LONGITUDE. 



Capella, or the quantity to be added to tlic obfcrved tranfit 

 to obtain the apparent right afcenfion. The apparent right 

 afcenlions are next reduced to mean right afceiifions for the 

 beginning of the year by Tables II. and III. obferving to 

 apply the contrary figns to thofe for a, Aquils, becaufe 

 now the mean place is to be deduced from the apparent, 

 whereas we deduced the apparent place of » Aquilae from the 

 mean. 



A feries of obfervations and calculations, fimilar to the 

 above, being continued for a great length of time, a catalogue 

 is to be formed, which, fuppofmg the inftrument to be per- 

 fcft, will be fubjeft to no other error than that of the 

 affumed right afcenfion of a Aquils, and with this error 

 every right afcenfion will be affefted. 



The fun is likewife to be obfcrved during the whole of 

 this procefs, and its right afcenfion deduced as in the above 

 example, and which will be fubjeft to the fame common 

 error as fubfifts in the right afcenfions of the flars. 



While this feries of obfervations is going on at the tranfit 

 inftrument, both the fun and flars are to be obferved afii- 

 duoufly with the mural quadrant, or any other inllrument 

 deftined to the determination of polar dillances. We need 

 not enter into the details of this procefs, as it has already 

 been minutely defcribed under Declination, but fliall 

 proceed to confider the ufe we are to make ot the refult. 



With refped to the ftars, it is evident that by this double 

 invelligation we have determined their places accurately, 

 both with refpeft to each other and to the equator, fo that 

 we might place them in their true pofitions on the celeilial 

 globe, provided no attention was required to be given to_ the 

 fituation of the ecliptic ; and this would be the cafe, if the 

 interfedion of a meridian pafTing through a Aquila: with 

 the equator, had been affumed as an arbitrary point of de- 

 parture in the fame manner, as we afTume a meridian pafTing 

 through Greenwich or Paris on the terrellrial globe, as a 

 ftandard to which terreftrial longitudes are referred. But 

 the great circle to which celellial longitudes are referred, is 

 required to pafs through the equinotlial point : it is the exat\ 

 polition, therefore, of this point which we are in fearch of, 

 and which is to be determined by the data we are now fup- 

 pofed to have coUefted. 



The continued feries of folar obfervations gives us the 

 obhquity of the ecliptic, and the declination of the fun at 

 the moment of obfervation, from which its right. afcenfion 

 may be ealily deduced by the folution of a right-angled 

 fpherical triangle ; but in making thefe computations, atten- 

 tion muHbe paid to the periodical ofclllations of the equator, 



and to the fecular variation of the ecliptic itfelf ; that is, the 

 right afcenlions mufl be calculated with the apparent oh- 

 liquity, that they may be reckoned from the apparent or 

 variable equinoftial point, in the fame manner as thofe deter- 

 mined by the tranfit inllrument, and with which they are now 

 to be coinpared. 



We have thus obtained a folar theory independent of the 

 fixed flars, and the pofition of the fixed liars independent of 

 the pofition of the ecliptic. It now only remains to combine 

 thefe operations, and to place the ecliptic in its due pofition 

 with refpedl to the fixed flars ; and this is done in the fol- 

 lowing maimer. 



We begin by comparing the right afcenfions of the fun 

 determined by the tranfit inllrument, with the right afcen- 

 fions determined on the fame day with the quadrant ; and if 

 they agree, it is a proof that the right afcenfion of a Aquilas 

 was rightly affumed ; if they differ, as will mofl probably be 

 the cafe, we mull proceed and endeavour to afcertain both 

 the quantity and the caufe of the difcordance. 



If we confider one fingle infulated obfervation, the dif- 

 cordance may arife either from an erroneous afl^umption itj 

 the right afcenfion of a. Aquilje, or from fome defeft in our 

 folar theory, or from fome error in the obfervation from 

 which the declination of the fun has been inferred. Novf, 

 though it would be impoffible to affign the true caufe of 

 the dilcordance from one fingle comparifon, yet the whole 

 feries will lead us to the truth, from this fortunate circum- 

 flance, that whatever error any defedl in the folar obfer- 

 vations produces in any one obfervation, the fame defeft will 

 produce an equal error, but with the contrary fign, in an 

 obfervation in which the fun is i8o degrees from its firfl 

 pofition. 



In felecling obfervations thus circumllanced, it mufl how- 

 ever be remembered, that although in theory we may deter- 

 mine the right afcenfion of the fun by trigono.iietrical calcu- 

 lation from any given declination, yet praclically, no exatt- 

 nefs can be expetted, except when the change of declination 

 is confiderable, which only happens near the equinoxes. The 

 exatt limits in which the comparifon may without impro- 

 priety be made, mull depend on the accuracy of the inllru- 

 ments, and on the confidence of the obferver in the correft- 

 nefs of his obfervations. In general, the period fhould not 

 be extended to more than fix or eight weeks on each fide 

 the equinox. 



When the feries of obfervations is complete, the refults 

 are to be arranged and compared as in the following 

 table : 



Let 



