The Elements of Natural or Experimental Philosophy (Volume 2) (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1813. Excerpt: ... NOTES OF PART IV. NOTE A. CHAP. V. Art. 7,0. Of the Precession of the Equinoxes. IF S, fig. 40., represent the sun, ABCD the earth, T its centre, EQ the equator, P, fi the poles, it will appear from note B, that the sun's disturbing force upon a particle at E, in the equator, in a direction parallel to TS, is, where/ am sun's force at T, r = TS, and EK = cosine of the arc AE, the sun's declination, KT being equal to the sine of the same. Now from the theory of the resolution of forces it follows, that this absolute force-----is to its effect in a direction perpendicular to the equator, as 1 (radius) to KT, so that in that direction the force becomes K KT, 0r, (calling EK x, and KT y) jl, r r Let ET = 1, P = periodic time of the earth, fi = that of a revolving body at the earth's surface (P. I. Art. 47), --= t, the force of gravity at the earth's surface = g; then /: g--: --, and 3yxf----(force upon E perpendicular to EQ): f:: 3yx: r; therefore force upon E perpendicular to the equator: g:: Zyxt2: 1. Let now d be the centre of gyration (vol. I. page 185), and Q the quantity of matter in the earth; then is the effect of the inertia of Q placed at d, to oppose motion, the same as that of the inertia of the earth; and by that centre's property ET2: dT2 ( ET2):: Q: Q = the quantity of matter to be placed at E for the same effect. Let q be the excess of the quantity of matter in the earth above that of its inscribed sphere, and (Newton's Princ. B. III. lemma 1 and 2) the action of the sun on the shell q to generate an angular velocity about an axis perpendicular to ABCD will be the same as it would be to generate an angular velocity in a quantity of matter--q placed at E. We may therefore suppose the sun to act perpendicularly to ET on $g at E, and to have...