HISTORY OF PHYSICAL ASTRONOMY.

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the planet round the sun. But here a difficulty occurs, the nature ofwhich it is necessary briefly to explain. The earth being the place fromwhich all observations are made, the position of a planet in the zodiac isdetermined by its geocentric longitude, or its angular distance from thevernal equinox relative to the centre of the earth. But, as the sun is thenatural centre of the planet’s motion, the theory of the latter assigns onlythe heliocentric longitude, or the distance from the vernal equinox relativeto the centre of the sun. In order, then, to compare the observationsof the planet with the results of theory, it is necessary to pass from thegeocentric longitude, derived immediately from observation, to the cor-responding value of the heliocentric longitude. This object may be ef-fected by a simple process of trigonometry, if we know the length of theradius vector of the planet, and the position of the earth in her orbit,corresponding to the time of observation. The former of these data maybe obtained from the tables of the planet, and the latter from the solartables. It is manifest, however, that if the tubular radius vector of theplanet be erroneous, the computation will be vitiated, and a false valuewill be assigned to the heliocentric longitude. The question then arises,how are we to pass from the geocentric longitude of the planet to theheliocentric longitude without complicating the result with the effect ofthe error of the radius vector. This object is accomplished per se for allobservations made when the planet is in opposition, for the sun, the earth,and the planet being then in the same straight line, the geocentric andheliocentric longitudes will necessarily coincide, and they will both retainthe same common value, whatever be the length of the planet’s radius vector.Even if the observations should not be made when the planet is actuallyin opposition, the heliocentric longitudes may be obtained free from theerrors of radius vector by skilfully combining together the observationsmade before and after opposition*. Mr. Adams in this manner deducedfrom the observations of Uranus twenty equidistant values of heliocentriclongitude, for the period included between 1780 and 1840. Comparingthese with the tabular values he obtained a corresponding series oferrors in heliocentric longitude, which, with those derived from theancient observations of tire planet, formed the data of his final investi-gation of the problem.

Mr. Adams commenced his researches by supposing the orbit of theplanet to be circular, and its mean distance from the sun double the meandistance of Uranus . It was probable from analogy that both these sup

* If we suppose the radius veclor of the tables to be loo small, then, before the eartharrives in opposition, the planet will appear behind its computed place; and, on the otherhand, when the earth has passed opposition, it will appear in advance of its computed place.Hence it is not difficult to perceive that these opposite effects may be destroyed by a suit-able combination of observations made before and after opposition. The same remarkwill manifestly apply, if the tabular radius vector be too large ; the only difference being,that in this case the planet before opposition will appear in advance of its computed place,and after opposition will appear behind it. After Kepler made the memorable discoverythat the orbit of Mars was not a circle, but retired within that curve towards the meandistance, his active imagination soon devised a theory in which the planet was supposedto move in an oval, the distance of which varied according to a certain law. This hypo-thetic orbit was, however, too much compressed in the sides to represent the true ellipse ofthe planet; and, accordingly, Kepler mentions that David Fabrieius, to whom he com-municated his theory, remarked to him that the observations of the planet before and afteropposition indicated that the distances of the oval were all too short. “ So nearly,” sayshe, “ did that astronomer anticipate me in the discovery of the true orbit of the planet,”—De Modbus Stella Martis, cap. Iv. p. 266.