The following five astronomical magnitudes, then, occur among the sides of this most useful triangle: viz., 1st, The co-latitude of the place of observation; 2d, the polar distance; 3d, the zenith distance; 4th, the hour angle; and 5th, the sub-azimuth (supplement of azimuth) of a given celestial object; and by its solution therefore may all problems be resolved, in which three of these magnitudes are directly or indirectly given, and the other two required to be found. (128.) For example, suppose the time of rising or setting of the sun or of a star were required, having given its right ascension and polar distance. The star rises when apparently on the horizon, or really about 34' below it (owing to refraction), so that, at the moment of its apparent. rising, its zenith distance is 90° 34'-ZS. Its polar distance PS being also given, and the co-latitude ZP of the place, we have given the three sides of the triangle, to find the hour angle Z PS, which, being known, is to be added to or subtracted from the star's right ascension, to give the sidereal time of setting or rising, which, if we please, may be converted into solar time by the proper rules and tables. (129.) As another example of the use of the same triangle, we may propose to find the local sidereal time, and the latitude of the place of observation, by observing equal altitudes of the same star east and west of the meridian, and noting the interval of the observations in sidereal time. The hour angles corresponding to equal altitudes of a fixed star being equal, the hour angle east or west will be measured by half the observed interval of the observations. In our triangle, then, we have given this hour angle Z P S, the polar distance P S of the star, and Z S, its coaltitude at the moment of observation. Hence we may find P Z, the co-latitude of the place. Moreover, the hour angle of the star being known, and also its right ascension, the point of the equinoctial is known, which is on the meridian at the moment of observation; and, therefore, the local sidereal time at that moment. This is a very useful observation for determining the latitude and time at an unknown station. CHAPTER III.' THE ACCURACY OF POINTING. OF THE NATURE OF ASTRONOMICAL INSTRUMENTS AND OBSERVATIONS IN GENERAL.-OF SIDEREAL AND SOLAR TIME.-OF THE MEASUREMENTS OF TIME.- CLOCKS, CHRONOMETERS. -OF ASTRONOMICAL MEASUREMENTS.-PRINCIPLE OF TELESCOPIC SIGHTS TO INCREASE SIMPLEST APPLICATION OF THIS PRINCIPLE. THE TRANSIT INSTRUMENT.--OF THE MEASUREMENT OF ANGULAR INTERVALS. METHODS OF INCREASING THE ACCURACY OF READING.-THE VERNIER. THE MICROSCOPE.- OF THE MURAL CIRCLE. THE MERIDIAN CIRCLE. - FIXATION OF POLAR AND HORIZONTAL POINTS. -THE LEVEL, PLUMB-LINE, ARTIFICIAL HORIZON. PRINCIPLE OF COLLIMATION.-COLLIMATORS OF RITTENHOUSE, KATER, AND BENZENBERG. OF COMPOUND INSTRUMENTS THEODOLITE. WITH CO-ORDINATE CIRCLES. THE EQUATORIAL, ALTITUDE, AND (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 The student who is anxious to become acquainted with the chief subject matter of this work, may defer the reading of that part of this chapter which is devoted to the description of particular instruments, or content himself with a cursory perusal of it, until farther advanced, when it will be necessary to return to it. 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 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 offers 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. 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 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. An 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 the 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 57th 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 all be 5700 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'oeuvre, 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. (132.) The great aim of the practical astronomer being numerical correctness in the results of instrumental 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: (133.) 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 tabulated 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 the relative magnitudes and the tension of their parts; and others of the like nature. (134.) 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. (135.) 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 principal classes. The first comprehends those which arise from an instrument not being what it professes to be, which is error of workmanship. Thus, if a pivot or axis, instead of being, as it ought, exactly cylindrical, be slightly flattened, or elliptical,-if it be not exactly (as it is intended it should) concentric with the circle it carries;-if this circle (so called) be in reality not exactly circular, or not in one plane; if its divisions, intended to be precisely equidistant, should be placed in reality at unequal intervals,—and a hundred other things of the same sort. These are not mere speculative sources of error, but practical annoyances, which every observer has to contend with. (136.) The other subdivision of instrumental errors comprehends such as arise from an instrument not being placed in the position it ought to bave; and from those of its parts, which are made purposely moveable, not being properly disposed inter se. These are errors of adjustment. Some are unavoidable, as they arise from a general unsteadiness of the soil or building in which the instruments are placed; which, though too minute to be noticed in any other way, become appreciable in delicate astronomical observations; others, again, are consequences of imperfect workmanship, as where an instrument once well adjusted will not remain so, but keeps deviating and shifting. But the most important of this class of errors arise from the non-existence of natural indications, other than those afforded by astronomical observations themselves, whether an instru ment has or has not the exact position, with respect to the horizon and its |
