124 ASTRONOMY. 
&c. The place o will consequently first see the part Hkih of the heavens, 
then JHhi, then KJHk, &c. Now, since we do not perceive the motion 
of the earth, we are led to imagine that it is the heavens that move, which, 
however, is only an illusion caused by the earth’s rotation. 
The flattened shape of the earth is also a consequence of its rotation. It 
is known from the theory of physics, that all parts of any body driven 
round in a circle with uniform velocity, endeavor to recede from the centre 
of this circle, which effort is called the centrifugal force. Let, in fig. 6, pl. 
6, AMBN represent an elastic globe with an axis AB, passing through the 
centre C. If now the globe be turned rapidly about AB, all its parts will 
move the faster, the more remote they are from the poles A and B, or the 
nearer they are to the equator MN; A and B moving only on themselves 
as poles. With a more rapid motion there willbe an increase of centri- 
fugal force, and those parts of the globe lying near the points M and N 
will separate more from the axis of rotation AB. Hence the spherical 
globe, AMBN, will finally assume the ellipsoidal shape, mBnA, and appear 
depressed or flattened. The earth, when first set in motion, must have 
been in precisely the same condition as the above globe, assuming, 
however, that at that time its matter was in a fluid or semi-fluid state. 
44. Thus the earth is not a perfect sphere, but an elliptical spheroid, in 
which the curvature of a meridian section at the equator is sensibly greater 
than at the poles, shown by measurements of degrees of latitude. Let 
NABDEF (pl. 6, fig. 9) represent a meridian section of the earth, C its 
centre, NA, BD, and GE, each a meridian arc, corresponding to a degree 
of latitude or to a degree of change in the meridian altitude of a star. 
Finally, let nN, aA, 0B, dD, gG, eH, be the direction of the plummet at the 
places N, A, B, D, G, E, of which N is situated in the pole, and E in the 
equator. If now any two neighboring vertical lines, as nN and aA, bB and 
dD, gG and eH, be prolonged to their intersections in X, y, z, then the 
angles NX A, ByD, GzE, will each amount to a degree, and consequently 
be all equal. Thus the small arcs NA, BD, GE, may be considered as 
circular arcs described about X, y, z, as centres. The points X, y, z, are 
called the centres of curvature, and the lines XN or XA, yB or yD, and 
2G or 2H, radii of curvature, by which the curvature at these points is 
determined and measured. Geometry teaches us that the intersections of 
all these vertical lines do not, as in the sphere, all fall in C, but must lie in a 
certain curve, Xy¥z, called the evolute. Vixperience has now shown that the 
terrestrial meridian is an ellipse, having for its major axis the equatorial 
diameter EF (fig. 9), and for its minor axis, the axis of the earth NS. 
This agrees also with the ratio of increase of the degree from the equator 
towards either pole. ‘The radius of curvature at E is the least, that at N 
the greatest. The dotted lines in fig. 9 represent the parts of the evolute 
belonging to the other quadrants. It is to the celebrated Bessel that we 
owe the most recent and authentic results from measurements of degrees 
According to him, a mean degree of the meridian is equal to 57013.109 
toises (364,576 English feet) ; half the major axis, or half the equatorial 
diameter to 3272077.14 toises (20,923,624 English feet) ; and half the minor 
124 
