An Introduction to Spherical and Practical Astronomy

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Ginn, 1891 - Least squares - 158 pages
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Page 110 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180 and less than 540. (gr). If A'B'C' is the polar triangle of ABC...
Page 75 - O between the equator and the pole and between the zenith and the horizon are both right angles, the altitude of the pole above the horizon is equal to the latitude of the place.
Page 143 - A weighted arithmetic mean is obtained by multiplying each value by some non-negative weight before summation and then dividing the sum of the products by the sum of the weights.
Page 5 - The longitude of a place is, therefore, measured by the arc of the equator intercepted between the meridian of the place and that of Greenwich ; or, which is the same thing, by the spherical angle at the pole included between these meridians.
Page 3 - ... the body. This last circle is nothing else than the meridian of the body. The horary angle is measured by the arc of the equator which has passed, or will pass, under the meridian of the observer, between the instant of observation, and the moment when the heavenly body is upon this same meridian. Azimuth. The azimuth of a body, is the arc of the horizon intercepted between the south point, and that in which a vertical circle passing through the zenith and the body, cuts the horizon. Amplitude....
Page 48 - ... fasten, to the up-and-down piece, the collar into which the telescope screws. This adjustment is not very liable to be deranged. Having now gone through the principle and construction of the sextant, it remains to give some instructions as to the manner of using it. It is evident that the plane of the instrument must be held in> the plane of the two objects, the angular distance of which is required: in a vertical plane, therefore, when altitudes are measured; in a horizontal or oblique plane,...
Page 107 - The polyconic projection is based upon the development of the earth's surface on a series of cones each one tangent to and having a common axis with the earth. In this projection a different cone is used to each parallel of latitude. Each cone has the parallel for its base and its vertex at the point where a tangent to the earth at the given parallel of latitude intersects the earth's axis. The...
Page iii - France, and his book is much used as a school text-book in Paris and elsewhere. EDUCATION AND TEXT-BOOKS. An Introduction to Spherical and Practical Astronomy. By Dascom Greene. 12mo, pp. 158. Boston: Ginn & Co.
Page 66 - DIFFERENCE OF LONGITUDE. The difference of longitude of two places on the earth's surface is the arc of the equator included between their meridians, or the corresponding angle at the pole. Fr: Difference de Longitude; Ger: Langenunterschied.
Page 123 - According to the theory, the most probable values of a series of related observations are those for which the sum of the squares of the errors is a minimum. Here is not the place to go into the details of the mathematical proofs of the Method of Least Squares...

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