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HISTOEY OF PHYSICAL ASTEOXGMY.
within 3 TT,Vinrth. part of tlieir observed values * * * § . Euler conceived thatthe disturbing action of the planets would offer unsurmountable difficultiestowards arriving at a complete theory of the moon's motion, and heasserted that this circumstance would for ever prevent astronomers fromreducing the error in the computed place of that body below 30" f. Thisstatement is well calculated to suggest the important character of theresults to which M. Hansen has been conducted by his researches in thepresent instance J.
The moon’s mass has been variously estimated by astronomers. Newton,by a comparison of his theory of the tides with observation, concluded thatit amounted to xgr.lnns-, the earth’s mass being supposed equal to unity §.Laplace similarly inferred from the height of the tides at Brest that themoon’s mass was equal to ^-Wg-H. This result is considerably less thanthat assigned by Newton; but Laplace conceives that on account of theinfluence of local circumstances on the height of the tides at Brest, thereal value of the moon's mass is even still less. He, therefore, determinedthe mass by other methods, and estimated its most probable value bytaking a mean of all the results. Three distinct methods offer themselvesfor this purpose, besides that suggested by the theory of the tides. Oneof these depends upon the fact that the force which retains the moon inher orbit, as indicated by her periodic time and observed distance, is duenot merely to the action of the earth, but to the united actions of theearth and moon. Hence, by computing the force in this maimer, weget the sum of the masses of the two bodies, and if the earth’s massis already known, the moon’s mass becomes known also. Adopting 57'12".Q3 as the mean parallax of the moon, Laplace obtained by thismethod Yi.-g for the value of her mass.
Another method for determining the moon’s mass is suggested by theinequality in the sun’s longitude, depending on the displacement of theearth from the common centre of gravity of the earth and moon. Sincethis is the point to which astronomers refer the computed place of theearth, it is clear that the motion of that body round it will generally causethe computed and observed places of the sun to differ. When the moonis in syzigees the inequality vanishes; for then the sun appears in thesame position, whether observed from the earth, or from the centre ofgravity of the earth and moon. It manifestly attains its maximum valueat the quadratures, where the lines drawn from the sun to the earth and
* See Poisson’s Memoire du Mouvement de la Lurie autour de la Terre, Mem. Acad,des Sciences, tome xiii. 1835.
+ “ Au reste je ne doute pas, qu’en corrigeant les Iieux. moyens de l’apogee et du nceuddans les tables ordinaires, on ne puisse par ce moyen parvenir a determiner le lieu de lalune a 30" pres. Or pour un plus haut degre de precision on ne saurait jamais l’esperera cause de 1’action des autres planetes a laquelle la Lune est assujetie.” Theorie de laLune, Prix de l’Academie, tome ix.
+ Since the preceding lines were written, we have ascertained that at the meeting ofthe Astronomical Society for September 1848, Mr. Airy communicated the correctionsof the elements of the lunar orbit, deduced from the Greenwich observations from 1750to 1830. When we consider the extent and accuracy of these observations, embracingthe united labours of Bradley, Maskelyne, and Pond; and the eminent talents of theastronomer who has superintended their reduction and discussion, we may confidently expectthat the results which have been obtained by means of them, will impart greater precisionto the lunar tables than any others of a similar character that have yet been arrived at.
§ Princip. lib. iii. prop. 37, cor, 4.