Page:The American Cyclopædia (1879) Volume VI.djvu/364

 356 EARTH It follows from the measurements that the compression of the earth is very nearly ^. But it is believed that the compression is different for different longitudes; in other words, that the earth is not a figure of revolu- tion. It will be interesting for the reader to compare the following three sets of results : First, as the result of comparing the best mea- surements before the recent Indian and Rus- sian observations, we have Earth's equatorial diameter 41,843,330 ft, or 7, 924*873 m.; po- lar diameter, 41,704,788 ft., or 7,898-634 m. ; difference of diameters or polar compression, 138,542 ft., or 26*239 m. ; ratio of diameters, 302-026 : 301-026; compression, s^Vinr; length of degree at equator, 362,732 ft. ; length of degree in lat. 45, 364,543-5 ft. Secondly, Sir John Herschel thus states the results obtained by Capt. A. R. Clark, R. E., from a combina- tion of all the results which have been ob- tained, and especially those resulting from the recent extension of the great arcs surveyed in India and Russia : " The earth is not exactly an ellipsoid of revolution. The equator itself is slightly elliptic, the longer and shorter diame- ters being respectively 41,852,864 and 41,843,- 096 ft. The ellipticity of the equatorial cir- cumference is therefore 4g 1 83, and the excess of its longer over its shorter diameter about two miles. The vertices of the longer diameter are situated in Ion. 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 ft. in length ; and consequently the most elliptic meridian (that of Ion. 14 23' and 194 23' E. of Greenwich) has for its ellipticity ^s-V-j, an( l tae least elliptic (that of Ion. 104 23' and 284 23' E. of Greenwich) an ellipticity of rsW-" Thirdly, Gen. Schubert, in the me- moirs of the imperial academy of St. Peters- burg, arrives (by a mode of reasoning which Sir John Herschel regards as less exact) to a similar but not identical conclusion. "He makes the ellipticity of the equator -g-gWi" savs Herschel, "and places the vertices of the longer axis 26 41' to the eastward of Capt. Clark's. His polar axis, as deduced from each of the three great meridian arcs, the Russian, Indian, and French respectively, is 41,711,019 ft., 41,- 712,534 ft., and 41,697,496 ft., 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 ft." It may be added that the figure of the earth as thus determined accords well with the observed change of rate in a pendulum set swinging in different latitudes, as also with the observed values of precession and nutation (the motions of the earth's globe caused by the attraction of the sun and moon on the protuberant mass round the equator). Next to the determination of the earth's figure, that of her density may be regarded as the most important terrestrial problem which men of science have attempted to solve. Newton was the first to show how the problem might be attacked, since he first showed that a plum- met would be deflected from the vertical by the attraction of a mountain. But Bouguer (born 1698) was the first to suggest that the method should be put in practice with direct reference to the problem of determining the earth's mass. The method is applied by means of the instrument called a zenith sector, a tel- escope with a graduated arc attached to its lower extremity and a plumb line to the upper. This telescope, pointed to the same star suc- cessively at two stations separated by a known distance, serves to show how much the centre of gravity changes in passing from one to the other ; and it is known that for each 100 ft. of horizontal distance on a north and south line, the change of direction is very nearly one sec- ond of angle. But if one of the stations be at the foot of a mountain, the same change of di- rection is not observed, because the attraction of the mountain deflects the plumb line ; and the effect is even greater if both the stations lie at the foot of a mountain, one on the north- ern side and the other on the southern. Thus, let us suppose that the two stations are sepa- rated by 4,000 ft. ; then the difference in the direction of gravity would be about 40" if the stations were on a plain ; but if a mountain separates them, this difference will be in- creased, because the positions of the lower ends of the plumb line, already tending to con- vergence in consequence of the fact that the earth's gravity is directed always toward the centre of the earth, are brought yet nearer to- gether by the mountain's attraction. If this difference is carefully determined, and if the geological structure of the mountain is known, as well as its general shape and dimensions, it becomes possible to compare the density of the earth with the known mean density of the mountain. This method was first applied by Bouguer in 1738, on the flanks of Chimborazo; but as both his stations were on the southern side, he was unable to determine the direction of the plumb line by means of such an instru- ment as the zenith sector; he failed accord- ingly to obtain any trustworthy results. But in 1772 Dr. Maskelyne proposed to the royal society to renew the experiment on some moun- tain in Great Britain. Schehallien was select- ed, and after a careful series of measurements and observations it was found that at stations separated by 4,364-4 ft. the difference in the direction of gravity was 54-6" instead of 42 "94", the difference due to gravity ; so that the dou- ble attraction exerted by the mountain was found to be 11'6". By a series of calculations devised by Cavendish and carried out by Dr. Hutton, the density of the earth was computed to be to that of the mountain as 17.804 to 9,933 ; and after carefully examining the geo- logical structure of Schehallien, Dr. Playfair inferred the probable mean specific gravity of the earth to lie between 4'56 and 4-87, that of water being unity. More recently Col. James, superintendent of the ordnance survey in Great Britain, has deduced a mean density