A Manual of Spherical and Pratical 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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J.B. Lippencott., 1864
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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 128 - It may also be defined as the sine of the angle of incidence divided by the sine of the angle of refraction, as light passes from air into the substance.
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 255 - Mean Time, suppose the altitude of the Pole Star, when corrected for the error of the instrument, refraction, and dip of the horizon, to be 46 17' 28
Page 55 - This time \ve shall have constant occasion to use, both because longitudes in this country and England are reckoned from the Greenwich meridian, and because the American and British Nautical Almanacs are computed for Greenwich time.* The difference between the local time at any meridian and the Greenwich time is equal to the longitude of that meridian from Greenwich, expressed in time, observing that 1* = 15. The difference between the local times of any two Fie- 10meridians is equal to the difference...
Page 593 - A/T of the planet's parallax, but also, hy the last-mentioned relation, that of the solar parallax.* The transits of Venus will afford 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...
Page 84 - The quantities a, c, &c. may be inserted in the table, and will thus complete the row of differences standing in the same line with the function from which 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 unit...
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 53 - The numbers here given, show, for Greenwich Apparent Noon, the distance of the mean Sun from the meridian, or the portion of time to be added to, or subtracted from, (according to the precept at the head of the column,) Greenwich...
Page 103 - ... 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 centre of the earth, and are called geocentric, or true, places. Those observed from the surface of the earth are called observed, or apparent, places. It must be remarked, however, that the geocentric places of the Ephemeris are also called apparent places when it is intended * See Attr.

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