To the Editor of the Sr,—The history of what are termed the Exact Sciences presents occasionally features as startling, as the most startling incidents, of which we read in novels or romances; with this difference that, in works of fiction, they are accepted as a matter of course, whilst, authoritative treatises of mathematics, they fre held to partake of the nature of a concrete impossibility. Nor is it always easy to Igive a clear exposition ofthe latter in popular lee guage. Net, with your permission, I will attempt to do so, in regard to one of the more remarkable cases, which occur in no less a work, than Sir Isaac Newton's Principia."
In Proposition XIX. of Book Il. of this celebrated treatise, the author, whose name it has immortalized, demonstrates that the Earth, a matter of theory, should be flattened at the poles or have the form of an orange; in the immediately following ition XX. he shows that, as a matter of fact, our planet rises at the poles and, consequently, has the shape of lemon. Modern Science has adoj the theory for the nek and. the obits figure of the Earth constitutes one of the fun da mental elements in the Newtonian System of Astronomy, as based on the principle of Universal Gravitation, with which that system stands or falls.
On the ground of actual geodetic measarements and pendalumexperiments, carried out in Newion's days, he computes, for every five degrees of latitude, a table of the length of the (seconds) pendulum" and of the "measure of one degree in the meridian the corresponding linear values regularly increasing from the equator towards the polis. But it 4s clear that. when the proportion ut the polar, to the equatorial, semi-axis of the Earth is known, its general shape is known; and a-suming it to be, as is universally done, a geometrical figure of revolution, that its proportions generally are known also. Hence, setting aside the intermediate values, the fundament tal numbers are given in Newton's table as follows atiende, RES" [MSa"she mertalen Length of the [Sfeasuroofone degree Feet. Linen, French Tolsen 8 T4689 $9,037
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Text read from the printed page and cleaned; old type leaves the occasional error.