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parallel to each other, both parallel to the horizontal bar, or rather perpendicular to the vertical axis of the instrument, round which the horizontal bar turns, by means of the spindle fitting into the socket at its centre; bring the bubble to the centre, by means of the levelling screws, turn the instrument round the vertical axis 180°,* and if the bubble remains in the centre, the axis of the spirit level, and consequently its parallel, the axist about which the telescope revolves, are perpendicular to the vertical axis of the instrument, and the latter, though not vertical, is in a vertical plane, perpendicular to the line of collimation. To make it vertical, which must be done every time an observation is made with the instrument, the above adjustments being completed, bring the bubble to the centre by means of the levelling screws, then turn the bar 90° on the vertical axis, and bring the bubble to the centre again; the vertical axis will then be truly vertical.

In connexion with this instrument two rectangular staves, called levelling staves, are used, divided into feet, tenths and hundredths of a foot. The staves are painted white, and the division lines are made very distinct, in black or red, the feet being numbered with distinct numerals. the hundredths are painted, the whole of each division, alternately white, and black or red. Two or three lengths of 6 feet of staff fit together by joints, so as to make a length of 12 or 18 feet. A plumb line suspended at the side of the staff, or in a groove covered, the lead part with glass so as to be visible, serves to place the staff exactly vertical.

In order to find the difference of level between two points of ground or the height of one above the other with these instruments, let an assistant hold one of the levelling staves vertically, standing upon one of the points in question, and another assistant the other staff, at some point in the direction of the second point; the observer turns the telescope, after the vertical axis of the instrument has been made truly vertical, and takes the reading cut by the horizontal wire, first on one of the levelling staffs, and then on the other recording them in separate columns of a field.

*If there is a horizontal compass box attached to the instrument this may be done by observing the number of degrees to which the needle points. If not, the instrument must be placed on the line of two staves, and between them, sighting first to one, and then to the other.

This axis, by the first adjustment, is identical with the line of collimation, or line of vision, when the intersection of the wires is brought upon an object. It is not the optical axis of the telescope, though it should be as nearly as possible, but the axes of the cylindrical parts of its tube, which are in contact with the y*.

‡ Not only feet, tenths, and hundredths may be distinctly read, but even thousandths, by estimation.

book, the one in the direction in which he is going, under the title of "forward readings," the other under that of reverse readings.* The staff on the given point of ground is now taken up and carried round the other (which is simply turned about where it stands), to a point still farther in the direction of the second given point; the level is also removed to a point between the levelling staves, and the process just described is repeated, and so on, till the second given point, between which and the first the difference of level is required, is reached, the last levelling staff being placed there. The difference between the sum of the direct readings and the sum of the reverse readings will be the difference of level of the two given points, or height of the one above the other.

To make a section of ground which is the intersection of a vertical plane with the surface of the earth, it is necessary to add three more columns to the field book, a column of differences, a column of heights, and a column of distances. The first contains the difference between each direct and reverse reading; the second contains the height of each point upon which the levelling staves are placed above a horizontal plane, assumed at pleasure, usually passing through the first point of the survey. Each number in the column of heights will be computed by adding the number of the column of differences to the preceding number in the column of heights; the first number in the column of heights is the

The level is always placed nearly half way between the two staffs, to avoid the error which would be occasioned by the difference between true and apparent level, the nature of which may be explained by the annexed diagram. Let the circle in the diagram be a vertical section of the earth through the point A, where the instrument is supposed to stand. The arc AM will be the line of true level, A and м being at equal distances from the centre of the earth c; the line AT tangent at A is the line of apparent level, determined by the optical axis of the

instrument. For a point on


the opposite side of A, from м, and at the same distance, the difference between apparent and true level will be the same. Hence the advantage of placing the instrument half way between the points whose difference of level is to be observed.

This should be entered with the negative sign, if the direct exceed the reverse reading.

same as taat adjoining in the column of differences.

