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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 deduced denote determine Diff difference of longitude diurnal motion earth eclipse employed Ephemeris epoch equal equations of condition equinox expressed formula geocentric given gives Greenwich mean hence horizon horizontal parallax hour angle instant instrument interpolation interval latitude logarithms lunar 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 673 - The squares of the periods of revolution of any two planets are proportional to the cubes of their mean distances from the sun.
Page 172 - The mean value of k f is about 57", which may be employed when a very precise result is not required. DIP OF THE HORIZON. 121. The dip of the horizon is the angle of depression of the visible sea horizon below the true horizon, arising from the elevation of the eye of the observer above the level of the sea.
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 = T 0 — T (382) in which (Art. 47) T...
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 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 105 - Parallax in altitude is, then, the angle at the heavenly body subtended by the radius of the earth. If the heavenly body is in the horizon as at H', the radius, being at right angles to AH', subtends the greatest possible angle at the star for the same distance, and this angle is called the horizontal parallax. The parallax is less as the bodies are farther from the earth, as will be evident from the figure.
Page 69 - Greenwich time; others, as the moon's parallax and semidiameter, 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:— Sun Moon Jupiter Mars Venus Error in RA OM 0.1 0.1 0.4 0.2 Error...
Page 196 - SECOND METHOD. — BY EQUAL ALTITUDES. 139. (A.) Equal altitudes of a fixed star. — The time of the meridian transit of a fixed star is the mean between the two times when it is at the same altitude east and west of the meridian ; so that the observation of these two times is a convenient substitute for that of the meridian passage when a transit instrument is not available. The observation is most frequently made with the sextant and artificial horizon ; but any instrument adapted to the measurement...
Page 74 - Ephemeris is employed, we can take the second differences into account in a very simple manner. In this work, 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...
Page 345 - The use of more has been found to add less to the accuracy of a determination than is lost in consequence of the greater fatigue from concentrating the attention for nearly twice as long. A large number of stars may thus be observed on the same night ; and it will be well to record half of them by the clock at one station and the other half by the clock at the other station, upon the general principle of varying the circumstances under which several determinations are made, whenever practicable,...