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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 limit 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 true longitude vernal equinox vertical circle whence zenith distance
Page 671 - The squares of the periods of revolution of any two planets are proportional to the cubes of their mean distances from the sun.
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, — T (382) in which (Art.
Page 3 - It is another characteristic feature of modern spherical astronomy, that the final formulas furnished to the practical computer are so presented as seldom to require accompanying verbal precepts to distinguish the species of the unknown angles and arcs; and this results, in a great measure, from the consideration of the general spherical triangle, or that in which the six parts of the triangle are not subjected to the condition that they shall each be less than 180°, but may have any values less...
Page 591 - Venus will aftbrd a far more accurate determination of this parallax than those of Mercury ; for, on account of its greater proximity to the earth, the difference in the duration of the transit at different places will be much greater, and the coefficient of AT: in the final equations proportionally great. Although the general method for eclipses may also be extended to the prediction of the transits of the planets (by Art. 322), yet it is more convenient in practice to follow a special method in...
Page 129 - The atmosphere, however, is not of uniform density, but is most dense near the surface of the earth, and gradually decreases in density to its upper limit, where it is supposed to be of such extreme tenuity that its first effect upon a ray of light may be considered as infinitesimal. The ray is therefore continually passing from a rarer into a denser medium, and hence its direction is continually changed, so that its path becomes a curve which is concave towards the earth. The last direction of the...
Page 69 - When this time is exactly one of the instants for which the required quantity is put down in the Ephemeris, nothing more is necessary than to transcribe the quantity as there put down. But when, as is mostly the case, the time falls between two of the times in the Ephemeris, we must ohtain the required quantity by interpolation.
Page 429 - AA'. It is, however, quite accurate enough for the purpose of determining the variation of the compass at sea, which is the only practical application of this problem. CHAPTER IX. THE MERIDIAN LINE AND VARIATION OF THE COMPASS. 272. THE meridian line is the intersection of the plane of the meridian with the plane of the horizon. Some of the most useful methods of finding the direction of this line will here be briefly treated of; but the full discussion of the subject belongs to geodesy. 273. By...
Page 69 - In the greater number of cases in practice, it is sufficiently exact to obtain the required quantities by simple interpolation ; that is, by assuming that the differences of the quantities are proportional to the differences of the times, which is equivalent to assuming that the differences given in the Ephemeris are constant.
Page 341 - A taps upon a signal key* at an exact second by his clock, thereby producing an audible click of the armature of the electro-magnet at B. The observer at B may not only determine the nearest second by his clock when he hears this click, but may also estimate the fraction of a second; and it would seem that we ought in this way to be able to determine a longitude within one-tenth of a second.
Page 24 - In this system the ecliptic is taken as the primitive circle, and the secondaries by which points of the sphere are referred to it are called circles of latitude. Parallels of latitude are small circles parallel to the ecliptic. The latitude of a point of the sphere is its distance from the ecliptic measured on a circle of latitude, and its longitude is the arc of the ecliptic intercepted between this circle of latitude and the vernal equinox. The longitude is reckoned eastward from 0° to 360°.