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trigonometrical measurement of the differences of level of all the stations of a survey; the other, by the use of the barometer, the principle of which is, in fact, identical with that of the sounding line. In both cases we measure the distance of the point whose level we would know from the surface of an equilibrated ocean: only in the one case it is an ocean of water; in the other, of air. In the one case our sounding line is real and tangible; in the other, an imaginary one, measured by the length of the column of quicksilver the superincumbent air is capable of counterbalancing.

(238.) Suppose that instead of air, the earth and ocean were covered with oil, and that human life could subsist under such circumstances. Let ABCDE be a


continent, of which the portion ABC projects above the water, but is covered by the oil, which also floats at an uniform depth on the whole ocean. Then if we would know the depth of any point D below the sea level, we let down a plummet from F. But if we would know the height of B above the same level, we have only to send up a float from B to the surface of the oil; and having done the same at C, a point at the sea level, the difference. of the two float lines gives the height in question.

(239.) Now, though the atmosphere differs from oil in not having a positive surface equally definite, and in not being capable of carrying up any float adequate to such an use, yet it possesses all the properties of a fluid really essential to the purpose in view, and this in particular, - that, over the whole surface of the globe, its strata of equal density are parallel to the surface of

equilibrium, or to what would be the surface of the sea, if prolonged under the continents, and therefore each or any of them has all the characters of a definite surface to measure from, provided it can be ascertained and identified. Now the height at which, at any station B, the mercury in a barometer is supported, informs us at once how much of the atmosphere is incumbent on B, or, in other words, in what stratum of the general atmosphere (indicated by its density) B is situated : whence we are enabled finally to conclude, by mechanical reasoning *, at what height above the sea. level that degree of density is to be found over the whole surface of the globe. Such is the principle of the application of the barometer to the measurement of heights. For details, the reader is referred to other works. +

(240.) Possessed of a knowledge of the heights of stations above the sea, we may connect all stations at the same altitude by level lines, the lowest of which will be the outline of the sea-coast; and the rest will mark out the successive coast-lines which would take place were the sea to rise by regular and equal accessions of level over the whole world, till the highest mountains were submerged. The bottoms of valleys and the ridgelines of hills are determined by their property of inter. secting all these level lines at right angles, and being, subject to that condition, the shortest and longest courses respectively which can be pursued from the summit to the sea. The former constitute the watercourses of a country; the latter divide it into drainage basins : and thus originate natural districts of the most ineffaceable character, on which the distribution, limits, and peculiarities of human communities are in great measure dependent.

* See Cab. Cycl. PNEUMATICS, art. 143.

+ Biot, Astronomie Physique, vol. 3. For tables, see the work of Biot cited. Also those of Oltmann, annually published by the French board of longitudes in their Annuaire; and Mr. Baily's Collection of Astronomical Tables and Formulæ.








(241.) The determination of the relative situations of objects in the heavens, and the construction of maps and globes which shall truly represent their mutual configurations, as well as of catalogues which shall preserve a more precise numerical record of the position of each, is a task at once simpler and less laborious than that by which the surface of the earth is mapped and measured. Every star in the great constellation which appears to revolve above us, constitutes, so to speak, a celestial station; and among these stations we may, as upon the earth, triangulate, by measuring with proper instruments their angular distances from each other, which, cleared of the effect of refraction, are then in a state for laying down on charts, as we would the towns and villages of a country: and this without moving from our place, at least for all the stars which rise above our horizon.

(242.) Great exactness might, no doubt, be attained by this means, and excellent celestial charts constructed ; but there is a far simpler and easier, and, at the same time, infinitely more accurate course laid open to us, if we take advantage of the earth's rotation on its axis, and by observing each celestial object as it passes our meridian, refer it separately and independently to

the celestial equator, and thus ascertain its place on the surface of an imaginary sphere, which may be conceived to revolve with it, and on which it may be considered as projected.

(243.) The right ascension and declination of a point in the heavens correspond to the longitude and latitude of a station on the earth; and the place of a, star on a celestial sphere is determined, when the former elements are known, just as that of a town on a map, by knowing the latter. The great advantages which the method of meridian observation possesses over that of triangulation from star to star, are, then, 1st, That in it every star is observed in that point of its diurnal course, when it is best seen and least displaced by refraction. 2dly, That the instruments required (the transit and mural circle) are the simplest and least liable to error or derangement of any used by astronomers. 3dly, That all the observations can be made systematically, in regular succession, and with equal advantages; there being here no question about advantageous or disadvantageous triangles, &c. And, lastly, That, by adopting this course, the very quantities which we should otherwise have to calculate by long and tedious operations of spherical trigonometry, and which are essential to the formation of a catalogue, are made the objects of immediate measurement. It is almost needless to state, then, that this is the course adopted by astronomers.

(244.) To determine the right ascension of a celestial object, all that is necessary is to observe the moment of its meridian passage with a transit instrument, by a clock regulated to exact sidereal time, or reduced to such by applying its known error and rate. The rate may be obtained by repeated observations of the same star at its successive meridian passages. The error, however, requires a knowledge of the equinox, or initial point from which all right ascensions in the heavens reckon, as longitudes do on the earth from a first meria dian.


(245.) The nature of this point will be explained presently; but for the purposes of uranography, in so far as they concern only the actual configurations of the stars inter se, a knowledge of the equinox is not necessary. The choice of the equinox, as a zero point of right ascensions, is purely artificial, and a matter of convenience : but as on the earth, any station (as a national observatory) may be chosen for an origin of lon.. gitudes ; so in uranography, any conspicuous star may be selected as an initial point from which hour angles may be reckoned, and from which, by merely observing differences or intervals of time, the situation of all others may be deduced. In practice, these intervals are affected by certain minute causes of inequality, which must be allowed for, and which will be explained in their proper places.

(246.) The declinations of celestial objects are obtained, 1st, By observation of their meridian altitudes, with the mural circle, or other proper instruments. This requires a knowledge of the geographical latitude of the station of observation, which itself is only to be obtained by celestial observation. 2dly, And more directly by observation of their polar distances on the mural circle, as explained in art. 136., which is independent of any previous determination of the latitude of the station ; neither, however, in this case, does observation give directly and immediately the exact declinations. The observations require to be corrected, first for refraction, and moreover for those minute causes of inequality which have been just alluded to in the case of right ascensions.

(247.) In this manner, then, may the places, one among the other, of all celestial objects be ascertained, and maps and globes constructed. Now here arises a very important question. How far are these places permanent ? Do these stars and the greater luminaries of heaven preserve for ever one invariable connection and relation of place inter se, as if they formed part of a solid though invisible firmament; and, like the great

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