The spheroidal form of the earth has also been proved by the variation in the lengths of pendulums for vibrat ing seconds in different parts of the earth. This was first discovered by Richer, who found that his pendu lum vibrated slower at Cayenne than at Paris, and that it was necessary to diminish its length in order to make it vibrate seconds. From a great number of observa tions, the length of a pendulum vibrating seconds at the equator is 439.224 lines, and the length of a pendu lum vibrating seconds at the poles 441.522 lines of a Paris foot. Hence it follows, that the force of gravity which causes the pendulum to vibrate is greater at the poles than at the equator; that the poles are nearer the earth than the equator; and that the earth is an oblate spheroid.
The compression of the earth's poles, and the accu mulation of matter at the equator, evidently arise from its diurnal rotation. The gravity of the equatorial parts is diminished by the centrifugal force arising from their rapid motion, while the gravity at the poles suffers no diminution. If the earth, therefore, were fluid, it would obviously assume a spheroidal form; and though we are not entitled to say, that it ever was in such a soft state as to yield to the effects of the centrifugal force, yet it is manifest, that even if it were originally spherical, and in its present consolidated state, it trwt have constantly been approximating to a spheroid.* form. Sec La Lunde Vistronomie,§ 2630, vol. iii. p. 1; La Place Sys teme tit Monde, p. 57; and Playfair, Edinburgh Trans. vol. v. p. 1. See also Physical ASTRONOMY, chap. vi; and EARTH.
In the article ATMOSPHERE, we intend giving a ge neral account of the chemical and physical properties of the mass of air which surrounds our globe. We shall now attend more particularly to those parts of the subject which are connected with astronomy.
As the atmosphere extends to a height of about 50 miles, and increases in density towards the surface of the earth, the light which is emitted from the sun, or planets, must suffer some change in passing through this immense refracting medium. Let us suppose that the atmosphere consists of beds of different densities A, B, C, ll, Plate XXXIX. Fig. 2. and that a ray of light RS enters it at S. Then, as the medium at S is denser than the medium at R, the ray will be bent or refracted into the direction ST, towards the perpendi Cular Sl. The medium at T being denser than at S, it
will be again bent at T, in the direction TU, towards the perpendicular T2. At U and V it will in like man ner be bent towards the perpendiculars U3, V4, so that it will arrive at the spectator at 0, in the direction VO ; and as objects are always seen in the direction of the ray which enters the eye, the ray RS, which has now been refracted into the direction Vo, will be seen in the line OVr. But since the density of the atmosphere in creases regularly, and is not composed of a succession of beds, the path of the ray, instead of being a polygon, RSTUVO will be a curve, and the object at R will be seen in the direction of the tangent to the curve, at the point 0 ; for the last elementary portion of the curve at O will coincide with the tangent. Therefore, if 0 be the spectator, H his horizon, the ray of light RS, enter ing the atmosphere at S, will move in the curve STO, and the object at R will be seen in the direction of the tangent Or; but RO is the path in which the ray would have reached the eye had there been no atmosphere ; therefore ROH is the real altitude of the sun, rOH the apparent altitude arising from refraction, and ROr the angle of refraction, or the difference between the true and apparent altitudes. This angle is obviously great est in the horizon, amounting to about 30'51", for the ray enters the atmosphere obliquely, and passes through a greater portion of it. At an altitude of 45° it amounts only to 57"; and in the zenith there is evidently no re fraction, as the rays enter the atmosphere perpendicu larly. These phenomena may be very simply illustrated, by placing a small body in the bottom of a vessel, and retiring to such a distance that it is just covered by the edge of the vessel. If water is poured into the vessel by another person, the rays proceeding from the object will be refracted upwards, and the object will become visible. The elevation of the object by the refraction of the water will be found less, in proportion as the eye of the observer approaches to a line perpendicular to the fluid surface. The effects produced in this experi ment are exactly the reverse of what takes place in the atmosphere ; for the body which emits the light is placed in the dense medium, and the observer in the rare one, from which cause the rays are bent from the perpendicular.