(205.) Geography is not only the most important of the practical branches of knowledge to which astronomy is applied, but it is also, theoretically speaking, an essential part of the latter science. The earth being the general station from which we view the heavens, a knowledge of the local situation of particular stations on its surface is of great consequence, when we come to inquire the distances of the nearer heavenly bodies from us, as concluded from observations of their parallax as well as on all other occasions, where a difference of locality can be supposed to influence astronomical results. We propose, therefore, in this chapter, to explain the principles, by which astronomical observation is applied to geographical determinations, and to give at the same time an outline of geography so far as it is to be considered a part of astronomy.

(206.) Geography, as the word imports, is a delineation or description of the earth. In its widest sense, this comprehends not only the delineation of the form of its continents and seas, its rivers and mountains, but their physical condition, climates, and products, and their appropriation by communities of men. With physical and political geography, however, we have no concern here.

(602.) In the progress of this work, we have more than once called the reader's attention to the existence of inequalities in the lunar and planetary motions not included in the expression of Kepler's laws, but in some sort supplementary to them, and of an order so far subordinate to those leading features of the celestial movements, as to require, for their detection, nicer observations, and longer-continued comparison between facts and theories, than suffice for the establishment and verification of the elliptic theory. These inequalities are known, in physical astronomy, by the name of perturbations. They arise, in the case of the primary planets, from the mutual gravitations of these planets towards each other, which derange their elliptic motions round the sun; and in that of the secondaries, partly from the mutual gravitation of the secondaries of the same system similarly deranging their elliptic motions round their common primary, and partly from the unequal attraction of the sun and planets on them and on their primary. These perturbations, although small, and, in most instances, insensible in short intervals of time, yet, when accumulated, as some of them may become, in the lapse of ages, alter very greatly the original elliptic relations, so as to render the same elements of the planetary orbits, which at one epoch represented perfectly well their movements, inadequate and unsatisfactory after long intervals of time.

The work here offered to the Public is based upon and may be considered as an extension, and, it is hoped, an improvement of a treatise on the same subject, forming Part 43. of the Cabinet Cyclopaedia, published in the year 1833. Its object and general character are sufficiently stated in the introductory chapter of that volume, here reprinted with little alteration; but an opportunity having been afforded me by the Proprietors, preparatory to its re-appearance in a form of more pretension, I have gladly availed myself of it, not only to correct some errors which, to my regret, subsisted in the former volume, but to remodel it altogether (though in complete accordance with its original design as a work of explanation); to introduce much new matter in the earlier portions of it; to re-write, upon a far more matured and comprehensive plan, the part relating to the lunar and planetary perturbations, and to bring the subjects of sidereal and nebular astronomy to the level of the present state of our knowledge in those departments.

The chief novelty in the volume, as it now stands, will be found in the manner in which the subject of Perturbations is treated. It is not — it cannot be made elementary, in the sense in which that word is understood in these days of light reading.

(864.) When we cast our eyes over the concave of the heavens in a clear night, we do not fail to observe that here and there are groups of stars which seem to be compressed together in a more condensed manner than in the neighbouring parts, forming bright patches and clusters, which attract attention, as if they were there brought together by some general cause other than casual distribution. There is a group, called the Pleiades, in which six or seven stars may be noticed, if the eye be directed full upon it; and many more if the eye be turned carelessly aside, while the attention is kept directed upon the group. Telescopes show fifty or sixty large stars thus crowded together in a very moderate space, comparatively insulated from the rest of the heavens. The constellation called Coma Berenices is another such group, more diffused, and consisting on the whole of larger stars.

(865.) In the constellation Cancer, there is a somewhat similar, but less definite, luminous spot, called Præsepe, or the bee-hive, which a very moderate telescope,—an ordinary night-glass for instance,—resolves entirely into stars. In the sword-handle of Perseus, also, is another such spot, crowded with stars, which requires rather a better telescope to resolve into individuals separated from each other. These are called clusters of stars; and, whatever be their nature, it is certain that other laws of aggregation subsist in these spots, than those which have determined the scattering of stars over the general surface of the sky. This conclusion is still more strongly pressed upon us, when we come to bring very powerful telescopes to bear on these and similar spots.

