The depth and form of the pools at the bottom depend upon the force of the current and the nature of the subsoil. If water is gently decanted into a full vessel, the influx current will only penetrate a short distance into the stagnant fluid below; but if the decanter is elevated, and the volume and force of the water increased, it will sink to a greater depth. The river as it flows down the gradient forming the rapid into the pool below, is governed by the same hydrostatic law. When small it will penetrate to a short distance below the surface, but when swollen it will sink to a greater depth. If large stones are embedded in the subsoil, they may deflect the current, and thereby prevent the bottom being scooped out to so great a depth as otherwise it would have been. But where bottom soils are equal, the depth of the pool will be directly as the altitude and force of the swollen current during the greatest floods.

The elevation of a bar above the general inclination of the river will, like the depth of a pool, depend upon the force of the current and the nature of the accumulated debris of which it is formed. If the ground is full of large stones, consisting of fragments of rock, they will accumulate during the natural formation of the channel by the flowing stream, and thus form a more elevated, acute, and permanent ridge across the current than when the stones are of a less size and rounded by attrition. But when the bar is composed of finer gravel, it will be "more flat," will give to the rapid a greater length, and be much more "liable to shift" in times of heavy floods than the previous example.

The depths and water-level lengths of the pools; the depths and hypotenusal lengths of the rapids from smooth water to smooth water, and the heights and lengths of the bars, require to be ascertained in the survey, and shown upon the longitudinal section; the breadths and depths are represented upon the transverse section; and the breadth, horizontal length, and direction of the river are shown upon the plan.

Pools, rapids, waterfalls, and cataracts are frequently known to anglers and others by their names; and these may require to be shown both upon the plan and sections.

It is seldom found advisable to change the course of a large river in a hilly country; on the contrary, the difficulty experienced is to confine them within the channels they have naturally scooped out for themselves; for unless the pools are of sufficient depth, and the bars formed with proper materials, it is impossible to prevent harm in storms of more than ordinary magnitude and duration.

When a survey is undertaken for the express purpose of supplying the necessary data required for embanking a river, so as to

prevent it from overflowing its banks, and for deepening the pools and improving the rapids, so as to obviate the shifting of the channel, the height and position of the embankments, and the materials of which the bar is formed, are the first matters of inquiry that engage the attention of the surveyor.

If the river has previously been allowed to overflow its banks during heavy floods, the confining of it within embankments will raise its surface level and increase its velocity and force.

The increase in the altitude of the river, at the top of the rapid, will be found in the majority of cases to endanger the stability of the bar, and hence the safety of the channel below. This arises from the increased velocity and force being produced by artificial means, whereas the defence is natural, the bar being formed by the river when flowing at a less depth.

Sometimes the stability of the bar and rapid may be increased by artificial means sufficient to counteract a greater force of current. This is done either by throwing in heavy stones in the smooth water immediately above the rapids whose bars are liable to be washed away, or by driving in piles and wattling them with small

timber.

As the breadth and depth of the river at the top of the rapid during a heavy flood are determined by the height and position of the embankments, they should be placed as far from the river's edge on both sides as the circumstances of the case will permit, the depth being inversely as the breadth.

When a river has left its bed, the same data are applicable in the formation of new bars and embankments in order to direct it back into its natural channel. Wherever the surface of the water is raised on the top of a rapid, the stability of the bar must be increased, and also the depth of the pool below; and this has to be done for several pools and rapids down the river, so as to restore the deranged balance of things to a state of equilibrium, similar to what is found in natural examples of stability.

When arable, meadow, or pasture lands have been washed away or covered with gravel, they require to be measured, so as to enable the landowner to settle questions of value with his tenants. In such cases a section to show the subsoil and drift is not unfrequently ordered.

When the course of a river has to be changed, a pool of considerable depth and length is best for the purpose, more especially if the bend is quick. A rapid should in such cases be avoided, if possible, as the concave bank and embankment are difficult to protect at the top of the rapid when the river is much swollen.

A ferry is generally at the narrowest and smoothest part of a pool, and a ford at the first smooth water immediately above a rapid; both require to be shown upon the plan, and also the ferryman's house and boat.

The piers of bridges should be protected by pools of sufficient depth to prevent harm to their foundations during the greatest flood.

