canal is not urged either way, except by those parts of the tube which are situate near the surface of the fluid.

For, from 1, any particle of the tube, set off 1 m, I n, equal to one another, and of any length less than the radius of the sphere of action of the particle.

If this particle urges the canal in one direction by its action at m, it urges it equally in the contrary, direction by its action at n*.

We will now see what action the canal sustains near the surface c e d. With a radius ef, equal to that of the sphere of action of the particles, and with the point e for a centre, describe the circular arc of p.

The canal e r is urged upwards by the resolved action of those particles of the section of the tube contained in the space of p do; and if this space be divided into two equal parts, by the horizontal line ef, the action of the part above this line draws the canal as much upwards as that of the lower part does. For from any point g, in the lower part, draw g e, g h equal to one another; the action of g on the part e h urges the canal neither upwards nor downwards; for its action on any point above h is counteracted by its action on another point at the same distance below e. But there are particles below h, and within the sphere of action of g, as at k, on which it exercises an unbalanced action tending to draw the canal upwards. Next, suppose i, in the upper part of the space of p do, similarly situate to g in the lower. Draw e i, which will be parallel to g h, and will evidently draw upwards that part of the canal below e, as much as g draws upwards the part below h.

The other end g, of the canal e nm, is urged upwards,

This is so plain, that one is astonished to find Mr. la Place, in his second method, making the chief part of the force, which elevates the fluid, reside at the junction of the two tubes. Sec "Supplément a la Théorie de l'Action Capillaire," p. 16. Clairaut also, in a theory, to which it has been lately the fashion to give very undeserved praise, falls into the same errour. "Figure de la Terre," p. 119. The false proposition, that a mass with a plane surface presses a slender column within it downwards, to which most of Mr. la Place's errours may be traced, has Clairaut for its original author. Haüy has the same figure, and nearly the same words.

in like manner, by the action of the space and w, equal to, and described in the same manner as, ofp do.

Now, suppose both sides of the section of the tube to revolve round the axes a b, a B; the cylindrical annulus generated by er is urged upwards by the action of the annulus generated by the circular space of p do; and that generated by g by that generated by ww. If we represent the action of the annulus generated by of p do by 2 r, that of the annulus generated by ≈≈ W will be 2 r'. By reasoning in the same manner with respect to all other cylindrical annuli within the sphere of action of the tube, and taking the sum of all the actions, it is plain, that the excess of the mass of the fluid in the leg A B over that inthe leg E F is as 2 r-2 r'.

But now, supposing all other things to remain the same, conceive the diameter of the tube to vary. A canal er, at the same distance from the side, in tubes of different diameters, will be equally attracted by all of them: for that part of the surface of the tube, which attracts the canal, is so small (by the hypothesis) that it may be considered as plane whatever be the tube's diameter.

Therefore, while the diameter of the tube varies, as the number of equal columns in a cylindrical annulus of given breadth,. at a given distance from the tube, but within the reach of its action, varies quam proxime as the diameter of the tube, while the force urging upwards each separate column is constant, it is easy to see, by collecting as before the sum of the forces acting on different annuli, that the excess of the mass in the leg A B over that in E F is as the diameter of the tube.

By combining both parts of the proposition, and supposing the diameter of the tube, and the attractions of its two ends to va y together, the excess of the mass in A B oyer that in E F will be as (2 r-2 r') x diameter. QED.

Cor. 1st. It is plain from the above demonstration, that Corollary 1. the mass of fluid, supported by a capillary tube, depends not in the smallest degree on the figure c a d of its surface, so that, if it were possible for us to make this surface take any other conceivable figure, the same mass of fluid would VOL. XXVII–OCT. 1810. K

still

still be supported. The figure of the surface is a secondary effect, exactly in the same manner as the catenarian form of a supported chain is a secondary effect; the cause being the pegs and the force of gravity.

When, however, I say, that the figure of the surface is of no consequence, I suppose that surface to be at a sensible distance below the orifice of the tube, otherwise the case will be very different: for,

Cor. 24, Suppose, in fig. 5, every thing to remain as before, excepting that the whole tube is made of one kind of matter, (the intensity of attraction for the fluid within it being r) and that the left hand branch terminates at yd, close to the surface of the fluid. I say that the difference of masses, in the two branches, will, in great measure, depend on the figure of that part of the surface of the fluid, at the orifice y d, which is near to y and d: and that we should have the greatest difference of masses if it were possible to make the fluid, at this orifice, take any figure as d xzy, perpendicular at the sides, and having every point of it's upper surface distant from and by a space greater than the radius of the sphere of action of the particles. And the difference of masses in this case, would be to the difference of masses when the surface is horizontal, as yd, at the orifice of the tube, as 2 to 1.