(777.) Besides the bodies we have described in the foregoing chapters, the heavens present us with an innumerable multitude of other objects, which are called generally by the name of stars. Though comprehending individuals differing from each other, not merely in brightness, but in many other essential points, they all agree in one attribute, — a high degree of permanence as to apparent relative situation. This has procured them the title of “fixed stars;” an expression which is to be understood in a comparative and not an absolute sense, it being certain that many, and probable that all, are in a state of motion, although too slow to be perceptible unless by means of very delicate observations, continued during a long series of years.

(778.) Astronomers are in the habit of distinguishing the stars into classes, according to their apparent brightness. These are termed magnitudes. The brightest stars are said to be of the first magnitude; those which fall so far short of the first degree of brightness as to make a strongly marked distinction are classed in the second; and so on down to the sixth or seventh, which comprise the smallest stars visible to the naked eye, in the clearest and darkest night.

(1.) Every student who enters upon a scientific pursuit, especially if at a somewhat advanced period of life, will find not only that he has much to learn, but much also to unlearn. Familiar objects and events are far from presenting themselves to our senses in that aspect and with those connections under which science requires them to be viewed, and which constitute their rational explanation. There is, therefore, every reason to expect that those objects and relations which, taken together, constitute the subject he is about to enter upon will have been previously apprehended by him, at least imperfectly, because much has hitherto escaped his notice which is essential to its right understanding: and not only so, but too often also erroneously, owing to mistaken analogies, and the general prevalence of vulgar errors. As a first preparation, therefore, for the course he is about to commence, he must loosen his hold on all crude and hastily adopted notions, and must strengthen himself, by something of an effort and a resolve, for the unprejudiced admission of any conclusion which shall appear to be supported by careful observation and logical argument, even should it prove of a nature adverse to notions he may have previously formed for himself, or taken up, without examination, on the credit of others. Such an effort is, in fact, a commencement of that intellectual discipline which forms one of the most important ends of all science. It is the first movement of approach towards that state of mental purity which alone can fit us for a full and steady perception of moral beauty as well as physical adaptation.

(401.) The moon, like the sun, appears to advance among the stars with a movement contrary to the general diurnal motion of the heavens, but much more rapid, so as to be very readily perceived (as we have before observed) by a few hours’ cursory attention on any moonlight night. By this continual advance, which, though sometimes quicker, sometimes slower, is never intermitted or reversed, it makes the tour of the heavens in a mean or average period of 27d 7h 43m 11s°.5, returning, in that time, to a position among the stars nearly coincident with that it had before, and which would be exactly so, but for reasons presently to be stated.

(402.) The moon, then, like the sun, apparently describes an orbit round the earth, and this orbit cannot be very different from a circle, because the apparent angular diameter of the full moon is not liable to any great extent of variation.

(403.) The distance of the moon from the earth is concluded from its horizontal parallax, which may be found either directly, by observations at remote geographical stations, exactly similar to those described in art. 355., in the case of the sun, or by means of the phenomena called occultations, from which also its apparent diameter is most readily and correctly found. From such observations it results that the mean or average distance of the center of the moon from that of the earth is 59.9643 of the earth's equatorial radii, or about 237,000 miles.

On Nebulæ

Although the cause is utterly unknown, and in the present stage of human cognoscence appears to be inscrutable, it is surmised that the exceptional bodies designated Nebulæ have a connection with double-stars (see Arago's Popular Astronomy, book xi. chapter xxiv.) while, as to colours, I have noticed in them pale tints of white, creamy white, yellow, green, and blue. It therefore follows that these incomprehensible but palpable evidences of Omnipotent power and design are not unnecessarily hauled in and appended to our dissertation upon Sidereal Chromatics.

