Synopsis
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. 1799 Excerpt: ...mv = /, then r'/Ti" = /,-a/"S, neglecting the other terms; but /---1-u A col. m v = I + 2 wxcof. mvt and /""!.-= 1-u x cos. "» = 1 + 3:t x cos. « v; hence, r = t +2 iv x cos. mv-zS-6:i-Sx cos. substitute this value of r into/-=r'yx 1-and we obt tin /-(1 + 2:c cos. mv-2S-6.1 Sx cos. mv) V x 1-e = V + 2Tt x col". n,-v 2S x r--6 5-col. mv x r--2 ":». x cos. wv x V, neglecting those terms where the product of die two sn.1!! qualities S and t enter. Now the two first tenm arc independent of e and S, and therefore we have nothing to do with them in our prelcnt enquiry, which is only to find the equations arising from the disturbing forces; but the other terms, depending upon e and.S, anlc from the disturbing forces; therefore the rc'p:ircd correction of the fluxion of the time is-2 Ji+e x V-iw x 36 + x col", mv x "o. Now if the orbit had been a perfect circle, and there had been no disturbing force, we should have had / = r, and / = v, and the motion being uniform, f would have been the mean longitude i and / being here constant, / must also express the mean longitude of tlie body P. Let therefore--the fluent of I'M x cos. mv x V arifin from the elliptic form of the orbit, and0-the fluent of-IT+Vx v--2:1 x 3A + x cos. mvxv arising ft m the disturbing forces; then / = r + «+P, therefore /--«-j3=vj that is, to lind the true place of the body, fust corrc.t the mean longitude by the elliptic equation (222), and ihcn apply the fluent of-Ty+exV-iw x 3S T'x ci f. mv x v with a contrary sif:n. If the o:bit be a circle, or if the cuentrieity be very final 1, for the correction vsc may all'umc only the fluent of--1 S t c x V vsith it's sign changed. 1115. The quantities here found are in terms of the r.i...
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