feet, then the whole pressure 3b d', in cwts.

7. If the gate be in form of a trapezoid, widest at top, then, if B and b be the breadths at the top and bottom respectively, and d the depth.

whole pressure in lbs. 314 [} (B

=

3

· b) + b] d2 whole pressure in cwts. (Bb) + b] d2, nearly. S. The weight of a cubic foot of rain or river water, is nearly equal to

cwt.

The pressure on a square inch, at the depth of THIR-ty feet is very nearly THIR-teen pounds.

Pressure on a square foot, nearly a ton at the depth of thirty-six feet. [The true depth is 35 84 feet.]

The weight of an ale gallon of rain water is nearly 10 lbs. that of an imperial gallon 10 lbs.

The weight of a cubic foot of sea-water is nearly of a cwt. These are all useful approximations.

Thus, the pressure of rain water upon a square inch at the depth of 3000 feet, is 1300 lbs.

And the pressure upon a square foot at the depth of 108 feet is nearly three tons.

9. In the structure of dykes or embankments, both faces or slopes should be planes, and the ex

DF D'

B

terior and interior slopes should make an angle of not less than 90°. For if A D' be the exterior slope, and the angle D' AB be acute, E D' perpendicular to A B is the direction of the pressure upon it; and the portion D' A E will probably be torn off. But when DA is the exterior face, making with A в an obtuse angle, the direction of the pressure falls within the base, and therefore augments its stability.

10. The strength of a circular bason confining water, requires the consideration of other principles.

The perpendicular pressure against the wall depends merely on the altitude of the fluid, without being affected by the volume. But, as professor Leslie remarks, the longitudinal effort of the thrust, or its tendency to open the joints of the masonry, is measured by the radius of the circle. To resist that action in very wide basons, the range or course of stones along the inside of the wall, must be proportionally thicker. On the other hand, if any opposing surface present some convexity to the pressure of water, the resulting longitudinal strain will be exerted in closing the joints and consolidating the building. Such reversed incurvation is, therefore, often adopted in the construction of dams.

In like manner, the thickness of pipes to convey water

h d

must vary in proportion to where h is the height of the

C

head of water, d the diameter of the pipe, and e the measure of the cohesion of a bar of the same material as the pipe, and an

inch square.

A pipe of cast iron, 15 inches diameter, and of an inch thick, will be strong enough for a head of 600 feet.

A pipe of oak of the same diameter, and 2 inches thick, would sustain a head of 180 feet.

Where the cohesion is the same, t varies as hd or as HDT hd t, in the comparison of two cases.

*

Example.-What, then, must be the respective thicknesses of pipes of cast iron and oak, each 10 inches diameter, to carry water from a head of 360 feet?

=

Here, 1st. for cast iron: HD (= 600 × 15) : T (= 1) :: h d ( 360 X 10 X 3 600 x 15 x 4

HD (= 180 X 360 x 10 x 2

180 x 15

10800

=

=

36000

= of an inch.

2dly. for oak:

360 × 10): t =

15) : T (= 2) :: hd ( = 360 × 10): t =

18 == 23 inches.

=

SECTION II.-Floating Bodies.

1. If any body float on a fluid, it displaces a quantity of the fluid equal to itself in weight.

2. Also, the centres of gravity of the body and of the fluid displaced must, when the body is at rest, be in the same vertical line.

3. If a vessel contain two fluids that will not mix (as water and mercury), and a solid of some intermediate specific gravity be immersed under the surface of the lighter fluid and float on the heavier; the part of the solid immersed in the heavier fluid, is to the whole solid as the difference between the specific gra

• To ascertain whether or not a pipe is strong enough to sustain a proposed pressure, it is a good custom amongst practical men to employ a safety valve, usually of an inch in diameter, and load it with the proposed weight, and a surplus determined by practice. Then, if the proposed pressure be applied interiorly, by a forcing pump, or in any other way, if the pipe remain sound in all its parts after the safety-valve has yielded, such pipe is regarded as sufficiently strong.

The actual pressures upon a pipe of any proposed diameter and head, may evidently be determined by a similar method.

vities of the solid and the lighter fluid, is to the difference between the specific gravities of the two fluids.

4. The buoyancy of casks, or the load which they will carry without sinking, may be estimated by reckoning 10 lbs. avoirdupois to the ale gallon, or 8 lbs. to the wine gallon.

5. The buoyancy of pontoons may be estimated at about half a hundred weight for each cubic foot.

Thus a pontoon which contained 96 cubic feet, would sustain á load of 48 cwt. before it would sink.

N. B. This is an approximation, in which the difference between and, that is, of the whole weight, is allowed for that of the pontoon itself.