For, in this latter case, when the surface of the fluid is yed, it is evident, from the reasoning used in the proposition, that the left hand mass is drawn upwards by a force as r, and the right hand mass by a force as 2 r; whence the difference of the masses is as r. But, if the left hand mass could stand at x z, and the column p become y', any such column, and consequently the whole left hand mass, would be urged neither upwards nor downwards by the branch y d of the tube: therefore the difference of masses would be entirely occasioned by the other branch, and would be

as 2 r.

Now, though we cannot make the fluid stand at x 2, we

* Mr. Haüy, explaining Abat's experiments after the ideas of la Place, falls, in consequence, into an erraur. 'See Traité de Physique,' tom. 1, p. 243, Ed. 2. le petit changement de figure lui donne plus de force,"

&c.

may

may give it the convex form & sy; and if c d was the sur face in the branch A B, when that in the other branch was

let this last become convex, as ♪s y, and the first shall be ; the difference of masses, in the latter case, being to that in the former in a ratio approaching the more nearly to that of 2 to 1, the higher we can make the convex surfaces, and the nearer its sides at y and dare to perpendicularity with day.

Here then is the true and simple explanation of Abat's experiment, which in no respect depends on the figure of the surface, in the fenfe that Mr. la Place means*.

Cor. 3rd. Let A B pr, fig. 6, represent a tube of such Corollary 3, intensity of attraction, that, if it be immersed in a fluid the horizontal surface of which is fc d, this surface shall undergo no alteration.

Suppose this tube cut off close to the surface; as, by this, the part of c (a quadrant to the radius of the sphere of attraction) to which half its effect is owing (by the proposition) is taken away, the intensity of attraction of the Jower part fcp must be doubled to preserve the equilibrium': and it plainly follows, that the intensity of attraction of the Aluid for itself is twice that which the tube before it was cut off had for the fluid.

May I not say, that so peculiar a demonstration, of a theorem easily proved in other ways, is of itself sufficient to establish the truth of this theory?

Cor. 4th. If, in fig. 4, we suppose the branch E F to Corollary 4, be cut off close to the surface (which I suppose horizontal) and then to be of the same intensity of attraction with the

After the same manner is explained another experiment mentioned by Mr. la Place, 1st. supplement, p. 60. Plunge a capillary tube into water, and, having closed the lower orifice with the finger, draw it out of the water. If we now remove the finger, the fluid will fall in the tube, and form a convex drop at the lower orifice. But, when it has ceased to descend, the height of the column always remains greater than the height of the water in the tube, above the level, when it was plunged in the fluid." This excess (says Mr. la Place) is owing to the action of the drop of water on the column.”

The true explanation is the same as that I have given above of Abat's experiment.

fluid it contains, we have the case of a common capillary tube; and the mass raised above the level of the surface of the fluid in the vessel is as (2 r-r') x diameter of the tube. From this corollary the explanation of the common phenomena is too simple to make it necessary for me to dwell on it.

Quicksilver

a ship

VI.

An Account of the Effects of Thirty Tons of Quicksilver escaping by the rotting of leathern Bags into the Bilge Water, on board the Triumph Man of War: communicated by Dr. BAIRD, Physician General to the Navy, to a Friend in London.

IN April, 1810, the Triumph man of war took on board taken on board thirty tons of quicksilver, contained in leather bags of 50lbs. each. These bags were picked up on the shore of Cadiz, from the wreck of two Spanish line of battle ships, lost in the storm immediately preceding, at the end of March, the above date. The collected bags were stowed below, in the bread room, after hold, and store rooms: in wet leathern they were saturated with salt water, and, in about a fortnight, all decayed and burst. In the act of collecting and endeavouring to save the quicksilver in casks, much of it found its way to the recesses of the ship, beyond the possibility of recovery. Some portion, however, was secreted by the men, who amused themselves in various ways with it, as cleaning their spoons, &c.

bags,

which burst.

The vapour of At this period bilge water had collected in the ship, the the bilge water stench from which was intolerable; and the carpenter's

whitened me.

tals, instead of mate, in the act of sounding the well, was nearly suffoblackening cated. The effect of the gas escaping from bilge water is them, manifested, by its changing every metallic substance in the ship black. But in this instance metals of every kind were coated with quicksilver; and a general affection of the mouth took place among the men and officers, to a severe

degree