which, he deduced this conclusion, on which, however, very
little reliance can be placed.The atmosphere of Venus has been analysed with the spectroscope by Vogel, and the existence of aqueous vapour is regarded as demonstrated. On the occasion of the late transit (1874) Tacchirii made spectroscopic observations, which seem more satisfactorily to establish the fact that there is water on Venus, than Vogel s observations.
Cassini and Montaigne imagined that they had observed a satellite accompanying Venus ; but this appears to have been an optical illusion arising from the strong light of the planet reflected back from the convex surface of the eye upon the eye-glass of the telescope, and thence reflected a second time back to the eye. During the transits of Venus in 1761 and 1769, and in the late transit of 1874, no trace of a satellite was seen ; and there can be now no doubt whatever that Venus is without a satellite.
The earth is the third member of the solar system in order of distance from the sun. From what has been already shown, in determining the relative position of the earth and the celestial bodies seen in our skies, we know that the earth is a globe, rotating on her axis once in a day, and circling around the sun in an orbit of great extent ouce in a year. In the present chapter we propose to present the results of more exact inquiries into the figure and motions of the earth.
It has been found by numerous and accurate experiments, that the lengths of arcs of 1 on the same meridian are greater in proportion as we advance nearer the pole. Hence, on account of the similarity of the isosceles triangles of which these arcs form the bases, their sides, or the terrestrial radii, must also be longer, and consequently the convexity of the earth is less towards the poles than at the equator. The surface of the earth is extremely irregular, even independently of the inequalities occasioned by mountains and cavities ; yet it has been discovered that the meridional curves differ almost insensibly from ellipses ; whence it is concluded that the figure of the earth is an ellipsoid of revolution about its shortest axis. In compar ing the results of the various measurements which have been made with the formulae belonging to the dimensions of such a body, this conclusion has been fully verified ; and the lengths of the arcs, the ellipticity, the distance of the pole from the equator, and, in short, all the elements of the spheroid, have been determined.
An arc of the meridian in India was measured by Colonel Lambton in the early part of this century. But its value has been much increased by Colonel Everest s extension of the arc. The arc of Lambton, extending from Punnae (lat. 8 9 35") to Damargida (lat. 18 3 15"), was measured after the model of the English trigonometrical survey. From Damargida, where Lambton s arc terminated, another was measured by Colonel Everest to Kaliana (lat. 29 30 48"), a space of 797 miles, covering an arc of 11 27 33", the latest geodetical improvements being introduced. The whole extent of Lambton s and Colonel Everest s operations includes a continuous arc of 21 21 (1477 miles). The work was rivalled in extent by a vast operation executed in Russia and other northern countries of Europe, by which an arc of 25 20 , extending from the banks of the Danube to the shores of the Arctic Sea, near the North Cape, was measured under the general super intendence and direction of W. Struve.
The arcs of India and of Russia include a space from lat. 8 to lat. 7 1 3 , with the exception of only about sixteen degrees, and are unquestionably the most important which exist for the determination of the earth s figure. When to them we add the French arc of 12 22 in a medium latitude, it will scarcely be necessary to take into account any other, at least for the northern hemisphere.
The following brief details of the Russian arc are taken from M. Struve s report of 1852:—
The southern extremity of the Russo-Scandinavian arc is Ismail on the Danube (lat. 45 20 ), the northern ex tremity is Fuglenaes, on the island of Qualoe, in Finn- marken (lat. 70 40 ). The interval from Tornea to Fuglenaes (4 49 ) was measured by Swedish and Norwegian engineers ; all the remainder by those of Russia, and, in particular, by M. Von Tenner, who, with M. Struve, from 1816 directed the whole operation.
The calculation of the figure of the earth from the com pleted Russian arc indicates an ellipticity somewhat greater than that generally received. The results obtained by Colonel Everest, on the other hand, by comparing his arc with those of Europe, give generally small ellipticities, that is, under -3^. The French and Indian arcs, for instance, give -gig-. The determinations by means of the pendulum are somewhat larger. The extensive observations of Colonel Sabine and Captain Foster concur in giving an ellipticity of ^-g-y-, but the French experiments by Duperrey and Freycinet lead to a result considerably greater. The discrepancy between the geodetical and pendulum results may, of course, be a real one depending on local variations of density. The astronomical determination from the lunar inequalities, which might be expected to concur with the results of the pendulum, gives -g-^-g- as a mean. Captain A. R. Clark, R.E., combining all the results obtained up to the year 1860, arrived at conclusions thus stated by Sir J. Herschel : " The earth is not exactly an ellipsoid of revolution. The equator itself is slightly elliptic, the longer and shorter diameters being respectively 41,852,864, and 41,843,096 feet. The ellipticity of the equatorial cir cumference is therefore ---5-5, and the excess of its longer over its shorter diameter about two miles. The vertices of the longer diameter are situated in longitude 14 23 E. and 194 23 E. of Greenwich, and of its shorter in 104 23 E. and 284 23 E. The polar axis of the earth is 41,707,796 feet in length, and consequently the most elliptic meridian (that of longitude 14 23 and 194 23 ) has for its elliptieity -5-^.5-, an d the least (that of longitude 104 23 and 284 23 ) an ellipticity of j^.^"
General Schubert, using a method which Sir J. Herschel justly regards as less trustworthy, " makes the ellipticity of the equator y-gVs , and places the vertices of the longer axis 26 41 to the eastward of Captain Clark s. His polar axis, as deduced from each of the three great meridian arcs, the Russian, Indian, and French respectively, is 41,711,000 feet, 41,712,534 feet, and 41,697,496 feet, the mean of which, giving to each a weight proportional to the length of the arc from which it is deduced, is 41,708,710 feet."
The figure and volume of the earth being thus determined, Earth s we require only to ascertain its mean density in order to mass . and know its mass. But this problem has not been solved, densit y- probably cannot be solved, with any very near approach to exactness. Various methods have been employed, the mere description of which suffices to show the difficulty and uncertainty of the subject.
neighbourhood of a mountain had been pointed out by
Newton[1] as a direct method of dealing with the problem of- ↑ De Mundi Systemate, 22. Newton, in a very remarkable passage of the Third Book of the Principia (Prop. X.), conjectures that " the quantity of matter in the earth may be five or six times greater than if the whole were composed of water."