Where the foundations of the piers of old bridges are so high as to form rapids, such data should be carefully shown upon the sections, and special attention drawn in any report that may accompany the survey relative to details of tear and wear, &c., that cannot be otherwise represented.

Lakes are sounded and the depths shown upon the plan, as in the case of the ocean.

In surveying waterfalls and cataracts the chief points that require attention are the peculiar geological strata of the rocks that form the bed of the river, the fracture and angles thus formed, and the wearing away of the bottom by the continuous action of the water. Such involves a large amount of work, but it is simple and easily performed by those who have a taste for drawing.

EXAMPLE VI.

GENERAL DIRECTIONS FOR THE SURVEY OF CANALS, IRRIGATIONWORKS, AND WARP-LANDS.

Surveys under this example are either of works that are finished or else to furnish data whereby others may be executed at some future period.

Canals.

In Canal-Surveying the levels are necessarily "water-levels" or "dead-levels," as they are sometimes termed in contradistinction from horizontal levels on which water flows.

When the canal is formed and in operation, the details of the vertical survey for the sections are of the simplest kind, as the levels can then be taken from the water, the normals from the height of the locks, and the lengths and breadths by measurement with the chain.

The details of the horizontal survey for determining the direction of the line of the canal, the area of land which it occupies, including the position of basins, quays, &c., and the severance of property which it has effected, are similar to what has already been given, and to the corresponding data in Railway-Surveying which will be found under that head, p. 385.

If the survey is made purposely to determine the levels and other data for a canal intended to be made, its details are more diversified and differ in many respects from those of a railway.

Under such conditions there are two levels given; viz., the lowest water level, and the highest one-the object of the canal being to raise the navigation from the former to the latter by means of a series of locks and dead levels, as from c to b in the annexed diagram. The first step in the survey is to find the difference and distance between the two given levels. This may be done either by the common levels and chain, as in the case of the river (Example IV.), or by the theodolite and chain. We shall adopt the latter, as it will illustrate a survey on the vertical plane conducted on the principles of plane trigonometry. The difference between this practice and that with the level will also be so pointed out as to be easily understood, the theodolite being in point of fact a spirit level.

The object of taking the levels is to find the height of the upper level above the lower one, which determines the number of locks on the line, and that of measuring the hypotenusal distances with the chain to find data for ascertaining the true lengths of the dead

U

levels or arcs that determine the length of the canal within the

survey.

The survey may be represented as lying between two arcs of two concentric circles on the vertical plane.

If, in the foregoing diagram (drawn on an exaggerated scale purposely to illustrate details which otherwise could not have been shown and made intelligible to the private student), we suppose abr to represent a section of the vertical plane, then ab and cd will be the two arcs between which the survey lies; the former showing the upper water level line, and the latter the lower one.

If we further suppose four locks on the line, such data will give three intervening arcs; and if we again assume that the three arcs subtend equal angles, then ce in the diagram will show the first lock, im the second, no the third, and ub the fourth ei will show the first intervening arc, mn the second, and ou the third.

The lines sought are therefore bd, ei, mn, and ou on the vertical plane.

The lines measured are the hypotenusal distances, and normals or vertical-offsets, the former lying between the theodolite and levelling-staff by the chain, and the latter by the levelling-staff.

The angles measured with the theodolite are those which each hypotenusal line makes with its horizontal level or tangent and sine, and the normals or portions of the two radii between which it lies.

In the diagram the hypotenusal line between the first two radii is the diagonal ci, which represents the first line measured with the chain. The first normal taken from the levelling-staff is represented by cy. The other diagonals, in and nu, may be drawn in a similar way; also their two normals at i and n; their two sines from i and n, and their two tangents from n and u-the construction of the second and third sector being similar to that of the first.

In each sector there are three right-angled plane triangles, and two oblique-angled triangles, with certain lines and angles, measured to find other lines and angles, by rules given in geometry and trigonometry. The triangles of the first sector only are completed, those of the other two being left for exercises to the student; and the three sectors have been made equiangular at the centre r, for the express purpose of illustrating some of the most remarkable properties of the circle, those properties most commonly met with in the practice of surveying. Two of the corresponding triangles of the three sectors are equiangular, but not equilateral, the sides increasing in length as the arcs and radii increase in length. The other three triangles are neither equiangular nor equilateral.