22

6. The principles of buoyancy are very ingeniously applied in Mr. Farey's self-acting flood-gate. In the case of common sluices to a mill-dam, when a sudden flood occurs, unless the miller gets up in the night to open the gate or gates, the neighbouring lands may become inundated; and, on the contrary, unless he be present to shut up when the flood subsides, the mill-dam may be emptied and the water lost which he would need the next day. To prevent either of these occurrences, Mr. John Farey, whose talent and ingenuity are well known, has proposed a self-acting flood-gate, the following description of which has been given in the Mechanics' Weekly Journal.

A A represents a vertical section of a gate poised upon a horizontal axis passing rather above the centre of pressure of the gate, so as to give it a tendency to shut close.

b

a a is a

lever, fixed perpendicular to the gate, and connected by an iron rod with a cask, b, floating upon the surface of the water, when it rises to the line, B, D, which is assumed as a level of the wear or mill-dam, B, C, E, F, in which the flood-gate is placed by this arrangement it will be seen that when the water rises above the dam, it floats the cask, opens the gate, and allows the water to escape until its surface subsides to the proper level at B, D; the cask now acts by its weight, when unsupported by the water, to close the gate and prevent leakage. The gate should be fitted into a frame of timber, H, K, which is set in the masonry of the dam. The upper beam, H, of the frame being just level with the crown of the dam, so that the water runs over the top of the gate at the same time that it passes through it to prevent the current disturbing the cask, it is connected by a small rod, e, at each end, to the upper beam, н, of the frame, and jointed in such a manner as to admit of motion in a vertical direction.

Any ingenious mechanic will so understand the construction from this brief account, as to be able to apply it to practice when needed.

7. By means of the same principle of buoyancy it is, that a hollow ball of copper attached to a metallic lever of about a foot long, is made to rise with the liquid in a water-tub, and thus to close the cock and stop the supply from the pipe, just before the time when the water would otherwise run over the top of the vessel.

8. This property, again, has been successfully employed in pulling up old piles in a river where the tide ebbs and flows. A barge of considerable dimensions is brought over a pile as the water begins to rise: a strong chain which has been previously fixed to the pile by a ring, &c. is made to gird the barge, and is then fastened. As the tide rises the vessel rises too, and by means of its buoyant force draws up the pile with it. In an actual case, a barge 50 feet long, 12 feet wide, 6 deep, and drawing two feet of water, was employed. Here, 50 x 12 x 16 7

50 x 12 x (6

2) X 유

=

=

192 × 74

=

1344 + 279 1371 cwt. = 66 tons nearly, the measure of the force with which the barge acted upon the pile.

SECTION III.-Specific Gravities.

1. If a body float on a fluid, the part immersed is to the whole body, as the specific gravity of the body to the specific gravity of the fluid.

Hence, if the body be a square or a triangular prism, and it be laid upon the fluid, the ratio of that portion of one end which is immersed, to the whole surface of that end, will serve to determine the specific gravity of the body.

2. If the same body float upon two fluids in succession, the parts immersed will be inversely as the specific gravities of those fluids.

3. The weight which a body loses when wholly immersed in a fluid is equal to the weight of an equal bulk of the fluid.

When we say that a body loses part of its weight in a fluid, we do not mean that its absolute weight is less than it was before, but that it is partly supported by the reaction of the fluid under it, so that it requires a less power to sustain or to balance it.

4. A body immersed in a fluid ascends or descends with a force equal to the difference between its own weight and the weight of an equal bulk of fluid; the resistance or viscosity of the fluid not being considered.

5. To find the specific gravity of a fluid or of a solid.— On one arm of a balance suspend a globe of lead by a fine thread, and to the other fasten an equal weight, which may just balance it in the open air. Immerse the globe into the fluid, and observe what weight balances it then, and consequently what weight is lost, which is proportional to the specific gravity as above. And thus the proportion of the specific gravity of one fluid to another is determined by immersing the globe successively in all the fluids, and observing the weights lost in each, which will be the proportions of the specific gravities of the fluids sought.

This same operation determines also the specific gravity of the solid immerged, whether it be a globe or of any other shape or bulk, supposing that of the fluid known. For the specific gravity of the fluid is to that of the solid, as the weight lost is to the whole weight.

Hence also may be found the specific gravity of a body that is lighter than the fluid, as follows:

6. To find the specific gravity of a solid that is lighter than the fluid, as water, in which it is put.-Annex to the lighter body another that is much heavier than the fluid, so as the compound mass may sink in the fluid. Weigh the heavier body and the compound mass separately, both in water and out of it; then find how much each loses in water, by subtracting its weight in water from its weight in air; and subtract the less of these remainders from the greater.