compare it with the quantity obtained from wheat flour prepared under our own inspection.

Thirty specimens of flour, from the harvests of 1827 and 1828, were, therefore, examined, and the gluten separated; and without taking any note of the other principles present, we found that, upon a mean, they gave 10.25 per cent. of gluten, perfectly dry and pulverized; whilst the flour, supposed to be adulterated, gave only from 6 to 6.5 per cent. of gluten in the same state. Hence it will be easy, by an operation of this kind, to tell whether a flour has been adulterated or not.-Jour. de Pharmacie.

12. Remark on a Passage of the Mécanique Analatique of Lagrange, by N. G. de Schulten.-Having attentively examined the beautiful theory of the equilibrium of an elastic thread, given by Lagrange, in the first volume of his Mécanique Analytique, p. 151, 159, Ed, Paris, 1811-15, I have found that an error has crept into it, to the correction of which I would the more especially direct the at-tention of mathematicians, as it exists in a work which is generally Land justly regarded as classical, and is latent there under so plausible an appearance, that it may have escaped the penetration even of the celebrated author to whom analysis is so deeply indebted.

The error in question regards the general expression for the tension of an elastic thread, composed of an element of an invariable length, which the author finds to be different from that which holds good for a thread with extensible or contractile elements, the difference being, according to him, such, that if in each case the tension be denominated, the equations of equilibrium are in the first

ds

λdz

Zdm-d. +ďa.Iď2z=0
Bds

eds2 dsds Ed's Ee dz

+d2. Id2y=0

+d.

Now I affirm, that in both one and the other of these two cases, it is only the equations (i.) which hold good. The (i.), although leadsing, as may be readily seen, to true equations of the curve of the 3thread, nevertheless do not give the true value of the tension. The

detailed analysis which has led me to this result, requiring too much space to be inserted here, for the present I shall only offer a general consideration, which appears to me suited to elucidate the subject, and the truth of which may be easily seen, viz. that the formation of general equations of equilibrium of a thread, the elements of which are attracted by any forces, either internal or external, must depend on those forces, and on the mutual actions of the elements; and lastly, on the positions and on the lengths of the elements themselves, all these elements being supposed actually in equilibrium: from whence it follows, that the property of the elements in question to change or not in length from the state of equilibrium cannot at all influence the form of these general equations, which, consequently, must remain the same for elements of invariable length, as for extensible or contractile elements (which, however, does not prevent the property in question from exercising a real influence on the final results of the calculation, by the modification which it occasions in the arbitrary contents introduced in the ulterior development of the general equations). As to the tension of the thread in equilibrium, of which the expression enters into the equations of the particular case now before us, it is clear that it is immediately derived from the forces and the mutual actions of which we have spoken, the expression of it being nothing else than that of one or other of the two parts, with contrary signs, of which the aggregate of all the forces affecting a given element of the thread in the direction of its length, is composed.

I shall add, that by proper reductions the (ii.) readily lead to the value of the tension A

(A+fXdm)dx+(B+fYdm)dy+(C+fZdm)dz

ds

which, as is manifest, is exactly the same in the case of a thread perfectly flexible of an invariable or variable length; a remark which appears to me interesting, and is not found in the works of Lagrange.

may

His error is derived from the very specious supposition, that, in the case of elements of invariable length, the variation of ds be suppressed in the expression of de, which, although true, when only the absolute value of de is in question, is not allowable in forming what the author calls the general equation of equilibrium, into which Sds should enter in every case, of which the author gives an example in the case of a thread perfectly flexible of an invariable or variable length.-Astronomische Nachrichte, 155.

13. Use of Plumbago instead of Oil in Clocks and Chronometers.It is well known that the gradual change of oil, when applied as a lubricating medium to those parts where friction takes place in clocks, watches, and other fine mechanical arrangements, has induced numerous persons to endeavour so far to purify the oil as to prevent or retard the injury occasioned to the going of the machine as much as possible. Mr. Hebert appears to have overcome this difficulty all at

once by discarding the oil altogether, and using instead well prepared plumbago. He first prepares the plumbago by repeatedly grinding and washing it over, by which means the gritty particles that occur, even in the best black lead, are removed, and which, if allowed to remain, would neutralize every advantage the pure plumbago is found to give. This done, the prepared substance is applied with a camel-hair pencil, either in the state of powder or mixed up with a drop or two of pure spirit of wine. It readily adheres to the surface of a steel pivot, as well as to the inside of the hole in which it runs, so that the rubbing surfaces are no longer one metal upon another, but plumbago upon plumbago. These surfaces, by their mutual action, speedily acquire a polish only inferior to that of the diamond, and then the retardation of the machine from friction is reduced almost to nothing, and wear and tear from this cause is totally prevented. An astronomical clock of Mr. Hebert's own making, of which the pivots, and holes, and teeth of the escape wheel had been covered on their rubbing parts with fine plumbago fourteen years before, was taken to pieces by a committee of the Society of Arts and examined; the surfaces of plumbago were found to be for the most part unbroken and highly polished, and neither the pivots nor sockets appeared, on examination with high magnifiers, to have undergone the slightest degree of wear.-Trans. Soc. Arts, xlvi. p. 48.

