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where is the collimation line correction, v = sin of angle of inclination corresponding to one division of bubble tube, equation 1, page 191, i the correction for inclination of bubble to upper surfaces of rings, p the pivot correction.

INSTRUCTIONS FOR PRECISE SPIRIT LEVELLING UNDER THE MISSISSIPPI River CommisSION.*

1. Before commencing operations the constants of the instruments will be determined. The most important of these is the value of one division of the level tube. This can best be determined by means of a level trier. It can also be determined in the field as follows:

Set up the instrument firmly, if possible mounting it on a wooden post, or better still, on a stone pier. Set up a rod in its tripod at such a distance that it can be distinctly read through the telescope. The distance should be at least 50 metres, or if the air is very still, 100 metres, and should be carefully measured. Adjust the instrument carefully, taking such length of bubble in the level tube that its ends will be about the middle or tenth graduated line on each side. Direct the telescope to the rod, and by means of the elevation screw cause the bubble to run to near one end of the level.

Carefully note the position of the three wires on the rod and the reading of the level. Now by means of the elevation screw cause the bubble to run to near the other end of the tube, and note the reading of the wire and bubble as before. One result for value of one division of level can then be obtained. This operation should be repeated ten times.

The elevation of the rod should be changed occasionally between sets, in order to avoid estimating the same part of the same centimetre on the rod. It will be sufficient to run the bubble five divisions each side of its central position.

If distance from instrument to rod

d, d'= distance through which eye and object ends of bubble move when run from near eye end to near object end

d+d'

= amount of displacement of bubble between two readings

2

r, r'corresponding means of three thread readings on rod, and

v = value of one division of level in seconds of arc.

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2. With the value of one division of the level, tables will be constructed showing the correction to be applied to a rod reading for an observed inclination of the level and for a distance determined by interval between extreme threads. If the level bubble is well ground, equal displacements of the bubble, say of two divisions, will correspond to equal displacements on the rod.

* Johnson, Theory and Practice of Surveying.

3. Before using the level or determining its value, the fastening of the tube in its case should be examined. One end should be clamped down just tight enough to prevent the tube from moving easily, but not tight enough to strain the glass. The other should be lightly clamped so that the tube may be free to expand and contract with temperature changes. The cotton packing at the ends should not exert a lateral strain on the tube. All level tubes will be numbered, and have their numbers marked on them.

4. In order to determine the inequality in the telescope rings, the instruments should be mounted on a stone pier or other firm support and carefully levelled. The level should be carefully adjusted, and the instrument clamped to prevent its moving in azimuth. Now with the eyepiece of the telescope over the elevating screw, note the reading of the bubble when level is set on telescope, both in direct and reversed position. Now reverse the telescope in the wyes and read the level as before. Several sets of observations should be made.

Let b, b'inclination of telescope as denoted by means of level readings with telescope direct and reversed, then the inequality of rings—

p = b - b'

4

Sixteen determinations of the value of p of two instruments in use on the Lake Survey gave probable errors of ±0.046′′ and ±0.041′′. The inequality may be expressed in seconds of arc if desired, but for purposes of computation is best expressed in terms of level divisions, as it can then be combined directly with the error of adjustment of level.

5. The centring of the object glass will be examined. This may be done as follows:-Draw out the eyepiece until the threads are no longer visible. Direct the telescope on some well-defined object, and when looking at it rotate the telescope on its wyes.

If the object remains steady, the object glass is sufficiently well centred. Should the object appear unsteady, the fault can only be remedied by a maker. The objective should be firmly screwed into the telescope.

6. The values of the wire intervals will be determined as follows:-Set up a rod at carefully measured distances of 10, 20, 30 to 100 metres from the instrument. Read the rod ten times at each distance. The rod may be altered in elevation, the level may be caused to change and the telescope may be rotated 180° (reversed) in order to change the position of the threads on the rod.

Taking the mean of the ten observed differences of readings of the extreme threads at each station occupied by the rod, a table will be constructed giving in metres the distance of the rod from the instrument for any observed difference of reading between extreme wires.

7. Unless the rods used have been previously compared with some known standard, they will be compared with each other and their relative lengths determined. This may be done by establishing two fixed points or two foot plates at equal distances from the instrument and differing in elevation about 2.7

metres. The distance should be about 10 metres. Determine the difference of elevation of the points by reading each rod on each point. A comparison of the resulting differences of elevation will give relative lengths of metres on rods.

Ten measurements with each rod will be determined. The elevation of the instrument will be slightly changed between each set in order to eliminate errors in estimating the millimetres. Each rod will be numbered and have its number marked on it. The rods should also be kept dry and provided with canvas covers to protect them when being carried to and from work.

The distance of the zero graduation above steel spur on which the rod stands will be well determined. This may be done with a right angle triangle and rule. It may also be determined by means of another levelling rod, the graduations of which commence at the foot of the rod, by determining the height of the instrument above some fixed point and subtracting it from the reading of the rod to be determined. The relative lengths of the rods must be known.

Whenever a bench mark is connected with in such a way that the rod is not placed directly on the bench mark, this quantity enters into the computation of difference of elevation.

8. Before commencing work at any time all adjustments will be carefully made.

The telescope will be collimated by having a rod set up at a distance of 50 metres and noting the position of the wires on the rod when the telescope is normal and when inverted or rotated 180° about its axis. The collimation error of the mean of the horizontal thread must not exceed 1.25 millimetres at a distance of 50 metres.

