September, 1912. 



KNOWLEDGE. 



magnitude in this region, but diminishes rapidh' for 

 stars beyond the sixteenth magnitude. This is 

 represented in the following table, where terminal 

 ratios are assumed which express the ap[)arent fart 

 that the star numbers have begun to diminish. 



The outer ring is three times as far away as the 

 inner by assumption, and if of identical constitution, 

 it should be one-ninth as bright. Since there is 

 approximate equalit}' betw een the rings, I have made 

 the outer ring nine times as great as the inner. 

 Taking the sums of the included numbers, we have : 



Inner ring= 10th to 14th + - ^'^ ~ ^^ mag. = 13-5M + 15M 

 = 28-5 M. ^ 



14 - 15 



Outer ring = — 

 = 255-M 



+ 16th to l.Sth mag. =^^ 15M + 240 M 



Number of stars per cubic light-year : 



Inner ring = 28,500.000/30,000 = 950. 

 Outer ring= 255,000,000/270,000 = 950. 



The star density is nearly one thousand per cubic 

 light-vear. The total number of stars in the galactic 

 zonc'lO" wide, is 255M + 28 oM = 283,500,000, or 

 79,000 stars per square degree for the combined 

 rings. A direct count on the photograph gave 78,000, 

 which agrees well enough. The distribution of stars 

 (tenth to eighteenth magnitudes) among the magni- 

 tudes, mav be represented by the sum of two curves, 

 one for each ring, as given in Figure 358. The 

 dotted line gives the star numbers resulting from the 

 compounding of stars in two rings whose separate 

 numbers are represented by the curves, r^, r,, whose 

 maxima correspond to about the fourteenth and 

 sixteenth magnitudes respectively. 



.Admitting that the Sun is situated midway between 

 two galactic condensations in a vacant, yet somewhat 

 central, region, an ideal axial section of the Galaxy, 

 which harmonizes known facts, is given in Figure 

 359. 



The star-ratio per successive magnitude is equal 

 to the ratio of brightness of stars one magnitude 

 apart, raised to the 3/2 power, or to (2 -512)'- = 

 3-981, provided the distribution is uniform. H. H. 

 Seeliger, from the stars of the Bonn Durchmusterung 

 and of the Southern Durchmusterung to the 9-5 

 magnitude, found the star-ratio per magnitude 

 = 3-85 for the Milky Way, but only 3-28 for the 

 galactic poles. The variation demonstrates that the 



■' " Old and New Astronomy," page 

 + Vol. XXXV, page 31. 



stellar distribution in distance, or in brightness, or 

 both together, cannot be uniform : evidently, the 

 limits of the Galax}- have been reached for 9-5- 

 magnitude stars, at least in a direction perpendicular 

 to the plane of the Milky Way. This becomes still 

 more noticeable in a comparison of Pickering's list 

 of stars within 2° of the North Pole with the 

 theoretical star-ratio, from which Ranyard concluded 

 that " instead of over fifteen thousand stars between 

 the fourteenth and fifteenth magnitudes, there are 

 less than four hundred, or only about one four- 

 hundredth [jart of the calculated number ; in other 

 words, about the number of stars which, according 

 to the space-ratio, would lie between the 9-5 and 

 10-5 magnitudes."* Either we must suppose that 

 there is an absorption of light in space much greater 

 than even that which I ha\e attributed to the distant 

 nebulae, or else the Galax\- is much more restricted 

 than has been supposed. .\ range of at least ten 

 magnitudes is known to occur in stars whose 

 distances are not dissimilar ; hence there is no need 

 of assuming that the excessively faint stars which 

 are massed in the Galaxy must be at distances of 

 thousands of light-years. Neither the faintness of 

 the light, nor the absence of proper motion, is a 

 sufficient reason for rejecting the ])laiii teaching (if 

 other modes of investigation. 



But in "Knowledge" for January, 1912,+ Dr. 

 Crommelin gives a stronger argument, which we 

 must examine more critically. He says: "It is 

 fairly well established that the Sun moves through 

 some four astronomical units per annum, which, if 

 unforeshortened, would give a star of sixty light- 

 years distance an apparent motion of one-fifth of a 

 second per annum ; the galactic stars certainly show 

 no motion approaching this amount, whence it 

 appears certain to me that the Galaxy is far more 

 than sixt\- light-years distant, so that all Professor 

 Verys estimates of nebular distances would need 

 muliplication by a considerable factor." 



In mv previous papers I have assumed that our 

 sun is itself a member of the galactic multitude, 

 though remote from the nuclei of condensation, and 

 that an unknown portion of the supposed solar 

 motion is common to the system and inay be shared 

 by large numbers of the galactic stars ; that is to 

 sa\-, no parallactic motion whatever would be found 

 if the Sun had the average motion of a galactic star, 

 and if the number of comparison stars could be 

 made indefinitelv great. 



To find the mean galactic motion, in this case, it 

 will be necessary to make a critical study of the 

 proper motions of the fainter and more distant 

 white nebulae from which the apex of the motion of 

 the Galaxy as a whole may eventually be recovered. 



The accepted value of the Sun's motion through 

 space has been derived from the relative motions of 

 a few neighbouring stars, assuming that, on the 

 whole, these are moving among themselves indis- 



