the height correfponding thereto; and in determining the quantity of effluent water, regard must be had to this inequality of velocity.

This mode of reafoning, however, is not conclufive; for though it may be just as far as relates to the number of infulated holes, it does not appear that the water will flow exactly in the fame manner when the threads thereof are united, as when they proceed from small separate apertures. As the refults of theory, however, upon this plan differ little from experiments, it may be useful to adhere to it till fome better method is difcovered. The quantity of water flowing through holes in a given time is not fo great as might be expected, because the water does not flow in a compact parallel stream, but contracts in diameter on coming out of the aperture, and this contraction extends to a distance nearly equal to half the diameter of the aperture. The diameter of the contracted fream is to the diameter of the aperture as 3 to 4, or as 3 to 4, or as 19 to 24, fo that its area to that of the aperture is as 10 to 16: it is nearly the fame thing when the water flows from lateral apertures.

This contracted ftream is a proof, that withinfide the veffel the lateral particles are directed towards the hole, with different degrees of obliquity, which obliquity may be decompofed into two forces, one parallel to the plane of the hole, which contracts the fluid; the other perpendicular to the fame plane, which occafions the efflux. This contraction takes place alfo when water paffes through tubes, and the contraction is at the entrance of the water into the tube, not at its going out, where it preferves its cylindric form. This contraction fenfibly diminishes the quantity of water that should be furnished by the tubes. To afcertain these facts, M. Bofiut made a great number of experiments, the refults of which follow. The apertures for the efflux of the water were all pierced perpendicularly in plates about a line thick, and the time of each experiment was reduced to 1 minute.

Conftant height of the water, 11 feet 8 inches 10 lines from the centre of each aperture.

Exp.

1. With a circular horizontal aperture, 6 lines diameter

2. With ditto, 1 inch diameter, 3. With ditto, 2 inches diameter 4. With a rectangular horizontal aperture, 1 inch by 3 lines

N° of cubic inc. difch. în 1 min.

2311

9281 37203

2933

5. With a fquare horizontal aperture, the fide inch

6. With two ditto, the fides 2 inches Conftant height 9 feet.

11817 47361

7. Lateral circular aperture, 6 lines diameter

8. Ditto, 1 inch diameter

Conftant height 4 feet.

9. Lateral circular aperture, 6 lines diameter

Conftant height 7 lines.

2018

8135

3353

5436

10. Ditto, 1 inch diameter

11. Lateral circular aperture, 1 inch diameter

628

From the above experiments M. Bollut drawi the following deductions:

I.' The quantities of fluid discharged in equal times from different fized apertures, the altitude of the fluids being the fame, are nearly to each other as the areas of the apertures. Thus in the 2d and 3d experiments the areas of the apertures are as 1 to 4, and the water discharged 9281 cu. bic inches; 37,203 is nearly in the fame ratio. 2. The quantities of water discharged, in equal times, by the fame aperture, with different alti tudes of the refervoir, are nearly as the fquart roots of the correfponding altitude of the water in the refervoir above the centre of the aperture! Compare the 8th and 10th experiments, in which the refpective altitudes of the refervoir were 9 and 4 feet, of which the fquare roots are 3 and 2; and we find the water discharged by the firft was 8135 cubic inches, the 2d 5436 cubic inches; nearly in the proportion of 3 to 2.

3. That, in general, the quantities of water discharged in the fame time, by different apertures and under unequal altitudes of the refervoirs, are to each other in a compound ratio of the areas of the apertures and the fquare roots of the altitudes.'

4. That on account of the friction, the smallest apertures discharge lefs water than those that are larger and of a fimilar figure, the water in the respective refervoirs being at the fame height.'

5. That of feveral apertures whose areas are equal, that which has the smallest circumference will difcharge more water than the others, the water in the refervoirs being at the fame altitude;' and this because there is less friction. Hence circular apertures are most advantageous, as they have lefs rubbing furface under the fame area.

