1908] on Recent Researches in the Structure of the Universe. ?>()b 



pictures of the sky as seen from points of view at a mutual distance 

 of a hundredth of a light-year. Our eye-distance of 16 light minutes 

 is thus increased more than 300-fold. True, this distance falls still 

 considerably short of that adopted by Heath, but it appears that, for 

 a considerable part of the stars, it is, though not nearly so great as 

 might be desired, still in a certain way sufficient. 



Cannot furnish Distance of Individual Stars. 



There is, however, a difficulty in the way, which prevents our 

 pictures from giving a stereoscopic view of the stars at all, and 

 thus prevents the determination of the distance of any star in 

 this manner. The difficulty is that the changed directions in which, 

 after the lapse of 150 years, we see the stars, is not exclusively the 

 consequence of the sun's motion through space, but is due also to a 

 real motion of the stars themselves. The two causes of displacement 

 which, in the case that we take the diameter of the earth's orbit as 

 eye-distance, are separable by means of a simple device, become 

 inseparable in the present case. 



In order to see whether this difficulty be or be not absolutely 

 insuperable, I will take a parallel case on the earth. 



Distance of Insect Cloud 



At a certain distance we observe a cloud of insects hovering over 

 a small pond. In order to evaluate the distance separating the 

 insects from our eye suppose that we make a photograph ; then 

 after a few seconds a second one from a slightly different standpoint. 

 It must be evident that even if we have used an instrument which 

 clearly shows the individual insects, the two pictures put in the 

 stereoscope will not furnish a stereoscopic view of them individually ; 

 on the contrary, the picture as seen in the stereoscope will be per- 

 fectly chaotic. The reason, of course, is that in the interval between 

 the taking of the two photographs the insects have moved. Does it 

 follow that no evaluation of the distance can be obtained ? 



The answer must be : of any individual insect, ?w ; but of the 

 cloud, as a whole, we can, provided that the cloud, as a whole, has not 

 moved ; or expressed more mathematically : provided that the centre 

 of gravity of the cloud has not moved we can derive the average 

 distance * of all the insects. We shall be sure of the immobility of 

 the centre of gravity if we know that the direction of the motions of 

 the insects is quite at random ; but this is by no means required. 



* The expression average distance ought, strictly speaking, to be replaced 

 by the distance corresponding to the average parallax. For clearness sake I 

 have ventured here and in what follows to substitute one expression for the 

 other. 



Vol. XIX. (No. 102) x 



