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from which the value of x is determined, once for all, for the same instruments.

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Then, if we wish to determine the volume of any body z, we subject it to experiment like the body z, and we have, in designating by h, b, the weight of the mercury c, d, for the body z:

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and on this occasion a being known, we deduce from it the value of z. The instrument is provided with several points of platina, so that various experiments may be made on the same bodies which control each other, and allow of an accurate mean.

The following are results obtained by this instrument, which, agreeing well with results directly obtained, enable us to place confidence in its indications.

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This coincidence induced me to employ the voluminimeter for determining the density of various substances, which the methods commonly employed could not accomplish. The following are my

results:

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The several woods experimented upon were reduced to powder by rasping, and dried at a temperature of about 100 degrees.

On a new shortened portable Barometer. By HERMANN KOPP.Ann. des Mines: (Ann. de Ch. t. vi.)

TRANSLATED FOR THE JOURNAL OF THE FRANKLIN INSTITUTE.

The instrument which I am about to describe, and which appears to be worthy the attention of philosophers and intelligent travelers, is

constructed on this principle:-"If a like volume of air in different states of condensation be compressed by a like quantity, and be at liberty to act on a column of mercury, this column will rise in proportion to the density of the compressed air before compression."

It is composed of two cylinders in their glass K, and i i communicating at the lower part by means of a bent tube p. In the cylinder K, is a solid piston. The cylinder i i is closed at its upper part, except that this part is traversed by a tube c d open at both ends. The body of the pump K, and the tube p, are filled with mercury, which, when the piston is at the highest point of its course, rises a few lines in the cylinder i i so as to leave the lower end of the tube ed open, which thus puts the air of the cylinder into communication with the atmosphere. To the tube c d there is adapted a platina wire whose two extremities, pointed and blackened, are fixed as a and b. On the same tube c d is traced an arbitrary scale whose zero is a little above, at a known and invariable distance from the points a and b.

Thus arranged, if the piston in K be depressed, the mercury will rise in ii will soon close the opening c, and then will compress the air in the cylinder. The piston is to be brought down until the mercury rises to a, for example. This compression will raise the mercury in the tube c d and from the height of this column, easily estimated by adding to the length indicated by the scale, the invariable distance from the point a, to the zero of this scale, the pressure of the atmosphere may be deduced.

To do this it will be sufficient to have determined by some previous trials, the constant relation which subsists, under the same circumstances, between the height of the common normal barometer, and that of the barometer now in question. This relation is determined by taking the mean of the relations of a certain number of observations made simultaneously with the two instruments; and when, on occasion, we wish to bring the heights given by the new barometer to the common barometric heights, we multiply them by this constant coefficient.

It is needless to say that at each observation the barometer must be placed vertically, and left to acquire an equilibrium of temperature with the ambiant air.

The second point b, serves to render the instrument double, so to speak, in order to make an experiment controling the former. The constant coefficient must, in this case, have been previously determined for that point.

A condition essentially needful in the construction of the instruments, is that the highest point b, must never be so high that the mercury, in reaching it, will rise in the tube higher than the upper part of the scale, and yet that it must come near it in order to profit by the whole length of the scale. The position which this point should occupy is easily determined. Let L be the length c d, D, the distance from b to c, then for the greatest possible barometric height

D
L-

H, we have D+ H<L; (L D and H estimated by the same

measure.)

This instrument, easily used, and, above all, easily and conveniently carried, has served me during a five months' journey. I subjected it to all sorts of trials, with respect to its solidity and invariability, and I am convinced that it gives barometric pressures with an error less than half a line, and more commonly with still greater exactness, although it is seldom more than 25 centimetres in height.

Memoir on a New Process of Chlorometry. By M. LASSAIGNE, (Compte Rendu de l'Acc.)

TRANSLATED FOR THE JOURNAL OF THE FRANKLIN INSTITUTE.

This process appears to me worthy of all preference to the chlorometer with an indigo test, by the unchangeableness of the proof liquor made use of, and by the exact and constant results which it furnishes. It rests on the precise knowledge of the proportion of any gaseous chlorine which is sufficient to decompose a determinate weight of pure ioduret of potassium, in order to become transformed entirely into chloride of potassium, and perchloride of iodine, both of them compounds soluble in water: the decomposition of this ioduret is easily marked by a small quantity of solution of starch, which, added to portions of ioduret at the moment of pouring in the chloric solution, gives immediately and successively the blue, violet, green, red, and yellow colors, as long as the smallest portion of free iodine remains. As soon as the decomposition is complete, the decolored liquor resumes the transparency and limpidity of distilled water;-this reaction enables us to appreciate the change much better than when we operate with the sulphuric solution of indigo, which, we know, remains always of a reddish yellow, more or less deep at the precise period of completing the test.

An equivalent of pure, dissolved, ioduret of potassium, requires, for its complete decomposition, six exquivalents of dry chlorine. The result is one equivalent of chloride of potassium, and one equivalent of perchloride of iodine IChs. From these data one litre of dry gaseous chlorine at a pressure of .76 m., weighing 3.208 grs., decomposes 2.482 grs. of ioduret of potassium.

