304 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1908. 



RESTRICTIONS. 



1. We will assume that the mixture is the same throughout the 

 whole of the system; 



2. We will not treat the different galactic latitudes separately. 

 The consequence will be that the resulting variations of density 



to which our discussion leads, will not represent the actual variations 

 which we would find if we traveled in space in any determined fixed 

 direction, but a variation which will represent some average of what 

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

 different regions of the sky. 



SIMPLIFIED TROBLEM. 



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 localized in space, and it would be possible to construct a 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 localize 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 dis- 

 tances 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 



