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adjustment altitude angular distance apparent approximate arithmetical mean assumed azimuth centre chronometer circle reading coefficient coincidence collimation axis computed constant declination axis declination circle deduced denote determined difference direction division elimination equal equations of condition equatorial star eye piece flexure follows formula given gives graduated Hence horizontal hour angle latitude lens limb magnifying power mean error measure meridian circle method of least micrometer thread microscopes middle thread moon's motion nearly normal equations number of observations object obtained ocular parallax parallel perpendicular pivots plane pole position angle position circle prime vertical probable error rays reduced refraction reversed revolved right ascension rotation axis screw semi-lens sextant sidereal sight line spirit level star substituted suppose telescope theodolite tion transit instrument transit threads tube unknown quantities vernier weight whence zenith distance zenith telescope zero
Page 97 - ... middle between them. The adjustment of the telescope when necessary is effected by means of two small opposing screws in the ring which carries it. • 85. The index correction. — Having made the preceding adjustments, it is necessary to find the point of the graduated arc at which the zero of the vernier falls when the two mirrors are parallel ; for all angles measured by the instrument are reckoned from this point (Art. 80). If this point is to the left of the actual zero of the scale by...
Page 307 - If the distance of the point from the origin, x=a> when v~ 0, c=2fa, and v*=2f(ax) ; (112) and since only the ordinates on the axis of x are involved, the velocity of the point on the curve depends not on the curve described, but on the difference of the ordinates...
Page 558 - The principle upon which it is proposed to solve this problem is, that the proposed observations should be rejected when the probability of the system of errors obtained by retaining them is less than that of the system of errors obtained by their rejection multiplied by the probability of making so many, and no more, abnormal observations.
Page 367 - N (the polar axis) is directed toward the elevated pole of the heavens, and it therefore makes an angle with the horizon equal to the latitude of the place (p.
Page 340 - ... general character than it possessed at first As now constructed, it can be used at all zenith distances, and may be regarded as designed for the comparison of any two nearly equal zenith distances in any azimuths. The method of finding the latitude by this instrument, now known as...
Page 92 - Sextant rests on the optical principle that " if a ray of light suffers two successive reflections in the same plane by two plane mirrors, the angle between the first and last directions of the ray is twice the angle of the mirrors.
Page 96 - Hold the instrument so that its plane shall be nearly vertical, and bring the direct and reflected images of the sea horizon into coincidence. Then incline the instrument until its plane makes but a small angle with the horizon ; if the images still coincide, the two glasses are parallel: consequently, if the index glass is perpendicular to the plane of the sextant, the horizon glass is also in adjustment. Any distant and well defined terrestrial object may be substituted for the star or the sea...
Page 15 - ... proportional to the quantity of light which falls on the surface of the two objectives respectively; but these surfaces are proportional to the squares of the diameters of the objectives, and hence the brightness of the images is proportional to the square of these diameters. On the other hand, let us suppose two telescopes, with object glasses of equal diameters, to have different magnifying powers; then one and the same quantity of light is distributed over the larger and over the smaller image,...
Page 94 - Fig. 1 represents the most common form of the sextant constructed upon these principles. The frame is of brass, constructed so as to combine strength with lightness; the graduated arc, inlaid in the brass, is usually of silver, sometimes of gold, or platinum. The divisions of the arc are usually 10' each, which are subdivided by the vernier to 10". The handle H, by which it is held in the hand, is of •wood. The mirrors M and m are of plate glass, silvered. The upper half of the glass m is left...
Page 50 - Hence we have f 00+? (180°+ 2)=3".58 sin (2 2+299° 30')+0".22 sin (42+4° 17') (30) The term in 4z is so small that we may suppose that it proceeds from the accidental errors of reading, and irregularities of the pivot, and we may, therefore, disregard it, as well as the subsequent terms in 6z, &c. BESSEL has shown* that if the section of a pivot which rests in a V is an ellipse, the centre of this ellipse will, as the instrument revolves, move in the arc of a circle the centre of which is the...