HCSTOBY OF 1'HtSlCAL' AS’iKONO',1 Y.

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magnitude in any particular instance depends upon the altitude of theobject above the horizon, and the state of the barometer and thermometerat the time of observation. It is obvious, therefore, that it cannot beconveniently combined in calculation with precession, aberration, or nuta-tion, the respective values of which depend on the position of the objectin the celestial sphere and on the time of observation. An objection ofa similar nature occurs, when the question relates to the combinationof the geocentric parallax with any other correction.

On the other hand, the inequalities of precession, aberration, and nuta-tion, offer obvious facilities for the invention of a method which may em-brace them all in one uniform process of calculation. For a long time,however, no vigorous effort appears to have been made with a view to theattainment of this desirable end. Astronomers continued to calculate thethree inequalities by separate processes, notwithstanding the analogy theybore to each other when considered merely in reference to the determina-tion of their numerical values. The reduction of any single observation,could, therefore, be effected only by executing a variety of distinct pro-cesses of calculation; and it was doubtless owing to the labour necessarilydemanded by such an operation, that vast masses of observations came tobe accumulated without being reduced at all.

About the year 1820 the subject began to attract serious attention, andmethods designed to facilitate the reduction of observations upon the prin-ciple of combination above referred to, were suggested by various astrono-mers, both in this country and on the Continent. Bessel at length pro-posed a method which, on account of its superior advantages, has supplantedall the others. The complete correction of a star’s place (in so far as pre-cession, aberration, and nutation are concerned), whether in right ascensionor in declination, is by this method expressed in terms of four products, eachproduct being composed of two factors, one of which depends on the placeof the star in the celestial sphere, and the other on the time of observation.The factors which depend on the time of observation are the same bothfor right ascension and declination, but those depending on the place of thestar are different. Hence the reduction of an observation, at least as faras relates to the three corrections above-mentioned, demands the com-putation of twelve constants, eight of which depend on the place of thestar, and four on the time of observation. Now, when the mean place of astar is once determined, the constants of the first-mentioned group may becomputed by an easy process, and it is manifest that when this is once ac-complished, the results will serve equally well for all observations of thestar. On the other hand the four constants which depend on the time ofobservation, will vary for every day of the year, and will even be differenton the same day of each successive year. Hence these constants, unlikethe former, will require to be calculated for each day of observation.They possess this peculiar advantage, however, that when once cal-culated for any day of the year, they will apply equally well to any star inthe heavens on that day.

The facility with which this method adapts itself to the computation of theapparent places of the stars by the aid of a catalogue of their mean places isvery obvious. The eight constants depending on the place of each star, maybe calculated once for all, and inserted in the catalogue. The four constantsdepending on the time of observation, cannot, of course, be included absolutelyin any catalogue; but their successive values may be calculated for a definiteperoid of time, so as to be applicable to any day of observation comprehendedwithin that period. These objects being accomplished, the determination