448.—Simple Theodolite.—The plain theodolite being of the cheapest construction may be stripped of its superior functions, which are used for testing its adjustments, and be made into a simple angle measurer for laying out or plotting small parcels of ground, small estates in building ground, local sewage, gas and water works, and many other cases of small surveys, for which purpose it will be found sufficient, with a saving of about half the cost of a perfect theodolite. The instrument shown above, Fig. 193, was designed by the author to meet the above cases. In this instrument there is no vertical arc. The telescope has a socket axis carried upon a single standard. The axis cannot be seen in the figure from interference of the telescope placed in front of it. The telescope is arranged to be fixed in a level position by means of the loose pin being pressed in a pair of holes. It may then be used as a level by means of the spirit level shown on the vernier plate. The horizontal circle is divided to read with a single vernier to 3' of arc by means of a hand magnifier which is placed in the case with the instrument. There are internal and external axes, each provided with clamp and tangent motions to the horizontal circle, as with the plain theodolite. It is supported on a tribrach, the legs of which are upon the plan, art. 249.

If it be made with two verniers and divided upon silver it becomes a useful light instrument for filling in details of superior triangulation. Weight, about 4¾ lbs.

449.—Examination and Adjustment of the Theodolite.—The description given of a transit theodolite, arts. 369 to 389, will show that this instrument is provided with means of adjustment in every requisite direction. Larger transit instruments possess the same means of adjustment, but in some parts these have greater refinement. Plain theodolites have the like methods, except in the case of the transverse axis, which is adjusted once for all by the maker. It will be necessary, therefore, to limit our space to a discussion of the examination and adjustments of the transit theodolite only, of which we have given a full description, arts. 369 to 389, noting only where variations occur from partial differences between this and others.

450.—A theodolite as it comes from a respectable maker is usually carefully adjusted in all its parts. If it has travelled a long journey it is, however, well for an experienced surveyor to put it through its various adjustments. The corrections, if any are required, will be generally very small, and these in all probability will be of the same kind as will occur in the use of the instrument and in the accidental conditions to which it may be subjected during conveyance from place to place upon a survey; therefore it is well to be familiar with them.

When a new instrument is received from the maker, it is necessary to observe attentively the manner of its packing as it lies in its case. It is well at first to lift the parts a few times gently out of the case and replace them, so that this may be done at any future time with certainty and without any risk of strain upon the instrument, remembering always that an instrument in conveyance is much more liable to be thrown out of adjustment by carelessly replacing it in its case than from its ordinary use, art. 42.

451.—For examination or adjustment of the theodolite the tripod stand should be at first firmly fixed with legs extended to an angle of about 70° to the ground, which should be solid and hard. As the telescope has to be brought to the height of the observer's eye, it is well to mention his stature in ordering an instrument. The tripods that are made for tall men are often awkward and unsteady if the legs are extended to bring the telescope down to the height of a short person. They may always be cut down and refinished by the maker. When the tripod is set up the toes should be each separately pressed down, so that future slips are impossible. This being done the instrument is taken from its case and grasped firmly by the body part under the horizontal circle, and placed on the tripod at once, then screwed firmly but not too tightly down upon its bearing surface. With a 6-inch transit theodolite the upper part is sometimes detached and packed separately in its case. Where this is so, after the body part is fixed on the tripod, the cleats on the top of the standards must be opened out, and the upper part of the instrument, lifted by its telescope, be slowly lowered into its bearings, being particular at the same time that the clips under the telescope embrace their stay-piece on the standard. The cleats must then be closed over the pivots. The instrument being set up to position, all levels may be adjusted to the centres of their runs, and every part clamped sufficiently to make the instrument firm, but in no case using violence to produce a strain in any part. The clamps or other fittings are afterwards separately released as they are required for examination or adjustment of the parts to which they relate.

