of the pane of glass and then through the opposite edge; and he has to determine the change in the direction of the distant house produced by this change of one foot in his own position. From this he is to estimate how far off the other mountain is. To do this, one would have to measure just about the amount of parallax that Bessel found in his star. And yet this star is among the few nearest to our system. The nearest star of all, Alpha Centauri, visible only in latitudes south of our middle ones, is perhaps half as far as Bessel's star, while Sirius and one or two others are nearly at the same distance. About one hundred stars, all told, have had their parallax measured with a greater or less degree of probability. The work is going on from year to year, each successive astronomer who takes it up being able, as a general rule, to avail himself of better instruments or to use a better method. But after all, the distances of even some of the one hundred stars carefully measured must still remain quite doubtful.
One general result of these measures of parallax may be set forth in this way: Imagine round our solar system as a centre (for in matters relating to the universe our whole system is merely a point), a sphere with a radius 400,000 times the distance of the sun. An idea of this distance may be gained by reflecting that light, making the circuit of the earth seven times in a second, and reaching us from the sun in eight minutes and twenty seconds, would require seven years to reach the surface of the sphere we have supposed. Now, the first result of measures of parallax is that within this enormous sphere there is, besides our sun in the centre, only a single star; namely, Alpha Centauri.
Now suppose another sphere, having a radius 800,000 times the distance of the sun, so that its surface is twice as far as that of the inner sphere. By the law of cubes the volume of space within this second sphere is eight times as great as that within the first. So far as can be determined, there are about eight stars within this sphere. We cannot be quite sure of the number, because there may be stars within the sphere of which the parallax is not yet detected; and of those supposed to be within it, one or two are so near the surface that we cannot say whether they are really within or without it. But the number eight is not egregiously in error.
We may imagine the spheres extended in this way indefinitely, but the result for the number of stars within them becomes uncertain owing to the increasing difficulties of measuring parallaxes so minute. The general trend of such measures up to the present time is that the number of stars in any of these spheres will be about equal to the units of volume which they comprise when we take for this unit the smallest and innermost of the spheres, having a radius 400,000 times the sun's distance. We are thus enabled to form some general idea of how thickly the stars are sown through space. We cannot claim any numerical exactness for this idea, but in the absence of better methods it does afford us some basis for reasoning.
Now we can carry on our computation as we supposed the farmer to measure the extent of his wheat-field. Let us suppose that there are 125,000,000 stars in the heavens. This is an exceedingly rough estimate, but let us make the supposition for the time being. Accepting the view that they are nearly equally scattered throughout space, it will follow that they must be contained within a volume equal to 125,000,000 times the sphere we have taken as our unit. We find the distance of the surface of this sphere by extracting the cube root of this number, which gives us 500. We may, therefore, say, as the result of a very rough estimate, that the number of stars we have supposed would be contained within a distance found by multiplying 400,000 times the distance of the sun by 500; that is, that they are contained within a region whose boundary is 200,000,000 times the distance of the sun. This is a distance through which light would travel in about 3300 years.
It is not impossible that the number of stars is much greater than that we have supposed. Let us grant that there are eight times as many, or one thousand millions. Then we should have to extend the boundary of our universe twice as far, carrying it to a distance which light would require 6600 years to travel.
There is another method of estimating the thickness with which stars are sown
