Page:Encyclopædia Britannica, Ninth Edition, v. 10.djvu/177

GEODESY appears as a vertical line about 10" in width. The best distance for this object is from one to two miles. It is clear that no correction is required to the angles measured by a theodolite on account of its height above the sea-level ; for its axis of rotation coincides with the normal to the surface of the earth, and the angles measured between (listant points are those contained between the vertical planes passing through the axis of the instrument and those poiiits. The theodolites used in geodesy vary in pattern and in size—the horizontal circles ranging from 10 inches to 36 inches in diameter. In Ranisden’s 36-inch theodolite the telescope has a focal length of 36 inches and an aperture of 25 inches, the ordinarily used magnifying power being 54 ; this last, however, can of course be changed at the requirements of the observer or of the weather. The pro- bable error of a single observation of a fine object with this theodolite is about 0"'2. Fig. 2 represents an altaziiniith theodolite of an im- proved pattern now used on the Ordnance Survey. The % W.J. ‘.15; z_y_,r_: FIG. ‘.?.—Altaziniuth Theodolite. horizontal circle of 14 inches diameter is read by three micrometer microscopes ; the vertical circle has a diameter of 12 inches, and is read by two microscopes. In the Great Trigonometrical Survey of India the theo- dolites used in the more important parts of the work have been of 2 and 3 feet diaiiieter,——-tlie circle read by five equidistant microscopes. Every angle is measured twice in each position of the zero of the horizontal circle, of which there are generally ten ; the entire number of measures of an angle is never less than 20. An examin- ation of 1407 angles showed that the probable error of an observed angle is on the average =l: 0'28. For the observations of very distant stations it is usual 165 to employ a lieliostat In its simplest form this is aplane mirror 4, 6, or 8 inches in diameter, capable of rotation round a horizontal and a vertical axis. This mirror is placed at the station to be observed, and in fine weather it is kept so directed that the rays of the sun retlecterl by it strike the distant observing telescope. To the observer the heliostat presents the appearance of a star of the first or second magnitude, and is generally a pleasant object for observing. .1strononu'cal Observations. The direction of the meridian is determined either by a theodolite or a portable transit instrument. In the former case the operation consists in observing the angle between a terrestrial object—generally a mark specially erected and capable of illumination at iiiglit——and a close circuinpolar star at its greatest eastern or western azimuth, or, at any rate, when very near that position. If the observation be made t minutes of time before or after the time of greatest azininth, the azimuth then will differ from its maximum value by sin 23 in seconds of angle, omitting smaller terms. Here the symbol 8 is the star's declination, 2 its zenith distance. The collimation and level errors are very carefully determined before and after these observations, and it is usual to arrange the observations by the reversal of the telescope so that collimation error shall disappear. If I), c be the level and collimation errors, the correction to the circle reading is b cot z i c cosec z, I: being positive when the west end of the axis is high. It is clear that any uncertainty as to the real state of the level will produce a corresponding uncer- tainty iii the resulting value of the azimuth,-—an uncer- tainty which increases with the latitude, and is very large in high latitudes. This may be partly remedied by observ- ing in connexion with the star its retlexion in mercury. In determining the value of “one division" of alevel tube, it is necessary to bear in mind that in some the value varies considerably with the temperature. By experiments on the level of I{amsden’s 3 foot theodolite, it was found that though at the ordinary temperature of G6’ the value of a division was about one second, yet at 32° it was about five seconds. The portable transit in its ordinary form lirirdly needs description. In a very excellent instrument of this kind used on the Ordnance Survey, the uprights carrying the tele- scope are constructed of niahegaiiy, each upright being built of several pieces glued and screwed together; the base, which is a solid and heavy plate of iron, carries a reversing apparatus for lifting the telescope out of its bearings, reversing it, and letting it down again. Thus is avoided the change of temperature which the telescope would incur by being lifted by the hands of the observer. Another form of transit is the German diagonal form, in which the rays of light after passing through the object glass are turned bya total reflexion prism through one of the trans- verse arms of the telescope, at the extremity of which arm is the eye—piece. The unused half of the ordinary telescope being cut away is replaced by a counterpoise. In this in- struiiient there is the advantage that the observer without moving the position of his eye commands the whole meridian, and that the level may remain on the pivots whatever he the elevation of the telescope. But there is the disadvantage that the flexiire of the transverse axis causes a variable collimation error depending on the zenith distance of the star to which it is directed ; and moreover it has been found that in some cases the personal error of an observer is not the same in the two positions of the telescope.

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