452.—Examination for Coincidence of Exterior and Interior Vertical Axes.—The theodolite being set up solidly, and all clamps fixed as above described, unclamp the lower or exterior axis clamp and set the vernier plate levels parallel with opposite pairs of parallel plate screws if the instrument adjusts on the parallel plate system, art. 193, or one level parallel with one pair of foot screws if it is made on the tribrach system, art. 234. Now adjust both levels. Turn the instrument half round (180°) and observe if the levels keep the centres of their runs. If they do so they are in adjustment to the exterior axis. If found imperfect, the adjustment by the capstan heads of the levels is set, by means of the tommy or pin which is provided in the instrument case, for half the error as it appears by the bubble, the other half being given by readjustment of the parallel plate or tribrach screws. In these adjustments it is necessary to be particular always to observe the bubbles after the hands have left the instrument, not during the adjustment, which produces strain upon the instrument. Now clamp the lower clamp and note if this clamping has disturbed the levels. If the levels are very sensitive it will do so in a slight degree, but the disturbance should be very small if the clamp is perfect. Now unclamp the vernier plate and note again if this clamp disturbs the levels: this should also affect them very little. Now observe the levels if they stand exactly as they did when the exterior axis was unclamped at their present position, and also at right angles to this. If they remain as before the axes are truly concentric. If they do not, there is no remedy except at the hands of the maker. The vertical axis to which the above examination applies is considered the most important part of the instrument, and the work should be thoroughly well done; nevertheless, if the levels are very sensitive, which they seldom are, such minute faults may be detected, that a small allowance may be made for imperfection of work, and the instrument still be considered a sound one. In the use of the instrument it is always well, after the circle is set either by the magnetic compass or by sighting a distant point for direction, to clamp the lower clamp and readjust the levels to the vernier plate. In this way the axis that will afterwards be used for triangulation will be vertical, and small errors due to want of coincidence of axes be eliminated.

453.—Examination of the Azimuthal Level.—This level, which is placed over the telescope, being made of superior sensitiveness to the vernier plate levels, is much more accurate for adjusting the vertical axis, but much slower in operation for testing. The verniers of the vertical circle should be accurately set to zero, in which position the run of the bubble should exactly agree with those on the vernier plate when placed parallel with them in any direction, but this level may also be considered by itself. Assuming the circle and verniers correct, or otherwise, it may be reversed over the axis by half turns in all positions over the parallel plate or tribrach screws, and adjusted by the capstan heads half the error, as before described, for the vernier plate levels.

454.—Examination of the Divisions and Centring.—The vernier plate being unclamped, the verniers, if two, should be brought approximately to 0° (360°) and 180°, and then the plate be lightly clamped. The microscopes or readers are then to be set truly radial with the zero reading of the verniers, and the tangent screw adjusted to make one of the readings, say the 360°, exact. The opposite reading, 180°, is then carefully examined, and the error discovered, if any, is due to the imperfection of centring, assuming the dividing perfect. At this point it is well to record the amount of difference. The same examination is then repeated with the 90° and 270°. In a properly centred and accurately divided 5-inch or 6-inch theodolite this difference will not amount to more than 1' error, in larger instruments proportionately less. Owing to the difficulties at all times of reading the circle correctly from difference of direction of light, and what is termed personal error, it is well to entirely repeat this examination, turning the instrument half round. It is also well to repeat the examination at what are termed the half points, 45°, 235°, and 135°, 315°. This will sometimes detect the error of centring, if there be any, in its true direction. The purpose of the two verniers is to discover this error. In practice the two readings are always taken, and the mean is considered as the true reading. Where there are a greater number of verniers exactly the same principle is followed, but the mean of three or more readings is taken, which of course assures great accuracy.

Examination of the telescope has been discussed arts. 107 to 115.

455.—Testing an Instrument for its Stability.—The stability of an instrument will depend principally upon the quality of the workmanship; but the same test will also indicate, at any time, whether the instrument has been submitted to sufficient wear to need the repair of the optician. For this examination the eye-piece of the telescope requires to be focussed against a piece of white paper held obliquely in front of the object-glass so as to throw a soft white light into the telescope. After the eye-piece is focussed, any distant point may be taken for a sighting object upon which to direct the telescope. This point should be focussed by the telescope so that its image falls centrally upon the intersection of the webs. The eye should then be shifted up and down or sideways within the range of clear vision of the webs in the eye-piece to ascertain that there is no parallax, that is, that the adjustments of the eye-piece and the telescope are in true focus upon the webs. This preliminary arrangement being made, which will serve in future examination for other adjustments, all parts of the instrument should be examined to see that the clamps are firmly clamped. The object to be used as an index or sighting point should be brought by the clamp and tangent motions exactly upon the intersection of the webs as they appear in the telescope, when the following examinations are to be made.

456.—Tripod Head Examination.—The telescope being sighted upon an index point, and all clamps screwed down and the tripod firmly fixed on the ground, take the tripod head of the theodolite in both hands and give it a twist of about a pound pull in one direction; then examine the telescope to see if the index point is displaced in the telescope. If it still stands correct give a like twist in the opposite direction and again examine the telescope. If it stands these opposite firm twists retaining its position the stand is good and in good order. If it does not, assuming good construction of stand, the remedy may be found in tightening up all its screws; but if its construction is bad it will not, even after this tightening, keep in order. There is no doubt that more inaccurate triangulation is caused by defective tripods than from any other cause whatever. A perfect instrument is useless on a bad tripod.

