Page images
PDF
EPUB

XXX. Intelligence and Miscellaneous Articles.

ON THE MAGNETIZATION OF SOFT IRON. BY M. P. JOUBIN.

THE phenomena of magnetization have as yet only been represented by empirical and approximate expressions; thus, for instance, the well-known formula of Fröhlich which is so frequently used does not show that the magnetic susceptibility passes through a maximum, a fact which is very important.

1. Let I be the intensity of magnetization, H the field, K the susceptibility, defined by the equation I= KH. In order to find another relation between these three magnitudes we may, with Rowland, trace a curve by taking for coordinates not I and H, but I as ordinate, and K or 4K as abscissæ. To each value of K two values of I correspond, and the centre of each chord is on a right line very slightly inclined to the axis of abscissæ, and the angular coefficient of which is negative. This curve is exactly a parabola (except near the axis of the ordinates) as Rowland has shown, who, however, represents it by a sinusoidal function. Thus it is that the equation

[blocks in formation]

represents exactly the magnetic condition of an iron investigated by Bosanquet, as shown in the following table. This example is taken at random among many others.

[blocks in formation]

2. The general aspect of these curves recalls in a striking manner the curves which give the densities of saturated fluids as a function of the temperature (MM. Cailletet and Mathias). To each value of the susceptibility (which replaces the temperature) correspond two values of the intensity of magnetization (or superficial density) which approach each other as K is increased, and merge into each other at the critical point. The maximum

intensity Im is nearly equal to three times the critical intensity I.; in fact in the preceding example Ic=478 and Im=1400, a third of which is 467. Now this property of ordinary fluids may be deduced from the equation of Van der Waals; we are thus led to inquire whether we may compare the magnetic properties to those of fluids.

3. Following Faraday, let us regard the field as occupied by tubes of force whose section o at each point is inversely as the field, H-1. In other words, instead of representing the intensity of the field by the number of lines of force per unit surface, let us define it by the section of unit tube. The coefficient K may then be written Io; this is the quantity of magnetism contained in the section of unit tube, just as the temperature is the quantity of heat contained in unit volume of a gas.

Between the superficial density I and the susceptibility K there is the same relation as between the cubical density d and the temperature T of a fluid, a relation expressed by the formula of Van der Waals. Given a fluid obeying this law,

[blocks in formation]

If it is gaseous and very far from its point of saturation, it virtually follows the law of Mariotte, and we may write pv=RT, from which is deduced the approximate law of its expansion,

[blocks in formation]

The expansion of unit volume is proportional to the absolute temperature. This expression leads us to Fröhlich's law.

Assume, in fact, that we can apply to magnetic phenomena the

same equation, in which we shall replace a by

1

T by K, and

I

[blocks in formation]

Admitting, in conformity with a well-known demonstration, that the pressure exerted against the external medium on the surface is proportional to Io, that is to say to KI, it will be seen that to write the equation p RKI, is to express a law analogous to that of Mariotte. We deduce from this,

=

[blocks in formation]

338

from which

Intelligence and Miscellaneous Articles.

This is Fröhlich's formula.

1 c Im-I HR H Hm

Now this formula holds very well with feebly magnetic bodies; we may from this conclude that in this case the pressure p is correctly valued. On the other hand, it does not agree with strongly magnetic bodies, for which the value of the pressure p is given by the formula of Van der Waals. From the known properties of this equation, the pressure corresponding to two values of I, corresponding to the same susceptibility K, is the same.

4. For a fluid, in proportion as the temperature T decreases the density of the saturated vapour decreases cotemporaneously with the tension; at the temperature at which the density becomes null, the tension is null also. Thus the second part of the equation of Van der Waals vanishes, and we deduce from it the value of the density of the liquid under the pressure null of its saturated vapour.

Applying the same method to the example mentioned above, the parabola cuts the axis of abscissæ at the point 4K=516; the corresponding value of I given by the equation of Van der Waals is I=1260. The direct measurement on the parabola gives 1256. This is an almost absolute coincidence.

