§ 15 Constitution of Liquid Veins: Sensitive Water-jets
We have thus far confined our attention to jets of ignited and unignited coal-gas—of carbonic acid, hydrogen, and air. We will now turn to jets of water. And here a series of experiments, remarkable for their beauty, has long existed, which claim relationship to those just described. These are the experiments of Felix Savart on liquid veins. If the bottom of a vessel containing water be pierced by a circular orifice, the descending liquid vein will exhibit two parts unmistakably distinct. The part of the vein nearest the orifice is steady and limpid, presenting the appearance of a solid glass rod. It decreases in diameter as it descends, reaches a point of maximum contraction, from which point downward it appears turbid and unsteady. The course of the vein, moreover, is marked by periodic swellings and contractions. Savart has represented these appearances as in Fig. 140. The part a n nearest the orifice is limpid and steady, while all the part below n is in a state of quivering motion. This lower part of the vein appears continuous to the eye; but the finger can be sometimes passed through it without being wetted. This, of course, could not be the case if the vein were really continuous. The upper portion of the vein, moreover, intercepts vision; the lower portion, even when the liquid is mercury, does not. In fact, the vein resolves itself, at n, into liquid spherules, its apparent continuity being due to the retention of the impressions made by the falling drops upon the retina. If, while looking at the disturbed portion of the vein, the head be suddenly lowered, the descending column will be resolved for a moment into separate drops. Perhaps the simplest way of reducing the vein to its constituent spherules is to illuminate the vein, in a dark room, by a succession of electric flashes. Every flash reveals the drops, as if they were perfectly motionless in the air.
Could the appearance of the vein illuminated by a single flash be rendered permanent, it would be that represented in Fig. 141. And here we find revealed the cause of those swellings and contractions which the disturbed portion of the vein exhibits. The drops, as they descend, are continually changing their forms. When first detached from the end of the limpid portion of the vein, the drop is a spheroid with its longest axis vertical. But a liquid cannot retain this shape, if abandoned to the forces of its own molecules. The spheroid seeks to become a sphere—the longer diameter, therefore, shortens; but, like a pendulum which seeks to return to its position of rest, the contraction of the vertical diameter goes too far, and the drop becomes a flattened spheroid. Now, the contractions of the jet are formed at those places where the longest axis of the drop is vertical, while the swellings appear where the longest axis is horizontal. It will be noticed that between every two of the larger drops is a third one of much smaller dimensions. According to Savart, their appearance is invariable.
I wish to make the constitution of a liquid vein evident to you by a simple but beautiful experiment. The condensing lens has been removed from our electric lamp, the light being permitted to pass through a vertical slit directly from the carbon-points. The slice of light thus obtained is so divergent that it illuminates, from top to bottom, a liquid vein several feet long, and placed at some distance from the lamp. Immediately in front of the camera is a large disk of zinc with six radial slits, about ten inches long and an inch wide. By the rotation of the disk the light is caused to fall in flashes upon the jet; and, when the suitable speed of rotation has been attained, the vein is resolved into its constituent spherules. Receiving the shadow of the vein upon a white screen, its constitution is rendered clearly visible to all here present.
This breaking-up of a liquid vein into drops has been a subject of frequent experiment and much discussion. Savart traced the pulsations to the orifice, but he did not think that they were produced by friction. They are powerfully influenced by sonorous vibrations. In the midst of a large city it is hardly possible to obtain the requisite tranquillity for the full development of the continuous, portion of the vein; still, Savart was so far able to withdraw his vein from the influence of such irregular vibrations that its limpid portion became elongated to the extent shown in Fig. 142. It will be understood that Fig. 141 represents a vein exposed to the irregular vibrations of the city of Paris, while Fig. 142 represents one produced under precisely the same conditions, but withdrawn from those vibrations.
