To Bessel is commonly assigned the credit of having first actually determined the parallax of a star with such certainty as to place the result beyond question. The star having the most rapid proper motion on the celestial sphere, so far as known to Bessel, was 61 Cygni, which is, however, only of the fifth magnitude. This rapid motion indicated that it was probably among the stars nearest to us, much nearer, in fact, than the faint stars by which it is surrounded.
After several futile attempts, he undertook a series of measurements with a heliometer, the best in his power to make, in August, 1837, and continued them until October, 1838. The object was to determine, night after night, the position of 61 Cygni, relative to certain small stars in its neighborhood. Then he and his assistant, Sluter, made a second series, which was continued until 1840. All these observations showed conclusively that the star had a parallax of about 0″.35.
While Bessel was making these observations, Struve, at Dorpat, made a similar attempt upon Alpha Lyræ. This star, in the high northern latitude of Dorpat, could be accurately observed throughout almost the entire year. It is one of the brightest stars near the Pole and has a sensible proper motion. There was, therefore, reason to believe it among the nearest of the stars. The observations of Struve extended from 1835 to August, 1838, and were, therefore, almost simultaneous with the observations made by Bessel on 61 Cygni. He concluded that the parallax of Alpha Lyræ was about one-fourth of a second. Subsequent investigations have, however, made it probable that this result was about double the true value of the parallax.
The third successful attempt was made by Henderson, of England, astronomer at the Cape of Good Hope. He found from meridian observations that the star Alpha Centauri had a parallax of about 1″. This is a double star of the first magnitude, which, being only 30° from the south celestial pole, never rises in our latitudes. Its nearness to us was indicated not only by its magnitude, but also by its considerable proper motion.
Although subsequent investigation has shown the parallax of this body to be less than that found by Henderson, it is, up to the time of writing, the nearest star whose distance has been ascertained. The extreme difficulty of detecting movements so slight as those we have described, when they take six months to go through their phases, will be obvious to the reader. He would be still more impressed with it when, looking through a powerful telescope at any star, he sees how it flickers in consequence of the continual motions going on in the air through which it is seen and how difficult it must be to fix any point of reference from which to measure the change of direction.
The latter is the capital difficulty in measuring the parallax. How shall we know that a star has changed its direction by a fraction of a second in the course of six months? There must be for this purpose some standard direction from which we can measure.
The most certain of these standard directions is that of the earth’s axis of rotation. It is true that this direction varies in the course of the year, but the amount of the variation is known with great precision, so that it can be properly allowed for in the reduction of the observations. The angle between the direction of a star and that of the earth’s axis, the latter direction being represented by the celestial pole, can be measured with our meridian instruments. It is, in fact, the north polar distance of the star, or the complement of its declination. If, therefore, the astronomer could measure the declination of a star with great precision throughout the entire year, he would be able to determine its parallax by a comparison of the measures. But it is found impossible in practice to make measures of so long an arc with the necessary precision. The uncertain and changing effect of the varying seasons and different temperatures of day and night upon the air and the instrument almost masks the parallax. After several attempts with the finest instruments, handled with the utmost skill, to determine stellar parallax from the declinations of the stars, the method has been practically abandoned.
The method now practiced is that of relative parallax. By this method the standard direction is that of a small star apparently alongside one whose parallax is to be measured, but, presumably, so much farther away that it may be regarded as having no parallax. In this assumption lies the weak point of the method. Can we be sure that the smaller stars are really without appreciable parallax? Until recent times it was generally supposed that the magnitude of the stars afforded the best index to their relative distances. If the stars were of the same intrinsic brilliancy, the amount of light received from them would, as already pointed out, have been inversely as the square of the distance. Although there was no reason to suppose that any such equality really existed, it would still remain true that, in the general average, the brighter stars must be nearer to us than the fainter ones. But when the proper motions of stars came to be investigated, it was found that the amount of this motion afforded a better index to the distance than the magnitude did.
The diversity of actual or linear motion is not so wide as that of absolute brilliancy. Stars have, therefore, in recent times, been selected for parallax very largely on account of their proper motion, without respect to their brightness. It is now considered quite safe to assume that the small stars without proper motion are so far away that their parallax is insensible.
Ever since the time of Bessel the experience of practical astronomers has tended toward the conclusion that the best instrument for delicate measurements like these is the heliometer. This is an equatorial telescope of which the object glass is divided along a diameter into two semicircles, which can slide along each other. Each half of the object glass forms a separate image of any star at which the telescope may be pointed. By sliding the two halves along each other, the images can be brought together or separated to any extent. If there are two stars in proximity, the image of one star made by one-half of the glass can be brought into coincidence with that of the other star made by the other half. The sliding of the two halves to bring about this coincidence affords a scale of measurement for the angular distance of the two stars.