apparatus of Venturi. These experiments, those which are given in the Hydrodynamics of D. Bernoulli, and those of many other philosophers whose names we shall not mention here, have put the phenomenon of pipes beyond all doubt. It is equally certain that this increase is owing to the liquid flowing in a full stream in the tube, which causes the contraction of the vein to disappear, and even changes it into a dilatation when the pipe is conical. But hitherto it has not been explained in a satisfactory manner why the fluid thus fills the tube adapted to a thin orifice. M. Hachette finds the sole, or at least the principal cause of it, in the adhesion of the fluid to the sides of the tube; that is to say, in the force which produces the capillary, and other similar phenomena.* The following are the experiments made to confirm this proposition :

EXPER. I.-The fluid in motion was mercury; the pipe was iron. When the mercury was perfectly pure, it had no affinity for the iron, and flowed out as it would have done had there been no pipe. But when the mercury was covered with a pellicle formed of an alloy of tin and other metals, this alloy covered the inside of the pipe, and in that case the mercury flowed in a full stream.

EXPER. II.-The fluid was water; the pipe was coated within with wax. The pipe was not filled, and the water flowed as if no pipe had been present. But it is always possible to force the water to moisten the wax; then the water fills the pipe, owing to the wax being replaced by the first coat of water which covers it. Hence the reason why a disc of glass at last adheres to water with the same force, whether or not it be covered with a coating of wax; for as soon as the wax is wetted, it is merely the action of water on water which determines the phenomenon, as M. Laplace has explained it in the theory of capillary action.

Another no less important fact, which M. Hachette has determined, is, that in a vacuum, or in air rarified to a certain degree, the phenomenon of pipes ceases to take place.† Thus having made

* Opinion of former Writers on the Cause of the Effects produced by Tubes.-M. Venturi states in a note (p. 23) that Gravesende and others have ascribed to the natural cohesion of the particles of water the increase of expanse in the additional descending tubes, and he observes that this cause is of very little importance. Before him, Bussut, Dubuat, had explained the effect of pipes by the viscosity of the water, the resistance of the fluid contained in the pipes, and the obliquity of the jets which strike the sides. At this time the phenomena of capillary tubes were scarcely known, and till now they had not been distinguished in the movement of fluids, which belongs to mechanics properly so called. Accordingly M. Bossut himself thought it requisite to adopt an hypothesis different from his own, presented by Venturi, as we see by the conclusion of a report made to the Institute on Sept. 7, 1797.-H. C.

+ On the Flowing of Liquids in a Vacuum.-This experiment must not be confounded with the one related in p. 15 of the work of M. Venturi. This philosopher says that, after having placed upon the receiver of an air-pump in which the mercury in the gauge stood at ten lines of height, a vessel to which a cylindrical pipe was fitted, he had observed that the time which the level of the liquid in the vessel took to sink was the same as if the experiment had been made in the open air, and by an orifice without a pipe, and of the same diameter as the pipe.

This fact being admitted, Venturi thought that he ought to ascribe the cause of the effects produced by the pipes to the action of the medium in which the experi

water run in a full stream through a tube under the receiver of an air-pump, and having rarified the air in the receiver, the author observed the fluid vein detaching itself from the sides of the pipe when the internal pressure was reduced to 23 centimetres of mercury, the external pressure being 0.76 metre. By thus diminishing the internal pressure, the effect of the external pressure is increased, which is transmitted to the pipe by means of the fluid contained in the vessel, and to which is added the pressure of that fluid. But there comes a point at which these two pressures are sufficiently great to detach the fluid vein from the sides of the pipe; in the same manner as a sufficient force detaches a disc from the surface of a fluid to which it adhered.*

Thus the flowing out of water in a vacuum or in rarified air agrees perfectly with the proposition of M. Hachette; and does not prove, as might be supposed, that the phenomena of pipes are owing to the pressure of the air in which that fluid flows-an opinion which would be obviously inconsistent with the two experiments just cited; for in these experiments the action of the air was the same, and yet the phenomena were different, according to the nature of the fluid and the matter of which the pipe was composed.

