The Story of the Heavens

by Robert S. Ball

When Bessel proposed to undertake the great research with which his name will be for ever connected, he determined to devote one, or two, or three years to the continuous observations of one star, with the view of measuring carefully its parallactic ellipse. How was he to select the object on which so much labour was to be expended? It was all-important to choose a star which should prove sufficiently near to reward his efforts by exhibiting a measurable parallax. Yet he could have but little more than surmise and analogy as a guide. It occurred to him that the exceptional features of 61 Cygni afforded the necessary presumption, and he determined to apply the process of observation to this star. He devoted the greater part of three years to the work, and succeeded in discovering its distance from the earth.

Since the date of Sir John Herschel's address, 61 Cygni has received the devoted and scarcely remitted attention of astronomers. In fact, we might say that each succeeding generation undertakes a new discussion of the distance of this star, with the view of confirming or of criticising the original discovery of Bessel. The diagram here given (Fig. 94) is intended to illustrate the recent history of 61 Cygni.

When Bessel engaged in his labours, the pair of stars forming the double were at the point indicated on the diagram by the date 1838. The next epoch occurred fifteen years later, when Otto Struve undertook his researches, and the pair of stars had by that time moved to the position marked 1853. Finally, when the same object was more recently observed at Dunsink Observatory, the pair had made still another advance, to the position indicated by the date 1878. Thus, in forty years this double star had moved over an arc of the heavens upwards of three minutes in length. The actual path is, indeed, more complicated than a simple rectilinear movement. The two stars which form the double have a certain relative velocity, in consequence of their mutual attraction. It will not, however, be necessary to take this into account, as the displacement thus arising in the lapse of a single year is far too minute to produce any inconvenient effect on the parallactic ellipse.

Fig. 94.—61 Cygni and the Comparison Stars.

The case of 61 Cygni is, however, exceptional. It is one of our nearest neighbours in the heavens. We can never find its distance accurately to one or two billions of miles; but still we have a consciousness that an uncertainty amounting to twenty billions is too large a percentage of the whole. We shall presently show that we believe Struve was right, yet it does not necessarily follow that Bessel was wrong. The apparent paradox can be easily explained. It would not be easily explained if Struve had used the same comparison star as Bessel had done; but Struve's comparison star was different from either of Bessel's, and this is probably the cause of the discrepancy. It will be recollected that the essence of the process consists of the comparison of the small ellipse made by the distant star with the larger ellipse made by the nearer star. If the two stars were at the same distance, the process would be wholly inapplicable. In such a case, no matter how near the stars were to the earth, no parallax could be detected. For the method to be completely successful, the comparison star should be at least eight times as far as the principal star. Bearing this in mind, it is quite possible to reconcile the measures of Bessel with those of Struve. We need only assume that Bessel's comparison stars are about three times as far as 61 Cygni, while Struve's comparison star is at least eight or ten times as far. We may add that, as the comparison stars used by Bessel are brighter than that of Struve, there really is a presumption that the latter is the most distant of the three.

We have here a characteristic feature of this method of determining parallax. Even if all the observations and the reductions of a parallax series were mathematically correct, we could not with strict propriety describe the final result as the parallax of one star. It is only the difference between the parallax of the star and that of the comparison star. We can therefore only assert that the parallax sought cannot be less than the quantity determined. Viewed in this manner, the discrepancy between Struve and Bessel vanishes. Bessel asserted that the distance of 61 Cygni could not be more than sixty billions of miles. Struve did not contradict this—nay, he certainly confirmed it—when he showed that the distance could not be more than forty billions.

Nearly half a century has elapsed since Struve made his observations. Those observations have certainly been challenged; but they are, on the whole, confirmed by other investigations. In a critical review of the subject Auwers showed that Struve's determination is worthy of considerable confidence. Yet, notwithstanding this authoritative announcement, the study of 61 Cygni has been repeatedly resumed. Dr. Brünnow, when Astronomer Royal of Ireland, commenced a series of observations on the parallax of 61 Cygni, which were continued and completed by the present writer, his successor. Brünnow chose a fourth comparison star (marked on the diagram), different from any of those which had been used by the earlier observers. The method of observing which Brünnow employed was quite different from that of Struve, though the filar micrometer was used in both cases. Brünnow sought to determine the parallactic ellipse by measuring the difference in declination between 61 Cygni and the comparison star.[38] In the course of a year it is found that the difference in declination undergoes a periodic change, and from that change the parallactic ellipse can be computed. In the first series of observations I measured the difference of declination between the preceding star of 61 Cygni and the comparison star; in the second series I took the other component of 61 Cygni and the same comparison star. We had thus two completely independent determinations of the parallax resulting from two years' work. The first of these makes the distance forty billions of miles, and the second makes it almost exactly the same. There can be no doubt that this work supports Struve's determination in correction of Bessel's, and therefore we may perhaps sum up the present state of our knowledge of this question by saying that the distance of 61 Cygni is much nearer to the forty billions of miles which Struve found than to the sixty billions which Bessel found.[39]

It is desirable to give the reader the means of forming his own opinion as to the quality of the evidence which is available in such researches. The diagram in Fig. 95 here shown has been constructed with this object. It is intended to illustrate the second series of observations of difference of declination which I made at Dunsink. Each of the dots represents one night's observations. The height of the dot is the observed difference of declination between 61 (B) Cygni and the comparison star. The distance along the horizontal line—or the abscissa, as a mathematician would call it—represents the date. These observations are grouped more or less regularly in the vicinity of a certain curve. That curve expresses where the observations should have been, had they been absolutely perfect. The distances between the dots and the curve may be regarded as the errors which have been committed in making the observations.