stones, about four inches thick, laid on a bed of hydraulic mortar, one inch thick, and covered by a similar coat of mortar, making the entire thickness of the lining six inches, has been found to answer all the required purposes. This lining should be covered, both at bottom and on the sides, by a layer of good earth, at least three feet thick, to protect it from the shock of the boats striking either of those parts.

The cross section of the canal and its tow-paths in deep cutting (Fig. 166) should be regulated in the same way as in canals

Fig. 166-Cross section of a canal in deep cutting.
E, side slopes of cutting.

of the first class but when the cuttings are of considerable depth, it has been recommended to reduce both to the dimensions strictly necessary for the passage of a single boat. By this reduction there would be some economy in the excavations; but this advantage would, generally, be of too trifling a character to be placed as an offset to the inconveniences resulting to the navigation, particularly where an active trade was to be carried on.

692. Summit level. As the water for the supply of the summit level of a canal must be collected from the ground that lies above it, the position selected for the summit level should be at the lowest point practicable of the dividing ridge, between the two branches of the canal. In selecting this point, and the direction of the two branches of the canal, the engineer will be guided by the considerations with regard to the natural features of the surface, which have already been dwelt upon.

693. Supply of water. The quantity of water required fo canals with a summit level, may be divided into two portions 1st. That which is required for the summit level, and those lev els which draw from it their supply. 2d. That which is wanted for the levels below those, and which is furnished from other

sources.

The supply of the first portion, which must be collected at the summit level, may be divided into several elements: 1st. The quantity required to fill the summit level, and the levels which draw their supply from it. 2d. The quantity required to supply losses, arising from accidents; as breaches in the banks,

and the emptying of the levels for repairs. 3d. The supplies for losses from surface evaporation, from leakage through the soil, and through the lock gates. 4. The quantity required for the service of the navigation, arising from the passage of the boats from one level to another. Owing to the want of sufficient data, founded on accurate observations, no precise amount can be assigned to these various elements which will serve the engineer as data for rigorous calculation.

The quantity required, in the first place, to fill the summit level and its dependent levels, will depend on their size, an element which can be readily calculated; and upon the quantity which would soak into the soil, which is an element of a very indeterminate character, depending on the nature of the soil in the different levels.

The supplies for accidental losses are of a still less determinate character.

To calculate the supply for losses from surface evaporation, correct observations must be made on the yearly amount of evaporation, and the quantity of rain that falls on the surface; as the loss to be supplied will be the difference between these two quantities.

With regard to the leakage through the soil, it will depend on the greater or less capacity which the soil has for holding water. This element varies not only with the nature of the soil, but also with the shorter or longer time that the canal may have been in use; it having been found to decrease with time, and to be, comparatively, but trifling in old canals. In ordinary soils it may be estimated at about two inches in depth every twenty-four hours, for some time after the canal is first opened. The leakage through the gates will depend on the workmanship of these parts. From experiments by Mr. Fisk, on the Chesapeake and Ohio canal, the leakage through the locks at the summit level, which are 100 feet long, 15 feet wide, and have a lift of 8 feet, amounts to twelve locks full daily, or about 62 cubic feet per minute. The monthly loss upon the same canal, from evaporation and filtration, is about twice the quantity of water contained in it. From experiments made by Mr. J. B. Jervis, on the Erie canal, the total loss, from evaporation, filtration, and leakage through the gates, is about 100 cubic feet per minute, for each mile.

In estimating the quantity of water expended for the service of the navigation, in passing the boats from one level to another, two distinct cases require examination:-1st. Where there is but one lock between two levels, or in other words, when the locks are isolated. 2d. When there are several contiguous locks, or, as it is termed, a flight of locks between two levels.

694. A lock is a small basin just large enough to receive a boat, in which the water is usually confined on the sides by two upright walls of masonry, and at the ends by two gates, which open and shut, both for the purpose of allowing the boat to pass, and to cut off the water of the upper level from the lower, as well as from the lock while the boat is in it. To pass a boat from one level to the other-from the lower to the upper end, for example-the lower gates are opened, and the boat having entered the lock they are shut, and water is drawn from the upper level, by means of valves, to fill the lock and raise the boat; when this operation is finished, the upper gates are opened, and the boat is passed out. To descend from the upper level, the lock is first filled; the upper gates are then opened, and the boat passed in; these gates are next shut, and the water is drawn from the lock, by valves, until the boat is lowered to the lower level, when the lower gates are opened and the boat is passed

out.

In the two operations just described, it is evident, that for the passage of a boat, up or down, a quantity of water must be drawn from the upper level to fill the lock to a height which is equal to the difference of level between the surface of the water in the two; this height is termed the lift of the lock, and the volume of water required to pass a boat up or down is termed the prism of lift. The calculation, therefore, for the quantity of water requisite for the service of the navigation, will be simply that of the number of prisms of lift which each boat will draw from the summit level in passing up or down.

