Fig. 29. O B D A dependent (by some mechanical movement) on the will of the observer, and in any required direction from one another. As these can, therefore, be made to approach to or recede from each other at pleasure, they may be brought in the first place to approach till they touch one another on one side, as at A C, and then being made by continuing the motion to cross and touch on the opposite side, as A D, it is evident that the quantity of movement required to produce the change from one contact to the other, if uniform, will measure the double diameter of the object A./ (201.) Innumerable optical combinations may be devised to operate such duplication. The chief and most important (from its recent applications,) is the heliometer, in which the image is divided by bisecting the object-glass of the telescope, and making its two halves, set in separate brass frames, slide laterally on each other, as A B, the motion being Fig. 30. B produced and measured by a screw. Each half, by the laws of optics, forms its own image (somewhat blurred, it is true, by diffraction,') in its own axis; and thus two equal and similar images are formed side by side in the focus of the eye-piece, which may be made to approach and recede by the motion of the screw, and thus afford the means of measurement as above described. (202.) Double refraction through crystallized media affords another This might be cured, though at an expense of light, by limiting each half to a circular space by diaphragms, as represented by the dotted lines. means of accomplishing the same end. Without going into the intrica cies of this difficult branch of optics, it will suffice to state that objects viewed through certain crystals (as Iceland spar, or quartz) appear double, two images equally distinct being formed, whose angular distance from each other varies from nothing (or perfect coincidence,) up to a certain limit, according to the direction with respect to a certain fixed line in the crystal, called its optical axis. Suppose, then, to take the simplest case, that the eye-lens of a telescope, instead of glass, were formed of such a crystal (say of quartz, which may be worked as well or better than glass,) and of a spherical form, so as to offer no difference when turned about on its centre, other than the inclination of its optical axis to the visual ray. Then when that axis coincides with the line of collimation of the object-glass, one image only will be seen, but when made to revolve on an axis perpendicular to that line, two will arise, opening gradually out from each other, and thus originating the desired duplication. In this contrivance, the angular amount of the rotation of the sphere affords the necessary datum for determining the separation of the images. (203.) Of all methods which have been proposed, however, the simplest and most unobjectionable would appear to be the following. It Fig. 31. is well known to every optical student, that two prisms of glass, a flint and a crown, may be opposed to each other, so as to produce a colourless deflection of parallel rays. An object seen through such a compound or achromatic prism, will be seen simply deviated in direction, but in no way otherwise altered or distorted. Let such a prism be constructed with its surfaces so nearly parallel that the total deviation produced in traversing them shall not exceed a small amount (say 5'.) Let this be cut in half, and from each half let a circular disc be formed, and cemented on a circular plate of parallel glass, or otherwise sustained, close to and concentric with the other by a framework of metal so light as to intercept but a small portion of the light which passes on the outside (as in the annexed figure,) where the dotted lines represent the radii sustaining one, and the undotted those carrying the other disc. The whole must be so mounted as to allow one disc to revolve in its own plane behind the other, fixed, and to allow the amount of rotation to be read off. It is evident, then, that when the deviations produced by the two discs conspire, a total deviation of 10′ will be effected on all the light which has passed through them; that when they oppose each other, the rays will emerge undeviated, and that in intermediate positions a deviation varying from 0 to 10', and calculable from the angular rotation of the one disc on the other, will arise. Now, let this combination be applied at such a point of the cone of rays, between the object-glass and its focus, that the discs shall occupy exactly half the area of its section. Then will half the light of the object lens pass undeviated—the other half deviated, as above described; and thus a duplication of image, variable and measureable (as required for micrometric measurement) will occur. If the object-glass be not very large, the most convenient point of its application will be externally before it, in which case the diameter of the discs will be to that of the object-glass as 707: 1000; or (allowing for the spokes) about as 7 to 10. (204.) The Position Micrometer is simply a straight thread or wire which is carried round by a smooth revolving motion, in the common focus of the object and eye-glasses, in a plane perpendicular to the axis of the telescope. It serves to determine the situation with respect to some fixed line in the field of view, of the line joining any two objects or points of an object seen in that field—as two stars, for instance, near enough to be seen at once. For this purpose the moveable thread is placed so as to cover both of them, or stand, as may best be judged, parallel to their line of junction. And its angle, with the fixed one, is then read off upon a small divided circle exterior to the instrument. When such a micrometer is applied (as it most commonly is) to an equatorially mounted telescope, the zero of its position corresponds to a direction of the wire, such as, prolonged, will represent a circle of declination in the heavens and the "angles of position" so read off are reckoned invariably from one point, and in one direction, viz., north, following, south, preceding; so that 0° position corresponds to the situation of an object exactly north of that assumed as a centre of reference,-90° to a situation exactly eastward or following; 180° exactly south; and 270° exactly west, or preceding in the order of diurnal movement. CHAPTER IV. OF GEOGRAPHY. THE PENDULUM. OF THE FIGURE OF THE EARTH.-ITS EXACT DIMENSIONS.-ITS FORM- HEIGHTS BY THE BAROMETER. (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. Astronomical geography has for its objects the exact knowledge of the form and dimensions of the earth, the parts of its surface occupied by sea and land, and the configuration of the surface of the latter, regarded as protuberant above the occan, and broken into the various forms of mountain, table land, and valley; neither should the form of the bed of the ocean, regarded as a continuation of the surface of the land beneath the water, be left out of consideration: we know, it is true, very little of it; but this is an ignorance rather to be lamented, and, if possible, remedied, than acquiesced in, inasmuch as there are many very important branches of inquiry which would be greatly advanced by a better acquaintance with it. (207.) With regard to the figure of the earth as a whole, we have already shown that, speaking loosely, it may be regarded as spherical; but the reader who has duly appreciated the remarks in art. 22 will not be at a loss to perceive that this result, concluded from observations not susceptible of much exactness, and embracing very small portions of the surface at once, can only be regarded as a first approximation, and may require to be materially modified by entering into minutia before neglected, or by increasing the delicacy of our observations, or by including in their extent larger areas of its surface. For instance, if it should turn out (as it will), on minuter inquiry, that the true figure is somewhat elliptical, or flattened, in the manner of an orange, having the diameter which coincides with the axis about th part shorter than the diameter of its equatorial circle; -this is so trifling a deviation from the spherical form that, if a model of such proportions were turned in wood, and laid before us on a table, the nicest eye or hand would not detect the flattening, since the difference of diameters, in a globe of fifteen inches, would amount only to th of an inch. In all common parlance, and for all ordinary purposes, then, it would still be called a globe; while, nevertheless, by careful measurement, the difference would not fail to be noticed; and, speaking strictly, it would be termed, not a globe, but an oblate ellipsoid, or spheroid, which is the name appropriated by geometers to the form above described. 300 (208.) The sections of such a figure by a plane are not circles, but ellipses; so that, on such a shaped earth, the horizon of a spectator would nowhere (except at the poles) be exactly circular, bnt somewhat elliptical. It is easy to demonstrate, however, that its deviation from the circular form, arising from so slight an "ellipticity" as above supposed, would be quite imperceptible, not only to our eye-sight, but to the test of the dipsector; so that by that mode of observation we should never be led to notice so small a deviation from perfect sphericity. How we are led to this conclusion, as a practical result, will appear, when we have explained the means of determining with accuracy the dimensions of the whole, or any part of the earth. (209.) As we cannot grasp the earth, nor recede from it far enough to view it at once as a whole, and compare it with a known standard of mea |