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of the mirror, care should be taken that the position of the eye is such that there will be no parallax. Such positions can be determined once for all when the mirror is at its greatest angle of elevation, by a second person reading the level directly while the observer finds the position from which the reading of the level in the mirror is the same. The notes will be kept in the form given in note-books. When once a number has been written down it must not be erased or made illegible. If wrong, a line will be drawn through it and the correct number written above.

The length of sights taken will depend on the condition of the atmosphere, but the rods should always be near enough to be seen distinctly. It will be seldom that lengths of sights greater than 150 metres can be taken. The back sight and fore sight corresponding to any instrument station must not differ in length by more than 10 metres, and the sum of the lengths of the back sights and fore sights between any two bench marks should be equal.

Whenever it is necessary that the line of levels should cross a river or other wide obstruction, a narrow place hould be irm points should be set upon the two banks; levels in good adjustment are set upon posts about 10 metres from each bench mark, and both levels go through the same operation.

The error of adjustment is first accurately determined. Call one of the levels A. A first reads on the bench mark near it, once with the telescope normal and once with the telescope inverted, then on the rod across the river five times with the telescope normal and five times with the telescope inverted. The error of adjustment of the level is again accurately determined. The rod across the river will need an extra vane. B performs the same operation simultaneously. A and B change places and repeat the observation at these new stations. The simultaneous levels eliminate refraction, the change of station eliminates curvature and small instrumental errors. Unless good results are obtained the levels should be repeated. If but one level can be used, the operation will be performed in the same order, but the time occupied in crossing must be as small as possible. With a single Kern level this process has given for a river 815 metres wide five results, the mean of which has a probable error of ±0.5 millimetre.

Permanent bench marks will be established at intervals of 3 miles along the river, and 5 miles on lines connecting the river line proper with the other levels or bench marks.

These bench marks will consist of a thoroughly verified tile 4 x 18 x 18 in. placed 3 ft. below the surface of the ground, and surmounted by a 4 in. wrought-iron pipe as a surface mark. The tile should have time to settle before levelling to it. Both tile and pipe will be suitably marked to designate the character of the point. In the centre of the upper surface of the tile a copper bolt will be leaded, the upper surface of which will be the point of reference. These bench marks will be placed where they can be easily found, and where they will not be disturbed. Property corners should be utilised where practicable. In addition to the above, benches should be established on permanent brick or stone structures by leading into them a horizontal copper bolt, with the letters U.S. P. B. M. and the number of the bench mark cut near A small hole in the centre of the bolt will be the point of reference.

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In connecting with a bench mark, if the bolt is vertical the foot of the rod

is placed directly upon it. If the bolt is horizontal in the wall of a building or other structure, it may be best connected in the following manner :-Set up the instrument in such a position and at such an elevation that the small hole in the bolt may be bisected by the middle thread without displacing the level by more than five divisions, using the elevating screw for making this bisection. Since the instrument can be raised or lowered about 2 centimetres by means of the levelling screws, the instrument can be placed in such a position by two or three trials.

Now bisect the bench mark with the telescope normal and also inverted, noting the reading of the level. Read the rod on the plate with the telescope in both positions. It is necessary to eliminate collimation by inverting the telescope, since the collimation of the middle wire is not the same as that of the three wires. The distance of bench mark from instrument must be determined and recorded.

Whenever work is stopped, at least two temporary bench marks should be established. These will consist of large nails or spikes driven their entire length vertically into the base of trees, or in the tops of sound stumps. When not in the vicinity of trees or stumps, wooden posts may be firmly set in the ground with their tops flush with the surface, and nails driven into them. When near the river temporary bench marks should be set every 2 kilometres. Every bench mark will be fully described in a note-book kept for that purpose. Its position with reference to the most prominent objects near it should be given by distance and direction. Public buildings, such as depôts, courthouses, churches, &c., are the best positions for permanent bench marks. In a village or town several permanent bench marks should be established to secure some one against loss.

If a railroad is crossed the elevation of the foot of the rail will be determined, and if levelling along a railroad, the elevation of the foot of the rail at depôts will be determined.