457.—General Examination of Fixed Parts.—The stand being found good by the above process, the general fittings of the instrument may be examined, after clamping all parts and directing the telescope to a distant point, by taking a quill pen by its root or pipe and pressing its feathered end upon one side of the eye-piece of the telescope sufficiently to bend the quill, and afterwards examining the telescope to see that the webs are not displaced from the index point. This may be done first to the right hand and then to the left. If the webs still cut the same object it is clear that the whole of the centres, fittings, clamps, and tangent screws of the horizontal circle are correct. If any displacement be discovered, the amount of difference between the right and left handed twists will be the total error due to imperfection of work or wear as the case may be. In exactly the same manner, but by pressing the eye-piece upwards and downwards, the transit axis and its fittings may be examined. If the instrument be not generally sound enough to bear the above tests, other critical adjustments become necessary. For the correction of faults that may be included in the above operations, the parts of the instrument must be separately examined.

458.—Examination of the Transit Axis.—The best means of adjusting this axis in a theodolite is by a striding level, art. 400. When this is not provided with the instrument, and it is often omitted for economy, the axis is generally better to be left as it is adjusted in this particular, by the maker. To adjust the transit axis the vernier plate bubbles are set exactly true by reversing angles of observation. The cleats are opened and the striding level is mounted above the instrument resting upon the pivots. The telescope is placed exactly over an opposite pair of parallel plate screws, or parallel with two screws if the base adjustment be on the tribrach principle. The striding level is then carefully observed and reversed on the pivots. If there be any difference in the run of the level bubble the transit axis is adjusted by raising or lowering the movable V on which one pivot rests by turning the capstan nuts until it is quite correct, if the instrument has this old-fashioned arrangement, or if not, by a few strokes of fine emery paper upon the V which is higher. This adjustment is almost superfluous, as the axis is generally set right at first, and is not subject to change, especially if solid without an adjustable V.

459.—For larger theodolites of 12 inches and over, the transit axis is much better adjusted by means of an artificial horizon, which will be described further on. By the use of this instrument in the northern hemisphere the pole star is first observed directly by the telescope, and then by its reflection from the horizontal surface of clean mercury placed on the ground at 12 feet or so from the instrument. If the star and its reflection cut the webs equally in directing the telescope by movement of its transit axis only from the one to the other, this axis must be truly horizontal. If the vernier plate be then turned a quarter of a revolution and the exterior axis a quarter of a revolution, the telescope transitted and observation be repeated, the verticality of the principal axis may be adjusted with perfect certainty. The principal axis should be moved one-eighth of a revolution all round and the bubble examined at every position to assure perfect adjustment. With the plain theodolite, Everest's and some others, the transverse axis is fixed to position by the maker, therefore cannot be adjusted.

460.—Examination and Adjustment of Webs, Lines on Glass, or Points.—The ordinary manner of webbing the diaphragm of a theodolite was shown Fig. 23. Horizontal angles are taken by the upper intersection of the diagonal webs or lines. A single web is placed horizontally for taking vertical angles: it is necessary that this should be nearly true. When the theodolite has its axis vertical, as shown by the vernier plate bubbles being in the centre of their runs, if one end of the horizontal web or line be set to cut a small distant object by sight in the telescope, the same object should keep on the web while the tangent screw of horizontal circle is moved a distance sufficient to traverse it, the hand being always taken from the screw while the observation is made. If it does not do so, the collimating screws should be lightly tapped with the back of a penknife in the direction to set it right. These screws have a slot in the body of the telescope, under the loose covering plate, sufficient to permit of this small adjustment.

461.—Adjustment of the Telescope to Vertical Collimation.—The eye-piece is first focussed as before against a piece of white paper held obliquely in front of the object-glass until the webs are sharply seen. The axis of the telescope is then examined for vertical collimation error. The method of doing this has been already described for a telescope placed in Y's, as it is in the Y-level, and the plain theodolite, art. 200. The only difference with the transit theodolite is that instead of turning the instrument in its Y's, the telescope is transitted, as it is termed, over on the transverse axis exactly half a revolution, or 180° as seen by the vernier reading; and the horizontal circle is moved also half a revolution, so that the telescope points again on the same distant point which is used for an object. If the webs or lines still cut the same point or small object, they are in vertical collimation, or truly in the optical axis of the telescope, as regards the vertical direction which this adjustment is intended to secure, presuming the circle has been correctly divided and centred and the verniers accurately set. If the webs or lines do not cut the same point, half the error is corrected by the top and bottom collimating screws near the eye-piece. This process is repeated until it is exact, being particular to observe, as before mentioned, that there is no parallax. This adjustment cannot be made with the plain theodolite; but the zero of altitude may be examined on both sides of the arc.

