relates to ascending tubes. positions.

The following relate to other

EXPER. 20.-The tube ABFE of Fig. 11, Experiment 15, was applied in the place of the tube B CQ O, in Fig. 7. The height of the water in the reservoir above the lower extremity of the tube was 41.5 inches. The four cubical feet of water were emitted in 22′′.

I applied the same conical tube ABFE, Fig. 11, to the orifice R, Fig. 8, to form an ascending jet a little inclined from the perpendicular. The height of the water of the reservoir above the upper extremity of the tube was twentythree inches. The expenditure of four cubical feet was made in 30".

The time of the expenditure in Experiment 15, was 25′′. And by comparing it with the present, we find nearly √41·5: √32·5=25′′: 22′′. And √23: √32·5=25′′ : 30′′.

EXPER. 21. The orifice R, Fig. 8, was circular, and 4·5 lines in diameter; the charge was 31.7 inches, and the jet declined a little from the perpendicular. The orifice being through a thin plate, afforded a cubical foot of water in 161". With an additional cylindrical tube of the same diameter, and ten lines in length, the cubical foot of water was emitted in 121".

Under a charge of fifty-six inches, the same orifice afforded by the vertical jet, a cubical foot in 123" through the thin plate, and in 91" with the same additional tube.

These two results being combined, give for the expenditure of vertical jets a mean ratio, between the thin plate and the cylindrical ajutage, of 100 to 134, which is also the ratio between the horizontal jets.

EXPER. 22.-I applied the glass tube QRT, Fig. 6, to the point S, Fig. 5, of the compound tube ACM N, the distance BS being twenty-four lines. In this situation the fluid T no longer rises in the tube. This proves that the lateral translation of the fluid in the cylindrical tube is made very near the place where the vein is contracted, and that, consequently, D R must briskly strike the side GM.

By this experiment we see that the distance BR at which the oblique filaments strike the sides of the tube, does not amount to twenty-four lines. Supposing DO=20 lines, the time which the particle D employs to pass through the space DO in my experiments is less than 0.01. Let us decompose the curve-lined motion DR according to the lines D O, O R. Let us suppose the acceleration through OR to be uniform, and it will be found that this acceleration is at least five times as great as that of heavy bodies. If the lateral force through OR were simply the mutual attraction of the particles of the water, this attraction in the particle D must not only overcome the inertia of the particle itself, but likewise that of the other particles nearer the axis, which follow D in its deviation through DR, and impress upon them a much greater sum of acceleration than that of gravity. Now the force of attraction of one particle of water is not greater than the natural gravity of a thread of water of the length of one line at most. The lateral communication of motion, which is the cause of the acceleration through OR, is, therefore, much greater than could have been produced by the mutual attraction of the particles of water.

PROPOSITION VII.

By means of proper Ajutages applied to a given cylindric Tube, it is possible to increase the Expenditure of Water through that Tube in the proportion of Twenty-four to Ten, the Charge or Height of the Reservoir remaining the same.

I shall here give an account of the different precautions necessary to be taken when the expenditure of water through a cylindrical tube of a given length is required to be the greatest possible.

*

1. The inner extremity of the tube AD (Fig. 13), must be fitted at A B with a conical piece of the form of the contracted vein; this increases the expenditure as 12-1 to 10. Every other form will afford less. If the diameter at A be too great, the contraction will be made beyond B, and the section of the vein will be smaller than the section of the tube.

2. At the other extremity of the pipe B Capply a truncated conical tube CD, of which let the length be nearly nine times the diameter C, and its external diameter D must be 18 C. This additional piece will increase the expenditure as 24 to 12.1, (Experiment 16). By this means the quantity of water will be increased by the two ajutages A B, CD, in the proportion of twenty-four to ten.†

The idea that this ratio will apply to long pipes is erroneous; for it must obviously decrease as the force necessary to produce motion increases; and, therefore, in long pipes will have very little effect. It may also be inferred that the effect of a truncated tube applied at the outer extremity will depend considerably on the velocity of the efflux. The Roman law, mentioned in the next

At Rome, the inhabitants purchase the right of conveying water from the public reservoirs into their houses. The law prohibits them from making the pipe of conveyance larger than the aperture granted them at the reservoir, as far as the distance of fifty feet.* The legislature was, therefore, aware, that an additional pipe of greater diameter than the orifice would increase the expenditure; but it was not perceived that the law might be equally evaded by applying the conical frustum CD beyond the fifty feet.

From the second rule we learn, that it is not proper to make the flues of chimneys too large in the apartments; but that it will be sufficient if they be enlarged at their upper terminations, according to the form CD, Fig. 13. This divergency of the upper part will carry off the smoke very well, even when it is not practicable to afford chimneys of sufficient length to the upper apartments. The same observation is applicable to chemical furnaces for strong fire.

3. The pipe B C ought to be straight, without elbows or curvatures. To the experiments which Bossut has made on this head, I shall add the following:

EXPER. 23. The two tubes ABC, DEF, Fig. 14. Plate II, are 15 inches long; their diameter is 14.5 lines. The conical portions A, D, have the form of the contraction of the vein of fluid, and are applied to the orifice P, Fig. 1, which is 18 lines in diameter, with 32.5 inches depth, or charge of superincumbent fluid. The elbows, or flexures, BC, EF, are made

paragraph has most likely limited the distance to that where the increase of expenditure would be inconsiderable for the size of pipe commonly used at the time.-ED.

* Fontin. de Aquæduct. Art. 205, 106 et 112. † Art. 631, et seq.

in the plane of the horizon. These two pipes are made of copper soldered with silver, and the workmanship carefully executed. The curvature B C was drawn out or bended, into the form of a quarter of a circle, by filling the tube with melted lead in order that it might preserve its diameter during the act of bending. The elbow D E F is constructed in a right angle. The expenditure through these two tubes was compared with that afforded through a right-lined cylindrical tube of similar dimensions, and in like circumstances. The four cubical feet of water flowed out of the cylindrical tube in 45"; out of the curved tube A BC in 50"; and out of the angular tube DEF in 70".

It is of importance that the tube B C, Fig. 13, Plate I, should be of an equal diameter throughout. It is not enough that care be taken that there should be no contraction; it is also necessary that it should not be enlarged at any part. For such enlargements have nearly the same bad effect in the expenditure as contractions. The pipe A O, Fig. 12, affords a much less quantity of fluid with the dilatations DE, H I, than if it were of a diameter equal to that at B throughout its whole length. The following experiment agrees with the theory.

EXPER. 24. The circular orifice A, Fig. 12, has the form of the contraction of the vein, and the remaining part of the tube is interrupted by various enlargements of its diameter. This tube is applied to the aperture P, Fig. 1. The dimensions of its parts measured in lines are as follow:-Diameter at A = 11.2. Diameter at B, C, F, G, &c., = 9. Length of BC= FG, &c., = 20. Length of C D E F G H, &c., = = = 13. Diameter of the enlarged parts each of the enlarged parts was variable. it was 38 lines, the second 76, and the result of the experiment was the same in both cases.

=

24. The length of The first time of trial