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Les équations de condition furent formées après l'addition de -1.200 aux x de 219, +0.100

mm

aux y de 219, +0.500 aux x de 222.

Les équations d'élimination sont:

6.160

- 36.506

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2.333

2.100

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Aux x de 233, nous ajoutons — 0.300, aux y +0.100. Les équations d'élimination

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94.74b28.18 c-4.53=0. - 12.72=0 .-15.70 0

71.04 c

- 8.65=0.

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Pour les couples de clichés 278 & 281, 280 & 283, je me borne à communiquer les nos d'ordre du Catalogue photographique du ciel pour les étoiles employées dans le calcul des constantes. Sur les clichés 278 et 281, p et r ont été calculées d'après 16 étoiles, savoir: pour le cliché 278, les nos 130, 134, 139, 144, 155, 156, 163, 176, 177, 200, 215, 217, 227, 229, 230, 231, qui pour le cliché 281 correspondent aux nos 21, 13, 34, 31, 46, 47, 71, 73, 72, 118, 134, 138, 144, 136, 147, 139.

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Dans les calcul des constantes pour les clichés 280 et 283, 13 étoiles ont été employées, savoir: pour le cliché 280, les nos 96, 113, 117, 118, 121, 129, 130, 131, 146, 155, 164, 165, 177, qui pour le 283 correspondent aux nos 4, 21, 16, 22, 27, 28, 29, 30, 41, 56, 54, 57, 68. Les résultats sont pour ce cas:

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Après exclusion de l'étoile no 155 du cliché 280, qui est aussi le n° 56 du cliché 283, et qui donne des erreurs restantes très considérables, on obtient les valeurs suivantes :

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Les chiffres ci-dessus prouvent combien la position d'une seule étoile peut influer sur la détermination des constantes des clichés. La quantité r-r, reste la même pour les deux clichés, mais descend de 0'.000300 environ après exclusion de l'étoile 155 (56).

X1

r

La comparaison des résultats relatifs aux sept paires de clichés traitées dans ce chapitre donne les valeurs suivantes pour (PP)-(P-Py1) et ("x-y1)-(-). Les quantités Pa1 Py .... sont les constantes de l'un des deux clichés, les quantités P P constantes de l'autre.

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Si l'on suppose que les chiffres ci-dessus constituent des écarts de la valeur exacte, 0, et si l'on donne à ces nombres des poids proportionnels aux nombres d'étoiles employées pour les calculer, on obtient en se basant sur ces données, comme erreurs probables d'une détermination de (P-Py1) — (Px.-Py) et de (1⁄2 — 1) — (—) à l'aide de 14 étoiles:

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2

r

R[(Px,—P11) — (Px,—Py)] =±0′.000047.

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Ces valeurs sont notablement plus grandes que celles qu'on a obtenues pour 14 étoiles à l'aide des clichés 412 a, b, c. Nous avions pour ces clichés (p. 20):

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On trouve une concordance plus grande en comparant les erreurs probables ici déterminées avec celles qu'on a calculées pour les clichés 412 a, b, c pour 74 étoiles. En effet, si l'on calcule les valeurs de R (p) et R (r), à l'aide des chiffres ci-dessus, en supposant que les constantes aient été calculées à l'aide de 74 étoiles, on a:

·R74 (?)=0′.0000103

R4 (r)=0.0000149.

Pour les clichés 412 a, b, c, on a trouvé

R4 (P)=0.0000055

R74 (1) =±0′.0000177.

III.

Discussion d'un certain nombre de clichés d'Eros.

Parmi les clichés sur lesquels l'Observatoire de Helsingfors a photographié la planete Eros pendant son opposition en 1900-1901, l'on en trouve plusieurs qui ont un grand nombre d'étoiles de repère communes. En effet, Eros fut photographié souvent deux et trois fois pendant la même soirée d'observation, ou bien encore deux ou trois soirées de suite; ce qui eut pour conséquence la représentation répétée de la même région à peu près du ciel sur plusieurs clichés. Ceux-ci sont par suite fort favorables à l'étude de la question que nous examinons dans ce travail. Les clichés d'Eros ont sur les clichés discutés plus haut cet avantage, que les étoiles communes sont réparties sur tout le cliché; les constantes sont ainsi plus exactement déterminées. Les positions employées à Helsingfors pour les étoiles de repère ont été publiées dans la Circulaire n° 12 de l'Observatoire de Paris. Je ne donne ici, par conséquent, que les numéros de B. D. pour les étoiles employées et leurs coordonnées rectilignes calculées et mesurées. Les clichés I, J et K ont 16 étoiles de repère communes, dont les coordonnées, exprimées en secondes d'arc, sont données dans le tableau suivant.

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