A Manual of Spherical and Practical Astronomy: Theory and use of astronomical instrumentsJ.B. Lippincott Company, 1874 |
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Common terms and phrases
angular distance azimuth centre chronometer circle reading coincidence collimation axis computed constant declination axis declination circle denote determined difference division east equations of condition equatorial star eye piece flexure follows formula given gives graduated heliometer Hence horizontal hour angle latitude lens limb magnifying power mean error measure meridian circle method micrometer thread microscopes middle thread moon's motion nearly normal equations number of observations obtained ocular optical axis 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 sin² spirit level star substitute suppose T₁ t₂ tan² telescope theodolite tion transit instrument transit threads tube unknown quantities vernier vertical circle weight whence zenith distance zenith telescope
Popular passages
Page 309 - 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 488 - Thus, the principle that the most probable values of the unknown quantities are those which make the sum of the squares of the residual errors a minimum, is not limited to the case of direct observations, but is entirely general. The principle is readily extended to observations of unequal precision. For if the degree of precision of the observations M, M', M".
Page 369 - ... carried out precisely in the same manner as with the zenith telescope. The different method of reversing the instrument by lifting it from its Vs instead of revolving directly about a vertical axis, does not in any way affect the principle, the essential condition of TALCOTT'S method being always observed, namely, that the relation of the level and the telescope is to be absolutely the same at the observations of both stars of the pair. CHAPTER IX. THE EQUATORIAL TELESCOPE. 242. THE equatorial...
Page 52 - 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...
Page 369 - 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 490 - A, or by comparing the errors which are committed with equal facility in the two systems. The errors to be compared must occupy in the two systems a like position in relation to the extreme errors, and we may select for this purpose in each system the error which occupies the middle place in the series of errors arranged in the order of their magnitude, so that the number of errors which are less than this assumed error is the same as the number of errors which exceed it.
Page 39 - ... index outside the microscope, or, indeed, wholly separate from it, the microscope being used exclusively to measure the fraction of a division. 24. The probable error of a reading of one microscope being e, that of the mean of m microscopes...
Page 94 - 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 105 - With a sextant thus furnished, we begin by directing the sight line towards the image in the mercury; we then move the index until the bubble plays, taking care not to lose the image in the mercury ; the reflected image from the sextant mirrors will then be found in the field, or will be brought there by a slight vibratory motion of the instrument about the sight line. It is found most convenient to attach the level to the stem which carries the reading glass, as it can then be arranged so as to...
Page 560 - 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.