanic Clouds are mixed up stars and 

 nebulfe. 



[The Clouds and the evidence they give have been 

 so clearly treated in your " Outlines of Astro- 

 nomy," that I have no reason for dwelling on the 

 significance of 10°. In conjunction with 5°-9° 

 the evidence seems to me absolutely conclusive as 

 to the association between stars and nebulse.] 



11°. Every one of the irregular nebula? is strangely 

 associated with star.s, which seem (but only seem) to 

 lie much nearer to us. Tour maps (in "Southern Obser- 

 vations ") and descriptions appear to me conclusive on 

 this point, even where you seem to avoid enforcing the 

 conclusion or to adopt a contrary one. If the coincidence 

 could be accidental in one case, could it in so many ? 



12°. The Orion nebula has long faint branches extend- 

 ing to e and i Orionis and condensing around those stars. 

 Can this be accidental ? And if not, does it not prove 

 these important points : first that a nebula may be no 

 farther ofi than hicid stars, and secondly that lucid stars 

 so far apart as e and i Orionis may belong to a single 

 system ? 



13°. All those stars mixed up with the Orion nebula 

 whose proper motions have been ascertained, have proper 

 motions singularlj' small, and coincident in direction — 

 indicating (in a new way) their belonging to one sy.stem. 



14°. The other stars in Orion have for the most part 

 the same characteristic proper motions (nor need excep- 

 tions at all perplex us, considering that we ought to 

 expect them in such eases). 



15°. All the stars in Orion (says Secchi) have similar 

 spectra. (Even if this remark is inexact the general 

 significance of what Secchi has observed cannot be mis- 



o 



understood.) 



[The last points go to prove the real oneness of the 

 Orion stellar and nebular system.] 

 16°. In particular regions of the heavens particular 

 spectral types prevail — indicating the existence of star- 

 systetns among the constellations — i.e., among lucid stars. 

 The evidence given by this fact, looked on as subsidiary 

 to the evidence for .star-streams, seems important. 



17°. In particular regions of the heavens the stars 

 seem to be drifting in a mass towards the same direc- 

 tions. 



[I send a rough copy of a portion of a map of 



proper motions I am preparing for next meeting 



of the Royal Astronomical Society.] 



18°. The proper motions of stars of .smaller magnitudes 



are not small enough (on the average) for the accepted 



views as to star-distances. I have taken the proper 



motions in Main's Catalogue of 1,167 stars common to 



Bessell's Catalogue and Greenwich Catalogue, and using 



the formula : — 



Mean proper motion = . /sum of square of 

 V proper motions. 

 I get: — 



Mean proper motion of stars of 1st 3 mags. = 0"-301 (^ , , 



next 3 mags. = 0"-302 J • ' 

 [I believe this result to be much more than suflB- 

 cient to prove 18"; but I do not by any means 

 accept it as it stands — or as otherwise than acci- 

 dental so far as its significance in regard to detail 

 is concerned. Its general significance is as trust- 

 worthy as it is obviotis. ] 

 19°. The same result follows from the small effect of 

 the correction due to the sun's proper motion, when esti- 

 mated with reference to the commonly-assumed stellar 

 distances. 



[I venture to point out that it is doubtful whether 

 Mr. Dunkin's result on this point is, as you sug- 

 gest, that which was to have been e.vpected. 

 Does not your reasoning, founded on the number 

 of stars which are moving hither and thither 

 with their real proper motions, apply both ways. 

 Every one of those stars is affected by the sun's 

 proper motion. I find by the ordinary rules for 

 determining means that the correction due to 

 the sun's motion ought to be exactly one-half of 

 the sum of the squares of the proper motions, if 

 the sun's motion is equal 

 to the average of stellar 

 motions. There is a 

 simple geometrical proof , 

 of this, the chief points 

 of which are as follows : 



— Let S A = displacement due to sun's motion, 

 S Si = S S; = motion of two stars in opposite 

 directions from S, foreshortened and really equal 

 to S A. Then, 



Sum of squares of opposite motions = Sj A- -f S^ A-, 

 Sum of sqtiares of ditto imcorrected^S Sj--|- S S;", 

 and former sum exceeds latter by 2 S A'- (one S A- 

 for each). 

 And the effect of foreshortening on all motions from 

 S, precisely corresponds to the effect of change of 

 position of S in diminishing S A. Hence for the 

 whole sphere there is an exact equality between 



