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Page 172 - The mean value of k' is about 57", which may be employed when a very precise result is not required. Fig. 17. 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 = T0 — T (382) in which (Art.
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 55 - - 10 meridians is equal to the difference of longitude of those meridians. In comparing the corresponding times at two different meridians, the most easterly meridian may be distinguished as that at which the time is greatest; that is, latest.
Page 19 - ... respectively north and south of the plane of the equator. The prime vertical is the vertical circle which is perpendicular to the meridian. The line in which its plane intersects the plane of the horizon is the east and west line, and the points in which this line meets the sphere are the east and west points of the horizon. The north and south points of the horizon are the poles of the prime vertical, and the east and west points are the poles of the meridian. * In this definition of the horizon...
Page 53 - A sidereal day is the interval of time between two successive upper transits of the vernal equinox over the same meridian.
Page 103 - ... 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 at the...
Page 21 - ... a great circle of the sphere whose plane is perpendicular to the axis ; hence the centre of the circle coincides with that of the sphere.
Page 74 - 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 value for any intermediate time may be found by simple interpolation, using the second differences...
Page 69 - This, however, is never the case; but the error arising from the assumption will be smaller the less the interval between the times in the Ephemeris ; hence, those quantities which vary most irregularly, as the moon's right ascension and declination, are given for every hour of 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...