know that is a wrong ellipticity, and we must try another, till we find one which will make the pressures equal. If we use a proper algebraical process, we can diminish the trouble of this so far as to reduce it all to a single trial; but still the principle of the process is exactly the same. And when we have found one ellipticity which does make the pressures equal, we are sure that we have got the right ellipticity for the earth; still limited, however, by our original supposition, that the earth is a fluid of equal density in every part, and is not more dense at the centre than near the surface; and if that original supposition be wrong, our conclusion will be wrong.
It was in this manner, assuming the earth to be a fluid no more dense at the centre than near the surface, and proceeding in every way as I have described, that Sir Isaac Newton inferred that the form of the earth would be a spheroid, in which the length of the shorter diameter or axis on which it turns, is to the length of the longer or equatoreal diameter, in the proportion of 229 to 230. And this, perhaps, may be considered as one of the most wonderful investigations in modern science.
With this proportion, as you will have perceived, is intimately connected the proportion of gravity at A and B, that is to say, of the attraction at A to the attraction diminished by centrifugal tendency at B. You must accept it as a result of mathematical investigation, of which I can give you no further explanation at present, that if you compare a point f in the line EA, with a point g in the line EB, such that Ef : EA : : Eg : EB, you then find the whole effective force at f, to bear the same proportion to the whole effective force at g, which that at A bears