The quantities of water, we find, expended in the foregoing experiments, are not nearly fo much as they ought to be, confidering the fize of the apertures and the altitude of the refervoirs. The quantity discharged is diminished confiderably by the friction, and by the contraction of the ftream; and probably on account alfo of the circular motion of the fluid: for the velocity which depends on the altitude of the refervoir is not fenfibly altered. The difference in the difcharge of water, fuppofing, 1. that the area of the ftream is the fame with that of the aperture; 2. that this ftream is contracted; is as 16 to 10: in other words, by fuppofing the area of the orifice to be diminished in the proportion of 16 to 10, we may determine with fufficient exactnefs the efflux of fluids from veffels where the furfaces are maintained at the same height.

SECT. III. Of the DISCHARGE of FLUIDS through ADDITIONAL TUBES.

IF the water, instead of flowing through an aperture pierced in a thin fubftance, paffes through the end of a vertical tube of the fame diameter as the aperture, there is a much greater discharge of water, because the contracted ftream is greater in the first inftance than in the fecond. In the following experiments, the constant height of the water in the refervoir, above the upper aperture of the tube, was 11 feet 8 inches to lines, the diameter of the tube 1 inch, LENGTHS

On comparing the three first experiments, it appears, that the longer the vertical tube is, the greater is the discharge of the water, because the contraction of the ftream is lefs; it is, however, always fomewhat contracted, even when it appears to fill the tube. By comparing the quantities of water discharged in the 3d and 4th experiments, we find the 2 difcharges, 12168 and 9282, are to each other nearly in the proportion of 13 to 10; but we have feen, that the water difcharged through a thin aperture without any contraction in the stream, would be to the fame aperture with a contracted ftream as 16 to 10.

Hence we may conclude, that, the altitude in the refervoir and the apertures being the fame, the discharge through a thin aperture without any contraction in the ftream, the discharge through an additional tube, and the discharge through a fimilar aperture with a contracted stream, are to each other nearly as the number 16, 13, and 10: these proportions are fufficiently exact for practice. Hence it is plain that an additional tube only destroys in part the contraction of the stream, which contraction is greatest when the water paffes through a thin aperture from a large refervoir.

If the additional tube, inftead of being vertical, or placed at the bottom of the reservoir, were horizontal or placed in the fide, it would furnish the fame quantity of water, provided it was of the fame length, and that the exterior aperture was at the fame distance from the furface of the water in the reservoir. If the additional tube, instead of being cylindrical, were conical, having its largest bafe nearest the reservoir, it would discharge a greater quantity of water. The most advantageous form that can be given, to obtain the greatest quantity of water in a given time by a given aperture, is that which the ftream affumes in coming out of the aperture; i. e. the tube must be of the form of a truncated cone, whose smallest base fhould be of the fame diameter as the aperture; the area of the small base should be to that of the larger base as 10 to 16; and the distance from one bafe to the other fhould be the femi-diameter of the largest base. The efflux of water will then be as abundant as it would be through a thin aperture equal to the smallest bafe, and where the ftream was not contracted. This form may be applied where it is neceffary to obtain a certain quantity of water from a river, an aqueduct, &c. by a canal or lateral tube.

On comparing the efflux of water through additional tubes of different diameters, and with dif; ferent altitudes of the water in the refervoirs, the following refults were obtained; the additional tubes were two inches long, and were vertical and placed at the bottom of the refervoir.

7

8

"That

From thefe experiments it results, 1. the discharge by different additional tubes, with the fame altitude of the refervoir, are nearly in proportion to the area of the apertures, or to the fquares of the diameters. 2. That the discharge of water by additional tubes of the fame diameter, with different altitudes of water in the reservoir, are nearly proportional to the square root of the altitude of the refervoir. 3. That in general the discharge of water in the fame time, through different additional tubes, with different altitudes of water in the fame refervoir, are to each other nearly as the product of the fquare of the diameters of the tubes by the fquare root of the altitude of the refervoirs." So that, additional tubes, tranfmitting water, follow (amongst themselves) the fame laws as through the thin orifice. The following table was formed from the foregoing experiments:

and the altitude of the reservoir above it, be the fame. This is a neceffary confequence of the equal preffure of fluids in all directions,

