་ which done reverse the telescope in its (Y's) that is, turn it end for end, which you must do carefully, that it may not disturb the vertical arc, and if the bubble resumes its former position in the middle of the tube, all is right; but if it retires to one end, bring it back one half, by the screw which elevates or depresses that end of the level, (capstanhead screw,) and the other half by the tangent-screw of the vertical arc; this process must be repeated until the adjustment is perfect. The third adjustment is that which makes the axis of the levels, on the vernier plate, parallel to that plate. Set the instrument as nearly level as can be done by the eye, fasten the centre of the lower horizontal limb, by the staffhead clamp, leaving the upper limb at liberty, turn the plate until the telescope is over two of the parallel platescrews; then bring the bubble of the level under the telescope to the middle of the tube, by the tangent-screw; now turn the upper limb half round, then, if the bubble returns to the middle, the limb is horizontal in that direction; but if not, half the difference must be corrected by the parallel plate-screws over which the telescope lies, and the other half, by elevating or depressing the telescope, by turning the tangent-screw of the vertical arc; having done which, it only remains to turn the limb over the other two parallel plate-screws, and by their motion, set it horizontal. Having now levelled the limb-plates by means of the telescope level, the other air-bubbles upon the vernier plate may be brought to the middle of their tubes by giving motion to the screws which fasten them in their places. The vernier of the vertical arc may now be attended to ; it is correct if it points to zero, when all the foregoing adjustments are perfect; any deviation in it is easily rectified, by releasing the screws by which it is held, and tightening them again after having made the adjustment, or, what is perhaps better, note the quantity of deviation as an index. error, and apply it more or less to each vertical angle observed. This deviation is best determined by repeating the observation of an altitude or depression in the reversed position, of both the telescope and verneir plate: the two reading will have an equal and opposite errors, one half their difference being the index error. Such method of observing angles is the very best, since the mean of any equal number of observations taken with the telescope reversed in its (Y's,) must be free from the effects of any error that may exist in the adjustment of the vernier. The Method of observing Angles with the Theodolite. Place the instrument exactly over the station from whence the angles are to be taken, this may be done by means of a plumb line, then it must be set level by the parallel plate-screws, bring the telescope over each pair alternately; one must be unscrewed while its opposite one is screwed up, until the two spirit levels on the vernier plate, keep their position in the middle of their tubes while the instrument is turned round upon its shaff-head. First, clamp the lower horizontal limb in any position, and direct the telescope to one of the objects to be observed, moving it, till the cross-wires and object coincide; then clamp the upper plate, and by its tangent-screw make the intersection of the wires bisect the object; now read off the two verniers, the degrees and minutes of one and the minutes only of the other, (also read the seconds of both if possible,) and take a mean of the reading. Next release the upper plate and move it round until the telescope is directed to the second object, and clamp it, make the intersection as before directed; then read off the two verniers, and the difference between their mean and the mean of the first reading, will be the angle required. Or thus clamp the upper to the lower plate at 360°, and bisect the first object by the clamp and slow motion of the lower limb; then, turn the upper plate until you cut the second object as before; this second reading will be the angle required: but both verniers will not read the same, and consequently the mean of them should be taken for the true angle. Now it appears, it matters not at what part of the lower limb the upper is clamped, so the angle is read off every time an object is bisected, for the difference between any two readings will be the angle subtended by the objects observed. It would also appear, that it is not necessary for the lower horizontal plate to have any motion; but its use is of the greatest importance, as it gives us the means of repeating the measure of any angle we may wish to determine with great accuracy. The magnetic bearing of an object is taken, by reading the angle pointed out by the compass-needle when the object is bisected: or, more accurately, by moving the upper plate, (the lower one being clamped,) till the needle points to zero, at the same time reading off the horizontal limb, then turning the upper plate about, bisect the object and read again; the difference between the two readings will be the bearing required. In taking angles of altitude or depression, it is necessary that the object should be cut by the intersection of the wires, and that after observing the angle with the telescope in its natural position, it should be repeated with the telescope turned half round in its (Y's;) the mean of the two will do away with any error that may exist in the line of collimation. Of the Vernier. A vernier is a graduated index, which serves to subdivide the smallest divisions of a graduated arc or straight line. The vernier, so called from its inventor, Mr. Peter Vernier, published in 1631. It is found on the principle, that if two plates be so graduated, that in a given space, one shall have N and the other N+1 divisions, each division of one shall be greater or less than each division of the other, by a quantity equal to each division of the latter or former, divided by N. To conceive this principle more fully, let there be two graduated arcs, (fig. 12,) each subdivided, the limb CD, into half degrees, and the vernier AB into such parts as that 30 of its subdivisions, make 29 of the subdivisions of the limb, each division of the vernier will then be less than a division of the limb by one-thirtieth of the latter, but each division of the limb being half a degree; hence, a division of the vernier is 30'-1'. Consequently each division of the vernier will give one minute. Now it is plain, that for any position of the vernier, the number of the division line on it which coincides with one on the limb must express the number of minutes that the zero of the vernier is past the division line on the limb. The arc to be read by the vernier index in any position, is the arc intercepted in the direction in which the degrees are numbered between the zero line of the limb and vernier. To read off any arc, suppose up to NM, is 10° on the limb and 11', or cuts of the vernier, since the divisions of the limb and vernier, coincide at the 11th division of the vernier. Hence the angle to be read off is 10° 11'. The limb and arc is always read off by the microscope. One side of the vertical arc is constructed to observe angles of altitude and depression, and the other side to give the difference between the base and hypothenusein link for one chain. Of Instrumental Parrallax. Instrumental parrallax is often the cause of much error in surveying and levelling. A "pencil" of rays, is a portion of light distinct from the rest. Rays are either parallel, converging, or diverging. The word focus, signifies a fire-place. A lens is a medium, having at least one surface convex or concave. The rays of light which proceeds from an object, and entering the eyes, convey to us the sense of vision, move in straight lines, unless turned from their course by refraction, and such portion as can enter the eyes may be considered as parallel straight lines; the more remote the object is, the nearer will this be the case. Let us now imagine the lens applied to the construction of a telescope, and figure 13 to represent a section of it; the image of an object at a distance, in the direction of C, would be formed at the point O, the focus of the object glass; let MN be the eye-glass, which is fixed in a slide. This eye-piece is no more than a microscope, to observe the image of the object at O; in order to do this, the eyeglass must be made to slide either in or out, such as to cause its focal point to coincide therewith, making that point the common focus of the two glasses. The observer can tell at once when this is the case, for he will obtain a perfect view of the object. Next, motion must be given to the slide by turning the milled head-screw, which gives motion to the slide by rack work; this will carry both wires and the focus of the eye-glass to coincide with the focus of the object-glass. When this is done, the adjustment of the telescope will be perfect, and |