When the fluid vein has been detached by rarifying the air as we have just stated, if we allow the air to enter again into the receiver, M. Hachette has observed that the water does not again begin to flow in a full stream. The contraction of the vein which took place in the rarified air continues to subsist, though the pressure of the atmosphere be restored. This, in the author's opinion, leads to the conclusion that the adhesion of that fluid to the sides of the pipe takes place only at the commencement of the motion, before that the fluid has acquired a sensible velocity in a direction which separates it from the side. To verify this conjecture, M. Hachette made the following experiment, which is the last that we shall notice:

The water flowed in a full stream through a pipe without the receiver of an air-pump. A small hole was made in this pipe very near the orifice. The external air then entered into the pipe, as ought to have happened according to the theory + of D. Bernoulli.

ment takes place. He did not remark that the contact of the liquid and of the sides of the pipe must precede the issuing out of the water, in order that it may run out from a full pipe. I have ascertained several times that the running of the liquid from a thin orifice, or from pipes, does not vary sensibly, whatever be the medium which surrounds the vessel, and that the liquid will run out in a full stream through a conical pipe with a maximum of divergence in a vacuum as well as ip the open air.-H. C.

* I repeated the same experiment in atmospheric air. The fluid vein was not detached from the sides of the pipe but under a pressure of a column of water, whose vertical height was 22.8 metres; so that the difference between the superior and inferior pressure was (228 10-33) 1247 centimetres in water, or 91 centimetres in mercury. The conduit of water not being vertical, we can draw no conclusion respecting the real pressure of the column of water in motion. I am preparing an apparatus to determine the point.-H. C.

+ Measure of the Negative Pressure in a Conical Pipe.-According to this theory (of Bernoulli), the sides of the conical pipe experience during the flowing of the

:

'It interposed itself between the water and the sides of the pipe. The contraction of the vein takes place in the inside of the tube, and the water ceases to flow in a full stream. This being the case, the opening made was exactly shut the adhesion of the water and pipe was not again produced, and the flowing of the water continued as if the pipe had not existed, so that it might have been removed or replaced without any change in the flow of the water. This experiment succeeded equally whatever was the direction of the jet. But care must be taken not to agitate the apparatus; for a very ́small lateral motion of the fluid vein causes it to adhere again to the moist sides of the pipe. It was probably from having neglected this precaution that M. Venturi, in p. 13 of his work, gives a result which appears contrary to that of M. Hachette.

PART III.-Figure of the Fluid Vein.

We have but little to say respecting this third part, which belongs entirely to descriptive geometry. It is in it that M. Hachette has been chiefly aided by two fellow labourers, who assisted him in his experiments, M. Girard, Draughtsman to the Polytechnic School, and M. Olivier, formerly a pupil in that school, and at present an officer of artillery. We find in it a description of the different forms of fluid vein corresponding to certain figures of the orifice. Figures upon a large scale representing the curve of the vein, and some of its sections, accompany the memoir. These figures have been constructed by a method sufficiently exact, which it would be difficult and superfluous to explain.

In this analysis of the memoir of M. Hachette we have pointed out most of the new experiments which belong to him, both respecting the contraction of the vein, and on the phenomenon of pipes; and we have stated the theory to which these experiments have led him. The Class may perceive by this statement what the author has added to the discoveries of his predecessors in this important branch of the mechanics of fluids, and be enabled to judge at the same time how much remains for him to do in order to com

liquid in a full stream an internal pressure less than the external pressure of the atmosphere. I measured the difference of these two pressures, which I call negative pressure, by means of a glass tube with two parallel vertical branches bent in the lower part. One of these branches was curved in its upper part, to fit it to the sides of the tube. Having first put mercury in the tube, the curved branch was filled with water, so that the water of that branch communicated directly with that which flowed through the conical pipe. The mercury rose in that branch during the flow of the liquid with a constant level, and I concluded that the height of the column of water which measured the difference of the pressures corresponded nearly to the initial height of the velocity which the water acquires in the conical pipe at the point of the insertion of the tube into this pipe. This result does not agree with the proposition of M. Venturi (p. 16 of his work). On that account I repeated the experiment several times; and I do not think that I am deceived in the conclusion which I have drawn from it. According to M. Venturi, the water would assume at the point of the insertion of the tube a velocity measured by the negative pressure augmented by the height of the constant level above the orifice. I must remark, however, that the result of his 15th expement (p. 27) confirms my conclusion. -H, C.

plete the investigation which he has begun. We think that in engaging M. Hachette to continue his labours, the Class ought to approve of this memoir, and order the printing of it in the Recueil des Savans Etrangers.

