other curves of the figure; their number showing their distance in feet above D. Around the point d, there is a small curve, also marked (3). By inspecting the table, it will be seen that d is 4 feet above D, and that the ground descends from d towards D and c d is therefore a small knowl, the top of which is cut off by the first plane. To show that the ground descends from d, even below the first curve (3), a plane is passed 1 foot below the first plane, or 2 feet above D; the curve of section is marked (2).

The second of the system of curves, or the one marked (6), must cut the line AD between b and c, the line EH between f and g, the line FI between k and l, and also between and I; it also cuts EH again between h and H, and the line DC between H and D.

The third curve, or the one passing 9 feet above D, passes through b, cuts the line EH between E and f, the line FI between i and k; thence it passes to p, and thence to the line DC, crossing it between I and L. There is also another curve determined by this plane, since it passes through the points C and 4, leaving the points t and s below it. This curve runs from C to p, and from p to q, as drawn in the figure.

q,

The fourth curve, marked (12), intersects the line AD between a and b, EH between E and f, FI at i, GL at m, and BC at B. There is also another curve lying around the point L: for the plane cuts GL between p and L, the line DC between C and L, and again between I and L.

The fifth curve, marked (15), cuts AD at a, EH between E and f, and AB at F. The sixth curve, marked (18), cuts AD between A and a, and AB between A and E. The proportional distances in all these cases are found as in the first example.

In looking on the little map that has been made, it is clearly indicated by the curves and shading, that the ground slopes from A to c, thence rises to d, and then slopes to D. It also slopes from A along the line AB; from E in the directions f and i, from F in the directions i and m, from G in the directions m and B, and from B in the direction Bqs. The ground also slopes from L to p, thence to 1 and h, and along to curve (2), and the point D: and on the other side

187. Thus far, we have said nothing of a plane of reference, which is any horizontal plane to which the levels of all the points are referred. In the first example, the plane of reference was assumed through the point A (Pl. 4, Fig. 6), and tangent to the surface of the hill in the second example, it was taken through D, the lowest point of the work.

188. After having compared all the levels with any one point, the highest and the lowest points are at once discovered, and the plane of reference may be assumed through either of them. As, however, in comparing the heights of objects, the mind most readily refers the higher to the lower, it is considered preferable to take the plane of reference through the lowest point. We say, for example, that the summit of a hill is 200 feet above a given plain, and not that the plain is 200 feet below the summit of the hill; so we say that a plain is at a given distance above a river, and not that the river is below the plain. This habit of the mind of referring the higher to the lower objects, suggests the propriety of taking the plane of reference through the lowest point, where there is no other circumstance to influence its selection. If, however, there are fixed and permanent objects, to which, as points of comparison, the mind readily refers all others, such as the court-house or church of a village, the market-house of a town, or any public building or monument, it is best to assume the plane of reference through some such point; for, it must be kept in mind, that the ends proposed in the construction of maps, are, to present an accurate view of the ground, its form, its accidents, and the relative position of objects upon it.

189. When the plane of reference is so chosen that the points of the work fall on different sides of it, all the references on one side are called positive, and those on the other, negative. The curves having a negative reference are distinguished by placing the minus sign before the number; thus ( ).

190. In topographical surveys, great care should be taken to leave some permanent marks, with their levels written on them in a durable manner. For example, if there are any rocks, let one or more of them be smoothed, and the vertical distance from the plane of reference marked thereon: or let

the vertical distance of a point on some prominent building, be ascertained and marked permanently on the building. Such points should also be noted on the map, so that a person, although unacquainted with the ground, could by means of the map, go upon it, and trace out all the points, together with their differences of level.

191. The manner of shading the map, so as to indicate the hills and slopes, consists in drawing the lines of shading perpendicular to the horizontal curves, as already explained.

192. In making topographical surveys, the great point is, to determine the curves which result from the intersection of the surface by horizontal planes.