The numbers in

the column of heights will be negative for points below the plane of reference. The third column contains the horizontal distances between points at which the levelling staves were placed, supposed to be measured with a tape or chain. To plot the section or profile of ground from such a field book, a horizontal line must be drawn to represent the section of the profile with the plane of reference; on this the numbers from the column of distances must be laid off from a scale of equal parts, and at the points of division ordinates or perpendiculars must be erected and taken from the scale of equal parts, equal to the numbers in the columns of heights; through the tops of these ordinates the section of ground required can then be traced with the hand. The following example of a field book, and the profile constructed from it, will serve to illustrate this subject.

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The mode of representing this is by means of horizontal sections formed by planes at regular intervals, one above another, these sections being all projected upon one horizontal plane, viz., that represented by the map.

To survey a hill for the purpose of drawing its horizontal sections upon a map, place an instrument for taking horizontal angles at the top of the hill, and plant stakes along lines diverging from this point down the hill, and take the horizontal angles formed by the vertical planes in which these lines lie; then level along the lines, taking the difference of level and distance at points where the slope changes. In order now from such a survey to plot the horizontal sections of the hill, draw on the map from the point A, corresponding to the one assumed on the top of the hill (supposed to have been previously determined in position on the map by tri

angulation or otherwise), a system of lines diverging from this point under


angles equal to the observed angles, and supposing, to render the conception definite, that the planes forming the horizontal sections are taken 10 feet apart, the points in which the projections of the sections cut the diverging line thus drawn, may be ascertained by proportion as follows:The difference of level between two points on one of these lines is to the horizontal distance between them, as 10 feet is to the horizontal distance from the upper point, at which a plane of section ten feet below this point would cut the diverging line. Commencing with the upper point of all, A, and determining thus the points a, b, c, d, at which the projection of the section 10 feet below cuts each of the diverging lines, it may be traced through them by the hand. In a similar manner another section 10 feet lower, and so on to the bottom of the hill. Where the sections are convex, are the ridges, or back bones of the hill; where the sections are re-entering are the ravines; and in general, the varying forms of the sections present to a practised eye an exact notion of the general configuration of the hill. In topographical maps these sections are drawn in pencil, and the hill shaded with irregular lines, in India ink, perpendicular to the sections, as seen between c and d, which is the direction in which water or alluvion would flow down the hill. These shading lines are best drawn with a pen of short coarse nib, and very short portions of a number of them at a time. The light should be supposed to fall obliquely in a certain direction, and the sides of the ravines towards the source of light will be darker than the opposite sides. The tops of the back bones will be quite light. The summits of the hills being usually more nearly perpendicular, will present deeper shades than the bases, which usually slope gently into the level ground.

Water is shaded by making the line of shore quite black, which should be first drawn all round the map, including the islands, then a second and finer line all round, as near the first as possible without touching it, then a third a little more distant, and so on, broader and broader, till the shadings from opposite shores meet midway.*


The problem ordinarily is to ascertain the shortest and cheapest route from one point to another on the surface of the earth, having no greater and more sudden elevations or depressions than are compatible with the nature of the locomotion to be employed upon it.†

The case frequently presented, not only for the whole route, but in minor instances, along its course, is that of a dividing ridge between two valleys, from one to the other of which it is necessary to pass.

It becomes necessary then to ascertain the lowest point of the dividing ridge. A good indication may be obtained proximately by a simple inspection of the course of the streams upon a map, inasmuch as the direction of their flow must be governed by the topography of the country over which they pass. One or two examples will sufficiently illustrate the principles which are to guide such an inspection.


If two streams run along two valleys, and tributaries proceed from near the same point A of the dividing ridge to empty into them, then the point A is a low point of the dividing ridge. For the waters accumulating for the formation of the


sources of the tributaries at the point a must flow from higher ground on both sides of this point.

Again, if two tributaries running at first nearly parallel to the principal streams, turn outward at a point ▲, this is a low point. For the *For further instruction in topographical drawing see an excellent little work by S. EASTMAN, U.S.A.

+ This will of course be modified by various circumstances, such as the greater or less difficulty of working the ground, from the nature of the soil; the vicinity of large towns, to pass through which the construction would turn aside, the existence of mines, or valuable products of any kind, for which it would afford transportation.

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