equinoctial and meridian is 38° 31' 20". The north and south poles of the heavens are the poles of the equinoctial. The east and west points of the horizon of a spectator are the poles of his celestial meridian. The north and south points of his horizon are the poles of his prime vertical, and his zenith and nadir are the poles of his horizon.

(124.) All the heavenly bodies culminate (i. e. come to their greatest altitudes) on the meridian; which is, therefore, the best situation to observe them, being least confused by the inequali ties and vapours of the atmosphere, as well as least displaced by refraction.

(125.) All celestial objects within the circle of perpetual apparition come twice on the meridian, above the horizon, in every diurnal revolution; once above and once below the pole. These are called their upper and lower culminations.

(126.) The problems of uranometry, as we have described it, consist in the solution of a variety of spherical triangles, both right and oblique angled, according to the rules, and by the formulæ of spherical trigonometry, which we suppose known to the reader, or for which he will consult appropriate treatises. We shall only here observe generally, that in all problems in which spherical geometry is concerned, the student will find it a useful practical maxim rather to consider the poles of the great circles which the question before him refers to than the circles themselves. To use, for example, in the relations he has to consider, polar distances rather than declinations, zenith distances rather than altitudes, &c. Bearing this in mind, there are few problems in uranometry which will offer any difficulty. The following are the combinations which most commonly occur for solution when the place of one celestial object only on the sphere is concerned.

(127.) In the triangle Z P S, Z is the zenith, P the elevated pole, and S the star, sun, or other celestial object. In this triangle occur, 1st, P Z, which being the complement of P H (the altitude of the pole), is obviously the complement of the latitude (or the co-latitude, as it is called) of the place; 2d, P S, the polar distance, or the complement of the declination (co-declination) of the star; 3d, ZS, the zenith distance or co-altitude of the star. If PS be greater than 90°, the object is situated on the side of the

equinoctial opposite to that of the elevated pole. If Z S be so, the object is below the horizon.

In the same triangle the angles are, 1st, Z P S the lower angle ; 2d, P Z S (the supplement of S Z O, which latter is the azimuth of the star or other heavenly body); 3d, P S Z, an angle which, from the infrequency of any practical reference to it, has not acquired a name.*

The following five astronomical magnitudes, then, occur among the sides and angles 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 subazimuth (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 ZPS, which, being known, is to be added to or subtracted from the star's right ascension, to give the sidereal

* In the practical discussion of the measures of double stars and other objects by the aid of the position micrometer, this angle is sometimes required to be known; and, when so required, it will not be inconveniently referred to as "the angle of position of the zenith."

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 obser vations 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 PS, the polar distance P S of the star, and Z S, its co-altitude 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.*

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 THE ACCURACY OF POINTING.-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 WITH CO-ORDINATE CIRCLES.-THE EQUATORIAL, ALTITUDE, AND AZIMUTH INSTRUMENT. THEODOLITE. -OF THE SEXTANT AND REFLECTING CIRCLE.-PRINCIPLE OF REPETITION. -OF MICROMETERS.-PARALLEL WIRE MICROMETER.-PRINCIPLE OF THE DUPLICATION OF IMAGES. THE HELIOMETER.-DOUBLE REFRACTING EYE-PIECE.-VARIABLE PRISM MICROMETER.

THE POSITION MICROMETER.

-OF

(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,

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.

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

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