Page:Popular Astronomy - Airy - 1881.djvu/258

244 by saying that "a body weighs more at the Pole than at the equator." And this statement is correct, if it be received with the proper caution. If we carried a pair of scales with proper weights from the Pole to the equator, the same weights which balanced a stone at the Pole would balance it at the equator, because the effect of gravity on both is altered in the same degree. But if we carried a spring-balance from the Pole to the equator, the spring would be more bent by the weight of the same stone at the Pole than at the equator. There is also another effect, to which I shall shortly allude, that a stone would fall further in one second at the Pole than at the equator.

Having computed the effective attractions at the Pole and at the equator, we must now examine what is the consideration to be applied in order to discover whether, with a certain supposition of ellipticity of the earth, this homogeneous fluid will be in equilibrium. The way in which Sir Isaac Newton proceeded is the same as that adopted by every other person who treats of the theory of fluids. You may conceive a cylindrical tube AE, open at both ends, to be put down from the Pole to the centre. Suppose you put down a similar pipe BE from the equator to the centre; and suppose that they communicate at the centre E—these imaginary pipes will not at all disturb the state of rest of the fluid, if it be at rest—by means of each of these pipes we shall ascertain the state of pressure of the fluid at the centre E. By the "state of pressure" I mean, the measure of that compression of the fluid at E, which would enable it to burst any shell that enclosed it at E, if there were no opposing pressure on the outside of the shell; and this measure is to