Capt. the Hon. C. L. Irby, H.M.S. Ariadne. Admiral Jones, 10, Curzon Street, May Fair. 1 The Rev. J. Kirkby, Sheerness Dockyard. Capt. Abraham Lowe, R.N. Capt. The Hon. J. A. Maude, H.M.S. Glasgow. Admiral the Right Hon. Earl Northesk, Commander in Chief, Plymouth. Rear Admiral Sir E. W.C. R. Owen, K.C.B. and M.P. Vice Admiral C. W. Paterson, Cosham, Hants. Capt. J. C. Ross, R.N. The Right Hon. Earl Spencer, K.G., &c. &c. . Henry Shiffner, R.N., Sompting Abbotts, Shoreham. . George F. Stow, H.M.S. Espoir. Capt. N. Thompson, H.M.S. Revenge. The Hon. G. Vernon, Ryde, Isle of Wight. Commodore J. C. White, R.N. The Right Hon. Lord Viscount Yarborough, 2 copies. CONTENTS. I. To convert longitude, or degrees into time, and conversely II. Depression of the horizon ... III. Dip of the horizon at different distances from the observer IV. Augmentation of the moon's semi-diameter V. Contraction of the semi-diameters of the sun and moon VI. Parallax of the planets in altitude.. VII. Parallax of the sun in altitude VIII. Meau astronomical refraction... IX. Correction of the mean astronomical refraction To find the latitude by the north polar star XI. Correction of the latitude deduced from the preceding table...... 20 XI. Mean right ascension of the sun... XIII. Equations to equal altitudes of the sun, part First.. XIV. Equations to equal altitudes of the sun, part Second XV. To reduce the sun's longitude, right ascension, and declination; and, also the equation of time, as given in the Nautical Almanac, to any given time under a known meridian XVI. To reduce the moon's longitude, latitude, right ascension, declin- ation, semi-diameter, and horizontal parallax, as given in the Nautical Almanac, to any given time under a known meridian 30 XVII. Equation of the second difference of the moon's place..... XVIII. Correction of the moon's apparent altitude XIX. To reduce the true altitudes of the sun, moon, stars, and planets, to their apparent altitudes ..... XXI. Correction of the auxiliary angle when the moon's distance from a XXII. Error arising from a deviation of one minute in the parallelism of the surfaces of the central mirror of the circular instrument of XXIII. Error arising from an inclination of the line of collimation to the plane of the sextant, or to that of the circular instrument of re- XXV. Correction of the logarithmic difference for the sun's, or star's appa- XXVI. Correction of the logarithmic difference for a planet's apparent XXVII. Natural versed sines, and natural sines XXVIII. Logarithms of numbers . XXIX. Proportional logarithms.... XXX. Logarithmic half elapsed time XXXII. Logarithmic rising. .... XXXIII. To reduce points of the compass to degrees, and conversely...... 89 XXXIV. Logarithmic sines, tangents, and secants to every point and quar- XXXV. Logarithmic secants to every second in the semi-circle XXXVI. Logarithmic sines to every second in the semicircle..... XXXVII. Logarithmic tangents to every second in the semicircle XXXVIII. To reduce the time of the moon's passage over the meridian of Greenwich to the time of her passage over any other meridian 100 XXXIX. Correction to be applied to the time of the moon's reduced transit in finding the time of high water at any given place...... 102 XL. Reduction of the moon's horizontal parallax on account of the spheroidal figure of the earth... XLI. Reduction of terrestrial latitude on account of the spheroidal A general traverse table, or difference of latitude and departure 106 XLIV. The mean right ascensions, and declinations of the principal fixed XLV. Acceleration of the fixed stars, or to reduce sidereal time into XLVI. To reduce mean solar time into sidereal time.... XLVII. Time from noon when the sun's centre is in the prime vertical; being the instant at which the altitude of that object should be observed, in order to ascertain the apparent time with the great- XLVIII. Altitude of a celestial object (when its centre is in the prime ver- tical), most proper for determining the apparent time with the XLIX. Amplitudes of a celestial object reckoned from the true east or L. To find the times of the rising and setting of a celestial object. ... 123 LI. For computing the meridional altitude of a celestial object, the latitude and the declination being of the same name LII. For computing the meridional altitude of a celestial object, the latitude and the declination being of contrary names ........ 138 LIII. The miles and parts of a mile in a degree of longitude at every |