Against these are to be set negative parallaxes of -0".09, -0".08 and several a little smaller, which are certainly unreal.
The presumption in favor of the actuality of one or more of the above positive values, which is created by their excess over the negative values, is offset by the following considerations: The area of the entire sky is more than 40,000 square degrees, or 10,000 times the area covered by the Helsingfors plates. We cannot well suppose that there are 1,000 stars in the sky with a parallax of 0". 10, or more without violating all the probabilities of the case. The probabilities of the case are therefore against even one star with such a parallax being found on the plates. Yet the cases of these four stars are worthy of further examination, if any of them are found to have a sensible proper motion.
On an entirely different plan is a survey just concluded by Chase with the Yale heliometer. It includes such stars having an annual proper motion of 0".05 or more as had not already been measured for parallax. The results, in statistical form, are these:
|2||stars have parallaxes between||+||9".20||and||+||0".25.|
|6||stars have parallaxes between||+||0".15||and||+||0".20.|
|11||stars have parallaxes between||+||0".10||and||+||0".15.|
|24||stars have parallaxes between||+||0".05||and||+||0'.10.|
|34||stars have parallaxes between||+||0'.00||and||+||0".05.|
|8||stars have parallaxes between||-||0".05||and||0".00.|
|5||stars have parallaxes between||-||0".10||and||-||0".05.|
|2||stars have parallaxes between||-||0".15||and||-||0".10.|
|92,||total number of stars.|
It will be understood that the negative parallaxes found for fifteen of these stars are the result of errors of observation. Assuming that an equal number of the smaller positive values are due to the same cause, and subtracting these thirty stars from the total number, we shall have sixty-two stars left of which the parallax is real and generally amounts to 0".05, more or less. The two values approximating to 0".25 seem open to little doubt. We might say the same of the six next in the list. The first two belong to the stars 54 Piscium and Weisse, 17h., 322.