4 6o POPULAR SCIENCE MONTHLY. 



reach a conclusion that can claim numerical exactness, we may reach one 

 that will give us a general idea of the subject. The first question at 

 which we aim is that of the number of stars within some limit of dis- 

 tance. It is as if, looking around upon an extensive landscape in an 

 inhabited country, we wished to estimate the average number of houses 

 in a square mile. On the general average, what is the radius of the 

 sphere occupied by a single star? If we divide the number of cubic 

 miles in some immense region of the heavens by the number of stars 

 within that region, what quotient should we get? Of course, cubic 

 miles are not our unit of measure in such a case. It will be more con- 

 venient to take as our unit of volume a sphere of such radius that from 

 its center, supposed to be at the sun, the annual parallax of a star 

 on the surface would be 1". The radius of this sphere would be 

 206,265 times that of the earth's orbit. We may use round numbers, 

 consider it 200,000 of these radii, and designate it by the letter E. 



Ri Ra Ra 



Fig. 3. 



Now, let us conceive drawn around the sun as a center concentric 

 spheres of which the radii are E, 2R, 3E, and so on. At the surfaces 

 of these respective spheres the parallax of a star would be 1", half a 

 second, one-third of a second, and so on. The volumes of spheres being 

 as the cubes of their radii, those of the successive spheres would be 

 proportional to the numbers 1, 8, 27, 64, etc. 



If the stars are uniformly scattered through space, the numbers hav- 

 ing parallaxes between the corresponding limits will be in the same 

 proportion. 



The most obvious method of determining the number of stars 

 within the celestial spaces around us is by measurement of their par- 

 allaxes. It is possible to reach a definite conclusion in this way only 

 in the case of parallaxes sufficiently large to be measured with an 

 approach to accuracy. In the case of a small parallax the uncertainty 