14. Description of a Microscopic Goniometer, by M. Raspail.-To obtain accuracy in delineating objects from a microscope, I constructed in pasteboard a model of the following instrument: a circular plate, 5.91 inches in diameter, having a perforation 3.15, and graduated on its inner circle, was placed on the object frame, so that its centre corresponded to the focus of the microscope. Two semicircles, one with a greater diameter than the other, and concentric with the disc, are moveable upon this in opposite directions, each having a hair stretched from one extremity to the other; this hair represented the common diameter. When I wished to measure an angle, I turned these semicircles in opposite directions, until the crossing of the hairs equalled the opening of the observed angle, the apex of which was exactly placed under their point of intersection. I had then only to count the degrees on the circular disc to obtain the value of the angle, taking into account the inversion of the images. But many considerable inconveniences resulted from this operation. With a considerable magnifying power, these hairs acquire too great thickness; and, on the other side, being obliged to place the object and the apparatus in the focus, and, consequently, to bring them near to each other, I could not help brushing the object almost every time that I turned round the crossed hairs.

I then devised the following process: I placed the two hairs in the interior of the microscope; one in the eye-tube, and applied against the upper surface of the interior eye-glass; and the other in the interior of the following tube, and applied almost against the infe

rior surface of the same glass. These hairs were each kept in their places by means of a circle of pasteboard exactly fitted to the sides of the tubes. When I wished to measure an angle of a crystal which I saw through the glasses on the object frame, I turned in opposite directions the eye-tube and the lower tube, until the crossing of the hairs gave me an angle corresponding to the angle I observed. Now, to measure the value of this angle, I placed toward the interior diaphragm of the microscope a graduated circle, and the thickness of which occupied only a very small space round the field of view of the microscope. This circle enabled me to count the degrees comprised between the opening of the two opposite angles; I then took the mean between the sum of them, and thus had the value of the mea sured angle. But the graduated circle, for which I was indebted to the skill of one of my friends, was of gelatine, and the impurities of this substance almost always render the degrees traced upon it indistinet, which would not be the case with a properly graduated circle of glass. This inconvenience may be remedied by the two following methods: when the value of an angle has been ascertained, it is only necessary to unscrew the tubes of the microscope immediately beneath the apparatus, then place on the side opposite to the eye-piece a diaphragm of pasteboard, with an aperture in the centre, and looking through this, the value of the angle which had been previously ascertained may be read off. A graduated circle, which would be very expensive, need not be placed in the interior of the microscope; it is only required to place horizontally, on the external eye-piece, a great circular plate, with an opening in the centre of the same diameter as the eye-piece. Two horse-hairs are then placed at right angles as diameters of this disc; these two hairs should be stretched by weights attached to their extremities. One of these horse-hairs is to be drawn above one of the hairs which is seen in the interior of the tube until they coincide exactly, which is the case when, by the effect of diffraction, the horsehair seems bordered on each side with a straight luminous edge, but which may be traced from one end to the other of that portion of the horse hair which is seen in the field of view. When this parallelism is obtained, by the same process the other external horse-hair is placed over the other internal one, at which time the external angle, or that obtained without the microscope, is the same as that within it. Nothing further is then to be done but to measure the required angle by placing delicately a circle graduated upon gelatine above the plate which supports the two hairs; the centre of which circle must coincide with the point of intersection of the two hairs. By this microscopic goniometer great accuracy is not to be hoped for; but for occasional purposes it will answer well.-Annales des Sciences Naturelles.

15. Lightning Rods.-In consequence of the powder magazine of Bayonne having been struck by lightning, the French Minister of War submitted certain questions to the Academy of Sciences on the subject. The conclusions of the report drawn up by the Section of Natural Philosophy of this eminent body deserve much attention.

The powder magazine of Bayonne, be it observed, was vaulted below the surface of the ground to exclude wet, and vaulted above to resist the effect of shells: so it might be compared to a hollow sphere, the interior of which would be difficultly accessible to the lightning; the comparison would be still closer, had it been cooled with hydraulic lime, so as to preclude the damp from penetrating.i i. The lightning injured the powder magazine at Bayonne, only because the lightning rod with which it was provided was badly constructed, the communication between it and the ground being insufficient.

ii. A lightning rod may be rendered fully efficient by making it penetrate deeply into water or damp earth; by burying the horizontal part of it; by covering it with ashes from an oven instead of charcoal imperfectly carbonized, and by directing a stream of water toward the subterranean part of the conductor.

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iii. That for powder magazines it is prudent to erect the lightning rod on a mast beside them.

iv. That in the case of magazines vaulted above and below, like that of Bayonne, and from which masses of metal of any considerable size are excluded*, it is unnecessary to employ lightning rodsA

v. But in the case of magazines not so vaulted, like those for temporary purposes, prudence requires the use of a lightning rod attached to a mast.

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1. On the influence of Liquefaction on the Volume and Dilatibility of certain Bodies, by G. A. Erman.-These investigations by M. Erman have been made only upon two bodies; the first an alloy of two parts of bismuth, one of lead, and one of tin; and the second, phosphorus. Water is the only substance which had previously been examined relative to this point of molecular philosophy.

The changes in volume were ascertained by hydrostatic weighings; those of the alloy being taken in olive oil, those of the phosphorus in water. As the process required the absolute dilatation of these two fluids to be accurately known, experiments were first set on foot with regard to olive oil, for the purpose of ascertaining the expression of its true dilatation: that of water had been previously ascertained.

Numerous experiments with the alloy at different temperatures were then made; and ultimately, the results expressed graphically, in the manner practised by meteorologists, by a line bounding the abscisses formed by the temperatures expressed in degrees of Reaumur's scale; the ordinates, the corresponding changes in volume, in parts of the primitive volume at zero. The following are consequences drawn from the simple inspection of the figure: the degrees are of Reaumur's scale.

The commission remarks that the ordinary iron work of a building, hinges, locks, cramp irons, staples, need not occasion any fears.

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