CHAPTERS ON THE STABS. 461 



of the latter may be equal to its whole amount. In this case the star 

 may be at any distance outside the sphere given by its measured par- 

 allax, or far within that sphere, so that no conclusion can be drawn. 

 It is, on the whole, useless to consider parallaxes less than 0".10; even 

 those having this value are quite uncertain in most of the cases. The 

 data at command for our purpose are the known individual parallaxes 

 and the statistical summary given by Dr. Chase as the result of his 

 survey, and quoted in our chapter on the parallaxes of the stars. This 

 survey was confined to stars whose parallax was not already measured, 

 and it brought out no parallax exceeding 0".30. 



The most careful search has failed to reveal any star with a par- 

 allax as great as 1", and it is not likely that any such exists. It is, there- 

 fore, highly probable that the first sphere will not contain a single 

 star except the sun in its center. 



Within the third sphere, the parallax at the surface of which is 

 0".33, we may place the following for stars with entire certainty: 



a Centauri Par .=0.75 



LI. 21,185 0.46 



61 Cygni 0.39 



Sirius 0.37 



There are two other cases in which the parallax is doubtful, though 



the measures as made bring the stars within the sphere 3R. They 



are: 



tf Herculis Par. — 0.40 



O. A. 18,609 0.35 



In the case of rj Herculis the proper motion is so small that 

 the presumption is strongly against so large a parallax, and the doubt- 

 ful parallax of the last star is so near the limit that it may be left 

 out of the count. The doubt in its case may be set off against a 

 doubt whether the parallax assigned to LI. 221,185 is not too large. 

 We assume, therefore, that four stars are contained within the sphere 

 3R, the volume of which is 3 3 = 27. This would give, in whole num- 

 bers, one star to 7 unit spheres of space. 



When we come to smaller parallaxes we find a great deficiency in 

 the number measured in the Southern hemisphere. The policy of 

 Gill, under whose direction or with whose support all the good measures 

 in that hemisphere were made, was to make a few very thorough de- 

 terminations rather than a general survey. Between the limits 0".20 

 and 0".33 are found: 



In the Southern Hemisphere 4 meas. (Gill) 



Northern " 2 " (Chase) 



" " 12" (Others) 



Total 18 



