Benjamin Franklin Papers

To Benjamin Franklin from Benjamin Vaughan, 31 December 1782

From Benjamin Vaughan

ALS: American Philosophical Society

Paris, Decr 31, 1782.

My Dear sir,

I inclose you an extract of a letter from Dr. Priestley to my brother William, on the subject of his late supposed discovery.3

At the same time I inform you that I have procured a small glass jar, for the purpose of observing the cause of the phœnomenon of the small bits of tea-leaves, which you find whirled to the centre of the bottom of your breakfast cup, when you stir your tea.

I had told you “at a hazard”, that as there were different velocities in the different ringlets of fluid that moved about the axis of your cup, if at any time the motion of your bitt of tea-leaf was checked, the different ringlets of fluid I thought might have an opportunity of exhibiting their difference of force, and that the outer ones might have balance enough in their favor to enable them to incline the tea-leaf inwards, towards the axis of the cup.— You then bid me observe bodies in the situation you described, and see whether my explanation would suit the fact.

I have accordingly made some observations by means of my small glass jar, as follows.— First, bodies whirling at the surface of a fluid, seem to move as carelessly as the fluid itself; generally proceeding circularly, sometimes where the motion is very slow yielding to the attraction of the glass at the side, and perhaps at other times after a long continued motion inclining to the axis of the jar. I observed a similar indifference in the motion of the particles whirling about, lower down, in the body of the fluid. Particles however which are heavier than the fluid, and which if stopped at the surface or watched in the course of their descent, appear indifferent in all their horizontal movements; yet, when they descend, and come to touch the bottom of the vessel, soon begin to shew an inclination to the centre.

This pretty sand of a blue color, which I inclose for you, will shew two of the cases which I allude to. Upon throwing it into the fluid which I had moved briskly round with the feather of a quill, a part of it remained at the top, where it moved round like a portion of the fluid; while that which descended, soon tended to the axis at the bottom of the jar. As the jar which I use, has a very steep bottom pointed upwards, this tendency to the centre lasts only while the whirl of the fluid is considerable; for afterwards & long before the fluid has lost its motion, the particles of sand will slide down the ascent and fall to the sides of the vessel, except in parts where it lodges.— To vary the experiment, I threw in pieces of a breakfast roll. The crusty parts will swim at the top, some pieces of the crum will descend, and a mixture of both will take any level of the water at pleasure, or change that level slowly enough for the purpose of observation. At the bottom I saw a great deal of your phœnomenon of the tea leaves; but it is only at the bottom.— At the bottom, when the water is first agitated, the crums and sand together, make an amusing appearance; for while some particles of the sand cover the apex of the bottom of the vessel, the rest of the sand flies about and above the apex, and the crums of bread fly round the whole, like birds darting and skimming round a little mountain that is laboring under some commotion.

On the whole, I am inclined to think that the principles which I guessed at, may turn out to be the right principles, for explaining all the appearances at the bottom of my jar.— If a boat is put in motion, and the moving power is made to act more on one side than the other, the boat will decline from the stronger moving power; that is, when the rudder by being turned to one side of the boat, clogs that side, and suffers the other side to move quicker, the boat in this situation declining from the greater force, turns inwards towards the retarded side.— Again. If I cut a round slice of cork, and place it on the surface of any fluid; and if I place a ruler in the direction of a tangent to the side of the round piece of cork, and draw a lancet swiftly along the edge of that ruler, the consequence will be, that the lancet striking the edge of the cork will drive it off nearly at right angles from the ruler.

A short application will shew perhaps, the action of these principles, in the case in question.— When the heavy body once touches the bottom of the jar, it loses some of that whirl, which it once had in equal degree with the fluid; and is therefore left liable to the impulse of the fluid which is still whirling. The blow it receives on its outer side, being greater than that which it receives on the inner side, its motion begins to acquire a tendency inwards, towards the center of the bottom. Being by its weight often sunk and rubbed against the bottom, the effect of this impulse is often repeated; and therefore if the impulse is strongly enough applied, the body will distinctly approach the axis, in spite of the slope upwards in the bottom.— Where the body is only a little heavier than the fluid, as in the case of the crum of a roll, the approach to the centre is less decided; because the body having a great tendency to swim while the water is moving swiftly, it touches seldomer, and with less force, than if it were heavier.

The form of the particles in question may likewise have great influence, as well as their weight; as in the case of your tealeaves; which, being usually oblong, afford a powerful lever to the action of the fluid.— It is also not to be forgotten, that the effect will always seem increased by the smallness of the vessel; because in small concentric circles taken at a given distance from each other, the difference of velocity will be much greater, than in large concentric circles, placed at a similar distance from each other.

