for the views AB, BC and stations a b. The points B, C, D, &c., for which there shall be a reading of the staff taken from the backward and forward stations of

the level, are called 'carrying points.' These are the points common to the readings taken at consecutive stations of the level.

Near the ends of the line of levels, as already stated, and at suitable intermediate points, 'bench marks' should be made on permanent objects, and their altitudes measured as points in connection with the line of section. These points need not be surveyed for the purposes of the section. Each day's levelling operations should commence on one and terminate on another 'bench mark.'

The engineer, before removing the level to a forward station, should reduce the 'fore' and 'back' readings, or measurements, to the datum line selected for the purpose. This reduction of the levels-altitudes-should be made in the field, at least for the carrying points. The operation will be readily understood from the following explanation, and an inspection of the illustration (fig. 54).

Let m and n be the readings of the staff at the carrying points A and B respectively, and d the altitude of A above the selected datum line; then will d+m be the altitude of the line of collimation of the level at a above the datum line; and, therefore, d+m-n (=d1) will be the altitude of the carrying point B above the same datum.

Putting my n1 for readings at B and C, observed from

D

b, we find the datum distance or altitude of line of collimation for this station of the level equal to d1+m1, and the like altitude of the carrying point C equal to d1+m1−n1 (=d2). Stating the observed altitudes (levels), at length we find the reduced altitude for C thus: d+m—n+m1—n1 = d2, or d+ (m+m1) — (n+n1) = d. This expressed in words is, the difference between the sums of the 'back' and 'fore' readings added to the initial datum altitude (datum altitude for first back reading point) will be the datum altitude (reduced level) for the extreme forward point. This, when reduced to a single station of the level, will be as above for d1. By deducting the readings for intermediate points from the corresponding datum altitude of the line of collimation, the altitudes of those points above the datum line will be obtained. It may be seen that the difference between the ‘back' and 'fore' readings is equal to the difference in the altitudes of the corresponding levelled points. This affords a convenient check on the arithmetical accuracy of the reductions for altitude.

In the operations just described there is not found a sufficient check on the results obtained, so that it becomes necessary to verify these by levelling between the ' bench marks.' The levels taken for this purpose are called 'check' levels, for which chain measurements and intermediate levels are not required. The levels for carrying points only may be taken, which points should be as near as may be at equal distances from the station of the level. As the check relates to the measurement of altitude, the absolute distance between the carrying points and the route selected will be, generally, immaterial. Should an error be detected between any two 'bench marks,' that part of the line of section should be relevelled in detail, and the point or points in error corrected.

The annexed 'Level Field-Book' will be found convenient and suitable for reducing in the field, without loss of time, the altitudes of the carrying points. The columns 1, 2, and 3 are placed on one page of a narrow

* The modern figures are those which the engineer should enter on the fieldbook, in the field, to record the measurements, and to obtain and verify the reduced altitudes (levels) of the carrying points. The antique figures are those which may be found subsequently in the office. Each levelled point, or reading, is on the same line as the corresponding reduced altitude.

blue-lined book, beside the columns 4 and 5, on the
next, or face, page. The blue lines on the one page
should correspond, in position, to those on the other, as the
book, when
open, makes only one page for the field work.

The following form of Level Field-Book has been adopted by many engineers :

It may be seen by an inspection of this form of Level Field-Book that to obtain the reduced altitudes (levels) of the carrying points, and their verification in the field, all the reduced altitudes must be found, and the sum of all the readings taken. Comparing the above form with the form of Level Field-Book already given, the advantages of the former are very manifest.