It contains the Sun's Semidiameter, Horizontal Parallax and Declination; the Time (mean, which by the addition of 0.19 sec. will be converted into sidereal) occupied by the Semidiameter in culminating or passing the meridian, the Equation or reduction of apparent to mean time, to be applied to apparent time in the manner indicated at the head of the column, the Sidereal Time, and the Obliquity of the Ecliptic. The epoch of all is Oh. Om., mean time, of the meridian of Greenwich. The apparent places of 30 of the principal fixed stars (pages 61 to 66) will be found very useful for determining the time, or latitude; for which purpose they are much to be preferred to the Sun. Reduction of Meridional Altitudes. A Table has been published for several years, in the English Nautical Almanac, for facilitating the reduction of the Latitude of a place, from observations made on the Pole star, at any time during its revolution around the Pole; which Table, when great accuracy is not wanted, or a good table of Logarithms is not at hand, will be found convenient. But as exactness is sometimes required, it was thought the insertion of a correct and general rule for the reduction of the Latitude, from altitudes of any star, might be useful and acceptable. Rule. To the log. co-sine of the star's distance from the meridian in degrees, add the log. cotangent of its declination; the sum (rejecting 10 in the index) will be the log. tangent of an arc (A) less than 90°. From the sum of the log. co-sine of A and the log. sine of the corrected altitude, subtract the log. sine of the star's declination, the remainder will be the log. sine of an arc (B). Then the Latitude is the sum or difference of B and A, according as the distance of the star from the meridian is greater or less than six hours; but, when the declination of the star is of the same name with, and is less than, the Latitude of the place, the supplement of their sum, and not their difference, is the Latitude. EXAMPLES. On the 23d of July, 1836, when the distance of the star a Ursa Minoris from the meridian was 6h. 7m. 27.9sec. (91° 51' 48"), its corrected altitude, at the church in Harris Street, Newburyport, was 42° 44' 13.93", and its declination 88° 25′ 53.54". What is the Latitude by this observation? cos. 91° 51' 48" cos. A 0° 3' 3.64" 9.9999998 sine 42 44 13.93 9.8316374 cot. 88 25 53.54 8.5120914 then BA (the star being more than six hours from the meridian)= 42° 48' 28.95", the Latitude. On the same evening, at the same place, when the star a Aquila was 10m. 73sec (2° 31′ 55′′) from the meridian, its corrected altitude was 55° 33′ 37.72", and its declination 8° 26' 27.13" north. log. cos. 2° 31' 55"+ log. co-tang. declination=log. tang. A 81° 33' 3.60" log. cos. A+log. sin. 55° 33′ 37′′.72-log. sin. dec.=log. sin.B 55° 38′ 25.56" Now, as the declination of the star is of the same name with, and is less than the Latitude, the supplement of the sum of A and B, 42° 48′ 30.84", is the Latitude. When, as is frequently the case, several altitudes of the same star have been obtained within a few minutes of each other, their reduction by this method is very simple, as two of the logarithms (the cotangent and sine of the declination) undergo no change. Boston, August 25th, 1837. AMERICAN ALMANAC FOR THE YEAR 1838, Being the latter part of the 62d, and the beginning of the 63d, year of the Independence of the United States of America; the 6551st year of the Julian Period; the latter part of the 5598th, and the beginning of the 5599th, year since the creation of the world, according to the Jews; the 2591st year (according to Varro) since the foundation of Rome; the 2585th year since the era of Nabonassar, which has been assigned to Wednesday the 26th of February of the 3967th year of the Julian Period, which corresponds, according to the chronologists, to the 747th, and, according to the astronomers, to the 746th year, before the birth of Christ; the 2614th year of the Olympiads, or the second year of the 654th Olympiad will begin in July, 1838, if we fix the era of the Olympiads at 775 years before Christ, or at or about the beginning of July of the year 3938 of the Julian Period; the latter part of the 1253d, and the beginning of the 1254th (lunar) year since the Hegira, or Flight of Mahomet, which is supposed to have taken place on the 16th of July of the year 622 of the Christian era. I. THE CALENDAR AND CELESTIAL PHENOMENA FOR THE YEAR. SIGNS OF THE PLANETS, &c. d Conjunction, or having the same Longitude or Right Ascension. Quadrature, or differing 90° in Opposition 66 แ The ascending, the descending node. An asterisk (*) prefixed to the conjunction of the Moon with a star or planet, indicates that the star or planet may be eclipsed in some part of the inhabited portion of the United States. The sign is prefixed to the latitude, or declination, of the Sun, or other heavenly body, when north, and the sign — when south; but the former prefixed to the hourly motion of the Moon in latitude, indicates that she is approaching, and the latter that she is receding from, the north pole of the ecliptic. The letters M. A., m. a., denote Morning and After noon. Length of the tropical year, commencing at the winter solstice 1837, and terminating at the winter solstice 1838, 365 5 40 49 Mean or average length of the tropical year 365 5 48 48 |