lations, may be useful results of a cursory perusal of this subject, without following the author into the more secret mysteries of abstruse formula. The third part of the work is one of no less interest, and is capable of assuming a more popular aspect. Sidereal astronomy is more popular in its character, because it is too remote to form a branch of practical mathematics, and it includes the principal field for general speculations about the origin or destiny of created matter, taken in its largest sense. The fourth part is a brief notice of the account of time and the history of the calendar.

The first effort of thought required in astronomy is to isolate oneself in space, and imagine that the world we live in is, physically speaking, but one of many; and that whatever is peculiar to this world, and however great or divine its privileges may be, yet, as far as we can judge of the material creation, it enjoys no absolute physical preeminence; it is no centre, no ruling power, no fulcrum by which to move the universe. If we rise from the surface, even so far as aëronautic expeditions or the ascent of lofty mountains enable us, the earth begins to subtend a smaller angle of vision, although a larger portion of the earth is seen.

'The greatest extent of the earth's surface which has ever been seen at once by man, was that exposed to the view of MM. Biot and Gay-Lussac, in their celebrated aëronautic expedition to the enormous height of 25,000 feet, or rather less than five miles. To estimate the proportion of the area visible from this elevation to the whole earth's surface, we must have recourse to the geometry of the sphere, which informs us that the convex surface of a spherical segment is to the whole surface of the sphere to which it belongs as the versed sine or thickness of the segment is to the diameter of the sphere; and further, that this thickness, in the case we are considering, is almost exactly equal to the perpendicular elevation of the point of sight above the surface. The proportion, therefore, of the visible area, in this case, to the whole earth's surface, is that of five miles to 8000, or 1 to 1600. The portion visible from Ætna, the Peak of Teneriffe, or Mowna Roa, is about one 4000th.'-P. 23.

This is an approach towards imagining the earth to be a planet. If we rise farther and look with the mind's eye when the material part of our nature can no longer follow, then we shall arrive at various stages, by which we may measure our distance, at each of which the earth will assume a more general character than it had done previously. At a distance of some fifty or sixty miles we shall probably be clear of the earth's outer coat of air, and then travel free in space without atmospheric phenomena such as refraction and reflection, causing the whole sphere of vision to be illuminated by the sun. All will, therefore, be dark except that portion of the sky whence the direct rays of the sun fall on the eye or the earth, and other heavenly bodies will be

seen in like manner according to their respective dimensions and power of light either direct or reflected. We shall then come to the moon's orbit, and if we happen to be travelling towards the sun, and the moon is also near us, we shall approach that body on its dark side, illumined only by the full earth, which will then be about four times the diameter of the moon as seen by us. In thus travelling, we must call to mind the laws of celestial perspective, by which the apparent situation of bodies in sight would be regulated. On this subject we will quote our author:

In celestial perspective, every point to which the view is for the moment directed, is equally entitled to be considered as the "centre of the picture," every portion of the surface of the sphere being similarly related to the eye. Moreover, every straight line (supposed to be indefinitely prolonged) is projected into a semicircle of the sphere, that, namely, in which a plane passing through the line and the eye cuts its surface. And every system of parallel straight lines, in whatever direction, is projected into a system of semicircles of the sphere, meeting in two common apexes, or vanishing points, diametrically opposite to each other, one of which corresponds to the vanishing point of parallels in ordinary perspective; the other, in such perspective has no existence. In other words, every point in the sphere to which the eye is directed may be regarded as one of the vanishing points, or one apex of a system of straight lines, parallel to that radius of the sphere which passes through it, or to the direction of the line of sight, seen in perspective from the earth, and the points diametrically opposite, or that from which he is looking, as the other. And any great circle of the sphere may similarly be regarded as the vanishing circle of a system of planes, parallel to its own.

