triangles. A theodolite measures the angles accurately. The stations from which the angles are observed should be so selected that none of the angles shall be very small, otherwise a slight mistake in an angle causes a great error in the opposite side of the triangle. Toward the conclusion of the process one of the sides of one or more of the triangles is measured and its length compared with that found by computation. This base of verification is taken as far distant from the first base as circumstances will admit. In one of the French operations the base of verification was between four and five hundred miles distant from the first base, and was seven miles in length, and yet the difference between its computed length and that obtained from its actual measurement did not amount to twelve inches.

§ 231. The following particulars show the accuracy which distinguishes these operations and the means taken to ensure it. A base of five miles in length was measured in Hounslow Heath with a steel chain of exquisite workmanship. The same base had been measured three years before with glass rods, and the two measurements differed only 2 inches. Sometimes rods of platina or of iron are used for measuring, and an allowance is made for the changes of temperature affecting the rods in the course of the operation. In later measurements rods composed of different metals put together so as to show the slightest contraction or expansion have been used.

In 1735 two scientific expeditions were sent from France, to determine the length of a degree of longitude in different latitudes. One degree was to be observed upon the equator, the other as near the poles as possible. One degree was measured in the valley of the river Tornea in Lapland. The base was measured on the frozen surface of the river, with a view to obtain as level a plain as possible; and rods of deal were employed instead of metal on account of the extreme cold. Two independent measures by two sets of observers differed only four inches. These operations were completed several years before the return of the Peruvian expedition, which had to contend with extraordinary difficulties caused by the ill-will and indolence of the natives, and by the localities. Their station was a

mile and a half above the level of the sea, and in some instances the heights of two neighboring signals differed more than a mile. To accomplish their measurements occupied nine years, three of which were employed in the determination of latitudes alone.

At the beginning of the French revolution, a measurement was made from Dunkirk to Barcelona, in order to ascertain the length of a quadrant of a meridian, and take the ten millionth part of it as a metre or universal standard. A metre contains 39.37 inches. This method of obtaining a standard of measure is not so good as the English mode, which consists in observing the length of the pendulum, which in a certain latitude, (that of London,) in a vacuum at the level of the sea beats seconds of mean time. The length of the pendulum is ascertainable without the use of any linear measure whatever; whereas in determining the French standard or the quadrant of the meridian, some linear measure already in use must be employed. And thus the very basis of their new system is expressed in terms of that in the place of which it is substituted. Arcs of longitude have also been measured in various other latitudes, and their observed lengths agree with their theoret ical lengths.

§ 232. By measuring degrees of the meridian we obtain the compression of the earth, while pendulum observations give us the ellipticity confounded with the effects of centrifugal force. The motions of the moon confirm the shape assigned to the earth. They cannot be accounted for on the supposition that the earth is a sphere, but they agree perfectly with the supposition that it is a spheroid. The ellipticity inferred from the lunar inequalities has an advantage not possessed either by measurements of degrees or by pendulum experiments, in being independent of local accidents, and thus showing the mean ellipticity of the

earth.

CHAPTER XI.

GENERAL PHENOMENA ON THE EARTH'S SURFACE.

Universal diffusion of Gravity over the Earth's Surface. Determination of the Earth's Mass and Density. Our Knowledge of the Earth's Surface. The Sea. Tides. Stability of the Ocean's Equilibrium. The Atmosphere. Clouds. Winds. Trade Winds. Use of the Atmosphere. Absorption and Diffusion of Light and Heat. Refraction. Twilight.

§ 233. The earth's exact diameter is important as a unit of measure for other bodies; its density is no less so as a standard of comparison for other planets.

