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aberration accuracy altitude ascension and declination assumed axis azimuth Bessel celestial sphere centre chronometer clock correction co-ordinates coefficient computed constant Corr corresponding curve deduce denote determine Diff diurnal motion earth eclipse employed Ephemeris epoch equal equations of condition equinox expressed formula geocentric given gives Greenwich Greenwich mean hence horizon horizontal parallax hour angle instant instrument interpolation interval latitude logarithms lunar mean meridian method moon nearly noon nutation obtain place of observation plane pole position precession precision prime vertical probable error proper motion quantity radius reckoned reduced refraction right ascension semidiameter sextant sidereal solar solar eclipse spherical star star's substitute sun's supposed surface taken temperature term tion transit triangle true true longitude vernal equinox vertical circle whence zenith distance
Page 223 - ... in the zenith. In such cases the two equal altitudes may be observed within a few minutes of each other, and all corrections, whether for change of latitude or change of declination, may be disregarded. CHAPTER VI. FINDING THE LATITUDE BY ASTRONOMICAL OBSERVATIONS. 160. BY the definition, Art. 7, the latitude of a place on the surface of the earth is the declination of the zenith.
Page 317 - CHAPTER VII. FINDING THE LONGITUDE BY ASTRONOMICAL OBSERVATIONS. 213. THE longitude of a point on the earth's surface is the angle at the pole included between the meridian of the point and some assumed first meridian. The difference of longitude of any two points is the angle included by their meridians. These definitions have been tacitly assumed in Art. 45, where we have established the general equation L = T0 T (382) in which (Art.
Page 542 - To find whether near a given opposition of the moon and sun a lunar eclipse will occur. The solution of this problem is similar to that of Art. 287, except that for the sun's semidiameter there must be substituted the apparent semidiameter of the earth's shadow at the distance of the moon ; and also that the apparent distance of the centres of the moon and the shadow will not be affected by parallax, since when the earth's shadow falls upon the moon an eclipse occurs for all observers who have...
Page 53 - A solar day is the interval of time between two successive upper transits of the sun over the same meridian. The solar time at any instant is the hour angle of the sun at that instant.
Page 74 - Ephemeris as functions of the time, are called the first differences; the differences between these successive differences are called the second differences; the differences of the second differences are called the third differences, &c. In simple interpolation we assume the function to vary uniformly; that is, we regard the first difference as constant, neglecting the second difference, which is, consequently, assumed to be zero. In interpolation by second differences we take into account the variation...
Page 103 - ... understood to be identical with the geographical or geodetic latitude. It has recently been attempted to show that the earth differs sensibly from an ellipsoid of revolution;* but no deduction of this kind can be safely made until the anomalous deviations of the plumb line above noticed have been eliminated from the discussion. CHAPTER IV. REDUCTION OF OBSERVATIONS TO THE CENTRE OF THE EARTH. 87. THE places of stars given in the Ephemerides are those in which the stars would be seen by an observer...
Page 1 - A MANUAL OF SPHERICAL AND PRACTICAL ASTRONOMY, embracing the general problems of Spherical Astronomy, the special applications to Nautical Astronomy, and the theory and use of fixed and portable Astronomical Instruments. With an Appendix on the method of least squares.
Page 690 - (722) Every observation throughout the year being employed to form such an equation, we can deduce from all the equations, by the method of least squares, the most probable values of AŁ and M. Those observations will have the greatest weight in determining A&, which are near the positive and negative maxima of the aberration, where the coefficient a has its greatest numerical values. These maxima occur for cos (O M} = 1 and cos (O M) = + 1 ; that is, for Q = 180° + M and O = M.
Page 74 - In this work, since the year 1 863, the difference given for a unit of time is always the difference belonging to the instant of Greenwich time against which it stands, and it expresses, therefore, the rate at which the function is changing at that instant. This difference, which we may here call the first difference, varies with the Greenwich time, and (the second difference being constant) it varies uniformly, so that its value for any intermediate time may be found by simple interpolation, using...
Page 69 - Greenwich time; others, as the moon's parallax and scmidiameter, for every twelfth hour, or for noon and midnight; others, as the sun's right ascension, &c., for each noon; others, as the right ascensions and declinations of the fixed stars, for every tenth day of the year. Thus, for example, the greatest errors in the right ascensions and declinations found from the American Ephemeris by simple interpolation are nearly as follows: Error in RA Sun Moon Jupiter Mars Venus O'.l 0.1 0.1 0.4 0.2 Error...