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HAO a great circle of the sphere, whose poles are Z N, be his celestial horizon ; Pp the elevated and

B Z

VUOSI

depressed POLES of the heavens: HP the altitude of the pole, and H P ZE O his meridian ; ET Q, a great circle perpendicular to P p, will be the equinoctial ; and if r represent the equinox, r T will be the right ascension, TS the declination, and PS the polar distance of any star or object S, referred to the equi. noctial by the hour circle PSTp; and BSD will be the diurnal circle it will appear to describe about the pole. Again, if we refer it to the horizon by the vertical circle ZSA, HA will be its azimuth, A S its altitude, and Z S its zenith distance. H and O are the north and south, and e w the east and west points of his horizon, or of the heavens. Moreover, if Hh, 00, be small circles, or parallels of declination, touching the horizon in its north and south points, H h will be the circle of perpetual apparition, between which and the elevated pole the stars never set; Oo that of perpetual occultation, between which and the depressed pole they never rise. In all the zone of the heavens between Hh and 00, they rise and set, any one of them, as S, remaining above the horizon, in that part of its diurnal circle represented by A BA, and below it throughout all the part represented by A Da. It

CHAP. II.

OF THE NATURE OF ASTRONOMICAL INSTRUMENTS AND OBSERV

ATIONS IN GENERAL, OF SIDEREAL AND SOLAR TIME. OF THE MEASUREMENT OF TIME. -CLOCKS, CHRONOMETERS, THE TRANSIT INSTRUMENT. OF THE MEASUREMENT OF ANGULAR INTERVALS. APPLICATION OF THE TELESCOPE TO INSTRUMENTS DESTINED TO THAT PURPOSE.OF THE MURAL CIRCLE. — FIXATION OF POLAR AND HORIZONTAL POINTS. THE LEVEL. -- PLUMB LINE. — ARTIFICIAL HORIZON. -COLLIMATOR, OF COMPOUND INSTRUMENTS WITH CO-ORDINATE CIRCLES, THE EQUATORIAL. -ALTITUDE AND AZIMUTH INSTRUMENT. — OF THE SEXTANT AND REFLECTING CIRCLE. — PRINCIPLE OF REPETITION. .

(102. Our first chapter has 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 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 appreciate either the truth of the theories themselves, or the degree of reliance to be placed on any of their conclu. sions 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 offers so close an approximation, in its nu.

merical results, to actual phenomena, as will justify him in receiving it as a true representation of nature.

(103.) 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 unacquainted 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 consi. dered that, owing to the application of telescopes to the purposes of angular measurement, every imperfection of structure or 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. An angle of one minute occupies, on the circumference of a circle of 10 inches in radius, only about 3} oth 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 mean surement of an angle. With the instruments now em. ployed in observatories, a single second, or the 60th part of a minute, is rendered a distinctly visible and appreeiable 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 dogth 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), 360 marks, dots, or cognizable divisions, which shall be true to their places within such minute 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 un. equally 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'ouvre, 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 imper. fections incident to every work the latter can place in his hands. He must, therefore, endeavour so to com. bine 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 in. strument 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.

(104.) The great aim of the practical astronomer being numerical correctness in the results of instru. mental measurement, his constant care and vigilance must be directed to the detection and compensation of errors, either by annihilating, or by taking account of, and allowing for them. Now, if we examine the sources from which errors may arise in any instrumental determination, we shall find them chiefly reducible to three principal heads :

(105.) 1st, External or incidental causes of error; comprehending such as depend on external, uncontrollable circumstances : such as, fluctuations of weather, which disturb the amount of refraction from its tabu. lated value, and, being reducible to no fixed law, induce uncertainty to the extent of their own possible magnitude ; such as, by varying the temperature of the air, vary also the form and position of the instruments used, by altering relative magnitude and the tension of their parts; and others of the like nature.

(106.) 2dly, Errors of observation: such as arise, for example, from inexpertness, defective vision, slowness in seizing the exact instant of occurrence of a phenomenon, or precipitancy in anticipating it, &c. ; from atmospheric indistinctness; insufficient optical power in the instrument, and the like. Under this head may also be classed all errors arising from momentary instrumental derangement, — slips in clamping, looseness of screws, &c.

(107.) 3dly, The third, and by far the most numerous class of errors to which astronomical measurements are liable, arise from causes which may be deemed instrumental, and which may be subdivided into two prin

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