In this example, the first column shows the stations; the second, the back-sights; the third, the distances from the level in each of its positions to the back staff; the fourth, the fore-sights; the fifth, the distances from the level to the forward staff; the sixth and seventh, are the columns of back and fore-sights, corrected by the difference of level. The corrections are thus made:-The difference of level in the table corresponding to 20 chains, is 5 tenths of an inch, which being subtracted from 9 feet 8 inches, leaves 9 feet 7.5 inches for the corrected back-sights; this is entered opposite station 1 in the sixth column. The dif ference of level corresponding to 32 chains, is 1.280 inches, which being subtracted from the apparent level, 1 foot 6 inches, leaves 1 foot 4.720 inches for the true fore-sight from station 1. The other corrections are made in the

same manner.

The sum of the back-sights being 44 feet 2.732 inches, and the sum of the fore-sights 9 feet 6.477 inches, it follows, that the difference, 34 feet 8.255 inches, is the true difference of level.

16. In finding the true from the apparent level, we have not regarded the effect caused by refraction on the apparent elevation of objects, as well because the refraction is different in different states of the atmosphere, as because the corrections are inconsiderable in themselves.

17. The small errors that would arise from regarding

the levelling staves at equal distances from the level. In such case, it is plain, 1st, that equal corrections must be made in the fore and back-sights; and, 2dly, that when the fore and back-sights are diminished equally, the result, which is always the difference of their sums, will not be affected.

This method should always be followed, if practicable, as it avoids the trouble of making corrections for the dif ference of true and apparent level.

The differences between the true and apparent level, being very inconsiderable for short distances, if only ordinary accuracy be required, it will be unnecessary to make measurements at all. Care, however, ought to be taken, in placing the levelling staves, to have them at as nearly equal distances from the level as can be determined by the eye; and if the distances are unequal, let the next distances also be made unequal; that is, if the back-sight is the longer in the first case, let it be made proportionably shorter in the second, and the reverse.

LEVELLING FOR SECTION.

18. Having decided upon the line along which a section is to be taken, let a permanent mark be made at the beginning of the line: this is called a bench-mark. A benchmark is made by drilling a hole in a rock, or by painting upon a rock or fence, or sometimes by driving a stake in the ground, with its upper end marked by a nail-head. Bench-marks should be made from time to time along the line, to serve as checks, in case a re-survey should become necessary.

The operations in the field are similar to those in the last example, and the field notes are kept in the same. manner, except that a new column is added for bearings, when it is necessary to make a plot of the line of survey. The total distance of each point above or below the starting point may be computed, and written in a separate column, paying particular attention to the signs. We annex an example, in which the heights are estimated in feet,

The fifth column shows the difference of level between any two consecutive positions of the levelling staff, and is found by subtracting the fore-sight from the corresponding back-sight, and giving to the remainder the proper sign. The sixth column shows the distance of each point above or below the bench-mark A, and is obtained by continual additions of the numbers in column 5. Thus,

(-12.20)+(-6.02)=-18.22; (-18.22) + 4.13 = -14.09;

and so on.

It will be seen that the point of termination is 37.79 feet below the starting point.

PLOTTING THE SECTION OR PROFILE.

19. The vertical distances being generally very small as compared with the horizontal distances, two different scales become necessary in plotting a profile. In order that the vertical distances may be fully exhibited in the plan, the scale used for them is much larger than is used for lines measured in a horizontal direction. This becomes absolutely necessary where long lines of profile, with a gentle slope, are to be plotted, as is always the case in the trial section of a railroad survey. We shall illustrate the manner of plotting, by drawing the section determined by the fieldnotes just given.

assume some point as A, to represent the point of beginning: lay off on the datum line, distances equal to the

measured distances 650, 700, 750, &c., feet to K, using in this case a scale of 1500 feet to 1 inch. At the points B, C, D, E, &c., thus determined, erect perpendiculars, making them equal, on a scale of 25 feet to the inch, to the corresponding differences of level taken from the field-book; through the points thus found, draw the irregular line APLM, and it will represent the surface of the ground along the line of level.

The bench-mark, between stations 7 and 8, is not plotted, as it is supposed to be out of the line of the section, and no distances are measured to it.

SECTION II.

TOPOGRAPHICAL SURVEYING.

21. Besides the surveys that are made to determine the area of land and the relative positions of objects, it is frequently necessary to make minute and careful examinations for the purpose of ascertaining the form and accidents of the ground, and to make such a plan as will distinguish the swelling hill from the sunken valley, and the course

37.79

22. This branch of surveying is called Topography. In surveys made with a view to the location of extensive works, the determination of the slopes and irregularities of the ground is of the first importance: indeed, the examinations would otherwise be useless.

23. The manner of ascertaining these irregularities is, to suppose the surface of the ground to be intersected by a system of horizontal planes at equal distances from each other; the curves determined by these secant planes, being lines of the surface, will indicate its form at the places of section, and, as the planes are nearer or more distant from each other, the form of the surface is more or less accurately ascertained.

If such a system of curves be determined, and then projected or let fall on a horizontal plane, it is obvious that the curves on such plane will be nearer together or farther apart, as the ascent of the hill is steep or gentle.

If, therefore, such intersections be made, and the curves so determined be accurately delineated on paper, the map will give such a representation of the ground as will show its form, its inequalities, and its striking characteristics.

24. The subject divides itself, naturally, into two parts. 1st. To make the necessary examinations and measurements on the field; and,

2d. To make the delineations on paper.

For the former of these objects, the theodolite is the best instrument; the common level, however, will answer all the purposes, though it is less convenient.

Before going on the field, it is necessary to provide a number of wooden stakes, about two feet in length, with heads. These stakes are used to designate particular points, and are to be driven to the surface of the ground. A nail should then be driven into the head of each of them, to mark its centre.

25. We shall, perhaps, be best understood, by giving an