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réduit depuis à 20", après un nouvel examen de fes Obier

vations.

Dans la révolution annuelle de la Terre, cet angle change de plan à tout moment, parce qu'il eft dans le plan de la Tangente de l'orbe annuel au point où fe trouve la Terre. C'est pour cela qu'il fait appercevoir des variations inégales dans les longitudes & latitudes, dans les afcenfions droites & déclinaifons des Etoiles, qui paroiffent décrire tous les ans une petite Ellipfe autour de leur vrai lieu: le grand axe de cette Ellipfe eft de 40′′, & le petit axe eft au grand, dans la raifon du Sinus de la latitude de l'Etoile, au Sinus total.

Ces inégalités font toujours en raifon des Sinus des arcs de la distance de la Terre ou du Soleil aux plans des cercles de longitude & de latitude de chaque Etoile, ou aux plans perpendiculaires à ceux-ci: parce que c'eft dans ces plans que les aberrations font nulles ou plus grandes.

A l'égard de l'aberration en déclinaison, la feule dont nous ayons befoin ici; elle eft nulle lorfque la Terre eft dans le point T (voyez Planche 6 Fig. 5) où l'Ecliptique AN fe trouve coupée par un grand cercle OET, mené du lieu E d'une Etoile, perpendiculairement à fon cercle de déclinaifon PED. Dans le Triangle rectangle CET, le point C eft le lieu de l'Etoile dans l'Ecliptique, CE fa latitude, & l'angle CET eft égal au complément de l'angle pEP, formé à l'Etoipar les cercles de latitude & de déclinaifon. Ayant donc calculé l'angle pEP, on peut trouver facilement le point T. Voici les Analogies dont nous nous fommes fervis.

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I. Comme le Sinus de complement de la latitude de l'Etoile, eft au Sinus de fon afcenfion droite comptée depuis le colure des Solftices; ainfi le Sinus de l'obliquité de l'Ecliptique, eft au Sinus de Pangle à l'Etoile pEP.

II. Comme le Rayon, eft au Sinus de la latitude de l'Etoile ; ainfi la Tangente de complement de l'angle à l'Etoile, eft à la Tangente de l'arc CT, qu'il faut ôter du lieu de l'Etoile pour avoir le point T, où fe trouve la Terre, quand l'aberration en déclinaifon eft nulle. A trois fignes de part & d'autre du point T, l'aberration eft la plus grande.

III. Comme le Sinus de Parc CT, au Sinus de l'angle PEp; ainfi 20" font à la plus grande aberration en déclinaison.

IV. Enfin, Comme le Rayon, eft à la plus grande aberration ainfi le Sinus de la diftance de la Terre ou du Soleil au point T, cu à fon oppofite, eft à l'aberration qui convient au lieu où se trouve la Terre au tems de l'Obfervation de l'Etoile.

On peut voir dans le Mémoire de M. Clairaut (page 226) les différens cas fuivant lefquels l'Etoile paroît s'éloigner ou s'approcher du Pole. Nous joignons ici (page lxxx) une Table particuliere que nous avons calculée pour chacune des Etoiles dont nous allons rapporter les Obfervations. On y trouve l'aberration de l'Etoile en déclinaifon qui convient aux vrais lieux du Soleil de 5 en 5 degrés. Les Lettres E, A qui font dans chaque colomne, fignifient que l'Etoile s'éloigne ou s'approche du Pole, fuivant la pofition de ces deux Lettres: celle qui eft à gauche, a rapport aux fignes de l'Ecliptique qui font à gauche dans la premiere colomne: & la Lettre qui eft à droite, a rapport aux fignes qui font à droite dans la premiere colomne.

§. II.

Des Réductions faites à cause de la préceffion des Equinoxes.

Nous avons calculé une Table du mouvement apparent des Etoiles en déclinaison, caufé par la préceffion des Equinoxes; on la trouvera ici (page lxxxj) de io jours en 10 jours. Les Lettres E, A fignifient, comme dans la Table de l'aberration, , que l'Etoile s'éloigne toujours, ou s'approche toujours du Pole arctique.

Il faut remarquer que les meilleurs Catalogues ne donnent pas la quantité précife du mouvement annuel en déclinaifon de la plupart des Etoiles, parce qu'il n'y eft calculé qu'indirectement. Nous l'avons déterminé par cette Analogie. (Voyez les Memoires de l'Académie, année 1741. page 247.)

Comme le quarré du Rayon, au produit du Sinus de l'obliquité de Ecliptique par le Sinus de l'afcenfion droite de l'Etoile, comptée depuis le colure des Solfices: ainfi la préceffion annuelle en longi

tude, que nous avons fuppofée de 50", eft au mouvement annuel en déclinaifon.

§. III.

De la Réfraction.

Enfin nous avons corrigé toutes nos Obfervations par la Réfraction. Car il eft certain par toutes les Théories Phyfiques, qu'elle s'étend jufqu'au Zenith précisément; & toutes les hypothefes s'accordent à la faire à peu près proportionnelle aux diftances au Zenith, depuis o° jufqu'à 15 ou 20°.

Entre toutes les hypothefes de Réfraction que différens Auteurs ont tâché d'établir, nous avons choifi celle de M. Bouguer (Méthode d'obferver fur mer la hauteur des Aftres, page 57 & fuivantes) tant à cause de la facilité avec laquelle on la peut calculer en tierces, que parce qu'elle s'accorde parfaitement vers le Zenith, à celle que M. D. Bernoulli a donnée, comme on le peut voir, en comparant la Table fuivante (page lxxxij) avec celle qu'on trouve dans l'Hydrodynamique page 222.)

Au refte le choix d'une hypothese étoit affez indifférent. Quelle qu'eût été celle que nous euffions adoptée, nous n'aurions pas trouvé des résultats fenfiblement différens de ceux que nous employons ici.

Table de l'aberration en déclinaison pour les Etoiles qui ont été obfervées en différens endroits du Royaume.

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7 E.A 12 17 E. A 33 | 15 E.A 47 10 A.E 52 4 E.A 49 2 A.E 31 19 A.E 12 19 A.E 19 317 A.E 3916

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54 19 10 28 18

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Table du Mouvement apparent en déclinaison,causé par la précession

des Equinoxes.

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