1908] on Recent Researches in the Structure of the Universe. 303 



we would find on all our travels if we successively directed them to 

 different regions of the sky. 



Simplified Problem. 



Our present problem will thus be confined to finding out : 



{a) The mixture law ; 



{h) The mean star-density at different distances from the solar 

 system. 



If time allows, I will, at the end of this lecture, say a few words 

 on the restrictions introduced, and the way to get rid of them. 



As it is not given to us to make such travels through space as 

 here imagined, we have to rely on more human methods for the 

 solution of our problem. 



Determination of Distance. 



It is at once evident that there would be no difficulty at all if it 

 were as easy to determine the distance of the stars as it is to determine 

 the direction in which they stand. For in that case the stars would 

 be locaHsed in space, and it would be possible to construct i true 

 model from which the peculiarities of the system might be studied. 



It is a fact, however, that, with the exception of a hundred stars 

 at most, we know nothing of the distances of the individual stars. 



What is the cause of this state of things ? It is owing to the 

 fact that we have two eyes that we are enabled not only to perceive 

 the direction in which external objects are situated but to get an idea 

 of their distance, to localise them in space. But this power is rather 

 limited. For distances exceeding some hundreds of yards it utterly 

 fails. The reason is that the distance between the eyes as compared 

 with the distance to be evaluated becomes too small. Instruments 

 have been devised by which the distance between the eyes is, as it 

 were, artificially increased. With a good instrument of this sort 

 distances of several miles may be evaluated. For still greater 

 distances we may imagine each eye replaced by a photographic plate. 

 This would even already be quite sufficient for one of the heavenly 

 bodies, viz. for the moon. 



At one and the same moment let a photograph of the moon and 

 the surrounding stars be taken both at the Cape Observatory and at 

 the Royal Observatory at Greenwich. Placing the two photographs 

 side by side in the stereoscope, we shall clearly see the moon " hanging 

 in space," and may evaluate its distance. 



But already for the sun and the nearest planets, our next neigh- 

 bours in the Universe after the moon, the difficulty recommences. 



The reason is that any available distance on the earth, taken as 

 eye-distance, is rather small for the purpose. However, owing to 

 incredible perseverance and skill of several observers, and by substi- 

 tuting the most refined measurement for stereoscopic examination, 



