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it became a point to ascertain whether the masses of metal were regularly crystallized. By cutting plates in different directions, from different parts of the same mass of lead, and examining their nodal lines, they did not agree with each other, and it appeared that a mass of metal, considered as a whole, does not possess the structure or properties of a body regularly crystallized, though each plate cut from it acts as if it belonged to such a body. And even if a large plate, which resembles a regularly crystallized substance, be cut up into smaller plates, these, by trial, will almost constantly be found to differ from each other.

These and other facts shew clearly that the metals have not a homogeneous structure, and yet at the same time that they are not regularly crystallized, but that they have a sort of semi-regular structure, as if, at the moment of solidification, several internal distinct crystals were formed, considerable in volume, but not having their homologous planes parallel to each other, so that, though each crystal is of regular structure, the whole mass is confused.

By examining crystallizations of metal, and especially of lead, obtained in the usual way from quantities in the act of solidifying, by pouring off the remaining fluid portion, this will easily be seen to be the case; and the distinct systems of crystals will be found to be the more extensive, the longer the time the metals have been retained in fusion, or the more frequently they have been fused.

A consequence of this structure is, that greater differences of elasticity will be observed in the same substance, by taking small plates than by using large ones, because then the number of crystals taken into the plates will be less. For the same reason a mass of metal examined in this manner will appear to be more regular in its structure as the mass is smaller.

Whether the plates of metal be taken from a large mass, or cast in moulds of the proper size, does not appear to make much difference; plates obtained in both ways will sometimes differ little, and sometimes much. The substance of the mould, its position, or the place of the jet by which the metal enters, appears to have no influence over the elasticity of the resulting plate, i. e. there is always one direction in which the resistance to flexure is the greatest. Neither does sudden cooling, nor the passage of an electric current along one of its diameters whilst in fusion and cooling, exert an appreciable effect on the phenomena; but the case is very different if a series of small blows be given to the mould as the metal solidifies: the formation of large crystalline systems is almost always then disturbed, and the resulting mass is of such uniform elasticity, that plates formed from it give only one sound, and the two nodal diameters can be produced across any part of it. It would be as interesting as important, to ascertain if the metals, whose crystalliza→ tion has been thus disturbed, have a tenacity equal to what they acquire under ordinary circumstances, and whether they do not acquire some new properties which may render this process useful in the arts.

Many causes, such as pressure, rolling, annealing, &c., may more or less alter the distribution of the elasticity of metals, but none of them appear to be of such a nature as to bring them to a homogeneous state. Thus, circular plates of lead, copper, tin, and brass, diminished to one-fourth of their first thickness by hammering, preserved nearly the same properties as they had immediately after fusion: their nodal systems were only a little changed in appearance, but the sounds accompanying them were at the same distance from each other as before.

Rolling produced similar effects, except that the crystalline systems were considerably extended in two directions parallel to each other, so that it does occasionally happen that plates of large size may present a structure approaching to regularity. This occurred with a plate of zinc, from which several discs were taken, so similar in properties, that the plate might be considered as regularly crystallized. A close examination of this plate in various directions gave such differences of elasticity as to lead to the conclusion, that the differences of resistance to flexure in different directions of the same mass of metal may be much greater than occurs even in some woods-as, for instance, the oak, beech, &c., and yet, as has been demonstrated in a former paper,: the extreme elasticities in the beech are to each other as 1 is to 16.

The influence of annealing appears to be very feeble, or even nothing, upon metals which have not been compressed; for discs of copper, which had been exposed for hours to a temperature near the point of fusion, gave the same sounds as before. But when the metals have first been pressed, then annealing slightly alters their tone and the disposition of the nodal lines.

The phenomena observed in the metals were found to occur also with glass, sulphur, common resin, copal, amber, plaster, slate, &c.; but the interval between the two sounds belonging to circular plates of these substances is always very small, rarely surpassing a major semitone: the two modes of division also shewn by the nodal lines, although they affect a fixed position, are so near to each other as mostly to give a rectangular cross. It is to be presumed, indeed, that a heterogeneous structure will be discovered in almost every solid substance, except perhaps those which are deposits of pulverulent matter, as chalk, for instance, which appears to approach very closely to homogeneity. Amongst all the bodies examined by M. Savart one only was found, namely, sealing-wax, in which the right-angled cross of nodal lines could be produced indifferently in any direction; but this substance, being a simple mixture of gum lac, turpentine, and cinnabar, we may imagine how the latter pulverulent body may prevent the particles of resin from arranging themselves regularly.

M. Savart concludes his memoir by an observation, apparently applicable to all bodies which crystallize irregularly, namely, that immediately after they have become solid, they vibrate sonorously with much greater difficulty than they do a few hours or days, or

even months later. It frequently happens, that a body which produced with difficulty only dull sounds, finally vibrated with such facility and energy, that its particles became disintegrated, and it flew to pieces upon the slightest agitation of its parts. From hence it appears to result that, during the solidification, many parts are, as it were, surprised in positions, from which they tend to depart, and that they acquire a permanent state of equilibrium only after a long time thus, if a circular plate of sulphur be cast in a mould, and endeavours be made, immediately after cooling, to produce sound from it, no sound can be obtained. After some days, sounds, more or less dull, may be obtained; if then the number of vibrations for any set of nodal lines be determined, and then the plate be left for a month or two after that time, it will be found to sound freely, and further, the same set of nodal lines, or mode of division, will give a greater number of vibrations; the sound may thus be raised sometimes a full tone. It is well known that sulphur, which has been recently fused, does not immediately recover its former properties; but no one suspected that it required whole months, and even a longer period, to fully restore them.-Annales de Chimie, xli. p. 61.