The drops into which the vein finally resolves itself are incipient even in its limpid portion, announcing themselves there as annular protuberances, which become more and more pronounced, until finally they separate. Their birthplace is near the orifice itself, and under even moderate pressure they succeed each other with sufficient rapidity to produce a feeble musical note. By permitting the drops to fall upon a membrane, the pitch of this note may be fixed; and now we come to the point which connects the phenomena of liquid veins with those of sensitive flames and smoke-jets. If a note in unison with that of the vein be sounded near it, the limpid portion instantly shortens; the pitch may vary to some extent, and still cause a shortening; but the unisonant note is the most effectual. Savart’s experiments on vertically-descending veins have been recently repeated in our laboratory with striking effect. From a distance of thirty yards the limpid portion of the vein has been shortened by the sound of an organ-pipe of the proper pitch and of moderate intensity.
I have also recently gone carefully, not merely by reading, but by experiment, over Plateau’s account of the resolution of a liquid vein into drops. In his researches on the figures of equilibrium of bodies withdrawn from the action of gravity, he finds that a liquid cylinder is stable as long as its length does not exceed three times its diameter; or, more accurately, as long as the ratio between them does not exceed that of the diameter of a circle to its circumference, or 3.1416. If this be a little exceeded the cylinder begins to narrow at some point or other of its length; nips itself together, breaks, and forms immediately two spheres. If the ratio of the length of the cylinder to its diameter greatly exceed 3.1416, then, instead of breaking up into two spheres, it breaks up into several.
A liquid cylinder may be obtained by introducing olive-oil into a mixture of alcohol and water, of the same density as the oil. The latter forms a sphere. Two disks of smaller diameter than the sphere are brought into contact with it, and then drawn apart; the oil clings to the disks, and the sphere is transformed into a cylinder. If the quantity of oil be insufficient to produce the maximum length of cylinder, more may be added by a pipette. In making this experiment it will be noticed that, when the proper length is exceeded, the nipped portion of the cylinder elongates, and exists for a moment as a very thin liquid cylinder uniting the two incipient spheres; and that, when rupture occurs, the thin cylinder, which has also exceeded its proper length, breaks so as to form a small spherule between the two larger ones. This is a point of considerable significance in relation to our present question.
Now, Plateau contends that the play of the molecular forces in a liquid cylinder is not suspended by its motion of translation. The first portion of a vein of water quitting an orifice is a cylinder, to which the laws which he has established regarding motionless cylinders apply. The moment the descending vein exceeds the proper length it begins to pinch itself so as to form drops; but urged forward as it is by the pressure above it, and by its own gravity, in the time required for the rounding of the drop it reaches a certain distance from the orifice. At this distance, the pressure remaining constant, and the vein being withdrawn from external disturbance, rupture invariably occurs. And the rupture is accompanied by the phenomenon which has just been called significant. Between every two succeeding large drops a small spherule is formed, as shown in Fig. 141.
Permitting a vein of oil to fall from an orifice, not through the air, but through a mixture of alcohol and water of the proper density, the continuous portion of the vein, its resolution into drops, and the formation of the small spherule between each liberated drop and the end of the liquid cylinder which it has just quitted, may be watched with the utmost deliberation. The effect of this and other experiments upon the mind will be to produce the conviction that the very beautiful explanation offered by Plateau is also the true one. The various laws established experimentally by Savart all follow immediately from Plateau’s theory.
In a small paper published more than twenty years ago I drew attention to the fact that when a descending vein intersects a liquid surface above the point of rupture, if the pressure be not too great, it enters the liquid silently; but when the surface intersects the vein below the point of rupture a rattle is immediately heard, and bubbles are copiously produced. In the former case, not only is there no violent dashing aside of the liquid, but round the base of the vein, and in opposition to its motion, the liquid collects in a heap, by its surface tension or capillary attraction. This experiment can be combined with two other observations of Savart’s, in a beautiful and instructive manner. In addition to the shortening of the continuous portion by sound, Savart found that, when he permitted his membrane to intersect the vein at one of its protuberances, the sound was louder than when the intersection occurred at the contracted portion.