Water, fpouting from a fmall ajutage, has fufficient velocity to carry it to the fame height as the water in the refervoir; but it never attains entirely to this height, being prevented by various concurring caufes; as, 1. The friction in the tubes between the refervoir and the ajutage: 2. The friction against the circumference of the aperture: 3. The refiftance of the air to the weight of the water at the top of the fpout; for this, having loft its motion, refts on the part below, and by its weight obftructs the motion of the column. The refiftance from this caufe is fo great, that the jet is frequently destroyed, the rifing water being by fits and starts preffed down to the very orifice from which it fpouts: but this inconvenience is remedied, by giving the jet a little inclination; for then the particles which have loft their motion upwards do not fall back as before, but fall off from the reft, and thus do not incumber the rifing fluid; hence fuch jets as are a little inclined will rife higher than those that are vertical.

When the ajutage is inclined to the horizon, the projectile force and the gravity of the water caufe the ftream to defcribe a parabola, whofe amplitude is greater in proportion to the height of the refervoir. When the ajutage is in an horizontal direction, the jet describes a femi-parabola. Jets of water rife higher in proportion as the aperture of the ajutage is large; because, 1. Of two jets proceeding from the fame refervoir with equal velocities, the largest undergoes lefs friction: 2. It has more mafs, and confequently more force to overcome obftacles. But though a large jet will rife higher than a small one, it does not discharge more water; for the difcharge is as the product of the aperture by the velocity at the moment of efflux; and this velocity is the fame in each, friction not being confidered.

To make large jets rife higher than small ones, the conduit-pipe must be large enough to furnish a fufficient quantity of water; for if these are narrow, fmall jets will rife higher than those that are larger. The diameter of the conduit-pipe fhould therefore bear a certain proportion to that of the ajutage, to make a jet rise to the greatest possible height. If we compare two different jets, and defire that each fhould attain its greatest altitude, the fquares of the diameters of the conduit-pipes must be to each other in the compound ratio of the fquares of the diameters of the ajutages, and the fquare root of the altitude of the reservoir. Thus, if we know the 'diameter that ought to be given to a conduit-pipe, to furnish water for the difcharge of a given ajutage, with a refervoir of a given altitude, we may determine the diameter of another tube, to feed a given ajutage with a refervoir of a given altitude.

Experience has fhewn, that, for an ajutage fix lines diameter, with a refervoir of 52 feet, the conduit-pipe should be about 39 lines; for an ajutage fix lines diameter, and a refervoir 16 feet, the conduit pipe 28 lines. There is no inconvenience in giving a conduit-pipe a greater diameter than

the above, but there would be a confiderable one in giving it a smaller.

From the comparison of feveral experiments made on jets d'eau, it appears, that the difference between the altitudes of vertical jets, and the altitudes of the refervoirs, is to each other as the fquares of the jet's altitude. If we know therefore, how far any jet falls fhort of the altitude of its refervoir, we may find by the rule of three, how much any other jet falls fhort of its refervoir. If we wish to know the altitude of the refervoir, we have only to add to the altitude of the jet the quantity found by the proportion. Conduit pipes fhould never be fixed at right angles to each other.

The following table will facilitate the application of the above principles. The firft column contains the altitudes of the jets; the 2d thofe of the refervoir; the 3d fhows, in Paris pints (36 of which make a cubic foot), the discharge during one minute, through an ajutage fix lines diameter, relatively to the altitudes of the 2d column. Knowing the discharge with an ajutage of fix lines by the rule of three, we difcover the discharge by any other ajutage with a refervoir of the fame height; as it has been proved, that the discharges are as the area of the ajutage, or as the squares of the diameters of these ajutages. In the 4th column appear the diameters for the conduit pipes of an ajutage fix lines diameter, relatively to the altitudes of the ad column.

Altitude of Alt. of the Discharge the jets. refervoir.

Ft. In.

in 1 min.

Diam. of the conduit pipes. Lines.

Feet.

Pints.