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accuracy adjustment altitude angle apparent applied approximation arithmetical mean ascension and declination assumed axis azimuth Bessel catalogue celestial sphere chro chronograph chronometer circle circumpolar stars co-ordinates coefficients collimation computation constant convenient corresponding culmination derived determined difference differential earth ecliptic elongation emersion employed ephemeris equal equations of condition equatorial intervals example expressed follows formula geocentric given gives Greenwich horizon hour-angle instant latitude limb logarithms longitude mean solar measured meridian method micrometer middle thread moon moon's right ascension multiplied Nautical Almanac normal equations nutation observatory obtained occultation parallax plane position precession prime vertical probable error proper motion reading reduced refraction screw semidiameter sextant sidereal star's stars observed Substituting subtract telescope tion transit instrument unknown quantities values vernier Washington weight write zenith distance zenith telescope
Page 157 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 301 - V's aa. Then the V's having been properly adjusted upon the pivot, h is loosened and the flat edge of the aperture in/ is pressed against the under side of the pivot by the spring /'. The elevation of the rod g above the glass plate is then measured by means of the spherometer.
Page 154 - The sine of the angle of incidence bears to the sine of the angle of refraction a ratio, which is always the same for the same two media and is called the index of refraction.
Page 122 - It may be denned as the angle formed with the plane of the equator by a line drawn from the place perpendicular to the surface of the "standard spheroid
Page 12 - It is a characteristic of the arithmetical mean, that it makes the sum of the squares of the residual errors a minimum. To illustrate this principle geometrically, suppose that several observations, made to determine the position in space of a point, A, give several positions around the true point, A- Connect the points given by observation by straight lines ; then the centre of figure or centre of gravity of the polygon...
Page 104 - ... Ascension, is the angular distance from the vernal equinox, measured on the equator. If a star is situated on the equator, then its right ascension is the number of degrees of the equator between the star and the vernal equinox. But if the star is north or south of the equator, then its right ascension is the arc of the equator intercepted between the vernal equinox and that secondary to the equator which passes through the star. Declination is the distance of a body from the equator, measured...
Page 25 - If, however, the observations are of unequal weight, the most probable value is found by multiplying each observation by its weight and dividing the sum of these products by the sum of the weights.
Page 122 - ... that in the spheroid considered in example 2 the resultant attraction at any point on the surface is proportional to the length of the normal between that point and the axis of revolution. 7. Express gravity on the surface of such a spheroid in terms of the latitude. [The latitude of a point on the surface is the angle made with the plane of the equator by the normal at the point. If E denotes the value of gravity at the equator, G the value in latitude A, and f the eccentricity of the generating...
Page 153 - When light passes from one medium into another, in a direction perpendicular to tha surface, it continues on in a straight line, without altering its course. When light passes obliquely from a rarer into a denser medium, it is refracted toward a perpendicular to the surface, and this refraction is increased or diminished in proportion as the rays fall more or less obliquely upon the refracting surface.