Page:Popular Science Monthly Volume 17.djvu/306

292 rotation. It was found, however, that Clark's calculations were considerably affected by certain anomalies probably existing in some of the geodetic calculations employed, and it seems that a majority of those competent to judge in these matters endorse the theory of a revolving ellipsoid.

By the term "figure of the earth" is understood the geometrical form of an ideal surface coinciding with the mean level of the sea, and prolonged in thought beneath the continents. In fact, geodetic calculations are always reduced to the sea-level, the altitudes of the stations being first determined from levels based on the nearest coast-line. The great difficulty is to accurately determine this level for a given station. For a long time it was supposed that the surface of the open sea was a horizontal; in other words, that it was parallel to the surface of liquids in repose, and perpendicular to the direction of the plummet line. But this definition is insufficient, as may easily be shown. The apparent vertical indicated by the plummet-line or determined at the level of the sea, is simply the direction of weight, which may be materially affected by local attractions due to an irregular distribution of the masses composing the soil. The vicinity of a mountain will deflect the plummet to a considerable degree, and a subterranean cavity may cause a deflection in the opposite way.

Let us now imagine the continents divided by a network of canals that connect all the seas, thus making of them one continuous sheet of water, as it were. Setting aside, for the purpose of the illustration, the oscillations caused by the tides, this sheet of water, assumed to be immovable, which represents the mean level of the sea, will exhibit elevations and depressions attributable to the local influences that deflect the plummet-line. The attraction of the continents causes a notable elevation of the sea-level along the coast, and a proportionate lowering of the mid-ocean. This influence of continents was described by M. Saigey in 1842, who gave as the probable height of the sea on the coasts of Europe thirty-six metres. Seven years later Mr. Stokes, the celebrated English physicist, attacked the question, bringing to bear upon it all the resources of mathematical analysis; and Philipp Fischer, in 1868, estimated that the disturbance of level due to the attraction of continents might amount to nine hundred metres. The mean level of the sea is, therefore, in all probability, an irregularly undulated surface, and the ideal or geometrical surface of the earth a regular spheroid, deviating but little from this average level, the accidental irregularity of which is in some way equalized.

The triangulations by which the terrestrial arcs are measured define the dimensions and configuration of this spheroid by the comparison of distances measured on the earth with the corresponding angular amplitude ascertained from the astronomical latitudes and longitudes of the stations. The most delicate part of the operations consists in ascertaining the local attractions that cause the deviations of the