I permitted a vein to descend, under scarcely any pressure, from a tube three-quarters of an inch in diameter, and to enter silently a basin of water placed nearly 20 inches below the orifice. On sounding vigorously a Ut2 tuning-fork the pellucid jet was instantly broken, and as many as three of its swellings were seen above the surface. The rattle of air-bubbles was instantly heard, and the basin was seen to be filled with them. The sound was allowed slowly to die out; the continuous portion of the vein lengthened, and a series of alternations in the production of the bubbles was observed. When the swellings of the vein cut the surface of the water, the bubbles were copious and loud; when the contracted portions crossed the surface, the bubbles were scanty and scarcely audible.
Removing the basin, placing an iron tray in its place, and exciting the fork, the vein, which at first struck silently upon the tray, commenced a rattle which rose and sank with the dying out of the sound, according as the swellings or contractions of the jet impinged upon the surface. This is a simple and beautiful experiment.
Savart also caused his vein to issue horizontally and at various inclinations to the horizon, and found that, in certain cases, sonorous vibrations were competent to cause a jet to divide into two or three branches. In these experiments the liquid was permitted to issue through an orifice in a thin plate. Instead of this, however, we will resort to our favorite steatite burner; for with water also it asserts the same mastery over its fellows that it exhibited with flames and smoke-jets. It will, moreover, reveal to us some entirely novel results. By means of an India-rubber tube the burner is connected with the water-pipes of the Institution, and, by pointing it obliquely upward, we obtain a fine parabolic jet (Fig. 143). At a certain distance from the orifice, the vein resolves itself into beautiful spherules, whose motions are not rapid enough to make the vein appear continuous. At the vertex of the parabola the spray of pearls is more than an inch in width, and, further on, the drops are still more widely scattered. On sweeping a fiddle-bow across a tuning-fork which executes 512 vibrations in a second, the scattered drops, as if drawn together by their mutual attractions, instantly close up, and form an apparently continuous liquid arch several feet in height and span (shown in Fig. 144). As long as the proper note is maintained the vein looks like a frozen band, so motionless does it appear. On stopping the fork the arch is shaken asunder, and we have the same play of liquid pearls as before. Every sweep of the bow, however, causes the drops to fall into a common line of march.
A pitch-pipe, or an organ-pipe yielding the note of this tuning-fork, also powerfully controls the vein. The voice does the same. On pitching it to a note of moderate intensity, it causes the wandering drops to gather themselves together. At a distance of twenty yards, the voice is, to all appearance, as powerful in curbing the vein, and causing its drops to close up, as it is when close to the issuing jet.
The effect of “beats” upon the vein is also beautiful and instructive. They may be produced either by organ-pipes or by tuning-forks. When two forks vibrate, the one 512 times and the other 508 times in a second, you will learn in our next lecture that they produce four beats in a second. When the forks are sounded the beats are heard, and the liquid vein is seen to gather up its pearls, and scatter them in synchronism with the beats. The sensitiveness of this vein is astounding; it rivals that of the ear itself. Placing the two tuning-forks on a distant table, and permitting the beats to die gradually out, the vein continues its rhythm almost as long as hearing is possible. A more sensitive vein might actually prove superior to the ear—a very surprising result, considering the marvellous delicacy of this organ.57
By introducing a Leyden-jar into the circuit of a powerful induction-coil, a series of dense and dazzling flashes of light, each of momentary duration, is obtained. Every such flash in a darkened room renders the drops distinct, each drop being transformed into a little star of intense brilliancy. If the vein be then acted on by a sound of the proper pitch, it instantly gathers its drops together into a necklace of inimitable beauty.
In these experiments the whole vein gathers itself into a single arched band when the proper note is sounded; but, by varying the conditions, it may be caused to divide into two or more such bands, as shown in Fig. 145. Drawings, however, are ineffectual here; for the wonder of these experiments depends mainly on the sudden transition of the vein from one state to the other. In the motion dwells the surprise, and this no drawing can render.58