276 A Short History of Astronomy [CH. x. 



in which the Cassinis had a considerable share, were made 

 during the i8th 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 vin., 

 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 cham- 

 pioned 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 i 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.* 



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 



* It is important for the purposes of this discussion to notice that 

 the vertical io not the linf drawn from the centre of the earth to the 

 place of observation. 



