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 parallax, 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 parallax as great as 1", and it is not likely that any such exists. It is, therefore, 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:
| α 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:
| η Herculis | Par. | —0.40 |
| O. A. 18,609 | 0.35 |
In the case of η Herculis the proper motion is so small that the presumption is strongly against so large a parallax, and the doubtful 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 33 = 27. This would give, in whole numbers, 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 determinations 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 | |||
