' LONGITUDE. 



(confidered as conftant forces) produce by their aftion on 

 the protuberant regions of the equator a flow periodical 

 revolution of the earth's axis about the pole of the ecliptic. 

 Bv this motion the cquinoftial points are carried backward, 

 and the pofitioi. of the equator among the fixed Itars changes 

 at every inftant. If the etfcft of this phenomenon was 

 firaply to caufe a change in the pofitionof the equinodtial 

 points, the difference of right afcenlion of ftars would not 

 be affefted by it ; but it mull be remembered, that tlic 

 right afcenfion of a ftar is determined by a perpendicular 

 drawn from the ftar to the equator ; now, the equator 

 changing its place, this perpendicular will change its place 

 alfo; that is, the ftar will be conftantly referred to a new 

 point on the equator, and hence the right afcenfion will 

 vary from two caufes ; one, the motion of the equinoftial 

 point, or point of departure, which will equally affedl every 

 ftar ; and the other from the change in the point of reference, 

 by which, according tD the definition, right afcenfion is de- 

 termined. It is the latter only of thele two caufes that 

 affefts the difference of right afcenfions. 



The folar and lunar nutations of the axis of the earth 

 arife from the unequal aftion of the fun and moon, by 

 which the precefTion of the equinoxes is not defcribed in the 

 uniform and iimple manner above mentioned. The reader 

 will fee under Nutation, that the axis of the es.rth never 

 points to its mean place ; hence the apparent equator never 

 coincides with the mean equator, or that circle which would 

 be the equator, if thefe periodical nutations did not exift. 

 Thefe derangements of the equator, and the correfponding 

 ofcillations of the equinoftial points, affeft' both the longi- 

 tudes and right afcenfions of the ftars, and hkewife their 

 declinations: their latitudes alone remain unchanged, for an 

 ofcillation in the axis of the earth produces no change in 

 the ecliptic, which depends only on the path which the cen- 

 tre of the earth defcribes in fpace, and which is not affefted 

 by the caufes we have above mentioned ; but the ecliptic it- 

 felf is deranged by the aftion of the neighbouring planets, 

 for thefe caufe the centre of the earth to take aftually a new 

 path in the heavens, though they are too diftant to derange 

 the parallelifm of the earth's axis by any unequal aiSlion on 

 the equatorial regions. The ecliptic, in confequence of this 

 difturbance, changes its point of interfeClion with the equa- 

 tor, which circle remains, from this caufe at leaft, unmoved, 

 and confequcntly the declinations of the ftars remain un- 

 changed ; but their longitudes are affefted, not only becaufe 

 the equinoftial point is difturbed, from which longitudes are 

 reckoned, but likewife becaufe each ftar is referred to a new 

 point on the ecliptic ; hence arifes a fecular variation in lon- 

 gitude, peculiar to each ftar. The right afcenfions are al- 

 tered by the change of pofition in the equinoftial point, 

 but this affefts every ftar ahke, and therefore produces no 

 change in the difference of right afcenfion ; in faft, the 

 effeft of this latter derangement enters as an element in the 

 conftant part of the preceffion common to all ftars. The 

 nature of all thefe changes, or equations, as they are tech- 

 nically called, has been, or will be, defcribed under their 

 appropriate terms, as Aberration, Nutation, Ecliptic, Secular 

 Variation, &c. &c. which fee refpeflively. 



Now the nicety and delicacy of the modern method of 

 reducing obfervations, confift in the exaft determination of 

 all thefe equations, and the due application of them to 



each feparate obfervation ; fo that inftead of the apparent 

 place, we make ufe of that in which we prcfume the 

 objeft would have appeared, had none of thefe periodicol 

 ofcillations exifted. Agreeable to this conception of the 

 fubjeft, we may define fome of the terms we have ufed 

 above with greater precifion than we have yet done. For 

 inftance, mean right afcenfion of a ftar, is the diltance of 

 the ftar's_ place correftcd for aberration, reduced to the 

 mean equator, from the mean vernal equinoftial point. Ap- 

 parent right afcenfwn, is the diftance of the liar's place re- 

 duced upon the apparent equator from the apparent equi- 

 noftial point. 



Mean declination, is the diftance of a ftar corrcfted for aber- 

 ration' from the mean equator. Apparent declination, is the ap- 

 parent diftance of the ftar from the apparent equator. The 

 mean equator, is an imaginary great circle of the heavens, 

 about which the apparent equator revolves without ever co- 

 inciding with it, in the manner already defcribed. Thea^- 

 parent equator, is that great circle of the heavens which 

 aftually correfponds with the equinoftial line on the earth, 

 whatever the pofition of the earth may be at the moment of 

 obfervation. 



If, with the mean right afcenfion, the mean dechnation, 

 and the mean obliquity of the ecliptic, we compute the 

 longitude of a ftar, that longitude will be its mean longi- 

 tude, that is, its place referred to the ecliptic will be reck- 

 oned from the mean equinox. 



If, with the apparent right afcenfion, the apparent de- 

 clination, and the apparent obliquity, we compute the longi- 

 tude, this will be reckoned from the apparent equinox. Side- 

 real time, (as ufed in thefe computations,) is that which has 

 elapfed fince the paffage of the apparent equinoftial point 

 over the meridian ; for aftronomers have not yet adopted a 

 mean fidereal time, which might be defined the interval which 

 elapfes from the paffage of the mean equinoStial point. This 

 latter method would be more fcientific than that now 

 in ufe, and would be a fimilar improvement to the fub- 

 ftitution of mean folar time for apparent folar time. Were 

 this latter mode adopted, an alteration muft be made in our 

 prefeiit tables of nutation, and the equation of the equinoxes 

 in right afcenfion, which now enters as common to all ftars, 

 would be omitted, as the fame quantity would previoufly be 

 applied to the error of the clock which is now applied to 

 the ftar. 



We have been led into this digreflion, and induced to 

 dwell rather at length upon thefe prehminary confidera- 

 tions, becaufe we do not, at this moment, recoUeft any 

 author that has entered much on the fubjeft, to whom we can 

 refer. 



The right afcenfion of a Aquilse then, being affumed as 

 near the truth as poflible, the right afcenfions of the other 

 ftars are to be inferred from it, by applying all the above 

 equations, and likewife a correftion for the error of the 

 clock. 



We fubjoin an example of one day's computation, taken 

 from the Greenwich Obfervations, 1809. The requifite 

 tables for thefe reduftions, for aberration, preceflion, nu- 

 tation, have been given under Declination (Tables 11. 

 and III.), and for applying the error of the clock to each 

 ftar, the following table will be found very ufeful. 



Table 



