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HISTORY OF PHYSICAL ASTRONOMY.

accounts better for the irregularities of the disturbed planet than anyother value which has been assigned. When the difficulty of makingobservations of the satellite is taken into consideration, it is manifest thatsome time must elapse before the value of this element can be establishedwith a degree of precision conformable to the present condition of PhysicalAstronomy.

In one of the preceding chapters allusion has been made to the long ine-quality in the moon’s epoch, which was the cause of so much embarrassmentto astronomers in the present century, but of which the existence was placedbeyond all doubt, and its true nature clearly established, by a discussion ofthe Greenwich lunar observations consequent upon their recent reduction.The complete explanation of this inequality by the theory of gravitation,was the reward of Professor Hansen’s researches on the subject. Mr.Airy, by the discussion of the same observations, detected also two smallperiodical inequalities in the moon's motion, neither of which had hithertobeen recognised by theory. The greater of these inequalities was in themoon’s latitude. It varied with the cosine of the moon’s true longitude,amounted at its maximum to 2".17, and was additive. The otherinequality was in the longitude. It varied with the cosine of the longitudeof the node, had a maximum value equal to 0".97, and was subtractive.These quantities are indeed very small, but such is the high degreeof precision which characterizes modern observation, and such is themathematical refinement attained in the correction of the lunar or planetaryelements by the discussion of masses of observations, that the existenceand true form of the inequalities was established beyond all doubt by Mr.Airy’s researches. Observation and theory were therefore once more atdirect issue, and it remained for the geometer to reconcile their discordanceby demonstrating the existence of the discovered inequalities, as necessarilydue to perturbative action. This important object has recently been ac-complished by the same geometer to whom the explanation of the longinequality in the epoch of the moon is due. Professor Hansen, by a pro-found investigation of the lunar theory, has discovered two inequalitiessimilar to those indicated by observation, and very nearly agreeing with themin their maximum values. The inequality in latitude was found by him toamount to 1".38. It arises from this circumstance, that the plane towhich the lunar orbit is inclined at an invariable angle is not the plane ofthe ecliptic as has been hitherto supposed, but a plane the position ofwhich Professor Hansen represents by the following conception :—“Takethe plane of the earth’s orbit in the position in which it was about threeyears ago ; let the nodes of this plane revolve backwards on the presentecliptic through 90°, without change of inclination; the plane so found isthe plane to which the uniformity of the inclination of the moon’s orbit isto be referred.”* The same train of investigation gave also the inequalityin longitude. M. Hansen obtained 0".50 for its maximum value. Thediscordance between M. Hansen’s results, and the values assigned to theinequalities by Mr. Airy, are not greater than such as may fairly beascribed to errors of observation. Thus the clouds which for a momentobscured the Newtonian theory of gravitation have been effectually dis-sipated, and a fresh conquest has been added to the long list of triumphswhich adorn its history.

With the foregoing brief allusion to the recent researches of M. Hausen

* Letter from Professor Hansen to the Astronomer Royal, Monthly Not. Ast. Soc.,June, 1849.