Therefore, in dissolving this quantity of ioduret of potassium in a litre of distilled water, a normal solution is prepared which requires for its total decomposition a volume equal to its own, of dry, gaseous, chlorine. For the operation we put into a glass vessel a measured quantity of the solution, and add to it a small quantity of solution of starch, (prepared by dissolving a gramme of starch in a hundred grammes of warm water, and filtering it when cold, or by rubbing in an agate mortar some dry starch, and treating it with 100 parts of cold water.) Put the starch solution into the crust with a bent neck, usually employed in chlorometric assays, and add it drop by drop to

the given solution of ioduret, mingled with starch solution, and stop at the moment in which the liquid, after passing through all the shades mentioned, becomes extremely clear. The quantities of chloric solution are in inverse ratio with the proportions of chlorine which they contain. The only precaution necessary in the assay, is to hold in the left hand the glass which contains the measured ioduret charged with eight or ten drops of starch solution, and twirling it round a little, pour into it from the right hand the chlorated solution contained in the crusts.

The determination of the value of an alkaline hypochlorite is effected in the same way in operating upon a recent solution of the salts made in the proportion of ten grammes to a litre of water. One condition only it is important to observe, in order that the operation be quickly and accurately performed; that is, to add to the test solution, charged with starch, a drop or two of concentrated sulphuric acid, for the purpose of disengaging chlorine, when the solution of hypochlorite is added. If this be not attended to, the operation is slow, and requires repeated additions, for to the coloring and discoloring produced by the first drops of hypochlorite in the non-acidulated proof liquor, succeeds spontaneously a fresh coloration which is soon destroyed by a few drops of hypochlorite, and this effect continues four or five times in succession, until the ioduret of potassium is decomposed.—Ann. des Mines, tom. iii, liv. 11.

FOR THE JOURNAL OF THE FRANKLIN INSTITUTE.

On the Diameter of Screws. By JAMES DEAN, A.M., A.A.S., &c., and late Prof. Nat. Phil. and Ast. Univ. Vt.; investigated in 1825. Every attentive student must have been surprised, on his first examining the investigation of the mechanical powers, at finding that the diameter of the screw was not an element in expressing the ratio of the power to the weight necessary to produce an equilibrium; and that, other things being equal, the diameter of the cylinder may vary ad infinitum, without, in the least, affecting that ratio. That reducing, or increasing, the diameter to an extreme degree, the distance of the threads remaining the same, will diminish the effect of any given power, will be universally admitted without any very nice reasoning on the subject; but it seems far from useless to ascertain the exact diameter, which, under any given circumstances, will enable a given power to produce the greatest effect, and it is very natural to look among the effects of friction for this as well as other deviations from abstract theory. Now the ratio of the friction to the pressure which produces it, has been found by Amontons, Parent, Coulomb, &c., to be very nearly constant between the same surfaces, and commonly about one-third. And as the writer cannot learn that friction is much considered in this country as a retarding and computable force, he takes the liberty of translating from Bossut's Mechanics, those sections in which he treats of friction as affecting inclined planes.

Fig. 1.

269. Let a body P, be placed on an inclined plane whose length is GH, height H I, and base GI; resolve the weight of the body, represented by the vertical line PD, into two other forces PC parallel, and P A perpendicular, to the inclined plane. It

is obvious that the force PC=PX

GI

HI

GH,

and the force PA=PXGH The first

of these two forces, called the relative

H

weight of the body, tends to make it slide down the plane, while the second produces a pressure on the plane, and causes a friction of the first species, so that putting n, for the ratio of the pressure, the fricGI =nPx If, therefore, the body be left entirely to itself, it GH will not descend unless its relative weight P C, be greater than the PXHI friction, that is, unless GH

tion

>nPx

GI
GH'

or HI>nxGI.

Hence, a body laid on an inclined plane, and left to the action of its weight only, will not descend unless the height of the plane is greater than the product of the base multiplied by the ratio of the friction to the pressure.

270. Let a body be ready to descend, or let its relative weight be equal to the resistance of friction H In x G I, or n=

HI
GI

Thus,

when the inclination of the plane is such that a body may be ready to descend by its own relative weight, the ratio of the friction to the pressure is that of the height of the plane to its base. Knowing, therefore, either of these ratios the other is known also.

Suppose, for example, the friction to be one-third of the pressure

HI

=

HI

, and by trigonometry the ratio. GI GI may be considered as that of the tangent of the angle of inclination.H GI to radius, and by trigonometric tables, this last ratio being 3, the angle H GI is about 18 26'. So that the friction being taken at one-third of the pressure, the angle of inclination of the plane must be about 18° 26', that the body may be on the point of descending by its own relative weight. If, on the contrary, the angle of the inclination of the plane be given, the ratio may be found by the tables, which is the value of n. This furnishes a very simple and convenient method of ascertaining friction by experiment. It is only necessary to lay the body on a plane at first very little inclined to the horizon, and gradually increase the inclination until the body begins to descend, and the ratio of height of the plane to its base is that of the friction to the pressure.

271. We will now consider a body which some power is ready to raise along an inclined plane, by overcoming its relative weight and friction. It is easy to find the general value of that power, but we shall confine ourselves to the two cases which most frequently occur,

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