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.

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.