IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I ^1^ iM ■- In 1111122 ^ ti& lllllio 1.8 1.25 U ill 1.6 - 6 " Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, NY. 14580 (716) 872-4503 f,' &y «' CIHM/ICMH Microfiche Series. CIHM/ICMH Collection de microfiches. Canadian Institute for Historical Microreproductions / Institut Canadian de microreproductions historiques »i':*-!!. Technical and Bibliographic Notes/Notes techniques et bibliographiques The Institute has attempted to obtain the best original copy available for filming. Features of this copy which may be bibliographically unique, which may alter any of the images in the reproduction, or which may significantly change the usual method of filming, are checked below. L'Institut a microfilm^ le meilleur exemplaire qu'il lui a dtd possible de se procurer. Les details de cet exemplaire qui sont peut-§tre uniques du point de vue bibliographique, qui peuvent modifier une image reproduite, ou qui peuvent exiger une modification dans la mdthode normale de filmage sont indiquds ci-dessous. D Coloured covers/ Couverture de couleur I I Covers damaged/ Couverture endommag^e I I Covers restored and/or laminated/ Couverture restaur^e et/ou pellicul6e Cover title missing/ Le titre de couverture manque H I I Coloured maps/ □ Coloured pages/ Pages de couleur Cartes g^ographiques en couleur D D D D Pages damaged/ Pages endommagdes Pages restored and/or laminated/ Pages restaurdes et/ou pelliculdes Pages discoloured, stained or foxed/ Pages d6color6es, tachet^es ou piqudes Pages detached/ Pages d^tachdes D Coloured ink (i.e. other than blue or black)/ Encre de couleur (i.e. autre que bleue ou noire) □ Showthrough/ Transparence □ Coloured plates and/or illustrations/ Planches et/ou illustrations en couleur D Bound with other material/ Relid avec d'autres documents D D Quality of print varies/ Quality indgale de I'impression Includes supplementary material/ Comprend du matdriel supplementaire D D Tight binding may cause shadows or distortion along interior margin/ La re liure serrde peut causer de I'ombre ou de la distortion le long de la marge intdrieure Blank leaves added during restoration may appear within the text. Whenever possible, these have been omitted from filming/ II se peut quG certainos pages blanches ajoutdes lors d'une restauration apparaissent dans le texte, mais, lorsque cela 6tait possible, ces pages n'ont pas dtd filmdes. D D Only edition available/ Seule Edition disponible Pages wholly or partially obscured by errata slips, tissues, etc., have been refilmed to ensure the best possible image/ Les pages totalement ou partiellement obscurcies par un feuillet d'errata, une pelure, etc., ont 6t6 filmdes d nouveau de fapon d obtenir la meilleure image possible. D Additional comments:/ Commentaires suppl6menraires; This item is filmed at the reduction ratio checked below/ Ce document est film^ au taux de reduction indiqud ci-dessous. 10X 14X 18X 22X 26X SOX 12X 16X 20X 28X 32X ails du tdifier une nage rata o >elure. Id H 32X The copy filmed here has been reproduced thanks to the generosity of: Library of Congress Photoduplication Service The images appearing here are the besi quality possible considering the condition and legibility of the original copy and in keeping with the filming contract specifications. Original copies in printed paper covers are filmed beginning with the front cover and ending on the last page with a printed or illustrated impres- sion, or the back cover when appropriate. All other original copies are filmed beginning on the first page with a printed or illustrated impres- sion, and ending on the last page with a printed or illustrated impression. The last recorded frame on each microfiche shall contain the symbol —^^ (meaning "CON- TINUED"), or the symbol V (meaning "END"), whichever applies. Maps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: 1 2 3 L'exemplaire film6 fut reproduit grdce d la g6n6rosit6 de: Library of Congress Photoduplication Service Les images suivantes ont 6t6 reproduites avec le plus grand soin, compte tenu de la condition et de la nettetd de l'exemplaire filmd, et en conformity avec les conditions du