On the Figure of the Earth. 293 
this line, as upon a base, he erects, in the direction of the meri- 
dian, a series of triangles, whose sides are successively connected, 
so that he can find the whole length of the arc of the meridian 
which crosses them. Having found the length of this arc, by 
whatever method he chooses to adopt, he then determines, by 
astronomical observations—not by a few, but by many thousands, 
the stars, or, to speak with more precision, the points in the hea- 
vens, towards which the two verticals produced to their two.ex- 
tremes are directed. But, since the earth is absolutely a mathe- 
matical point, when compared to infinite space, the arc of the- 
heavens, intersected by the produced ‘parts of the verticals, is the 
same as that which might be observed from their point of con- 
course. He thus measures the angle which they include, and the 
instruments give the number. of degrees, minutes, seconds, and . 
even fractions of seconds, which correspond to it : for it is neces- 
sary to observe the most scrupulous precision, when we are mea- 
suring an object so immense by means.so diminutiye. Similar 
observations, repeated on various points of the same arc of the - 
meridian, discover how the verticals produced to these points 
incline mutually in given distances ; but the law of these inclina- 
tions is precisely the geometrical character which specifies the 
curvature, and the degree of curvature of the earth’s surface, in 
the direction of the meridian, which has been taken. Operations 
analogous to this will also give this curvature in other directions, 
—for example, from east to west, by following the course of the 
same parallel, as is done at present from Brest to Strasburgh : 
and the united results so obtained, in different countries, com- 
pletely determine the form of the earth. 
‘The other method, founded upon observations of the pen- 
dulum, is more circuitous, and appears, at first view, to have no 
connection with the proposed object. In this method we have 
nothing to do with bases, triangles, or with any geometrical. or 
actual measurement of the earth’s surface, the observer not 
haying even the necessity to cast his eyes upon the surface at all. 
He merely brings with him a small metal ball, quite round, some 
metal wire, a clock, an astronomical circle, and a small iron rule. 
When arrived at one of the stations which he has chosen, he shuts 
himself up in some strong secluded building, where he is free from 
any exterior motion or noise. Then taking his metal ball, he 
suspends it to one end of his wire, by means of a small round 
leather cap, so exactly fitted to the ball, that contact alone shall 
be suflicient to make them adhere. He attaches the other end 
of the wire toasteel fulcrum, like the fulcrum of a balance, which 
he sets upon a plane of agate stone, exceedingly smooth, firm, 
and made perfectly horizontal ; he then puts the pendulum in 
motion, counting the number of vibrations which it makes in any 
pe 
‘ given 
