EXPER. 27. Place a floating body at the surface of the fluid, of sufficient magnitude to prevent the formation of the cavity. If the fluid be much agitated, the cavity will take place at the lower part, and air will introduce itself through the opening E F. Whence it follows that the pressure of the atmosphere on the upper surface of the fluid is not the cause of the cavity, which assumes the shape of a funnel. The air does not enter, but because it finds an empty space formed by the centrifugal force.

EXPER. 28.-When the fluid remains in a state of tranquillity without eddies, the vessel empties itself in forty seconds; but when the circular motion takes place, the evacuation is accomplished in fifty seconds, more or less. It cannot, therefore, be said in general terms, that the whirling stream absorbs and draws down bodies through the opening E F, with more force than if no such circulation took place.

EXPER. 29.- Pour a stratum of oil upon the water of the vessel. As soon as the funnel forms itself, the oil rushes down and issues out before the greatest part of the lower water, upon which it rested. The portions of oil partake less of the rotation of the lower water; having less density, they likewise recede less from the axis than the water; in consequence of which, as they occupy the interior part of the funnel, and are unsupported, they flow out first.

EXPER. 30.-Every other small body which floats on the water in the vessel acts in the same manner as the oil, provided its dimensions be very small. If the volume of the body be somewhat greater, while it approaches the cavity, to fall therein, its extremity, which is nearest the axis, comes into a place where the circulation is more rapid. This rapidity of motion impressed at one extremity of the floating body, is transported, by the laws of mechanics, to its centre of gravity, which is more remote from the axis in a situation where the circular motion

is slower; consequently, the body recedes from the edge of the cavity into which it was about to fall. It returns a short time afterwards, is again repelled, and these alternate motions continue as long as the circumstances which produced them. Lastly, if the body which floats at the surface of the liquor after the funnel has been formed, be of sufficient size to cover the whole cavity, it destroys the funnel in the upper part, and sometimes also in the lower. The reason is, that the body itself cannot turn round its centre but according to the law,

1

r

v=r; it, therefore, destroys by friction the law v = in the parts of the fluid in contact with it, and, consequently, it destroys the funnel itself.

PROPOSITION XII.

The lateral Communication of Motion takes place in the Air as well as in Water.

The stream of air, which moves in the midst of a body of air at rest, produces undulations and eddies round its current in the same manner as in water. These may be observed in the smoke which rises from a furnace, and produces a remarkable` aspect, when it issues like a dark tree from an agitated volcano. They may likewise be seen, in the particles which float in an obscure chamber, when a ray of the sun shines in, and the observer blows through them.

If the general wind comes, for example, from the south, it frequently happens that the north side of a mountain is at the same time struck by a north wind. This partial and local wind is nothing but the eddy produced by the mountain itself acting as an obstacle against the principal wind, from the south. It is probably from the same cause, that the wind sometimes

acts in the contrary direction on the sails of a vessel, when they are too obliquely presented to its stream.

The vapour of water which issues from the eolipile carries the surrounding air with it, and drives it against the burning coals opposite to the stream of aqueous vapour. It must not, therefore, be concluded that the aqueous vapour is itself in this case decomposed to maintain the combustion of charcoal.

It is known that the flues of chimneys assist the rising of smoke by their figure; concerning which we have drawn some inductions, in the Seventh Proposition.

In organ-pipes, the air which issues out of the side opening (lumiere) rubs laterally against the extremity of the column of the air included in the pipe. It rubs it on one side in the longitudinal direction, and is, as it were, an elastic file acting upon an elastic surface. Though the column of air be fluid, its parts are, however, so far intermixed together, that the tremulous motion excited at the place of friction is soon communicated laterally through the whole thickness of the column, which receives vibrations of such a kind, that they are an equilibrium with each other, and with the velocity of the stream which affords the friction. For this effect, it is requisite that the column should divide itself at different points or nodes, distributed through the length of the tube.* It is by repeated actions that the wind which issues from the side aperture impresses at length upon the whole column contained in the pipe, a movement of vibration greater than that which the laws of impulse, and of the lateral communication, would permit it to make by a single impulse. In the hautboy, and other similar instruments, having a mouth-piece, or reed, the cause which excites the tremulous motions does not act sideways on the air contained in the pipe; but strikes the column

* Mémoires de l' Acad. an. 1762, page 431.

directly in the middle for which reason it communicates its vibrations with so much the more effect to the whole mass.

In like circumstances, the force of sound, which is propagated in the atmosphere, depends on the magnitude of the section of the air which is at the extremity of the pipe, and the amplitude of the vibrations of this section. It is this surface which strikes the atmosphere, and communicates the pulsations. For this reason, conical divergent pipes afford a stronger sound than those which are cylindrical; and these last afford a stronger sound than pipes which are conically divergent. The first cause of the sound which acts at the mouth end of the pipe would never, of itself, excite such strong pulsations in the atmosphere, as it does excite by the lateral communication in the air contained in a divergent conical pipe.

The explanation of this phenomenon may be understood by observing, 1st, That if a number of elastic bodies be disposed in progression, the first will impress upon the last, by the intermedium of the others, more velocity than would be communicated by the immediate stroke: 2. The vibrations excited in the pipe have a certain permanence, which permits them to receive an increase of force by the united effect of successive impulsious: whereas, in the open atmosphere, every pulsation is transient and single.

Is not the augmentation of sound in the speaking trumpet in part owing to the same cause of the lateral communication of motion, rather than to the mere reflection of the sonorous lines from the sides of the tube itself?

I call those resonant vibrations, which take place in a tube

* It is known that the material of which a pipe is made does not perceptibly affect the sound. V.

when sound is excited; and I call those propagated vibrations, or pulsations, which transmit the sound through the atmosphere. I have already pointed out a difference, which appears to me to take place between these two kinds of vibrations; namely, that the former have a certain permanence and connexion with each other, so that each succeeding impulse excites, supports, and reinforces the former; whereas, those pulsations which succeed each other in the atmosphere by the repeated action of the resonant body, are single, and independent of each other.

But the following is a much more remarkable difference between these two kinds of vibrations. When at the extremity of a pipe A B C, a resonant vibration is made in the section of air, B C, Fig. 2, Plate I., experience shews that this vibration becomes the centre of pulsations propagated all round in PS Q. For, on whatever side the observer is placed, whether at P or at Q, he will hear the sound of the pipe A B C nearly as much as at S. But when there is no pipe, and the vibration at C B is a simple pulsation propagated through the open air from A to B ; in this case the pulsation is not propagated laterally and completely to P and Q, like the resonant vibration; but is contained almost entirely in the limits BZ and C Y, with a divergence of between 15 and 20 degrees. This fact has been disputed by various philosophers; but it cannot be questioned, since it is well known that we do not hear the echo, or reflected sound, from the plain surface, unless we place ourselves in the line of reflection, or very near it. If the pulsation of the echo were propagated all round, before the reflecting surface, diverging from thence as a centre, ought we not to hear the echo in every situation whatever, before that reflecting surface? We must, therefore, admit, with regard to sonorous pulsations propagated in the atmosphere, certain exceptions, and even limits, with regard to the lateral communication of motion which we have pointed out in the first proposition, and in the fifth, with regard to water.