it is perhaps requisite to give some description of the mode of adjusting the vertical circle. Where the supports are high enough to allow the telescope to pass when turned round in a vertical plane, all the adjustments are the same as in the altitude and azimuth circle. [Cuict.s.] When the telescope is too long for this, the circle must be lifted out of its v's, in order to bring the line of sight again upon the object to be bisected, and then set down again. The operation is, in fact, the same, whatever be the nature of the vertical arch, and the adjustment is to be effected either by altering the level or the horizon tal wire until the reading is tho same in both positions of the telescope. If the observer has a Y love!, or collimator, he can set the cross of his level-wires horizontal, and this being bisected by the telescope of the theodolite, the vernier must be made to read zero, and the bubble of the level be brought to the middle by its proper screws. Or if the observer possess two stands (and there is a great convenience in having more stands than ono iu surveying), ho may place tho stands at a considerable distance from each other, and, fixing the instrument on one stand, and a mark of exactly the same height as the telescope-axis on the other, observe the mark, noting its elevation or depression. Now, exchanging the instrument and mark, he must re-observe the depression or elevation exactly as before. On drawing the figure, it will be seen that if light move in a straight line, —elevation at lower station=90—depression at higher station +the angle between perpendiculars to the earth's surface at each station, which last quan tity is known from the distance between the stations, and may be easily calculated, that is, depression — elevation = a known angle. But if the zero is wrong, depressions will be increased while elevations are diminished, and rice versa, so that depression observed — elevation observed — the known angle, instead of being = 0, will be + 2 error of the vernier, which may be corrected accordingly either by the adjust ment of the level or of the horizontal wire. Or, lastly, if the telescope has so much motion as that a star can be observed directly and by reflexion from mercury or any other fluid, the index-error of the verti cal circle may be most accurately determined thus :—Take any star in the meridian, and having observed it directly, observe it immediately after by reflexion. If great nicety is required, the observations should be repeated alternately several times, and the partial results reduced to the meridian. The mean reading between the meridian altitude and meridian depression is the reading which corresponds to the horizon, and the difference of this from 0, or scolding as the circle reads altitudes or zenith distances, is the error of the instrument, which may either be corrected or allowed for. This method, though very accu rate, requires some knowledge of the time, and is rather restricted by the choice of stars. It is nearly as safe to observe a star not far from the east or west point, first directly, then by reflexion, and lastly, directly, making the contacts at following whole minutes, or at even or odd minutes if the interval of a minute is not sufficient. As the stars rise nearly uniformly in this part of the heavens, the mean of the first and third observations should give an altitude equal to the depression observed midway. The discrepancy between these results will be the double index-error as before, which may be corrected or allowed for. By some of these methods the index-error of the vertical circle or sector is to be found.
In some of the older theodolites the telescope rides in v's at the top of the vertical arch, and is reversible as a level. The horizontal posi tion of the telescope 1'6 can therefore be found as in any other level, and the verniers of the vertical circle set to zero when the telescope is horizontal. The vertical angles measured by these instruments are not, however, to be greatly depended on. They are usually greatly out of balance in all positions of the telescope, except the horizontal position, and therefore they make better levels than altitude instru ments. This error may be partially got rid of by having a second level fixed to the instrument which is parallel to the plane of the vertical cirele, and adjusted to the telescope-level when that is horizontal. If this supplementary level is pretty well graduated, it will show the tilt which is given the plane of the instrument by want of balance, and so give the correction required.
It may be as well to mention here that the principal adjustment being that of setting the plane of the theodolite horizontal, or, more correctly speaking, the principal axis vertical, any horizontal level any where placed is sufficient for the purpose, though the cross-levels are a little handier. A box-level is convenient, if a stand and repeating-table are used, to bring the planes nearly horizontal, and to make both ends of the bubbles visible at first.
Many surveyors give themselves and the instrument-maker a great deal of unnecessary trouble by being very difficult on the chapter of excentricity, which they confound with error of division. The English dividing-engines, up to the present time, do not divide the circles upon their centres ; and therefore it frequently happens that the point round which the circle turns is not the point round which it is divided. When this error is not absolutely monstrous, the only effect is that one vernier gains what another loses, and that the mean of two opposite, or of three, four, or more equidistant readings, is precisely the same as if there were no excentricity. The advantage of a little excentricity that it gives yen the benefit of an unbiassed reading at every vernier as well as the : again, if all the verniers are recorded, it is a check on the dishonest observer, who might read one vernier and set down the rest. The instrument-maker must please his ignorant customer, and so either hammer his circle after it is divided, which may deform his work, or have an adjustment, which injures its solidity.
In Itanaaden's great theOdolite, and several others which have been made, the circle is read off by micrometer microscopes. Sometimes the microscopes revolve with the telescope (as the verniers do in our figure) ; sometimes the microscopes are fixed, and the circle revolves with telescopes, as in Ramsdcn's theodolite.
Ertel of Munich has made several astronomical theodolites in which the rays entering into the telescope are reflected along the horizontal axis by a prism. The observer therefore looks in at tho end of the horizontal axis, whatever the position of the star may be. The eye and body of the observer are more satisfactorily placed, and the sup ports are kept close and snug to the horizontal circle. The instrument is well adapted to one of its principal objects, observing stars at their passage over the prime vertical [Taman]; but there is some troublo in finding an object when you have no better direction to look for it than your eye affords. Excellent latitudes have been determined by instruments of this clans used in the prime vertical, and even the small vertical circle seems from some accounts to possess more power than from its dimensions we should have thought probable. As a general rule, the greater the number of readings, the less the effect of bad division, but beyond a limited number, the trouble and difficulty of reading-off is found in practice to counterbalance the advantage. Two opposite readings annul the effect of excentricity ; three or four equi distant readings destroy such an error as would arise from the circles becoming elliptic after it WAS divided, or any error which follows the same law. In small stoutly-made theodolites we think two the most convenient number, and they can be much more conveniently read off than a larger number. When the circle is so much as 8 inches in diameter and the telescope good, we should prefer three or tour readings. The vertical circle or sector may have two opposite readings. For many matters connected with surveying on the most extensive and accurate scale, see the memoirs published of the English, Scotch, and Irish Trigonometrical Survey; and the 'Base Mdtrique,' or accouut of the French measurement of an are of the meridian, although that survey was conducted by a different instrument. Similar opera tions have been carried on in many countries during the last seventy or eighty years, and the memoirs which relate to these surveys contain the best information which can be had on the subject.
It should be mentioned that Mr. Simms has introduced a Transit Theodolite, or portable altitude and azimuth instrument, for the use of the scientific traveller and engineer. The ordinary vertical arc of the theodolite is extended to a complete circle, and is read by two opposite verniers. The range of the telescope is unlimited, and by means of a diagonal eye-piece observations can be made in the zenith. The axis is perforated for illumination of the field of view. The instrument is 8 inches in diameter.