Bessel's observations of 61 Cygni were commenced in August 1837, immediately on the establishment at the Königsberg observatory of a magnificent heliometer, the workmanship of the celebrated optician Fraunhofer, of Munich, an instrument especially fitted for the system of observation adopted; which being totally different from that of direct meridional observation, more refined in its conception, and susceptible of far greater accuracy in its practical application, we must now explain.

(809.) Parallax, proper motion, and specific aberration (denoting by the latter phrase that part of the aberration of a star's light which may be supposed to arise from its individual peculiarities, and which we have every reason to believe at all events an exceedingly minute fraction of the whole,) are the only uranographical corrections which do not necessarily affect alike the apparent places of two stars situated in, or very nearly in, the same visual line. Supposing then two stars at an immense distance, the one behind the other, but otherwise so situated as to appear very nearly along the same visual line, they will constitute what is called a star optically double, to distinguish it from a star physically double, of which more hereafter. Aberration (that which is common to all stars), precession, nutation, nay, even refraction, and instrumental causes of apparent displacement, will affect them alike, or so very nearly alike (if the minute difference of their apparent places be taken into account) as to admit of the difference being neglected, or very accurately allowed for, by an easy calculation. If then, instead of attempting to determine by observation the place of the nearer of two very unequal stars (which will probably be the larger) by direct observation of its right ascension and polar distance, we content ourselves with referring its place to that of its remoter and smaller companion by differential observation, i. e. by measuring only its difference of situation from the latter, we are at once relieved of the necessity of making these corrections, and from all uncertainty as to their influence on the result. And for the very same reason, errors of adjustment (art. 136.), of graduation, and a host of instrumental errors,

which would for this delicate purpose fatally affect the absolute determination of either star's place, are harmless when only the difference of their places, each equally affected by such causes, is required to be known.

(810.) Throwing aside therefore the consideration of all these errors and corrections, and disregarding for the present

the minute effect of specific aberration and the uniformly progressive effect of proper motion, let us trace the effect of the differences of the parallaxes of two stars thus juxtaposed, or their apparent relative distance and position at various seasons of the year. Now the parallax being inversely as the distance, the dimensions of the small ellipses apparently described (art. 805.) by each star on the concave surface of the heavens by parallactic displacement will differ, the nearer star describing the larger ellipse. But both stars lying very nearly in the same direction from the sun, these ellipses will be similar and similarly situated. Suppose S and s to be the positions of the two stars as seen from the sun, and let ABCD, abed, be their parallactic ellipses; then, since they will be at all times similarly situated in these ellipses, when the one star is seen at A, the other will be seen at a. When the earth has made a quarter of a revolution in its orbit, their apparent places will be Bb; when another quarter, Cc; and when another, D d. If, then, we measure carefully, with micrometers adapted for the purpose, their apparent situation with respect to each other, at different times of the year, we should perceive a periodical change,

both in the direction of the line joining them, and in the distance between their centers. For the lines A a and Cc cannot be parallel, nor the lines Bb and Dd equal, unless the ellipses be of equal dimensions, i. e. unless the two stars have the same parallax, or are equidistant from the earth.

(811.) Now, micrometers, properly mounted, enable us to measure very exactly both the distance between two objects which can be seen together in the same field of a telescope, and the position of the line joining them with respect to the horizon, or the meridian, or any other determinate direction in the heavens. The double image micrometer, and especially the heliometer (art. 200, 201.) is peculiarly adapted for this purpose. The images of the two stars formed side by side, or in the same line prolonged, however momentarily displaced by temporary refraction or instrumental tremor, move together, preserving their relative situation, the judgment of which is no way disturbed by such irregular movements. The heliometer also, taking in a greater range than ordinary micrometers, enables us to compare one large star with more than one adjacent small one, and to select such of the latter among many near it, as shall be most favourably situated for the detection of any motion. in the large one, not participated in by its neighbours.

(812.) The star examined by Bessel has two such neighbours, both very minute, and therefore probably very distant, most favourably situated, the one (s) at a distance of 7′ 42′′, the other (s) at 11' 46" from the large star, and so situated, that their directions from that star make nearly a right angle with each other. The effect of parallax therefore would necessarily cause the two distances Ss and Ss to vary so as to attain their maximum and minimum values alternately at three-monthly intervals, and this is what was actually observed to take place, the one distance being always most rapidly on the increase or decrease when the other was stationary (the uniform effect of proper motion being understood of course to be always duly accounted for). This alternation, though so small in amount as to indicate, as a final

result, a parallax, or rather a difference of parallaxes between the large and small stars of hardly more than one third of a second, was maintained with such regularity as to leave no room for reasonable doubt as to its cause, and having been confirmed by the further continuance of these observations, and quite recently by the exact coincidence between the result thus obtained, and that deduced by M. Peters from observations of the same star at the observatory of Pulkova*, is considered on all hands as fully established. The parallax of this star finally resulting from Bessel's observation is 0"-348 so that its distance from our system is very nearly three parallactic units. (Art. 804.)

of

(813.) The bright star a Lyra has also near it, at only 43" distance (and therefore within the reach of the parallel wire or ordinary double image micrometer) a very minute star, which has been subjected since 1835 to a severe and assiduous scrutiny by M. Struve, on the same principle of differential observation. He has thus established the existence of a measurable amount of parallax in the large star, less indeed than that of 61 Cygni (being only about a second), but yet sufficient (such was the delicacy of his measurements) to justify this excellent observer in announcing the result as at least highly probable, on the strength of only five nights' observation, in 1835 and 1836. This probability, the continuation of the measures to the end of 1838 and the corroborative, though not in this case precisely coincident, result of Mr. Peters's investigations have converted into a certainty. M. Struve has the merit of being the first to bring into practical application this method of observation, which, though proposed for the purpose, and its great advantages pointed out by Sir William Herschel so early as 1781 †, remained long unproductive of any result, owing partly to the imperfection of micrometers for the measurement of

* With the great vertical circle by Ertel.

It has been referred even to Galileo. But the general explanation of Parallax in the Systema Cosmicum, Dial. iii. p. 271 (Leyden edit. 1699) to which the reference applies, does not touch any of the peculiar features of the case, or meet any of its difficulties.

distance, and partly to a reason which we shall presently have occasion to refer to.

(814.) If the component individuals S, s (fig. art. 810.) be (as is often the case) very close to each other, the parallactic variation of their angle of position, or the extreme angle included between the lines A a, C c, may be very considerable, even for a small amount of difference of parallaxes between the large and small stars. For instance in the case of two adjacent stars 15" asunder, and otherwise favourably situated for observation, an annual fluctuation to and fro in the apparent direction of their line of junction to the extent of half a degree (a quantity which could not escape notice in the means of numerous and careful measurements) would correspond to a difference of parallax of only

of a second. A difference of 1" between two stars apparently situated at 5" distance might cause an oscillation in that line to the extent of no less than 11°, and if nearer one proportionally still greater. This mode of observation has not yet been put in practice, but seems to offer great advantages.*

(815.) The following is a list of stars to which parallax has been up to the present time more or less probably assigned:

Although the extreme minuteness of the last four of these results deprives them of much numerical reliance, it is at least certain that the parallaxes by no means follow the order of magnitudes, and this is farther shown by the fact that a Cygni, one of M. Peters's stars, shows absolutely no indications of any measurable parallax whatever.

*See Phil. Trans. 1826, p. 266. et seq. and 1827, for a list of stars well adapted for such observation, with the times of the year most favourable. The list in Phil. Trans. 1826, is incorrect.

† Groombridge's catalogue of circumpolar stars.