A familiar illustration of this is often to be had by attending to the lines of light seen in the air, when the sun's rays are darted through apertures in clouds, the sun itself being at the time obscured behind them. These lines which, marking the course of rays emanating from a point almost infinitely distant, are to be considered as parallel straight lines, are thrown into great circles of the sphere, having two apexes or points of common intersection-one in the place where the sun itself (if not obscured) would be seen. The other diametrically opposite. The first only is most commonly suggested when the spectator's view is towards the sun. But in mountainous countries, the phenomenon of sunbeams converging towards a point diametrically opposite to the sun, and as much depressed below the horizon as the sun is elevated above it, is not unfrequently noticed, the back of the spectator being turned to the sun's place. Occasionally, but much more rarely, the whole course of such a system of sunbeams stretching in semicircles across the hemisphere from horizon to horizon (the sun being near setting), may be seen. Thus again, the streamers of the Aurora Borealis, which are doubtless electrical rays, parallel, or nearly parallel to each other, and to the dipping needle, usually appear to diverge from the point towards which the needle, freely suspended, would dip northwards (i. e. about 70° below the horizon and 23° west of north from London), and in their upward progress pursue the course of great circles till they again converge (in appearance) towards the point diametrically opposite (i. e. 70° above the horizon, and 23° to the eastward of south), forming a sort of canopy overhead, having that point for its centre. So also in the phenomenon of shooting stars, the lines of direction which they appear to take on certain remarkable occasions of

periodical recurrence, are observed, if prolonged backwards, apparently to meet nearly in one point of the sphere; a certain indication of a general near approach to parallelism in the real directions of their motions on those occasions.'-Pp. 67—69.

Arrived at the moon, suppose we rested for a short time on its inhospitable shores, and had our material substance restored to us. We should then be struck not only with the barren ruggedness of the moon's surface, or, if our taste lay that way, be delighted at the ample field before us for the investigation of volcanic remains; but we should find the necessity of managing without any air to breathe, and probably without many other terrestrial comforts. Anxious to depart from a position so little suitable, it will, however, be satisfactory to discover an extraordinary facility in bounding up from its surface; for in proportion to the size of any body, so is its power of retaining any weight on its surface. Advancing onwards towards the sun, we shall soon leave the earth and moon, as a little system by itself, far behind us, and belong for a time to the neighbourhood of Venus, our old home being thenceforth nothing but a planet, and Venus to its short-sighted inhabitants the centre of all things. We shall then approach the world of Mercury, with its rapid change of seasons and burning climate; thence we shall be absorbed in the magnificence of the sun, gradually enlarging before our eyes as we near its tremendous globe. A thin atmosphere will probably meet us, visible on earth as the zodiacal light. If haply we escape destruction from the proximity of the sun, and wend our way onward, we shall again cross the paths of the inferior planets, and of mother earth, and thence pass Mars, various broken fragments of what may once have been a planet, then Jupiter with its satellites, Saturn with its ring, Uranus, and long neglected Neptune, each one for a time being the principal town as it were of their respective counties. A wandering comet will meanwhile appear at uncertain intervals. Still going on, the whole solar system will become a remote object of vision, only on a par with many others that surround us. Another sun with its revolving planets will then perhaps claim our attention as coming in the way of our flight, to be left again for another, through all the wonders of sidereal phenomena, of which more hereafter; for enough has now been said to claim for the astronomer the privilege of being a citizen of the universe, with no local habitation for his speculations.

We will now, however, descend to the earth and begin to look about us from this our observatory. A few notices from the interesting chapter on Astronomical Instruments may here seem appropriate, as being the means by which all the facts of the science are laid down with that accuracy that alone warrants

the establishment of principles and of theories derived from them.