The elevation of the zeros of all water gauges and also the gauge bench marks will be determined.

The datum planes of cities along the line of levels will be connected with and their elevations deduced.

Frequent connections will also be made with the United States Engineer bench marks between St Paul and Grafton.

In reducing the observations the nearest tenth of a millimetre will be retained. The distance will be taken out from the table to the nearest metre. The limit of discrepancy in closing a polygon will be—

5 millimetres

distance in kilometres

The distance referred to is the entire length of the polygon from bench mark I to bench mark 2 and back to bench mark 1, and the limit of discrepancy refers to the polygons between successive bench marks. If the discrepancy exceeds the prescribed limit, then the entire polygon must be re-run one or more times, or until the difference of the means of the direct and reverse results is within the limit.

The notes will kept in the following form :

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CHAPTER IV.

ADJUSTMENT OF INSTRUMENTS.

Chain. From pulling through fences or other causes the chain is liable to become lengthened or shortened, and must be tested and adjusted from time to time. The best way to test the chain is to compare it with a steel tape, noting also whether the half-chain or 50 links mark is exactly 33 ft. If the chain is too short, it must be lengthened by straightening out any links which may have become bent, or by inserting one or two of the spare rings connecting the links, some of these being always provided on the chain for this purpose. If the chain is too long, some of these rings must be taken out. A Government standard of all kinds of English measures has been established in Trafalgar Square, London, by means of permanent bronze marks let into the granite plinth of the terrace wall in front of the National Gallery. There is also a standard in the Guildhall belonging to the Corporation of London, and similar marks are established in nearly every city or town by the burgh surveyor, in some central position.

Theodolite. The adjustments of the theodolite may be divided into the Temporary Adjustments and the Permanent Adjustments.

TEMPORARY ADJUSTMENTS.-These are the adjustments which must be attended to each time the instrument is set up.

1. To Set up the Instrument over a Station. This is effected by means of the plumb bob and plumb line attached to the vertical axis of the instrument, which is brought over the point first roughly by means of the legs and then exactly by the adjusting screws or sliding plate. When there are no adjusting screws or sliding plate the plumb bob is brought over the point by means of the legs only, pressing into the ground one leg or another until

the plumb bob is exactly over the point. In accurate work see that the levelling up of the instrument does not disturb the position of the plumb bob, and if so, readjust and level up again.

2. To Level up the Instrument. By this is meant making the horizontal plates and y, Fig. 52, truly horizontal, and the vertical axis truly vertical. It is effected by means of the two spirit levels attached to the upper or vernier plate t. Rotate the instrument horizontally until one of the levels v is parallel to one pair of the levelling screws g'. By means of these screws bring the bubble of this level to the centre of its run, and by the third screw, or if there are four levelling screws, by means of the other pair of screws, bring the bubble of the other level to the centre of its run. Now rotate the instrument horizontally through 180°, and see if the bubbles of the two spirit levels still remain in the centre of their runs. If they do, the adjustment is effected; but if not, then the spirit levels are not parallel to the upper plate t. In this case correct half the deviation by means of the capstan screws attaching the levels to the upper plate, and half the deviation by the levelling screws g', and repeat the operation until the bubbles remain in the centre of their runs while the instrument is rotated into any position. The plates and y should be clamped together by the screw a' during this adjustment.

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As this adjustment is so liable to get out, it is here described under the head of temporary adjustments, although the adjustment of the levels themselves parallel to the plate t might be called one of the permanent adjustments; the levelling up by means of the screws g' being strictly speaking the temporary adjustment.

A more exact adjustment may be made by means of the large level attached to the telescope. Set the vernier of the vertical circle to zero and bring the telescope over one pair of screws. Now level it up by the levelling screws g. Turn the instrument horizontally through 180°, and if the bubble of the telescope level deviates from the centre of its run, correct half the deviation by the tangent screw r of the vertical circle and half by the levelling screws g. Repeat the operation until the bubble remains in the centre of its run, when the instrument is turned through 180°. Now turn the horizontal platest and y (clamped) through 90° so that the telescope is over the third screw, or when there are four levelling screws, over the other pair of screws, and again level up

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