July 9, 1908] 



NA TURE 



^2>7 



comparing the number of the stars of absolute magnitude 

 35 in the two shells. The values obtained from the magni- 

 tudes 05 and 1-5 may be neglected. Owing to the exceed- 

 ingly small number of stars, they must necessarily lead to 

 intrustworthy results. From all the rest I found that the 

 i-nsity in the tenth shell must be about 64 per cent, of 

 lat in the ninth shell. The proportion between the 



■nsities in the other shells was determined in exactly the 

 ime way. 



A slight defect in our results was then discovered. We 

 should exceed the limits of the time allowed for this lecture 

 by entering into a consideration of this defect. It must 

 be sufficient to state that it was not difficult to remove it. 

 .\heT that it appeared that the density in the first six of 

 our shells is nearly the same. The density in these shells, 

 that is, in the neighbourhood of our sun, is such that 

 about 2000 stars of a luminosity exceeding one-hundredth 

 that of the sun must be contained in a cubic Ught-ccnttiry. 

 Aher the sixth shell the density diminishes gradually at 

 such a rate that in the eleventh shell the density has fallen 

 to about 30 per cent, of what it is in the vicinity of the 

 solar system. 



In what precedes we tried to give a solution of the 

 problem put at the beginning of this lecture — a solution, 

 however, which embraces only that part of the universe 

 which is contained within a distance of about 2000 light- 

 years from our solar system. Is there no possibility of 

 getting bevond this distance? 



I think there is, but, of course, you will not be 

 astonished to find that the certainty of our conclusion 

 diminishes as we get deeper and deeper into the abysses 

 of space. 



One of the reasons why the method thus far applied 



breaks down beyond the eleventh shell is that our data 



I about proper motion are not refined enough to determine 



this motion with sufficient accuracy as soon as it is below 



i" in a century. Even the somewhat greater motions are 



rather uncertain. The proper motions thus cannot help 



us much beyond a certain distance. But we have still one 



valuable element for the solution of our problem. This 



, element Is the total number of stars separately for the 



r' apparent magnitudes. Thanks mainly to the photomctrlcal 



I researches at the Harvard Observatory, It has become 

 possible to determine with considerable accuracy the total 

 number of stars of the first, second, &c., to the eleventh 

 magnitude ; with a fair degree of accuracy even those for 

 the magnitudes down to the fourteenth (inclusive). 



The density in the shells beyond the eleventh, not only 

 for the stars down to the eighth apparent magnitude, but, 

 according to what has been said a moment ago, also for 

 the apparent magnitudes of nine, ten, &c., to fourteen, has 

 I0 be determined In such a w.ay that the addition of all 

 the numbers In any one vertical column of Fig. 4 produces 

 just these totals for the corresponding apparent magni- 

 tudes. 



It can be proved that after the eleventh shell the density 



must, on the whole, continue to diminish. If we assume 



that this diminution Is gradual and proportional to the 



increase In distance, it becomes very easy to determine 



the rate of this diminution, and consequently the distance 



at which the density becomes zero, that is, the distance 



at which we reach the limit of the stellar system. We 



cannot enter into fuller particulars here. It must be 



sufficient to say that in this wav we are led to conclude 



that the further diminution of density must be slow, so 



; slow that in the assumption made above the limit of the 



■ system Is only reached at a distance of some 30,000 light- 



f years. 



Hypotheses Underlying the Results. 

 In conclusion, a few words on the question. In how 

 fir are the results now obtained to be considered as 

 r^tabllshed ? 



The answer must be, They can be considered to be 

 established only In so far, and no further, than we can 

 trust the truth of the hypotheses which still underlie our 

 reasoning. 



For future consideration there thus remains the question. 

 In how far can we test the validity of these hypotheses? 

 These hypotheses are the following : — 

 (i) The mixture was assumed to be the same at greater 

 and smaller distances from the solar system. 



NO. 20IQ. VOL. 78] 



(2) The same was done for different distances from the 

 gala.xy. 



(3) The universe was assumed to be transparent, that is, 

 it was assumed that the absorption of light in space is 

 zero. 



Can we get rid of these hypothetical elements? 



I think we can, at least to a very great extent. 



As to the first. Our Fig. 4 already goes far in enabling 

 us to judge whether it is true or not. For evidently both 

 our sixth and our ninth shell give the nature of the 

 mixture, at least of the stars of absolute magnitude 3-5 

 to 6-5. Therefore, so far as these stars are concerned, we 

 are able to see whether or not the mixture is the same 

 at the distance of 650 light-years as it is at the distance 

 of 170 llght-jears. Likewise, the figure enables us to 

 make the comparison In other cases. As soon as we 

 possess the necessary data for a longer range of apparent 

 magnitudes, say down to the fourteenth or fifteenth, we 

 shall be able to dispense to a very large extent with our 

 first hypothesis. 



As to the second, the possible variation of the mixture 

 with the distance from the Milky Way, It Is largely only 

 the question of treating the stars in different galactic 

 latitudes separately. .So far as I can see, there are no 

 particular difficulties in the way of such a separate treat- 

 ment, at least not since the nature of certain anomalies 

 in the distribution of stellar motions has been elucidated. 



.Ibsorption of Light in Space. 



Last, not least. Is the universe really absolutely trans- 

 parent? There are reasons which make this seem very 

 doubtful. .•\ couple of years ago I obtained some evidence 

 in the matter which shows that the absorption of light 

 in space, if it exists to an appreciable amount, must at 

 least be so small that over a distance of a hundred light- 

 years not more than a few per cent, of the light can be 

 lost. To determine so small an amount to within a small 

 fraction of its total value will be a difficult task Indeed. 

 .Still, we can even now see definite ways, which, given 

 the necessary data for very faint stars and nebula;, will 

 probably enable us to overcome this last difficulty. 



This want of data for very faint stars, which, ^ in the 

 present investigation, makes itself felt at every step, has 

 led a number of astronomers to concerted action. 



The express purpose of their cooperation Is to collect 

 data of every kind for stars down to the faintest that can 

 practically be reached. As complete observation and treat- 

 ment of these numberless stars Is out of the question, the 

 plan is confined to a set of samples distributed over the 

 ivhole of the sky. 



Conclusion. 



If, at the end of this lecture, somebody summarises what 

 has been discussed by saying that the results about the 

 structure of the universe are still very limited and not yet 

 free from hypothetical elements, I feel little Inclined to 

 :ontradict him. But I would answer him by summing up 

 in another w.ay, viz. : — • 



Methods are not wanting which, given the necessary 

 observational data obtainable in a moderate time, may lead 

 us to a true, be It provisionally still not very detailed, 

 insight into the real distribution of stars in space. 



I think this time need not exceed some fifteen years. 

 They to whom such a time may still seem somewhat long 

 may be reminded of the fact that we shall have finished 

 our work before any but a very few of our nearest neigh- 

 bours in space can be aware of the fact that we have 

 begun, even if we could send them a message now by 

 wireless telegraphy travelling at the speed of light. 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE. 



St. Andrews. — Besides the gifts of DIplodocus to the 

 British Museum and to the museums of Paris and Berlin, 

 Dr. Andrew Carnegie has, at the instigation of Dr. 

 Holland, presented a neatly mounted example (cast) of the 

 hind limb of DIplodocus to the University Museum, St. 

 .'\ndrews — another of the very munificent donations which 

 mark the period of office of the late Rector of the 

 University. 



