HISTORY OF PHYSICAL ASTRONOMY.

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In order to render observations of the planets available as elements oftheoretical research, it is necessary to reduce them from the place of ob-servation to the sun, the physical centre of the planetary system. Twosteps are requisite for this purpose. The first consists in reducing theapparent position of the planet from the place of observation to the centreof the earth. To this end it is indispensable to obtain a knowledge ofthe diurnal or geocentric parallax, in other words, the apparent displace-ment occasioned by viewing the body from a point on the surface of theearth instead of its centre. The second step in the reduction of a planetaryobservation, consists in transferring the position from the centre of theearth to the centre of the sun. This object is effected by means of theannual or heliocentric parallax. When once the absolute magnitude of theterrestrial orbit has been determined by means of the solar parallax, theheliocentric parallax of any planet, is readily ascertained by the aid ofKepler’s third law. The reduction of a planetary observation is thusultimately made to depend upon the evaluation of the solar parallax. Theprogress of researches on this important subject has already been brieflyalluded to in one of the preceding chapters.

After the astronomer has succeeded in tracing the laws of the variousprinciples which exercise an influence on the apparent positions of thecelestial bodies, and has determined their maximum effects with alldesirable precision, there still remains the laborious task of computing thedisplacement occasioned by them corresponding to any assigned instant.Various expedients have been devised with a view to abbreviate thetoilsome calculations attendant upon this operation. In the Connai'ssancedes Temps for 1760, there appeared tables having for their object, to faci-litate the computation of aberration and nutation for a few of the principalstars. Similar tables continued to be published in the volumes for thesubsequent years, the numbers of stars to which they were adapted, gradu-ally increasing, until at length it amounted to 510 in the volume for 1806.In the same year tables designed to facilitate the calculation of aberrationand nutation were published by Cagnoli and De Zach. Cagnoli’s tablesappeared in the form of an appendix to a catalogue of 501 stars which hepublished at the same time *. They were applicable only to the stars con-tained in the catalogue. De Zach’s tables were attached to a catalogue of1830 zodiacal stars ; but their application was confined to 494 of the prin-cipal stars in the catalogue-j\ In 1812, the last-mentioned astronomergave an important extension to his previous labours by the publica-tion of tables of aberration and nutation, adapted to a catalogue of 1440stars j. A defect of these tables consisted in the omission of the solarnutation, an element of displacement which, although of inconsiderable im-portance compared with the other corrections, is capable of exercising avery sensible influence on the delicate investigations of sidereal astronomy.

It cannot fail to excite surprise that, until a very recent period, nogeneral methods were devised by astronomers, having for their objectto facilitate the reduction of observations, by combining together in onehomogeneous system of calculation, as far as was practicable, the separateprocesses for determining the various inequalities which affect the ap-parent positions of the celestial bodies. With respect to refraction, its

* Catalogue de 501 6toiles, suivi des Tables relatives d’Aberration et de Nutation;Mod., 1807.

+ Tabulae Speciales Aberrationis et Nutationis, &c.; 2 tom. 8vo., Gotha, 1807.

f Nouvelles Tables d’Aberration et de Nutation pour 1440 etoiles, 8vo., Marseille ,1812.