wires to coincidence with the image of those of the collimator by an appropriate mechanism communicating the requisite small amount of movement to the speculum in its cell.* See Phil. Trans, 1833, pp. 448-9, where this application of the collimating principle used by the author since 1833, is first described. See also “ Results of astronomical observation at the Cape of Good Hope,” preface, p. xiv. It is to be presumed that Mr. Stoney in bringing before the British Association in 1856, this application of the collimating principle as a novelty has been unaware of this its prior use since he has not alluded to it. The direct reference of objects to the collimating cross, described in the text, would seem to have been overlooked by him. These remarks apply to the report of the contents of his paper published in the “ Athenæum" of August 30th, 1856. CHAPTER IV. OF GEOGRAPHY. OF THE FIGURE OF THE EARTH. — ITS EXACT DIMENSIONS. — ITS FORM THAT OF EQUILIBRIUM MODIFIED BY CENTRIFUGAL FORCE. VARIATION OF GRAVITY ON ITS SURFACE. STATICAL AND DYNAMICAL MEASURES OF GRAVITY. -THE PENDULUM.-GRAVITY TO A SPHEROID. OTHER EFFECTS OF THE EARTH'S ROTATION. -TRADE WINDS. DETERMINATION OF GEOGRAPHICAL POSITIONS. OF LATITUDES. OF LONGITUDES. CONDUCT OF A TRIGONOMETRICAL SURVEY.-OF MAPS. - PROJECTIONS OF THE SPHERE. MEASUREMENT OF 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 compre , hends 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 K 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 ocean, 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 minutiæ 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 zooth 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 tth 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. a (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, but somewhat elliptical. It is easy to demonstrate, however, that its deviation from the circular form, arising from so very slight an “ellipticity” as above supposed, would be quite imperceptible, not only to our eyesight, but to the test of the dip-sector; 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 measure in any degree commensurate to its own size, but can only creep about upon it, and apply our diminutive measures to comparatively small parts of its vast surface in succession, it becomes necessary to supply, by geometrical reasoning, the defect of our physical powers, and from a delicate and careful measurement of such small parts to conclude the form and dimensions of the whole mass. This would present little difficulty, if we were sure the earth were strictly a sphere, for the proportion of the circumference of a circle to its diameter being known (viz. that of 3•1415926 to 1.0000000), we have only to ascertain the length of the entire circumference of any great circle, such as a meridian, in miles, feet, or any other standard units, to know the diameter in units of the same kind. Now, the circumference of the whole circle is known as soon as we know the exact length of any aliquot part of it, such as 1° or zooth part; and this, being not more than about seventy miles in length, is not beyond the limits of very exact measurement, and could, in fact, be measured (if we knew its exact termination at each extremity) within a very few feet, or, indeed, inches, by methods presently to be particularized. (210.) Supposing, then, we were to begin measuring with all due nicety from any station, in the exact direction of a 0 . meridian, and go measuring on, till by some indication we were informed that we had accomplished an exact degree from the point we set out from, our problem would then be at once resolved. It only remains, therefore, to inquire by what indications we can be sure, lst, that we have advanced an eract degree ; and, 2dly, that we have been measuring in the exact direction of a great circle. (211.) Now, the earth has no landmarks on it to indicate degrees, nor traces inscribed on its surface to guide us in such a course. The compass, though it affords a tolerable guide to the mariner or the traveller, is far too uncertain in its indications, and too little known in its laws, to be of any use in such an operation. We must, therefore, look outwards, and refer our situation on the surface of our globe to natural marks, external to it, and which are of equal permanence and stability with the earth itself. Such marks are afforded by the stars. By observations of their meridian altitudes, performed at any station, and from their known polar distances, we conclude the height of the pole; and since the altitude of the pole is equal to the latitude of the place (art. 119.), the same observations give the latitudes of any stations where we may establish the requisite instruments. When our latitude, then, is found to have diminished a degree, we know that, provided we have kept to the meridian, we have described one three hundred and sixtieth part of the earth's circumference. (212.) The direction of the meridian may be secured at every instant by the observations described in art. 162. 188.; and although local difficulties may oblige us to deviate in our measurement from this exact direction, yet if we keep a strict account of the amount of this deviation, a very simple calculation will enable us to reduce our observed measure to its meridional value. (213.) Such is the principle of that most important geographical operation, the measurement of an arc of the meridian. In its detail, however, a somewhat modified course must be followed. An observatory cannot be mounted and dismounted at every step ; so that we cannot identify and measure an exact degree neither more nor less. But this is |