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aberration altitude apparent place argument arithmetical mean ascension and declination axes azimuth called celestial sphere centre circle of latitude compute constant quantity correction corresponding cosine cotang deduced denote determined Diff differential coefficients diurnal motion earth easily equa errors of observation expression find the following fixed ecliptic following equation following form formulae function given hence horizon hour angle integral interpolation introduce logarithms lower culmination mean noon meridian moon multiply number of observations numerical values nutation obliquity orbit order to find parallax plane pole positive axis precession probable error probable values proper motion radius refraction residual errors right ascension rising or setting semi-major axis sidereal sidereal day sine spherical squares star substitute subtract tables tangent Taylor's theorem tion triangle unknown quantities vernal equinox vertical circle wish to find zenith distance
Pàgina 375 - The cubes of the mean distances of the planets from the sun are proportional to the squares of their times of revolution.
Pàgina 105 - When the sun is north of the equator the days are longer than the nights in the northern hemisphere ; and when the sun is south of the equator the reverse of this is the case; and in the southern hemisphere, of course, similar changes take place. At the equator the day is always 12 hours long, but at 8° 34' north or south of it, the length of the day extends to 12 J hours.
Pàgina 5 - C cos a — cos B cos C and changing the letters we get the following three equations, which correspond to the formulae (2), biit again contain angles instead of sides and vice versa: cos A = sin B sin C cos a...
Pàgina 113 - The cause of this motion is shewn, by physical astronomy, to arise from the attraction of the sun and moon on the excess of matter at the equatoreal parts of the earth.
Pàgina 3 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Pàgina 196 - For since (—) and (c—} are the differential coefficients \dtJ \dtJ of a and cT, if the heliocentric place of the planet is changed whilst the place of the earth remains the same, the second members of the two equations give the places of the planet at the time T? but as seen from the place which the earth occupies at the time t. Note. The motion of the earth round the sun and the rotation on the axis are not the only causes which produce a motion of the points on the surface of the earth in space,...
Pàgina 161 - Atmospheric currents, in high latitudes, when undisturbed, are westerly, particularly in the winter season. If storms and gales revolve by a fixed law, and we are able, by studying these disturbing causes of the usual atmospheric currents, to distinguish revolving gales, it is likely that voyages may...
Pàgina 74 - ... remain fixed in the celestial sphere. If we lay a great circle through the pole and the star, the arc contained between the star and the equator is called the declination and the arc between the star and the pole the polar-distance of the star. The great circle itself is called the declination -circle of the star. The declination is positive, when the star is north of the equator and negative, when it is south of the equator. The declination and the polar -distance are the complements of each...
Pàgina 5 - A = cos B cos C — sin B sin C cos a ; and changing the signs of the terms, we obtain, cos A = sin B sin C cos a — cos B cos C.
Pàgina 324 - If then we substitute in place of the indeterminate co-ordinates a;, y, z the co-ordinates of a place on the surface of the earth, referred to the same system of axes, we obtain the fundamental equation for eclipses. For this purpose we must first determine the position of the line joining the centres of the two bodies. But if a and d be the right ascension and declination of that point, in which the centre of the more distant body is seen from the centre of the nearer body or in which the line passing...