J 30 On the Atiiihimr TiJti. [Ffin 



It is obvious that this is no other than the preceding theory of tlie 

 tides, the moon's orbit being the oblong splieroid, which wants only 

 a rotatory motion round its axis to exhibit the phenomena of the 

 ebb and flow. 



That the eccentricity of the moon's orbit is materially aiFected by 

 gravitation is an admitted fact — the point at issue is the mode of 

 application. And it may be observed in the outset, that the expo- 

 sition given in the preceding passage is contrary to all analogy. All 

 the planets, primary as well as secondary, move in nearly similar, 

 that is to say, elliptical, orbits : it would be natural, therefore, to 

 expect that one law should regulate them all ; yet the cause of their 

 approaching and receding, of their increasing and diminishing 

 curvature, is explained by an application of the principles of gra- 

 vity, differing very widely indeed from that contained in the para- 

 graph just quoted. 



The planets are retained in their eccentric orbits by a beautiful 

 combination of these two laws, viz. that gravity or the centrifugal 

 force is governed by nearly the stjuares, while velocities and the 

 centrifugal forces are governed by the I'ules, of the distances. The 

 centrifugal forces increase or decrease more rapidly than the gravi- 

 ties ; while therefore gravity, preponderating in the higher apsis, 

 makes the planet approach to the sun, the centrifugal force pre- 

 vailing in the lower apsis, enlarges the curve and makes it again 

 . recede from him, and by their combined actions the planet con- 

 tinues to revolve from the one apsis to the other. That the eccen- 

 tricity of tiie moon's orbit is governed by the general law which 

 regulates the other planets, and not by the difference of the attrac- 

 tions of the sun and the earth, is abundantly obvious ; for at the 

 period of opposition the moon is acted upon by the sum of the 

 attractions of the sun and the earth, instead of being affected by 

 their difference ; and we have the testimony of JNIr. INI'Lauriu 

 himself to this view of the subject. In a paper on the Path of 

 Secondary Planets, written some years after his Theory of the Tides, 

 and when tlie difficulties of that theory did not trammel his mind, 

 Mr. ISI'Laurin, alter explaining why the moon, whose gravity at 

 the CGiijunction is greater towards the sun than its gravity towards 

 the earth, d«es not abandon the earth, proceeds thus : " But it 

 may contribute towards removing this difficulty to o!)serve that if 

 the velocity of the moon at the conjunction was less than that 

 which is requisite to carry a body in a circle there round the sun, 

 supposing this body to be acted on by the same force which acts 

 there on the moon (i. e. by the excess of lier gravity towards the 

 sun above her gravity towards the earth) then the moon would 



pins prpp que la (errc, cJ en rprouve line action plus considerable; la difference 

 <Je.-. attiactions du .olfil siir ccs deux cfirps tend done alors a dimiiiutr la pesanteur 

 do lii Iui:e ler? la Icne. P.ireilleracnt dans ies Kppo-iiioiis de la lune au soloil, re 

 satellite, plus (!|nignc< du suli-il que la terie, eji e>.t faiblrracn! attlir ; la diffrrenec 

 de rac-iiou du btdeil una di-ac encore a diuintier ia. pcta'iicur dc la luue," &c 



