Page:Chance, love, and logic - philosophical essays (IA chancelovelogicp00peir 0).pdf/216

 than 180° by an amount proportional to the area of the triangle; or,

Third, space is unlimited but finite, (like the surface of a sphere), so that it has no infinitely distant parts; but a finite journey along any straight line would bring one back to his original position, and looking off with an unobstructed view one would see the back of his own head enormously magnified, in which case the sum of the three angles of a triangle exceeds 180° by an amount proportional to the area.

Which of these three hypotheses is true we know not. The largest triangles we can measure are such as have the earth's orbit for base, and the distance of a fixed star for altitude. The angular magnitude resulting from subtracting the sum of the two angles at the base of such a triangle from 180° is called the star's parallax. The parallaxes of only about forty stars have been measured as yet. Two of them come out negative, that of Arided ([Greek: a] Cycni), a star of magnitude 1-1/2, which is —0."082, according to C. A. F. Peters, and that of a star of magnitude 7-3/4, known as Piazzi III 422, which is —0."045, according to R. S. Ball. But these negative parallaxes are undoubtedly to be attributed to errors of observation; for the probable error of such a determination is about ± 0."075, and it would be strange indeed if we were to be able to see, as it were, more than half way round space, without being able to see stars with larger negative parallaxes. Indeed, the very fact that of all the parallaxes measured only two come out negative would be a strong argument that the smallest parallaxes really amount to +0."1, were it not for the re