695. Let a boat, on its way up, be supposed to have arrived at the lowest level supplied from the summit level; it will require a prism of lift to ascend the next level above, and so on in succession, until it reaches the summit level, from which one prism of lift must be drawn to enable the boat to enter it. From this it appears that but one prism of lift is drawn from the summit level for the passage of a boat up. Now, in descending on the other side, the boat will require one prism of lift to take it to the next level, and this prism of lift will carry it through all the successive locks, if their lifts are the same. For the entire passage of one boat, then, two prisms of lift must be drawn from the summit level.

This boat will thus leave all the locks full on the side of the ascent, and empty on the side of the descent. Now the next boat may be going in the same, or in an opposite direction, with respect to the first. If it follows the first, it will evidently require two prisms of lift for its entire passage, and will leave the locks in the same state as they were. If it proceeds in an opposite direction, i will require a prism of lift to ascend to the summit

'evel; but, in descending, it will take advantage of the full lock, left by the preceding boat, and will therefore not draw from the summit level for its descent to the next; the same will take place at every level until the last, where it will carry out with it the prism of lift, which was drawn from the summit level for the preceding boat, so that in this case it will draw but one prism of lift from the summit level. If the two boats had met on the summit level, the same would have taken place: therefore, when the boats alternate regularly, each will require but one prism of lift for its entire passage. But as this regularity of alternation cannot be practically carried into effect, an allowance of two prisms of lift must be made for the entire passage of each boat.

In calculating the expenditure for locks in flights, a new element, termed the prism of draught, must be taken into account. This prism is the quantity of water required to float the boat in the lock when the prism of lift is drawn off; and is evidently equal in depth to the water in the canal, unless it should be deemed advisable to make it just sufficient for the draught of the boat, by which a small saving of water might be effected.

696. Locks in flights may be considered under two points of view, with regard to the expenditure of water: the first, where both the prism of lift, and that of draught, are drawn off for the passage of a boat; or second, where the prisms of draught are always retained in the locks. The expenditure, of course, will be different for the two cases.

To ascertain what will take place in the two cases, let a case be supposed, in which there is a flight of locks on each side of the summit level, to connect it with the two next lower levels. In the first case, a boat, arriving at the foot of the flight, finds all the locks of the flight empty, except the lowest, which must contain a prism of draught to float the boat in. To raise the boat, then, to the upper level, all the locks of the flight must be filled from the summit level, which will require as many prisms of lift as there are locks, and as many prisms of draught as there are locks less one; or, representing by L the prism of lift, D the prism of draught, and n the number of locks in the flight, the total quantity of water, for the ascent of the boat, will be represented by

n L + (n − 1) D ;

(1).

In descending, on the opposite side, the boat will require a prism of lift and one of draught at the first lock; but to enter the second another prism of draught in addition will be required, and this entire quantity will be sufficient to take it through all the remaining locks of the flight: this quantity will therefore be rep resented by

so that for the entire passage of the boat, the total expenditure will be represented by

The flight, on one side, is thus left full after the passage of the first boat, and on the other side, empty. If a second boat, then, follows directly after the first, the prism of lift must be drawn from the lowest lock to admit the boat, this prism is then supplied from the lock next above, and so on to the summit level; so that but one prism of lift will be drawn off for the ascent of this boat, and it will require one of lift, and two of draught, to carry it down the opposite flight. If, therefore, the total number of boats which follow in this order, including the first, be represented by m, the total expenditure will be represented by

(n + 1) + (n + 1) D + (m − 1) 2L + (m − 1) 2D.. L 21+ (4).

If the second boat, instead of following the first, arrives in the opposite direction, or alternates with it, the expenditure for its ascent will be represented by the formula (1), and for its descent it will be nothing, since it finds the opposite flight filled, as left by the first boat; but if the locks had been emptied, then the passage of the second boat would have taken place under the same circumstances as that of the first.

It will be unnecessary here to go farther into these calculations for the various cases that may occur, under the different circumstances of passage of the boats or of empty or full flights; the preceding gives the spirit of the method, and will give the means for entering upon a calculation to allow for the loss or gain by the passage of freighted or of empty boats, following any prescribed order of passage. These refinements are, for the most part, more curious than useful; and the engineer should confine himself to making an ample allowance for the most unfavorable cases, both as regards the order of passage and the number of boats.

697. Feeders and Reservoirs. Having ascertained, from the preceding considerations, the probable supply which should be collected at the summit level, the engineer will next direct his attention to the sources from which it may be procured. Theoretically considered, all the water that drains from the ground adjacent to the summit level, and above it, might be collected for its supply; but it is found in practice that channels for the conveyance of water must have certain slopes, and that these slopes, moreover, will regulate the supply furnished in a certain time, all other things being equal. In making, however, the survey of the country, from which the water is to be supplied to the summit level, all the ground above it should be examined, leav