The Cavendish experiment, as it is often called, has since been repeated by various other experimenters in modified forms, and one or two other methods, too technical to be described here, have also been devised. All the best modern experiments give for the density numbers converging closely on 5-1∕2, thus verifying in a most striking way both Newton’s conjecture and Cavendish’s original experiment.
With this value of the density the mass of the earth is a little more than 13 billion billion pounds, or more precisely 13,136,000,000,000,000,000,000,000 lbs.
220. While Greenwich was furnishing the astronomical world with a most valuable series of observations, the Paris Observatory had not fulfilled its early promise. It was in fact suffering, like English mathematics, from the evil effects of undue adherence to the methods and opinions of a distinguished man. Domenico Cassini happened to hold several erroneous opinions in important astronomical matters; he was too good a Catholic to be a genuine Coppernican, he had no belief in gravitation, he was firmly persuaded that the earth was flattened at the equator instead of at the poles, and he rejected Roemer’s discovery of the velocity of light. After his death in 1712 the directorship of the Observatory passed in turn to three of his descendants, the last of whom resigned office in 1793; and several members of the Maraldi family, into which his sister had married, worked in co-operation with their cousins. Unfortunately a good deal of their energy was expended, first in defending, and afterwards in gradually withdrawing from, the errors of their distinguished head. Jacques Cassini for example, the second of the family (1677-1756), although a Coppernican, was still a timid one, and rejected Kepler’s law of areas; his son again, commonly known as Cassini de Thury (1714-1784), still defended the ancestral errors as to the form of the earth; while the fourth member of the family, Count Cassini (1748-1845), was the first of the family to accept the Newtonian idea of gravitation.
Some planetary and other observations of value were made by the Cassini-Maraldi school, but little of this work was of first-rate importance.
221. A series of important measurements of the earth, in which the Cassinis had a considerable share, were made during the 18th century, almost entirely by Frenchmen, and resulted in tolerably exact knowledge of the earth’s size and shape.
The variation of the length of the seconds pendulum observed by Richer in his Cayenne expedition (chapter VIII., ([§ 161]) had been the first indication of a deviation of the earth from a spherical form. Newton inferred, both from these pendulum experiments and from an independent theoretical investigation (chapter IX., [§ 187]), that the earth was spheroidal, being flattened towards the poles; and this view was strengthened by the satisfactory explanation of precession to which it led (chapter IX., [§ 188]).
On the other hand, a comparison of various measurements of arcs of the meridian in different latitudes gave some support to the view that the earth was elongated towards the poles and flattened towards the equator, a view championed with great ardour by the Cassini school. It was clearly important that the question should be settled by more extensive and careful earth-measurements.
The essential part of an ordinary measurement of the earth consists in ascertaining the distance in miles between two places on the same meridian, the latitudes of which differ by a known amount. From these two data the length of an arc of a meridian corresponding to a difference of latitude of 1° at once follows. The latitude of a place is the angle which the vertical at the place makes with the equator, or, expressed in a slightly different form, is the angular distance of the zenith from the celestial equator. The vertical at any place may be defined as a direction perpendicular to the surface of still water at the place in question, and may be regarded as perpendicular to the true surface of the earth, accidental irregularities in its form such as hills and valleys being ignored.[123]
The difference of latitude between two places, north and south of one another, is consequently the angle between the verticals there. Fig. 78 shews the verticals, marked by the arrowheads, at places on the same meridian in latitudes differing by 10°; so that two consecutive verticals are inclined in every case at an angle of 10°.