racters of anterior sinus and gape; and, besides E. Scouleri, at least two species have been determined. A very closely related genus, Offa, has also been indicated. M'Coy's "Daphnia primava" belongs to Cypridina proper; and twelve other Carboniferous species have been established. A modified form of carapace, without any exact modern analogue, characterizes the new genus Cypridinella, with seven species. De Koninck's genus Cypridella (restricted) has seven species; and a form intermediate to this and Cypridina is described as Cypridellina, with eight species. Sulcuna (with two species) is an exaggerated modification of Cypridella. Cyprella of De Koninck (restricted) has two species. The recent Bradycinetus, Sars, and Philomedes, Lilljeborg, appear to have their prototypes in the Carboniferous Limestone, with one species each. Rhombina, a new genus, is a less easily recognized Cypridinal form, with an Irish and a Belgian species.

The recent Polycope, Sars, belonging to a different family, and represented by three Carboniferous species, was the last described in the memoir; but Cytherella, belonging to an allied group, is known in the Mountain-limestone and Coal-measures; and Leperditia, Entomis, Beyrichia, Kirkbya, and other paleozoic genera, abound, together with forms referable probably to Cythere, Cypris, Candona, &c., which will be treated of in a future paper.

XXXVIII. Intelligence and Miscellaneous Articles.

ON THE PERMANENT MAGNETISM OF STEEL. BY E. BOUTY. 1

THE phrase "coercive force" has ever expressed only a somewhat vague comparison between the phenomena of the magnetization of steel and friction. This bringing together of two orders of phenomena so complex is altogether artificial, and absolutely excludes the facts which relate to the temporary magnetization of steel.

Wiedmann has, more profitably, brought the phenomena in question into comparison with those which depend on elasticity in solid bodies, especially the phenomena produced by torsion. Although this comparison does not constitute a theory properly so called, it has the advantage of expressing a real physical relation; for torsion modifies the magnetic state of a bar, and modifications of that state can in turn modify the torsion to which the bar has previously been submitted. A great number of facts relative to magnetization or demagnetization are conveniently interpreted in this system; but the following phenomena can only with very great difficulty be adapted to it.

It has long been known that a certain temporary magnetism can be superposed to a permanent magnetism opposite in direction, and that the latter may reappear, sometimes even integrally, after the influence of the external forces has ceased. For example, if a bar of magnetized steel be submitted to the action of a current too feeble to demagnetize it entirely, during the action of the current a diminution of the magnetism of the bar is observed, which may go

so far as to the apparent reversal of the poles, whereas after the cessation of the current the bar is found to be still magnetized in the original direction.

The following fact, which I have observed, appears to me still more curious. I take a bundle formed by the combination of four square bars of the same length. It is tempered hard and magnetized immediately; its magnetic moment is measured; lastly it is taken to pieces, and the magnetic moment measured of each bar separately. It is found that the sum of these moments is very considerably greater than the magnetic moment of the bundle. If the bars be united in twos, the sum of the moments of the pairs is intermediate between those of the whole bundle and of the separate bars. When, finally, the bundle is reconstructed, the magnetic moment also returns to its former value.

In this experiment the bundle, which, innocent of all anterior magnetization, has only once undergone the action of the magnetizing spiral, is in an absolutely normal condition at the moment of the first separation; and no new force appears to intervene, to which one might attribute the observed augmentation of the permanent magnetism. It is true that, in separating the bars, we suppress their reciprocal reaction; and we know that in each of them it acted in the opposite direction to that of the permanent magnetism; but this suppression can only have effect on the temporary magnetism. Thus, even in a normal bar, a certain degree of permanent magnetism is found to be superposed to a temporary magnetism of the opposite direction.

