## 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, Volume 1 |

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aberration accuracy altitude ascension and declination assumed astronomical 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 result right ascension semidiameter sextant sidereal solar solar eclipse spherical star star's substitute sun's supposed surface taken temperature term tion transit triangle true longitude vernal equinox vertical circle whence zenith distance

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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 28 - To show as clearly as possible how the formulae of Spherical Trigonometry are thus converted into formulae of Spherical Astronomy, let us first consider a spherical triangle ABC, Fig. 3, in which there are given the angle A, and the sides b and c, to find the angle B and the side a. The general relations between these five quantities are [Sph. Trig. Art. 114]* cos a = cos c cos b -)- sin c sin b cos A ~| sin a cos B = sin c cos b — cos c sin b cos A...

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 84 - Avhich we set out. The law of the coefficients in (71) is that the coefficient of any odd difference is obtained from that of the preceding odd difference by introducing two factors, one at the beginning and the other at the end of the line of factors, observing as before that these factors are respectively greater and less by unity than those next to which they are placed; and the coefficients of the even differences are obtained from the next preceding even differences in the same manner. The factors...

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.

Page 53 - A sidereal day is the interval of time between two successive upper transits of the vernal equinox over the same meridian.

Page 643 - We shall call the maximum angle subtended by the mean distance of the earth from the sun, at the distance of the star, the constant of annual parallax of the star, or, simply, its annual parallax. If then we put ANNUAL PARALLAX. p = the annual parallax, a = the mean distance of the earth from the sun, J = the distance of the star from the earth, we have sin p -. a 7 or, if we take a = 1, according to the usual practice, we have, for so small a quantity,

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 : — Sun Moon Jupiter Mars Error In RA OM 0.1 0.1 0.4 Error In...

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 542 - HFE = the sun's semi-diameter minus his horizontal parallax (—s— p); therefore half the angle subtended by the section of the shadow is equal to the sum of the parallaxes...