Feb. 5, 1816.

(Signed)

AMPERE, GIRARD, and POISSON,
Commissioners.

The Class approves of the report, and adopts its conclusions.

Observations on the Method of obtaining a constant Discharge from a given Orifice, and on the Changes in the Quantity of the Liquid discharged which results from Obstacles placed at small Distances from the Orifice.

M. Hachette has communicated his observations to the meeting of the Societé Philomatique of Feb. 10, 1816. They are a continuation of the memoir on which M. Poisson has written the preceding report. We shall extract from it what relates to obstacles struck by the fluid vein at small distances from the orifice.

D. Bernoulli thought that these obstables did not change the quantity of fluid that flowed out; and he mentions in the fourth section of his Hydrodynamics an experiment in support of his opinion; but the flow lasted too short a time to deduce from it an exact comparison between the quantities of liquid that flowed out. The influence of the obstacle is very obvious in the following experiment :

A fluid vein flowed out of a great vessel by a circular horizontal orifice 20 millimetres in diameter, and fell into a vessel placed at a great distance from the orifice. The level of the water in the vessel sank about six decimetres in 10′ 21′′. The plane face of an obstacle was presented at different distances from the orifice on which the jet fell perpendicularly.

These distances, expressed in millimetres, being

128m 80m 50m

24m

4m

the corresponding times of the sinking of the level are

10′ 21′′ 10′ 25′′ 10′ 26′′ 11′ 13′′ 15′ 54′′ This shows us that at the distance of 128 millimetres (5.039 inches) the obstacle produces no effect; but at four millimetres (0.157 inch) the time is increased rather more than one half.

ARTICLE IX.

Determination of the primitive Form of Bitartrate of Potash,
By W. Hyde Wollaston, M.D. F.R.S.

MY DEAR SIR,

(To Dr. Thomson.)

March 26, 1817.

I YESTERDAY took up again the examination of the form of supertaṛtrite of potash; and as I found it by far the most difficult I

ever undertook to investigate, I am unwilling that the share of labour bestowed upon it should be lost, and commit it to writing without delay.

Imagine a prism the section of which is a rectangle, having its sides nearly as 8 to 11. Let it be terminated at each end by dihedral summits placed transversely, so that the sides of one summit meet in one diagonal, and the sides of the opposite meet in the other at an angle of 794. You have then a form to which all the modifications of this salt may be referred, and from which they may be calculated.

But, though this be a convenient primary form for consideration of the subject, it may perhaps not be correctly the primitive form, since all the faces that I have named cannot be obtained by fracture. The prism splits most readily in the direction of its broader side, without difficulty in the direction of its diagonals, with some difficulty in the direction of its narrow side, but not at all in the direction of those faces which I have represented as terminal.

It might, therefore, be regarded as a rhombic prism, which also splits in its two diagonals, terminated by dihedral summits arising from its sides (instead of its angle), and transversely placed as before.

But of these views I prefer the former, on account of a third view of the matter (which, indeed, is the first I had of the subject). You have but to conceive the former prism shortened till the sides are reduced to nothing, and the summits will then comprise a scalene tetrahedron, the sides of which are four similar triangles, inclined to one another at 7940, 77°, and 534°.

Conceive this tetrahedron moved in the direction of its shortest diagonal, it describes the first prism, and the splits of that prism are in the planes described by all the edges of the tetrahedron. I will inclose a model unfolded, which you may easily reunite by warming the cement at the corners.

Yours very faithfully,

W. H. WOLLASTON.

ARTICLE X.

Appendix to the Essay on the Chemical Compounds of Axote and Oxygen. By John Dalton.

(Read to the Manchester Society, December, 1816.)

I. Experiments on the Combination of Nitrous Gas and Oxygen, with a View to ascertain the Maximum and Minimum.

CLASS I.-Experiments over Water.

EVERY attentive observer must have seen with surprise the variable proportions in which nitrous gas and oxygen unite. Whether