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41. Calculation of potential V for a homogeneous sphere

42. Attraction of a homogeneous body nearly spherical on par-

ticles, external and internal

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

particles, external and internal

40

41

ib.

57

ART.

95. Geodesy affords a test of the earth’s having been fluid or not

96. Length of an arc of meridian

98. Formulæ for finding the semi-axes and ellipticity by Two

Arcs : arcs which are most likely to give best results.

99. Examples, from the English and Indian Arcs

100. The probable causes of deviation from the mean ellipticity

in the ellipticity deduced from particular arcs

101. A comparison of arcs on 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. Proposit

Propositions suggested by Captain A. Clarke's 'Article on

the Figure of the Earth in the Volume of the British

Ordnance Survey

104. Deviation of the mean arc from the elliptic form

105. Formulæ for correcting the observed latitudes to make

them suit the general curve. Examples .

107. Application of the Principle of Least Squares to find the

mean figure of the earth

108. Results from British Ordnance Survey

109. Ellipse which best suits the observations

110. Local departures from the mean figure in India

112. Ellipse which most nearly accords with the mean ellipse and

with the calculated deflections of the vertical

114. Difference in length, and distance at mid-latitude, of two

arcs having same extremities

116. Indian Arc compared with the mean ellipse

117. The difference between geodetical and astronomical ampli-

tudes arises solely from local attraction

118. Effect of local attraction on the mapping of a country

119. Geodesy gives no evidence regarding change of level

120. Effect of local attraction on the SEA-LEVEL

122. 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 nearly 600 feet higher than at Cape Comorin

from these causes

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ATTRACTIONS AND LAPLACE'S

FUNCTIONS.

1. THE Law of Universal Gravitation teaches us, that every particle of matter in the universe attracts every other particle of matter with a force varying directly as the mass of the attracting particle and inversely as the square of the distance between the attracted and the attracting particles. Taking this law as our basis of calculation, we shall investigate the amount of attraction exerted by spherical, spheroidal, and irregular nearly-spherical masses upon a particle, and apply our results in the second part of this Treatise to discover the Figure of the Earth. We shall also show how the attraction of irregular masses lying at the surface of the Earth

may

be estimated, in order afterwards to ascertain whether the irregularities of mountain-land and the ocean can have any

effect on the calculation of this figure.

CHAPTER I.

ON THE ATTRACTION OF SPHERICAL AND SPHEROIDAL

BODIES.

PROP. To find the resultant attraction of an assemblage of particles constituting a homogeneous spherical shell of very small thickness upon a particle outside the shell: the law of attraction of the particles being that of the inverse square.

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attraction be so obosen that equals ina unit of mass at the socistance, the elementary mass at Pon in the

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y Wholt oliminate from this equation by means of

yo = + x2 – 2cr cos , d

e

ym dy

2c

prdr sitruction of P on C in CO=

1 +

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i sin e

76 obtain the attraction of all the particles of the shell we Thatrate this with respect to and y, the limits of being 1 and 27, those of y being cấr and c+r;

prdr

c-go? , attraction of shell on C=

2c

prdr

c? 1+

dy

ya
47 prédr_mass of shell

πρrdr-
ca

(2x + 2x)

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