5. From this point the equation of Van der Waals can no longer represent the phenomenon, for the fluid can no longer exist in the liquid state; a change of state takes place, and the representative curve changes suddenly. This is also the case with magnetism; it is from this point that the curve is no longer parabolic. There is a change of state corresponding to the passage from the liquid to the solid state.

In fine, the phenomena of the magnetization of iron are analogous to those presented by a saturated fluid, and might be calculated by the same formulas; I propose to try if we can find experimentally a reduced equation independent of the magnetized body.

Feebly magnetized bodies are subject to laws analogous to those of liquids at a distance from their point of saturation.—Communicated by the Author, from the Comptes rendus, Jan. 8, 1894.

ON THE EXPERIMENTAL INVESTIGATION OF THE ROTATIONAL COEFFICIENTS OF THERMAL CONDUCTIVITY. BY CH. SARET.

In the very amiable and indulgent notice which the Archives de Genève has published of my Eléméns de Crystallographie physique, M. Curie has proposed a method by which the existence

or absence of rotational coefficients of thermal conductivity in crystals may be ascertained in a simple manner.

I wish here to point out briefly the principle of an analogous method which I was led to try some time ago, and which, as I have subsequently learned, is identical with the method proposed by Boltzmann for the investigation of Hall's phenomenon.

If a point sufficiently distant from the edge of a thin crystallized plate be heated, the isothermal curves obtained by Senarmont's method are ellipses, whatever be the values of the coefficients of rotation.

If instead of working with a continuous plate the plate is split by a straight saw-cut in the direction of a radius from the centre of heating, the isothermal curves will be scarcely modified, and will shorten on each side of the slit if the coefficients of rotation are null, but will exhibit a break in the same region if the coefficients are not null. In this case the flow from the centre tends to follow a spiral line; there should be an accumulation of heat on one of the edges of the slit and a falling off on the other.

The experiment may be made still more simply. Instead of sawing the plate it is sufficient to heat a point of the rectilinear edge. If the coefficients of rotation are not zero the isothermal line must undergo a spiral modification, and the distances at which it cuts the edge of the plate on the right and left of the point heated are not equal.

This method is not very certain: it is better to cut the plate by a saw-cut in two halves, which are then adjusted in a suitable support in their original position, leaving a slight interval between the two edges of the slit. By heating a point of this the spiral deformation should be separately produced on each piece, and the isothermal will present discontinuities in the opposite direction at the two points where it meets the slit.

I have tried these various methods on plates of gypsum; in no case have I observed a discontinuity indicating an appreciable spiroidal deformation of the isotherms. I hope to pursue these experiments.

What we have said applies to thin plates perpendicular to the axis of rotation. It will be seen in like manner that on heating by Jannettaz's method a point in a face cut in an unlimited crystal, parallel to the axis of rotation, isotherms should be obtained which are not symmetrical in reference to that diameter which is parallel to this axis. The fact that this deformation has not hitherto been noticed appears to prove that the coefficients of rotation are always zero, or at any rate very small.-Bibliothèque Universelle, No. 4, 1893.

MECHANICAL ENERGY OF MOLECULES OF GASES.

To the Editors of the Philosophical Magazine.

GENTLEMEN,

Will you kindly allow me to ask, through the medium of your Philosophical Magazine,' whether there has ever been published a statement of the Amounts of Mechanical Energy of the Molecules of different Gases? and if so, where it is to be found?

If there has been no such publication, I beg leave to say that by calculating the mean molecular velocities per second at 0° C. of a considerable number of gases, simple and compound, from their molecular weights and the square roots of those weights (or of the specific gravities) in the usual manner, and multiplying the squares of those velocities by the molecular weights, I have observed that the resulting products are alike in amount, and therefore the quantities of mechanical energy of the molecules of gases at the same temperature and pressure are equal.

As it is possible that this general truth has been already observed and published (although during extensive reading on cognate subjects I have not seen it), I make the above statement with great diffidence.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]
« PreviousContinue »