An

'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. It may be thought an easy thing, by one acquainted with the niceties required, to turn a circle in metal, to divide its circumference into 360 equal parts, and these again into smaller subdivisions,—to place it accurately on its centre, and to adjust it in a given position; but practically it is found to be one of the most difficult. Nor will this appear extraordinary, when it is considered that, owing to the application of telescopes to the purposes of angular measurement, every imperfection of structure of division becomes magnified by the whole optical power of that instrument; and that thus, not only direct errors of workmanship, arising from unsteadiness of hand or imperfection of tools, but those inaccuracies which originate in far more uncontrollable causes, such as the unequal expansion and contraction of metallic masses, by a change of temperature, and their unavoidable flexure or bending by their own weight, become perceptible and measurable. angle of one minute occupies, on the circumference of a circle of 10 inches in radius, only about th part of an inch, a quantity too small to be certainly dealt with without the use of magnifying glasses; yet one minute is a gross quantity in the astronomical measurement of an angle. With the instruments now employed in observatories, a single second, or a 60th part of a minute, is rendered a distinctly visible and appreciable quantity. Now, the arc of a circle, subtended by one second, is less than the 200,000th part of the radius, so that on a circle of 6 feet in diameter it would occupy no greater linear extent than part of an inch; a quantity requiring a powerful microscope to be discerned at all. Let any one figure to himself, therefore, the difficulty of placing on the circumference of a metallic circle of such dimensions (supposing the difficulty of its construction surmounted), 260 marks, dots, or cognizable divisions, which shall all be true to their places within such narrow limits; to say nothing of the subdivision of the degrees so marked off into minutes, and of these again into seconds. Such a work has probably baffled, and will probably for ever continue to baffle, the utmost stretch of human skill and industry; nor, if executed, could it endure. The ever varying fluctuations of heat and cold have a tendency to produce not merely temporary and transient, but permanent, uncompensated changes of form in all considerable masses of those metals which alone are applicable to such uses; and their own weight, however symmetrically formed, must always be unequally sustained, since it is impossible to apply the 'sustaining power to every part separately: even could this be done, at all events force must be used to move and to fix them; which can never be done without producing temporary and risking permanent change of form. It is true, by dividing them on their centres, and in the identical places they are destined to occupy, and by a thousand ingenious and delicate contrivances, wonders have been accomplished in this department of art, and a degree of perfection has been given, not merely to chefs d'œuvre, but to instruments of moderate prices and dimensions, and in ordinary use, which, on due consideration, must appear very surprising. But though we are entitled to look for wonders at the hands of scientific artists, we are not to expect miracles. The demands of the astronomer will always surpass the power of the artist; and it must, therefore, be constantly the aim of the former to make himself, as far as possible, independent of the imperfections incident to every work the latter can place in his hands. He must, therefore, endeavour so to

combine his observations, so to choose his opportunities, and so to familiarize himself with all the causes which may produce instrumental derangement, and with all the peculiarities of structure and material of each instrument he possesses, as not to allow himself to be misled by their errors, but to extract from their indications, as far as possible, all that is true, and reject all that is erroneous. It is in this that the art of the practical astronomer consists,-an art of itself of a curious and intricate nature, and of which we can here only notice some of the leading and general features.'-Pp. 75-77.

Every astronomical observation is practically a mean of various errors. In the most exact of physical sciences, no absolute exactness is pretended to from one observation alone or even from many. A great portion of the observer's labour that never ceases and allows him no rest, is in discovering the faults of his instruments.

'With regard to errors of adjustment and workmanship, not only the possibility, but the certainty of their existence, in every imaginable form, in all instruments, must be contemplated. Human hands or machines never formed a circle, drew a straight line, or erected a perpendicular, nor ever placed an instrument in perfect adjustment, unless accidentally; and then only during an instant of time. This does not prevent, however, that a great approximation to all these desiderata should be attained. But it is the peculiarity of astronomical observation to be the ultimate means of detection of all mechanical defects which elude by their minuteness every other mode of detection. What the eye cannot discern nor the touch perceive, a course of astronomical observations will make distinctly evident. The imperfect products of man's hands are here tested by being brought into comparison under very great magnifying powers (corresponding in effect to a great increase in acuteness of perception) with the perfect workmanship of nature; and there is none which will bear the trial. Now, it may seem like arguing in a vicious circle, to deduce theoretical conclusions and laws from observation, and then to turn round upon the instruments with which those observations were made, accuse them of imperfection, and attempt to detect and rectify their errors by means of the very laws and theories which they have helped us to a knowledge of. A little consideration, however, will suffice to show that such a course of proceeding is perfectly legitimate.'—Pp. 79, 80.

Astronomical instruments are not all telescopes, as some youthful amateurs expect when they go into an observatory; telescopes, indeed, may be attached to most, but they are not generally or principally for the purpose of magnifying. An observatory, therefore, is not to be judged by the possession of the telescope of greatest power, as the use of such instruments is quite distinct from the more ordinary duties of an observer. These consist in the measurement of angles, and telescopic power is chiefly wanted to help in pointing an instrument with accuracy and clearly define its outline, rather than to increase its size. The mere examination of heavenly bodies to ascertain their individual peculiarities is a minor branch of astronomy compared with a knowledge of their motion, as discovered by minute changes in angular measurement.