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 deter

minations 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:

In the above figure let 1, 11, 12, &c., represent the successive stations occupied by the instrument; BM, a', a", &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 I - BM. Rod 1 is then read and immediately afterward rod 2. The time elapsing between these readings commonly will not exceed 1 minute, and should not exceed 5 minutes. The instrument is then carried to 11 and rod 1 to a', the distances a 11 and 11-a1 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 I 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.

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

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 should be chosen. Firm 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 × 18 × 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 it. A small hole in the centre of the bolt will be the point of reference.

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 I, 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 be kept in the following form :—