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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 /