For the transit theodolite, adjustment by means of a collimator, art. 229, is much more convenient and exact, as lateral and vertical errors in the position of the webs can be detected in one operation. When a Y-level is at hand, this may be used as a collimator if it is first set to solar focus.

462.—Examination for Perpendicularity of Transit Axis and Telescope.—The whole of the lower part of the instrument retaining its position with all clamps firm, open the cleats upon the top of the standards so as to release the transit axis. Now release one of the clip screws and gently lift the upper part of the instrument out of its bearings. Turn the telescope the reverse way upwards, which will be in this case bubble downwards. Release the clamp and turn the clips to the reverse position of the telescope, and reverse the position of the pivots in their bearings. If the telescope be now directed to the same point as before, and the webs still fall upon it, the telescope adjustment is at right angles to the transit axis.

463.—Examination of the Magnetic Needle.—If the needle be placed in a circular box, as shown in the engraving, Fig. 30, it admits of no adjustment. If it is placed in a trough, Fig. 161, it admits of adjustment generally by lateral screws to a portion of its division. If the needle is used for a survey, it is set to the zero of the horizontal circle by clamping the vernier plate and bringing the northern vernier to zero, then releasing the exterior axis and bringing the needle by the motion of the lower tangent screw to the zero of its circle. The corrections of the needle for giving true north have been discussed, art. 132. It is difficult to read an ordinary edge-bar needle correctly, it is also difficult to mount it perfectly true. It may be read at both ends, and if the 0° and 180° points cut the line fairly it is considered correct; if not, the mean of the difference may be taken. In some instruments a microscope is mounted over the needle point that the needle may be adjusted to a web; but British surveyors seldom feel confident of surveys by the magnet, and for triangulation generally prefer to employ a certain number of distant fixed points, the bearings of which are at first as accurately ascertained as possible, for referring objects, rather than to refer frequently to the magnet. When the needle is out of use it should always remain lifted off its centre. When the instrument is put by for a long period it is better to place it in a vertical position and free the needle, so that it rests in the magnetic meridian, in order to preserve its magnetism as much as possible.

464—Use of the Theodolite.—In setting up a theodolite, place the tripod nearly over the position in which it is to be used. This is frequently the socket hole formed in the earth by the removal of a ranging pole or picket, to be described Chapter XVII. Then, after it is set up, suspend the plummet from the hook, which will be found inside the head of the tripod. If the ground be solid and level, then by shifting the toes of the tripod slightly, and firmly pressing them down one by one, the centre of the plummet may be brought easily within about ·25 of an inch of its true position. The theodolite is then placed on its tripod, observing that the telescope is in a position easy to be used. The centre of the picket-hole, when this is used for a station, is generally taken by guess-work, which is considered near enough. It may be taken with a little more refinement by placing, in the same hole, a short false picket of nine inches or so in length, but of the same diameter as the ordinary picket, the top of which is cut off smooth and polished, and has lines sawn across its centre inlaid with ebony, described in Chapter XVII. The false picket is carried about with the theodolite. With Everest's and many other forms of theodolites the hook is fixed under the axis of the instrument. In this case it is usual to set the theodolite before adjusting it to the station, as there is no separate hook to the tripod, which also occurs with all framed stands.

465.—Where there is no hook to the tripod an excellent plan is to have a false centre, which may be a piece of turned wood with a hole through it, to fix on the top of the tripod head. The plummet cord adjusts through the hole. This false centre is also convenient where the axis adjusts to position by a mechanical stage. Fig, 194 shows a false centre formed of a piece of ivory with two slots to permit the cord to loop over and yet hang centrally.

466.—It may be observed that if the tripod be set up out of level, which it must necessarily be in many cases, the hook, if attached to the stand and following its inclination, will not hold the cord at a truly vertical position to the axis. Surveyors commonly allow a little for this inclination. It is much more accurate to have the cord suspended directly from the axis of the instrument when it is constructed to admit this. Then if a false centre be used the plummet should be suspended a second time from the axis hook. With the kind of runner shown in the figure this need take little time, as it is instantly detached and replaced.