Page:Popular Astronomy - Airy - 1881.djvu/260

246 BE, we have to consider that there is a longer column of fluid, of which every part is pulled downwards by a smaller attraction. And therefore (on the principles which I have just explained in reference to a head of water) by choosing a proper ellipticity of the spheroid, or in other words, choosing a proper proportion of length of the columns AE and BE, the pressures per square inch which these columns produce at the centre E may be made exactly equal.

And now comes into account the fundamental property of fluids, namely, the equality of pressure in all directions. When the fluid is in a state of rest, the pressure per square inch at E must be the same, whether it is estimated by the pressure which it exerts in sustaining the column EA, or by the pressure which it exerts in sustaining the column EB. This is the fundamental property of fluids, upon which (as a matter of science) I shall not speak at greater length; I shall merely remind those who have to do with steam boilers, or Bramah's presses, or other engines in which fluids are in a state of violent compression, that there is equal tendency to burst upwards, downwards, or sideways. Therefore when we have gone through the investigation, taking into account what is the attraction of the spheroid on every part of the fluid in each column, what is the amount of the centrifugal tendency in each part of the column EB, and what is the length of each of the pipes, on an assumed ellipticity of the earth; and when we have thus found, by considering each pipe separately, the pressure at E where the two pipes join, we must have the two pressures equal. And if the ellipticity which we have assumed for the earth will not make these two pressures equal, we shall