The horizontality of the horizontal wires will be examined by moving the telescope in azimuth so that the rod shall appear to move through the field of the telescope. If the threads are horizontal, the reading on the rod will be the same, the position of the level, which should be closely watched, remaining the same. If the threads are found to be not horizontal, they will be made so by turning the telescope a small amount in the wyes. When the thread wires have once been made horizontal, small screws which abut against projection of wye above elevating screw should be so adjusted that when they press against this projection the wires are horizontal. If the vertical thread is then inclined, as shown by the plumb line attached to the rod, it must remain so.

To make the axis of the level parallel to the upper surface of the rings, it is necessary to make the vertical planes passing through them parallel and to make them equally inclined to the horizon.

To make the lateral adjustment, raise the clips fastening the level to the telescope, and revolve the level about the telescope a short distance each side of the vertical. If the bubble runs in opposite directions when on opposite sides of the vertical, the level is to be adjusted by means of the opposing horizontal screws at one end of the level until such is not the case.

To make the vertical adjustment, raise one of the clips and read the level in its direct position and also when it is reversed on the telescope. The difference between the differences of end readings in each position is four times the error of adjustment, and is to be corrected by the opposing vertical screws at one end

of the level case. The error of adjustment must not be allowed to exceed two divisions of the level. Care must be taken that the telescope rings are free from dust when adjusting the level. After having made the vertical adjustment, it will be necessary to examine the lateral adjustment again, since making one of the adjustments affects the other.

To make the level and vertical axis of revolution perpendicular to each other, loosen the small clamp screw at one end of the horizontal bar fastened to the vertical axis, and by means of the elevating screw raise or lower that end of the upper horizontal bar until the telescope can be rotated 180° from any position, and have the level reading the same in both positions.

To adjust the level attached to the rod, set up the rod in its tripod in such a position that when a plumb line is attached to the small hook near the top of the rod, the point of the plumb bob shall coincide with the point of a small cone attached to the rod near its foot. Now bring the level bubble to the centre by means of the levelling screws. In making this adjustment, the rod should not be exposed to the wind, as the plumb line is influenced thereby. This adjustment will be made at least once each day.

Each time that the instrument is placed on a station its axis will first be made vertical by means of the levelling screws in such manner that the telescope may be turned around the horizon without the bubble of the level running a great number of divisions. The telescope is finally made horizontal by means of the elevating screw. The inclination at the moment of observing must not ordinarily exceed three divisions of the level and never five divisions. The instrument when in use ought always to be sheltered from the sun and wind. It is carried from station to station without being dismounted, but the level should be taken off and carried in the hand. The small clamp screw at the end of horizontal bar and the large screw which fastens the instrument immovably to the tripod should both be turned tight before moving the instrument.

The rods must be placed on the plates which accompany them, and held in a vertical position as indicated by the spherical level attached. It is advisable to always use the same rod with the same foot-plate. In placing the foot-plates, great care should be taken that they be horizontal, on firm ground, and not liable to change. The surface of the ground, if not firm or level, should be removed.

The errors of adjustment will be determined at beginning and end of each series of observations: that is to say, after having mounted the instrument and before dismounting it, and in all cases at least once each day. If the instrument has been deranged by a jar, the corrections must be determined anew.

The error of collimation will be determined by two readings of the rod at a distance of 50 metres when the telescope is in its normal position and two when it is rotated 180° in the wyes. The difference between the means of the two readings, after being corrected for the inclination of the level, must not exceed 2.5 millimetres at that distance, and commonly should not exceed I millimetre. The error of the adjustment of the level will be determined by reading the level four times when direct and four times when reversed on the telescope, reversing it between each reading.

The error of adjustment must not exceed two level divisions, and commonly should not exceed one. All the details of the determination of the errors of adjustment must be entered in the note-book in their proper place. It is always advisable to have the errors of adjustment as small as possible, and necessary that they be well determined. The time of making these determinations will be recorded in the note-book.

In all work along the main line of levels each observer will duplicate his own work by running over the line in opposite directions, preferably under similar conditions as to illuminations, &c.

While connecting two bench marks the order of using the rods will be as follows:

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B.M.

In the above figure let 1, 11, 12, &c., represent the successive stations occupied by the instrument; BM, a', a3, &c., the positions occupied by rod 1; and a, a2, &c., the positions occupied by rod 2. The instrument having been set up at 1, rod I is placed on BM, and rod 2 at a, making distance 1-a equal to IBM. Rod 1 is then read and immediately afterward rod 2. The time elapsing between these readings commonly will not exceed I minute, and should not exceed 5 minutes. The instrument is then carried to 11 and rod I to a', the distances a-11 and 11-al being equal. Rod 2 will then be read, and immediately afterward rod 1. The instrument will then be taken to 12, and the rods read in the order 1, 2. Work will be continued in this manner until the other bench mark is reached. Rod I must be placed on this bench mark, which will be the regular order if there have been an even number of instrument stations. If there have been an odd number of instrument stations, at the last station use rod 1 for both back sight and fore sight. When levelling the rate of progress in favourable weather will be about 1 kilometre per hour. After having properly levelled the instrument at any station, and having made the vertical thread coincide with the centre line of the rod, the observation will be made and recorded in the following order :-First the level will be read, the tenths of the division being estimated; then the position of the threads on the rod will be read, the millimetres being estimated; and finally the level will be read again. The observer will then read the rod a second time to make sure that no error has been made. The recorder will then take the differences between the readings of the middle and extreme wires to guard against errors, and if these differences denote any error, the observations must be repeated. If an error exists it will be shown by too great a difference between the differences. This is a most important check, and must not be neglected. These differences will also serve as a check upon the distances between the instrument and rods.

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The recorder should also check the level readings to make sure that errors of whole divisions have not been made. This may be done by summing up the readings and noticing the length of the bubble. In reading the level by means

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