At the surface of the fluid, there are yet two farther circumstances worthy of remark. First; if the swimming body projects out of the fluid, the resistance it will meet with from the air will a little retard its motion and when this motion is revived by the impulse of fluid placed at different distances from the axis, it may be seen to tend some little towards the axis, even at the surface. And next; at the surface, we see the operation of two other principles; namely attraction to the sides, and attraction between the swimming bodies respecting each other.— Perhaps there is a little attraction subsisting between the particles at the bottom; but it is less than at the top, where at best it is very feeble. The intangling of the particles one with another, may be of more consequence; for they may assume the form & nature of a lever, and in consequence become much more seriously acted upon, than when they are separate.

So much at present for these tea-leaves.— When we were talking on the subject of them, I remember some one stated an assertion that the heaviest bodies had always most disposition to quit the centre, in the case of centrifugal forces. I mention it by the by, that I suspect this position was not truly understood in the quarter whence it came. The heavy body does not tend to quit the centre with more velocity than the light body; but, in consequence of having more force to overcome obstacles, it eventually moves more effectually, & therefore faster.— If I tie one end of a string to the centre of a board and move that board swiftly round its centre, the momentum given to the particles of the string will not be sufficient to keep it stretched; but if I fasten a bullet to the other end of the string, the momentum of a heavy bullet not being to be put in comparison with the disposition of the string to remain curled & crooked, the string will become both straightened and stretched. In this situation however, every particle in the string gets as far from the centre, as its circumstances permit; but the bullet having most momentum from its contents, and most sphere of action from the parts of the string to which it is fastened, takes the most circuit in its motion.

There was another fact suggested in the conversation, not more difficult to explain than the above. If water and lead are supposed to be put into different tubes which have each one of their ends joined in a common centre, if the whole is put in motion from that centre, we expect that the lead will be found at the farther extremities of the tubes, instead of the water; and very properly so; for the bullet without tending to have a swifter motion than the water has nevertheless power to displace the water when the water becomes stationary, and to put itself in its stead at the farther end of the tube. If the tubes were indefinitely prolonged, the water or even a piece of cork in the water, would go on just as fast as the bullet, other things being equal; but the moment a stop is put to their progression, then the bullet, adding its force to that column of water of which it makes a part, overcomes all the other columns, and drives on to the obstacle, as the only way of securing its own rest.— In this, the bullet acts precisely as it would in a case of gravity. Where there is no resistance, it moves no faster than a feather towards the earth. But when resistance occurs, though it is only from a medium as thin as the air, a difference is immediately perceived in favor of the motion of the bullet. And the moment a bullet is put upon the surface of water at rest, though the bullet begins with being stationary, like the water, yet it will penetrate and displace the water, as long as it finds water and passage left for its motion.

As to a third supposed fact, which I think was mentioned, namely that of separating bodies of different gravities spread through a fluid, by including them in a vessel to which a centrifugal force is given, it seems only another consequence of these principles. The heaviest bodies without tending faster from the centre in their origin than the lighter ones, yet by moving more powerfully, will always (where fair play is given them) be found at the bottom of the vessel; that is, as far as possible from the centre of motion. And as the centrifugal force may easily be made more violent than the force of gravity, separations of the particles may possibly be made in this way, which gravity in the common way of its operation cannot effect.

None of these principles, I apprehend, will be found at all inconsistent with the fact of our tea-leaves. Originally, these leaves set out (not with a centrifugal force resembling the other cases,) but with much the same force that belonged to that precise ringlet of fluid in which it stood, when the parts received their first motion; and this force, as soon as gravity carried them to the bottom and exposed them to friction, they soon lost. The inclination they afterwards acquired towards the centre, depended on principles still more different from the common centrifugal force, than the first motion they had.— It is easy however to imagine this force combined with a centrifugal force, by supposing a whirling motion given to a fluid that has light and heavy particles immersed in it; and, when the phœnomenon of the tea-leaves &c. has begun to work, then to suppose the vessel and its contents swiftly swung round a common centre. The whirling and centrifugal motions will then be exhibited on the same bodies.

As I have seldom found any of these questions fail to yield, sooner or later, to a little patience and thinking, I should now turn to the discussion of the cause of the agitation attending the surfaces of oil & water, when they are in contact with each other in any quantity, and affected by a vibrating motion; but at present, the time of both of us is, I hope, better occupied. At some future moment of your leisure, and when you are less fatigued than at present, I shall beg to call your attention to this & other subjects, which you have started in your writings and conversation. In the mean time, I am, my dearest sir, your most devoted, affectionate, & grateful,

Benja: Vaughan

[Note numbering follows the Franklin Papers source.]

3The extract is undated. In it, Priestley expresses doubt about his calculation of “the weight of water in air.” For his description of the experiment to convert purified water into “permanent air” see the extract of his letter to BF of Dec. 12.

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