contrat de filmage. Les exemplaires originaux dont la couverture en papier est imprim6a sont filmds en commen9ant par le premier plat et en terminant soit par la derniilire page qui comporte une empreinte d'impression ou d'illustration, soit par le second plat, salon le cas. Tous les autres exemplaires originaux sont filmds en commenpant par la premidre page qui comporte une empreinte d'impression ou d'illustration et en terminant par la dernidre page qui comporte une teiie empreinte. Un des symboles suivants apparaitra sur la dernidre image de cheque microfiche, selon le cas: le symhr :? —m- signifie "A SUIVRE", le symbole V fcjgnifie "FIN". Les cartes, planches, tableaux, etc., peuvent dtre film6s d des taux de reduction diffdrents. Lorsque le document est trop grand pour dtre reproduit en un seul clich6, il est filmd d partir de Tangle supdrieur gauche, de gauche d droite, et de haut en bas, en prenant le nombre d'Images ndcessaire. Les diagrammes suivants iilustrent la mdthode. 1 2 3 4 5 6 i ^ U. S, Ho^^^'-'^ ^- -^-^ ^ 9^^ ^^» 1> coK^EECTionsrs TO HANSEN'S TABLES OF THE MOON. PREPARED AND PRINTED FOR THE UBlt OF THE ■i AMERICAN EPHEMERIS AND NAUTICAL ALMANAC. i WASHINGTON : aOVERNMENT PRINXrNO OFFICE. 1878. ..-^ In the RcsearcheH on ihe Motion of the Moon* to Im' |)ro(»tUit<Kl in Api^ndix IT of the Washington Observations for 1875, it is Hhown that the larjfe deviations of Hanson's hmar tahles from oKservations will almost entirely disappear by substituting for the empirical term an eini)irical alteration of the other term (hie to the action of Venus, and by making suitable alterations in the elements of mean motion. The entire secular and long \v:v'\od tmrecstions may be formuljite<l as follows: Put Vj = 21".47 sin (8 V — 13 E + 274° 14'). (The on>iririe}d term.) (Vy A == 18 V - 16 E - (/. T = time after 1800.0, counted in centuries. Then the sum of the corrections in question is : — Vj— l'M4 — 2y".17T — 3".76T'^-15".5cos A. o For the present purposes, the most convenient way of applying these corrections is to omit Table XLI, Arg. 30, which contains V,, and to rephu-e it by the sum of the above terms, omitting the first ; this sum being tabulated as a function of the time. Table XLI, liowever, contains the constiuit 21".49, which will hi oniittetl with the table, and must therefore l)e ajjplied in the new table. The quantity by which table XLI must be replaced is therefore 20".36 - 29".17 T — 3".76 T^ — 16".5 cos A. this is to be reduced to Hansen's units by lx;ing multiplied by the factor 212.6. The result is shown for the Iwginning of each tenth year of the present century, and interiM>lated to every year from 1880 to 1900 in the first of the follow- ing tiibles. This is followed by a corrected table XXXIV, in which the t«rm 0".335 sin (2 «7 — 4 .7' + 2 w — 4 to'), is removed and replaced by — 0".285 sin i2g — 4 .9' + 2 w — 4 w'), conformably to the results given on p. 439 of Hansen's Darleffung. lieducing the correction to Hansen's units, it is — 131 sin (2 «7 — 4 (7' + 2 «j — 4 w'). This quantity being tabulated and applied to Hansen's Table XXXIV, we have the corrected table here given. No further corrections than these are now proposetl, because they would of necessity, in the present stiite of the lunar theory, ha purely provisional, and would prove a sounti of trouble in revising the theory. With these corrections it is intended to employ Hansen's Tables in the Americsin Ephenieris for 1883. SIMON NEWCOMB. ' Abstract in Sillinian's Juuntal for November, 1877. )bscrvation8 for tirely disappear Vonus, and by 'iHitioiis may be XLI, Arg. 30, a; tabulated as a li tlie table, and jrofore r the lieginning it of the follovv- TABLE XLI. Argument. The year of the Chriitian era. Year. Ineq. Year. Ineq. 1800 +7603 1880 -223s — 768 — 146 1810 6835 1 881 — 2381 — 946 -'45 1820 5889 1882 —2526 — mo -145 1830 4779 1883 — 2671 —1256 —144 1840 3523 1884 -2815 —'363 -144 1850 2160 1885 -2959 —1446 -143 i860 + 714 1886 — 3102 —1473 —"43 1870 — 759 1887 -3245 —1476 —142 1880 -2235 1888 -3387 —1433 - 141 1890 -3668 1889 -3528 -'356 — 140 1900 —5024 1890 —3668 isen's units, it is re given. tent stiite of the 883. ^COMB. %r /