1908] on Recent Researches in the Structure of the Universe. 313 



is about two-tliirds, of that in the 9th shell. A similar conclusion is 

 obtained by comparing the number of the stars of absolute magni- 

 tude 3 • 5 in the two shells. The values obtained from the magnitudes 

 0-5 and 1*5 may be neglected. Owing to the exceedingly small 

 number of stars, they must necessarily lead to untrustworthy results. 

 From all the rest I found that the density in the 10th shell must be 

 about 64 per cent, of that in the 9th shell. The proportion between 

 the densities in the other shells was determined in exactly the same 

 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. After that it appeared 

 that the density in the first six of oui* 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 light-century. After the 6th 

 shell the density diminishes gradually at such a rate that in the 11th 

 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 beyond this distance ? 



Stak-density for Distances Exceeding 2000 Light-ybaes. 



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 in the abysses of space. 



One of the reasons why the method thus far applied breaks 

 down beyond the 11th shell, is that our data about proper motion 

 are not refined enough to determine this motion with sufficient 

 accuracy as soon as it is below 1" 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 apparent magnitudes. 

 Thanks mainly to the photometrical researches at the Harvard 

 Observatory, it has become possible to determine with considerable 

 accuracy the total number of stars of the 1st, 2nd, etc., to the 11th 

 magnitude ; with a fair degree of accuracy even those for the magni- 

 tudes down to the 14th (inclusive). 



The density in the shells beyond the 11th, not only for the stars 

 down to the 8th apparent magnitude, but according to what has 

 been said a moment ago, also for the apparent magnitudes of 9, 



