In the first column are entered the distances between the several stations, which, being successively added to the preceding total, give the total distances of each station from the starting point: in the next column are entered the distances of the stations from the instrument; and in the third are

entered the bearings of the stations from the instrument. In the fourth and fifth columns are entered the readings of the staves; and in the sixth column the heights above datum of the several stations are computed by adding the back reading to the height last found, and subtracting the fore reading from the sum. The seventh and eighth columns are added for performing the reduction of the measured distances to horizontal distances, when the slope is sufficient to render this reduction necessary. In carrying forward the distances to the next page of the book, the total reduced horizontal distance should be carried to the top of the first and second columns instead of the total measured distance along the slope; but such substitutions should not be made at any other part of the page, as it would interfere with the proof of the distances by adding up the second column, which ought to produce the last distance entered in the first. The levels are proved by subtracting the sum of the numbers in the sixth column from the sum of the numbers in the fifth, when the remainder should be the height above datum of the last station recorded at the bottom of the page.

To facilitate the reduction of the measured distances to the corresponding horizontal distances, the following table showing the reduction upon each 100 feet for each foot difference of level should be inserted in the field book:

When it is required to plot the section on a large scale, and to show every undulation of the surface, it is not necessary to remove and re-set the instrument to obtain the height, above datum of every point necessary to be known for this purpose; but, besides reading the staff at the back and fore station, it may be read off from the same place of the instrument, at as many intermediate points as may be deemed

desirable; and these readings, being entered both as back and fore readings, will produce the same effect as back and fore readings of the same points obtained in different positions of the instrument. The distances from the instrument of these points should be omitted from the second column; but, the distances between them being entered successively in the first column, their respective distances from the instrument may at any time be determined, if required. The height of the instrument itself may be entered in this way as an intermediate sight; and, as the same height that is added as a back reading is subtracted again as a fore reading, any error in this reading will not at all affect the levels afterwards taken, and, provided it be not greater than the limit within which distances can be laid down and estimated upon the plot, is of no moment. Now, in taking the section of a line of any considerable extent, the scale is seldom sufficiently large to admit of less than six inches being laid down or estimated upon the plot, and consequently an error of two or three inches in the intermediate sights would be immaterial. When observations are made out of the line, to be levelled, in order, for instance, to obtain the height of this line above neighbouring rivers, canals, roads, &c., the readings are to be entered in the same manner as for other intermediate sights; and, the column of bearing and distance being left blank, no mistake can be made in drawing the section. The bearing and distance of such points, if desirable to be noted, must be entered in the space left for remarks.

For the purpose of reference on any future occasion, in order either to check the accuracy of the levels already obtained, or for the convenience of commencing a new series in some other direction, marks should be left upon some convenient fixed points upon which the staff has been held, and the reading noted with the greatest possible care. These bench marks, as they are called, should ordinarily be left at about every half-mile of distance, and may be either on or off the line. In the latter case the readings are to be recorded in the manner already explained for points out of the line. The hooks and tops of gates, copings, sills, or steps of doors, &c., are commonly used for bench marks, and the mark must be made exactly on the point upon which the staff has been held. A stout stake may be driven into the ground for a bench mark, and is by many persons preferred to any other.

When a section of considerable length is to be plotted, the horizontal distances cannot be laid down on as large a scale

as is necessary for the vertical heights above datum, in order that the section may be of any practical use, without making the plot of most unwieldy dimensions. It is therefore usual to make the vertical scale much larger than the horizontal one: thus 4 inches to a mile for the horizontal distances, with one inch to 100 feet for the vertical distances, is a usual combination. In the accompanying figure we have drawn the portion of a section from the portion of the field book at page 109, making use of a scale of 1 inch to 800 feet for the horizontal distances, and of a scale of 1 inch to 200 feet for the vertical distances

A G is ruled for the datum line; on it are set off from A, the horizontal distances at the points B, C, D, E, F, G, according to the horizontal scale of 1 inch for each 800 feet, and through the points A, B, C, D, E, F, and G, are drawn lines Aa, Bb, &c., perpendicular to A G; on these lines are set off the vertical distances to the points a, b, c, &c., according to the vertical scale of 1 inch for each 200 feet; and the line a g, passing through all the points a, b, c, &c., will represent the required section. A line is drawn between the stations E, F, at the proper distance from the datum line to represent the level of the canal; and proceeding in this manner, and making any remarks that may seem desirable, opposite the corresponding points of the section, the work will be completed.

Having now explained the construction and use of the most accurate instruments for tracing the level of any portion of country, we proceed to notice the water level, a very simple instrument, adapted to give a rapid delineation of any portion of country, an object frequently of greater importance than accuracy. It can be made by any workman, will cost but a few shillings, and requires no adjustment when using it.

"A B is a hollow tube of brass, about half an inch in diameter,

and about 3 feet long; c and d are short pieces of brass tube of larger diameter, into which the long tube is soldered, and are for the purpose of receiving the two small bottles, e and f. the ends of which, after the bottoms have been cut off, by tying a piece of string round them when heated, are fixed in their positions by putty or white lead; the projecting short

axis, g, works (in the instrument from which the sketch was taken) in a hollow brass cylinder, h, which forms the top of a stand used for observing with a repeating circle; but it may be made in a variety of ways, so as to revolve on any light portable stand. The tube, when required for use, is filled with water (coloured with lake or indigo), till it nearly reaches to the necks of the bottles, which are then corked for the convenience of carriage. On setting the stand tolerably level by the eye, these corks are both withdrawn, which must be done carefully, and when the tube is nearly level, or the water will be ejected with violence; and the surface of the water in the bottles, being necessarily on the same level, gives a hori zontal line in whatever direction the tube is turned, by which the vane of a levelling staff is adjusted."

The instrument, however, with which observations upon the level of a country may be most expeditiously made, and generally with greater correctness than with the water level, is the reflecting level. This instrument consists merely of a piece of common looking-glass, l, one inch square, set in a frame fixed against a plate of metal weighing about a pound, and suspended from a ring, r, by a twisted wire, w, so that it may swing freely, but not turn round on its axis of suspension. A fine silk thread, tt, is stretched across the center of the mirror, and a small opening, o, at one side of the mirror.