462 POPULAR SCIENCE MONTHLY. 



Of the Northern results three are exactly on the limit, 0".20, and 

 several others are doubtful, and probably too large. The most likely 

 Dumber for the Northern hemisphere seems to be 12, and if we estimate 

 an equal number for the Southern hemisphere we shall have 24 in 

 all. Adding the four stars within the sphere 3E, we shall then have a 

 total of 28 within the sphere 5R, of which the volume is 125. This 

 gives between 4 and 5 space units to a star. 



Let us now consider the space between the spheres 5R and 10E, 

 including all stars whose parallax lies between the limits O'MO and 

 0".20. Of these the numbers are: 



Southern Hemisphere 6 (Gill) 



Northern " 15 (Chase) 



15 (Others) 



Eeasoning as before, we may assume that the number of stars be- 

 tween the assigned limits is 60, making a total of 88 within the sphere 

 10R. The volume of space enclosed being 1,000 units, this will give 

 one star to 12 units of space. 



How far can we rely on this number as an approximation to the 

 actual number of stars within the tenth sphere? The errors in the 

 estimate are of two classes, those affecting the parallax itself and those 

 arising from a failure to include all the stars within the sphere. The 

 very best determinations are liable to errors of two or three hundredths 

 of a second, the inferior ones to still larger errors. Thus, it may 

 happen that there are stars with a real parallax larger than the limit 

 of which the measures fall below it and are not included, and others 

 smaller than the limit which, through the errors of measurement, are 

 made to come within the sphere. As we have seen in the chapter 

 on the parallaxes, it is quite possible that there may be a number of stars 

 with a measurable parallax whose proximity we have never suspected 

 on account of the smallness of the proper motion. We can only say 

 that the nearer a star is to the system the more likely its proximity is 

 to be detected, so that we are much surer of the completeness of our 

 list of large parallaxes than of small ones. Hence, there may well be 

 a number of undetermined parallaxes upon or just above the limit O'MO. 



The most likely conclusion we can draw from this examination 

 seems to be that in the region around us there is one star to every 

 8 units of space; or that a sphere of radius, 2E, equal to 412,500 radii 

 of the earth's orbit, corresponding to a parallax of 0".50, contains one 

 star. This is a distance over which light would pass in 8£ years. 



We next see how far a similar result can be derived from statistics 

 of the proper motions. It seems quite likely that nearly all proper 

 motions exceeding 1" annually have been detected. The number 

 known is between 90 and 100, but it can not be more exactly stated 

 because there is some doubt in the case of a number which seem to 