Besides the methods of diverging and parallel sections, we may assume a point on the surface of a hill, place the level there, and run a line of level round the hill, measuring the angles at every turn or change of direction: such a line will be a horizontal curve. Then, levelling up or down the hill, a distance equal to the vertical distance between the horizontal curves, let a second curve be traced; and similarly for as many curves as may be necessary,

This method, however, is not as good as the methods before explained.

193. Besides representing the contour of the ground, it is often necessary to make a map which shall indicate the cultivated field, the woodland, the marsh, and the winding river. For this, certain characters, or conventional signs, have been agreed upon, as the representatives of things, and when these are once fixed in the mind, they readily suggest Those which are given in

the objects for which they stand. Plates 5 and 6, have been adopted by the Engineer Department, and are used in all plans and maps made by the United States Engineers.

It is very desirable that a uniform method of delineation should be adopted, and none would seem to be of higher authority than that established by the Topographical Beaureau. It is, therefore, recommended, that the conventional signs given in Plates 5 and 6, be carefully studied and closely fol

CHAPTER VII.

Of Surveying Harbours.

194. There are two objects to be attained in the survey of a harbour.

1st. To survey the shore along high or low water mark, to trace its windings, to note the points and inlets, and to ascertain and fix the places at which rivers and creeks discharge themselves. And,

2dly. To discover the channels, their direction, depth, and width; the position of shoals, the depth of water upon them, the nature of the bottom, and in short, whatever may contribute to easy and safe navigation.

To determine the principal points and trace the shore.

195. Having provided a boat and crew, row once or twice around the harbour, mark the more important and prominent points; at which, let station-staves with flags upon them be erected.

Then, measure a base line, and form a series of triangles, having their angles at the stations already chosen. Let the angles of these triangles be measured with the theodolite, and their sides calculated; after which, the high or low water mark may be traced along the shore with the compass, as hereafter explained.

Let us suppose that Plate 6 is a map of a harbour to be surveyed.

We see, by inspecting it, that the upper end of the lake at A, the termination of the harbour at B, the rocks at C, the point at D, the fisheries at E, and the two bays at F and G, are all prominent points. At these points, therefore, let station-flags be placed. Then, measure the distance from A to B, for a base line, and let the work be begun at A.

Remove the staff at A, and place, by means of a plumb-line, the axis of the theodolite over the station. Then, having levelled the instrument, bring the 0 of the eyeglass vernier to coincide with the 0 of the limb, and tighten the clamp-screw of the vernier plate. Loosen the lower clamp-screw, and turn

the body of the instrument until the telescope comes nearly on the base line AB: then tighten the clamp-screw K, and by means of the lower tangent-screw L, and the thumb-screw Z, bring the intersection of the spider's lines to coincide with the bottom of the staff at B. Then, direct the lower telescope to the same point, without moving the limb.

Having thus placed the instrument, examine the opposite vernier, and if it stands exactly at 180°, enter the direction from A to B, 00, as in the field notes below.

But if the reading of the opposite vernier exceeds 180°, enter half the excess for the direction. If the reading is less than 180o, take half of what it falls short, from 360°, and enter the remainder for the direction from A to B.

The two verniers are used to avoid any error which might arise from a defective graduation of the limb, or from an imperfect centring. A false centring, is when the centre of the limb or vernier plate is out of the axis of the instrument, and when this is the case, it is a fruitful source of error.

Both verniers should be read at every observation, and a mean between the readings taken for the true direction.

Having thus placed the instrument, loosen the clamp-screw of the vernier plate, and direct the telescope to station E Note the degrees, and take a mean between the readings of the two verniers for the minutes, and enter the result opposite direction AE, as in the field notes. Do the same for the station G, and then enter in a column to the right, the angle formed by the lines which join the stations. The angle will either be the difference of the readings, or the difference between 360° and the larger reading, plus the smaller reading.

Having sighted to all the stations which can be seen from A, remove the instrument and replace the station staff.

Take the theodolite to B, the other extremity of the base line. It is now required to place the instrument in such a manner that the horizontal limb shall have the same relative