It will be recollected by all who are really concerned about the matter, that, when the wondrous revelations of Lord Rosse were communicated to the public, certain buzzing popinjays, who hang about and obstruct the avenues to the temple of science, vociferously proclaimed that the Nebular Theory had received its coup de grace from the castle at Parsonstown. Now this crude conceit was assuredly not imbibed from his Lordship's statement, he having most pointedly said, that “now, as has always been the case, an increase of instrumental power has added to the number of clusters at the expense of the nebula; properly so called; still it would be very unsafe to conclude that such will always be the case, and thence to draw the obvious inference that all nebulosity is but the glare of stars too remote to be separated by the utmost power of our instruments.”

(130.) Our first chapters have been devoted to the acquisition chiefly of preliminary notions respecting the globe we inhabit, its relation to the celestial objects which surround it, and the physical circumstances under which all astronomical observations must be made, as well as to provide ourselves with a stock of technical words and elementary ideas of most frequent and familiar use in the sequel. We might now proceed to a more exact and detailed statement of the facts and theories of astronomy: but, in order to do this with full effect, it will be desirable that the reader be made acquainted with the principal means which astronomers possess, of determining, with the degree of nicety their theories require, the data on which they ground their conclusions; in other words, of ascertaining by measurement the apparent and real magnitudes with which they are conversant. It is only when in possession of this knowledge that he can fully appretiate either the truth of the theories themselves, or the degree of reliance to be placed on any of their conclusions antecedent to trial: since it is only by knowing what amount of error can certainly be perceived and distinctly measured, that he can satisfy himself whether any theory oifers so close an approximation, in its numerical results, to actual phenomena, as will justify him in receiving it as a true representation of nature.

(131.) Astronomical instrument-making may be justly regarded as the most refined of the mechanical arts, and that in which the nearest approach to geometrical precision is required, and has been attained.

DOUBLE STAR COLOURS CONTINUED

Opening remarks

In consecution of this fascinating subject, we will now follow the period of 1844, the date of the “Cycle,” by that of 1860, the year in which the Hartwell Continuation appeared; after a further advertence to most of its matter, and considerable correspondence on the several points connected therewith. It has been suggested to me that some colours may undergo pulsations, but the adduced instances are mostly at low altitudes, where atmospheric influences are prevalent; and there may be a want of rigorous correction of the residual spectrum of the refracting telescope. But embarrassments in the outset of any enterprize only enhance the value of proven examples.

It may be noted—en passant—that a slight perturbation pervaded the minds of observing neophytes on the averment pronouncing that there are only three primary colours, namely— red, yellow, and blue; and that the other four—orange, green, indigo, and violet—are de facto produced by combinations of the former, and are therefore secondary or compound colours. This is, however, comparatively easy, as well to suggest as to adopt; but when an arrogant Goethe—unversed even in first principles—steps forward in the pride and panoply of popularity to explain the physiological and chemical qualities of the same, in order to demolish the “nauseous precepts of Newton,” we are really taken aback by his temerarious effrontery.

(346.) In the foregoing chapters, it has been shown that the apparent path of the sun is a great circle of the sphere, which it performs in a period of one sidereal year. From this it follows, that the line joining the earth and sun lies constantly in one plane; and that, therefore, whatever be the real motion from which this apparent motion arises, it must be confined to one plane, which is called the plane of the ecliptic.

(347.) We have already seen (art. 146.) that the sun's motion in right ascension among the stars is not uniform. This is partly accounted for by the obliquity of the ecliptic, in consequence of which equal variations in longitude do not correspond to equal changes of right ascension. But if we observe the place of the sun daily throughout the year, by the transit and circle, and from these calculate the longitude for each day, it will still be found that, even in its own proper path, its apparent angular motion is far from uniform. The change of longitude in twenty-four mean solar hours averages 0° 59′ 8″°.33; but about the 31st of December it amounts to 1° 1′ 9″°.9, and about the 1st of July is only 0° 57′ 11″°.5. Such are the extreme limits, and such the mean value of the sun's apparent angular velocity in its annual orbit.

(348.) This variation of its angular velocity is accompanied with a corresponding change of its distance from us.