The powerful attraction which the earth, in consequence of its superior bulk, has for bodies on its surface, prevents our perceiving the attraction they exercise on one another. It may be shown however by balancing a small mass in such a manner that it may be moved by the slightest influence, and then bringing a large body into its neighborhood; or by ascertaining the deflection of the plumb line caused by the vicinity of a mountain; or by comparing the length of a pendulum vibrating seconds in a plain, and on the summit of a mountain. A balance of torsion is in fact a horizontal pendulum. It may be applied to a mountain or to much smaller attracting bodies. If two equal balls of lead are suspended from the opposite extremities of a slender bar of wood, and this is suspended at its centre by a very fine wire, the only force required to move the balls will be that which suffices to produce a slight twisting of the wire that suspends the rod. Now if a large mass of lead be brought into the neighborhood of each ball, (the rod having been previously hanging at rest,) its attraction will cause the rod to turn round, until the small balls have come into the same line with the large masses. If the masses be now moved a little further, the balls will follow them; twisting the wire from which the rod is suspended still more. Now, as the force which is required to produce any amount of alteration in the position of the rod can be

ascertained in another way, the actual amount of the attraction which the masses exercise over the balls may be determined; and this may be compared with the earth's attraction. From the knowledge of these facts, the quantity of matter in the earth may be compared with that in the masses of lead; for the weight of the earth is just as much greater than that of the masses of lead, as the force with which it attracts the balls exceeds that with which the masses attract them, proper allowance being made for their difference of distance. When the actual weight of the earth is known, we may estimate its density as compared with water; since we may easily calculate the weight of a globe of water of equal size. And from the weight and density of the earth, that of the other planets and of the sun may be ascertained.

§ 234. A beautiful proof that the attraction of gravity is diffused through separate portions of the earth is the fact that mountains draw a plumb line out of the perpendicular.

By ascertaining the exact amount of the deviation and obtaining the specific weight of the mountain, the specific weight of the earth, or its weight compared with the mountain and consequently with a globe of water of the same size, may be learned. The mountain Schehallien in Scotland was thus examined. It was measured from its base to its summit, its component parts examined, and its specific gravity determined. Assuming that the spirit in the levels of the instruments would be attracted toward the mountain, or that the plumb lines by which the instruments are rectified would deviate from a perpendicular to the horizon, it is plain that observations on the fixed stars, taken on opposite sides of the mountain, would differ from each other by double the amount of deviation.

§ 235. The meridian zenith distances of certain stars were observed first on the north and then on the south side of the mountain. They gave a constant error of 11" more than could be accounted for by the difference in latitude of the stations. The mountain therefore deflected the plumb lines from the perpendicular 53". From the actual attraction of the mountain its attraction

at the distance of the earth's centre was to be calculated. The comparative powers of attraction of the earth and the mountain, and their relative sizes being known, their relative densities could be determined. After a year's labor in reducing these data it was found that the density of the earth was to that of the mountain as five to three, or nearly five times the density of water, or nearly double that of rocks near the surface. It is of about the density of silver ore throughout. Since the density of the earth is so much greater than the average specific gravity of rocks on the surface, it follows that the internal matter must be more dense than the superficial layers.

§ 236. While we thus by reasoning learn the size and mass of the earth, how little do we actually know of it. Even its surface is not yet wholly known to us. The ancients thought a fiery impassable zone separated the northern from the southern regions; the polar circles have proved equally impenetrable to the most zealous efforts of the moderns. The interiors of the continents are yet unexplored, so that enough remains to stimulate the curiosity and enterprise of man for ages yet to come. Enough of the surface has been explored to prove to us that its nature is every where the same. Every where there are traces of convulsive change; every where fire and water leave their traces. Huge rocks have been melted and cast up; water has worn them away and left the sand and the pebbles to tell of the slow destruction it has wrought. To water also we owe all the plains and habitable spots of the earth. It is still busy bringing all things to its own level. All over the globe there is no sameness, each country has its characteristic scenery, every where there is variety. Even the bottom of the sea has its risings and its abysses, fit abodes now for its varied inhabitants, and perhaps the peaks and valleys of a world to be upheaved hereafter. But beyond this very outer surface we cannot penetrate. The deepest mines are but as a scratch on the surface of a model globe, the highest mountains are not five miles high. The ocean has not been sounded below 27,600 feet. The deepest mines do not penetrate more than 2,231 English feet, or ‰ of the earth's radius be