The Story of the Heavens by Sir Robert Stawell Ball (fantasy books to read .txt) 📕

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.

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. Bruennow, 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. Bruennow 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 Bruennow employed was quite different from that of Struve, though the filar micrometer was used in both cases. Bruennow 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.

Perhaps it will be thought that in many cases these errors appear to have attained very undesirable dimensions. Let us, therefore, hasten to say that it was precisely for the purpose of setting forth these errors that this diagram has been shown; we have to exhibit the weakness of the case no less than its strength. The errors of the observations are not, however, intrinsically so great as might at first sight be imagined. To perceive this, it is only necessary to interpret the scale on which this diagram has been drawn by comparison with familiar standards. The distance from the very top of the curve to the horizontal line denotes an angle of only four-tenths of a second. This is about the apparent diameter of a penny-piece at a distance of _ten miles_! We can now appraise the true magnitude of the errors which have been made. It will be noticed that no one of the dots is distant from the curve by much more than half of the height of the curve. It thus appears that the greatest error in the whole series of observations amounts to but two or three tenths of a second. This is equivalent to our having pointed the telescope to the upper edge of a penny-piece fifteen or twenty miles off, instead of to the lower edge. This is not a great blunder. A rifle team whose errors in pointing were more than a hundred times as great might still easily win every prize at Bisley.

We have entered into the history of 61 Cygni with some detail, because it is the star whose distance has been most studied. We do not say that 61 Cygni is the nearest of all the stars; it would, indeed, be very rash to assert that any particular star was the nearest of all the countless millions in the heavenly host. We certainly know one star which seems nearer than 61 Cygni; it lies in one of the southern constellations, and its name is a Centauri. This star is, indeed, of memorable interest in the history of the subject. Its parallax was first determined at the Cape of Good Hope by Henderson; subsequent researches have confirmed his observations, and the elaborate investigations of Dr. Gill have proved that the parallax of this star is about three-quarters of a second, so that it is only two-thirds of the distance of 61 Cygni.

61 Cygni arrested our attention, in the first instance, by the circumstance that it had the large proper motion of five seconds annually. We have also ascertained that the annual parallax is about half a second. The combination of these two statements leads to a result of considerable interest. It teaches us that 61 Cygni must each year traverse a distance of not less than ten times the radius of the earth's orbit. Translating this into ordinary figures, we learn that this star must travel nine hundred and twenty million miles per annum. It must move between two and three million miles each day, but this can only be accomplished by maintaining the prodigious velocity of thirty miles per second. There seems to be no escape from this conclusion. The facts which we have described, and which are now sufficiently well established, are inconsistent with the supposition that the velocity of 61 Cygni is less than thirty miles per second; the velocity may be greater, but less it cannot be.

For the last hundred and fifty years we know that 61 Cygni has been moving in the same direction and with the same velocity. Prior to the existence of the telescope we have no observation to guide us; we cannot, therefore, be absolutely certain as to the earlier history of this star, yet it is only reasonable to suppose that 61 Cygni has been moving from remote antiquity with a velocity comparable with that it has at present. If disturbing influences were entirely absent, there could be no trace of doubt about the matter. _Some_ disturbing influence, however, there must be; the only question is whether that disturbing influence is sufficient to modify seriously the assumption we have made. A powerful disturbing influence might greatly alter the velocity of the star; it might deflect the star from its rectilinear course; it might even force the star to move around a closed orbit. We do not, however, believe that any disturbing influence of this magnitude need be contemplated, and there can be no reasonable doubt that 61 Cygni moves at present in a path very nearly straight, and with a velocity very nearly uniform.

As the distance of 61 Cygni from the sun is forty billions of miles, and its velocity is thirty miles a second, it is easy to find how long the star would take to accomplish a journey equal to its distance from the sun. The time required will be about 40,000 years. In the last 400,000 years 61 Cygni will have moved over a distance ten times as great as its present distance from the sun, whatever be the direction of motion. This star must therefore have been about ten times as far from the earth 400,000 years ago as it is at present. Though this epoch is incredibly more remote than any historical record, it is perhaps not incomparable with the duration of the human race; while compared with the vast lapse of geological time, such periods seem trivial and insignificant. Geologists have long ago repudiated mere thousands of years; they now claim millions, and many millions of years, for the performance of geological phenomena. If the earth has existed for the millions of years which geologists assert, it becomes reasonable for astronomers to speculate on the phenomena which have transpired in the heavens in the lapse of similar ages. By the aid of our knowledge of star distances, combined with an assumed velocity of thirty miles per second, we can make the attempt to peer back into the remote past, and show how great are the changes which our universe seems to have undergone.

In a million years 61 Cygni will apparently have moved through a distance which is twenty-five times as great as its present distance from the sun. Whatever be the direction in which 61 Cygni is moving--whether it be towards the earth or from the earth, to the right or to the left, it