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HISTOKY OF PHYSICAL ASTBONOMY.

that considerable uncertainty still rests upon this point. It is fortunatethat the very circumstance which renders it so difficult to ascertain themass of this planet with precision, should also in a great measure relievethe astronomer from the embarrassment of an erroneous evaluation.

The perturbations of Venus , though very minute, are more considerablethan those of Mercury, on account of her greater proximity to the otherplanets. The principal disturbing body is the earth, hut even in thiscase the greatest inequality in longitude does not exceed 10". Laplacecomputed the terms of perturbation as far as the third powers of theeccentricities and inclinations, but he neglected those of higher orders,under the impression that they were too minute to be appreciable byobservation. Mr. Airy, however, has discovered among the terms of thefifth order a sensible inequality, depending on the action of the Earth .It takes 240 years to pass through all its values, although its greatestmagnitude does not exceed 2."9. We shall presently have occasion tomention the circumstance which gave rise to the detection of this interest-ing inequality.

Halley's tables of Venus were those which were held in most esteem byastronomers throughout the last century, until they were supplanted bythose of Lalande towards its close. In 1810, Lindenau published tablesfouuded on the Greenwich observations, and on those made on thecontinent during the present century. They are the tables now generallyused by astronomers.

The mass of Venus is an element of physical astronomy, which has oc-casioned much research. As the planet is unaccompanied by a satellite,its mass can only he determined by means of the perturbations it pro-duces in the motions of the other bodies of the system. These, how-ever, are so very small, that until recent times no dependence could beplaced on the results derivable from them. Lagrange, in his famousresearches on the planets which appeared in the Berlin Memoirs for1781-82-83, determined the mass of Venus , by assuming the densities ofthe planets to vary in the inverse ratio of their mean distances from thesun. In this manner he found a value for the mass of the planet, whichexceeded the value of the earth’s mass, nearly in the proportion of threeto two. This mil manifestly result from his hypothesis, when we con-sider that the volumes of Venus and the Earth are nearly equal, and thatthe mean distance of the latter from the sun, exceeds that of the formernearly in the proportion of three to two. That this estimate, however,greatly exceeded the real value, was evident from the result which La :grange arrived at, relative to the displacement of the Earth ’s orbit by theaction of the other planets. In this case, the principal disturbing bodiesare Jupiter and Venus , and as the mass of the former of these planetswas sufficiently well known, it was clear that any discordance betweentheory and observation ought to be referred to an error in the mass of thelatter. Lagrange computed by theory, the displacement of the terrestrialorbit, and obtained 61". 5 for the secular diminution of the obliquity ofthe ecliptic; hut as the observations of astronomers generally gave lessthan 50" as the real value, it hence followed that the mass of Venus wastoo great, and that the hypothesis on which its determination was foundedwas erroneous. Delambre, while engaged in the construction of his solartables, determined the mass of Venus by means of the periodic inequa-lities which she occasions in the Earth’s longitude. Clairaut had pre-viously sought to determine the mass of the planet by this method, but