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42. Attraction of a homogeneous body nearly spherical on an ex-
ternal particle
43. Ditto on an internal particle
44. By choosing the origin at the centre of gravity, and taking
the radius of the sphere of equal mass as a standard, the
general radius of the body is simplified
45. Attraction of a body consisting of nearly spherical shells on
an external particle
46. Ditto on an internal particle
38
39
40
41
42
CHAPTER IV.
ATTRACTION OF BODIES NOT SPHERICAL NOR SPHEROIDAL.
47. Object of this chapter
48. Attraction of a slender prism on a particle towards either
49. Attraction of a slender pyramid on a particle at its vertex; also of a frustum .
51. Attraction of an extensive plain of given depth or thickness
on a point above it.
43
ib.
44
ART.
PAGE
55.
Attraction of a rectangular mass on a particle in the plane of
one of its sides
46
48
56. Examples. Takal K'hera, Schehellien, Arthur's Seat
57. Method of calculating the attraction of extensive tracts of
mountain-country
58.
Law of Dissection of the mountain-mass into compartments,
such that the attraction of each is proportional to the aver-
age height of the mass standing on it.
60. Numerical calculation of the dimensions of these compart-
61.
Remarks on the application of these results to the Himma-
layas, (62) to the Ocean, and (63) to the interior of the
Earth
64. Effect on the plumb-line of a slight but wide-spread defect or
excess of density in the interior of the Earth
57
65.
Example: a space equal to 3-100,000ths of the volume of the
Earth and excess or defect of density equal 1-100th of
Earth's density
58
FIGURE OF THE EARTH.
CHAPTER I.
FIGURE OF THE EARTH, CONSIDERED AS A FLUID MASS, AND
THEREFORE CONSISTING OF STRATA NEARLY SPHERICAL.
68. A homogeneous mass of fluid, every particle attracting ac-
cording to the inverse square of the distance, can revolve
with a uniform velocity round an axis, if it be in the form
of an oblate spheroid of ellipticity, the angular velocity
and gravity being the same as in the Earth
63
69. This is a stable form
66
72. If the central parts alone attract the same is true, but the ellipticity is
73. Equation of equilibrium, if the mass consist of nearly spheri-
cal strata of varying density
68
79. It decreases towards the centre
80. Ellipticity of the surface in the case of the Earth
81. Conditions enumerated, which must be satisfied if the Earth
derived its form from being a fluid mass
82. Test of the law of density used, by its application to calculate
Precession
84. Argument drawn by Mr Hopkins from Precession that the
crust is of considerable thickness .
85. Remarks on Professors Hennessy and Haughton's calcula-
tions
86. Argument drawn from the present aspect of the surface of the
Earth in mountains, plains, and oceans
77
78
79
80
8883
85
CHAPTER II.
FIGURE OF THE EARTH, ON THE SOLE HYPOTHESIS OF THE
SURFACE BEING A SURFACE OF EQUILIBRIUM AND
90. Clairaut's Theorem, generalized by Professor Stokes: Re-
marks on the result of Pendulum experiments, and the
ellipticity thence deduced
92. Ellipticity determined from the motion of the Moon in lati-
tude
94. The centre of the Earth's volume coincides with the centre of
its mass; and the axis of revolution is a principal axis
CHAPTER III.
THE FIGURE OF THE EARTH, DETERMINED BY GEODETIC
OPERATIONS.
95.
96.
This affords a test of the earth's satisfying the conditions of
Length of an arc of meridian; also of longitude
97. Formulæ for semi-axis major and ellipticity.
98. Examples, to show how much small errors in the observed
amplitude affect the calculated ellipticity
98
99
100
99. Error in the computed ellipticity arising from an error in
one or both of the amplitudes of the arcs compared. Arcs
which are most likely to give best results
100. A comparison of arcs in various parts of the Earth's surface gives an average form agreeing with the hypothesis that the Earth acquired its general form from being in a fluid state
102. The probable causes of deviation from the mean ellipticity
in the ellipticity deduced from particular arcs
104. Effect of an uncorrected error in the amplitude, or of using
the mean ellipticity instead of that of the local arc, upon
the mapping of a country. Example from the northern
part of the Indian Arc
106. Effect of disturbing forces upon the sea-level
101
102
107. Examples, along the coast of Hindostan, arising from the
attraction of the Himmalayas and the deficiency of attrac-
tion of the Ocean lying on the south. The sea-level at
Karachi is more than 600 feet higher than at Cape Comorin
from these causes
110. Propositions suggested by Captain A. Clarke's Article on
the Figure of the Earth in the Volume of the British
Ordnance Survey