9. On the Solidification of Plaster, by M. Gay Lussac.-Every one knows the property which plaster possesses, when deprived of its water by heat, of becoming solid with that fluid. The consistency which it acquires is very variable, and the purest plasters are precisely those which acquire least hardness. The cause has been attributed, in Paris plaster, to the presence of a few hundredths of carbonate of lime; but, without doubt, erroneously; for the heat necessary to bake the plaster is, in the small way, not above 300° F., and, in the large way, is never carried to the degree necessary to decompose the carbonate of lime. Besides, calcined plaster rarely contains free lime, and the addition of that base to those plasters, which have but little consistence, does not sensibly improve them. I think that we must search for the difference of consistency, which is acquired by different plasters, when mixed with water, in the hardness which they possess in their natural uncalcined state; a hardness which we cannot explain, but must take as a natural fact. That stated, I suppose that a hard plaster-stone, having lost its water, will acquire greater consistency when returning to its first state than a plaster-stone naturally softer. It is in some degree the primitive molecular arrangement which is reproduced. We find, in the same way, that when good fused steel has its carbon removed by cementation with oxide of iron, it will give, by a new cementation with carbon, a steel much more homogeneous and perfect than that obtained in the same circumstances by the cementation of iron.-Annales de Chimie, xl. p. 436.

10. Formula for reducing a Mercurial Thermometer in high Temperatures. If q denote the degrees of a mercurial thermometer, n

the number of degrees between the points of congelation and ebullition, s the number of degrees at the boiling point, and cal. q the degrees of the true augmentation of heat corresponding to the state q of the thermometer, the following expression is correct :

11. Determination of the Mathematical Law, according to which the Elastic Force of Steam increases with the Temperature. By M. Roche, Recueil Indust. p. 285.-It has already been ascertained-i. That a small increase of temperature augments considerably the elastic force of vapour. ii. That this force increased nearly in geometric progression, for each increase from 30° of: Fahrenheit's scale, or 131 of Reaumur's, or 16 of the centigrade thermometer; the elastic force doubling successively for the successive augmentations of 16 from the boiling point 100.

Nevertheless, it appears, from experiments made both in France and England, that the tensions of vapours depart from this law at high temperatures, and different empirical formulæ, more or less exact, have been proposed to represent the law of the elastic force; that of M. Laplace, inserted in the Traité de Physique of M. Biot, is of the form F 760m × 10m + bi2 + c i3 + &c., in which F denotes the elastic force estimated in millimeters: 760m the height of the column of mercury equivalent to the pressure of the atmosphere, and a, b, c, &c., constant coefficients, which M. Laplace endeavoured to determine by experiment; he found a 0.154547, b≈ 0.00625826, &c.

Such a formula is very complicated, and to apply it to high temperatures, the terms i3, i*, &c., must be employed; i representing the excess of the temperature above 100°. But a simple formula may be obtained by observing that the elastic force of steam increases for each element of temperature by a quantity, which is in a ratio composed of the existing elastic force and of the increase which I denominate the expansive heat, and which is proportional to the product of the temperature by the density it would give to the vapour, or to the quotient of this temperature, by the volume which it tends to give to the vapour, according to GayLussac's law of dilatation. We see, then, that the true law will be, that the elastic force increases in a geometrical progression when the expansive heat increases in arithmetical progression, and as this expansive heat, denoting by the excess of temperature above 100, would be proportional to

100° + x

or

100+ x

8+0.03 (100 + x) 11 +0.03 x

(0°, being the coefficient of the dilatation or the increase of volume for each degree); and as

the increments may be considered as proportional to the quotient,

and the elastic force may be expressed by the formula

m being a constant coefficient, and 760m the pressure of the atmosphere; this formula, by employing logarithms, becomes

If F be known by experiment, n will be obtained by resolving the preceding equation, which will give

n =

11 +0.03 x

(log F-log 760m)..

Now, if the values of n, which I call the logarithmic modulus of the elastic force of steam, be taken according to the table of elastic forces drawn up by the Institute, and inserted in the Traité de Physique of M. Pouillet, the mean value of n will be found = 0.17; the other values differing but little from it, the formula then becomes

In a memoir which I presented to the Institute, in the month of February, 1827, and which was referred to the examination of the committee charged with investigating high temperatures in steamengines, I shewed how the modulus of steam of other liquids might be found, and their density calculated therefrom; and I found that the maximum of the elastic force of water takes place at a temperature of about 770°, where its density is nearly equal to that of the liquid, the pressure amounting to more than 4000 atmospheres."

12. Destruction of Vermin in Ships by Steam. By letters from India, it appears that the application of steam has been found wonderfully efficacious in cleansing ships from vermin, and especially the white ant. A steam-boat (the Comet) was placed alongside a merchant-vessel, and steam from its boiler conveyed by a very simple system of pipes into the hold of the latter, the apertures to which were closed as well as they could be. The operation was continued for several hours; and there is no reason to believe that it was not effectual, and will prove a valuable process in the navy. Besides the direct object of cleansing the ship, another advantage accrued, from the discovery of every leaky place existing, by the oozing of the water through them, in which way leaks were made manifest, that could not be found out otherwise. The expense is