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aberration according accurate altitude apparent applied approximate assumed axis azimuth becomes beginning centre chronometer circle clock co-ordinates computed condition constant correction corresponding declination deduced denote determine difference direction earth eclipse effect employed Ephemeris equal equations error EXAMPLE expressed formula given gives greater Greenwich height hence horizon hour angle increase instant interval known latitude limb limit longitude mean meridian method moon moon's nearly nutation observed obtain parallax plane pole position practical preceding precession precision probable proper motion quantity reduced refraction regarded respectively result right ascension semidiameter sidereal simple sin² sphere star substitute sufficient sun's suppose surface taken term tion transit triangle true vertical whence zenith distance
Page 164 - 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 309 - ... more and more diverge from the truth. The methods referred 'to in the preceding articles are, therefore, generally to be preferred. 212. The latitude may also be found from two altitudes by the simple method proposed by Captain SUMNER, for which see Chapter VUL 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...
Page 30 - 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 665 - The squares of the periods of revolution of any two planets are proportional to the cubes of their mean distances from the sun.
Page 585 - ... 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 of the transits of the planets (by Art. 322), yet it is more convenient in...
Page 86 - 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 215 - ... the condition that the sun should be near the prime vertical may then be satisfied within a few minutes of noon; and in case the ship's latitude is exactly equal to the declination, it will be satisfied only when the sun is on the meridian in the zenith. In such cases the two equal altitudes may be observed within a few minutes of each other, and all corrections, whether for change of latitude or change of declination, may be disregarded. CHAPTER VI. FINDING THE LATITUDE BY ASTRONOMICAL OBSERVATIONS....
Page 55 - A sidereal day is the interval of time between two successive upper transits of the vernal equinox over the same meridian.
Page 73 - ... instant. When the sun is on a meridian in west longitude, the Greenwich apparent time is precisely equal to the longitude, that is, the Gr.
Page 188 - ... will be fully discussed in Vol. II. It will there be seen, also, that the time may be found from transits over any vertical circle. 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...