1814.] On Ike Aniilunar Tide. 13 V 



indeed abandon the earth ; for in that case the moon, having less 

 velocity than would be necessary to prevent her from descendin,;^ 

 within that circle, she would approach to the sun and recede from 

 the earth. But tliough the absolute velocity of the moon at the 

 conjunction be less than the velocity of the earth in the annual 

 orbit, yet her gravity towards the sun is so much diminished by her 

 gravity towards the eartli that her absolute velocity is still much 

 superior to that which is requisite to carry a body in a circle there 

 about the sun that is acted on by the remaining force only. There- 

 fore, from the moment of the conjunction, the moon is carried 

 without such a circle, receding continually from the sun, to greater 

 and gj-eatcr distances, till she arrive at opposition, where, being 

 acted on iii the sum of those tv/o gravities, and her velocity being 

 now less than what is necessary to carry a body in a circle there 

 about the sun that is acted upon by a force that is equal to that 

 sum, the moon thence begins to approach to the sun again. Thus 

 she recedes from the sun, and approaches to it, by turns; and iu 

 every month her path has two apsides, a perlhelium at the conjunc- 

 tion, and an aphelium at the opposition, between which she is 

 always carried, in a manner similar to that in which the primary 

 planets revolve between their apsides."* 



* After slating th.it tlie law of gravity in regard to tiie planets varies recipro- 

 rally as tlse square of the distance, Laplace, with similar views, ijrocceds thus : — 

 " Son inouvement elliptic ne luissc aucuii doule a cctegard. Pour le faire voir, 

 suivous ce niouvemcnt, en fais!-ant partir la plancjte, du periliOlie, la viiesse est 

 alors a son niaxiniwii, et sa tendance a s'eloigner du soloil, reinportaut siir sa 

 pcjautcur vers cet astre, son rayon vecteur auguientc, et forme dfs angles obtus 

 avec la direction de son mouvemeut ; la pesantcur vers le ^oleil, decompobce siii- 

 vant cclte direction, diininue done de plus en plus la vitesse jusqu'a ce que la 

 plaui'i- ait uClcint son aphclie. A ce point, Ic rayon vecteur redevient perpcndicii- 

 Jain- a lacourbe ; la viiesse est a son miiiiiiium et la tendance a s'uloigner dii soloil 

 ctant moindre que la pesanteiir solaire, la planele s'en rapproclie en decrivant l;i 

 seconde parlie de son ellljire. Dans cette partie sa pe^antenr vers Ic soleil, accroit 

 sa viiesse comine aujiar.'iranl, «lle I'avoit diniiniiue, la planute se retrouve au 

 periiitlie, .avec sa vite^sc primitive, el reconiDience un nouvclle revolminn sem- 

 Ijlable a la preetdcnte." — Sijsl. p. 191. l.aplace has not exposed himself to sucli 

 a direct charge of inconsistency as Mr. Al'I.aurin; but there occurs, it is ap];rc- 

 hended, the same contradictory principles; for it jsdillicuU to anticipate how the 

 n)oon, which is a satellite of tiie earth, is to be excluded from the fullowiiig 

 trencral observation. Alludin:; to the satellites of .lupilcr, he says, " ils uous 

 ii'fcront ])r'r la proin])ti(ude de leur revolutions tons les ;;r;ind! chanf^emcns que le 

 lewips ne devcloppe qu'a\ec une extrrnie lenteur, dans le- stiatcmc planetaire, dont 

 celiii dcs snleViUn est Viiunge." — Sj/si. p. 2'l.S. If the satellites are governed by the 

 same princij)les as the planets, which is the position here maintained, tiiid which 

 Air. M'l.aurin illuslralcs in the jiassajje already quoted, thru it is to be inferred 

 from tlie statements of Al. Laplace that the elipl/ity of tlio moon's orbit, like tliut 

 "f liicplantli, i> owing to Uic combination uf the la-ivs of motion and gravity, 



{To fit conlinr.ed.) 



I J 