It would therefore be very natural to recur to an old hypothesis, according to which the condition, whatever it may be, which corresponds to the conservation of a certain permanent magnetism, is communicated, in the conversion into steel or in the tempering, only to a certain number of molecules, the others retaining their former properties. If we remark (1) that the laws of the temporary magnetism of steel appear to be identical with those of induced magnetism in soft iron, (2) that the development of permanent magnetism is eminently variable from one sort of iron or steel to another, and for one and the same sort according to sometimes insignificant physical conditions, we shall be led to examine more closely than has been done yet the consequences of this hypothesis. Let us consider a cylinder of elemental dimensions, but of very great length relatively to its diameter. Let us suppose the two kinds of magnetic elements scattered at random, but in a determinate proportion, in all parts of the cylinder, and a magnetic force F acting in the direction of the axis. If the molecules devoid of coercive power existed alone, the cylinder would take a magnetic moment FAv,-Av representing the volume of the cylinder, and k a coefficient which depends on the density of the molecules. In the same way the molecules endowed with coercive power, if they were alone, would take a magnetic moment qFAv.

If we suppose the coefficients of induction k and q constant (which is sensibly true for small values of the inductive forces), and designate by e a coefficient dependent on the grouping of the mag

netic elements of both kinds, we find that the magnetic momer.t communicated to the cylinder by the force F will be, taking account of the reactions of the two sorts of molecules.

M=

k+q+2ckq F▲v;
1–ckq

after the cessation of the force F, they will retain a moment

m=q

(1+ck)2 F▲v. 1-ckq

This quantity is what is ordinarily called the permanent magnetism. The temporary magnetism, which disappears on the cessation of the force F, is

μ=M-m=kFav.

It is thus seen that the two coefficients of temporary and permanent magnetism ordinarily determined are not quantities of the same kind. The quantity q, analogous by the part it plays to k, is obtained by dividing the ordinary coefficient of magnetism by (1+ck)2

It is evident, and verified without difficulty in a particular case, that the total magnetic moment M is intermediate to those which would be produced by the same force F acting on two cylinders equal to the first, each comprising only one sort of molecules, with the same total density. But it is not the same with the residual moment m, which, for a given value of q, is as much greater as the coefficient k of temporary magnetism itself is greater; and as the coefficient k relative to soft iron is enormous, it is seen that the addition of a certain quantity of soft iron to the hardest steel may augment the residual magnetism of the latter. The employment of armatures of soft iron at the extremities of magnetic bundles, in order to increase their power, comes to the support of our assertion. We will also remark that, according to M. Jamin, the varieties of steel the richest in carbon and tempered the hardest do not present the greatest residual magnetic moments-which is what should be if the molecules of soft iron in them are very rare, as we must suppose them to be. We reserve to ourselves to return to this subject subsequently, and to develop the results by calculation and experiment.

The complete theory of the phenomena of breaking, on which we were engaged in a preceding communication, required a rigorous knowledge of the two functions of temporary and permanent magnetism of steel. Let us consider two bodies, A and B, submitted to one and the same inductive force, but united invariably the one to the other. After the cessation of the inductive force the body A remains under the action of B, and conserves, apart from the residual magnetic moment which would remain to it after its separation from B, a moment (of the same or the contrary direction) produced by the influence of B, and which is permanent only so long as the union between A and B subsists. This magnetic excess might be named the subpermanent magnetic moment. In the experiment

so far as to the apparent reversal of the poles, whereas after the cessation of the current the bar is found to be still magnetized in the original direction.

The following fact, which I have observed, appears to me still more curious. I take a bundle formed by the combination of four square bars of the same length. It is tempered hard and magnetized immediately; its magnetic moment is measured; lastly it is taken to pieces, and the magnetic moment measured of each bar separately. It is found that the sum of these moments is very considerably greater than the magnetic moment of the bundle. If the bars be united in twos, the sum of the moments of the pairs is intermediate between those of the whole bundle and of the separate bars. When, finally, the bundle is reconstructed, the magnetic moment also returns to its former value.

In this experiment the bundle, which, innocent of all anterior magnetization, has only once undergone the action of the magnetizing spiral, is in an absolutely normal condition at the moment of the first separation; and no new force appears to intervene, to which one might attribute the observed augmentation of the permanent magnetism. It is true that, in separating the bars, we suppress their reciprocal reaction; and we know that in each of them it acted in the opposite direction to that of the permanent magnetism; but this suppression can only have effect on the temporary magnetism. Thus, even in a normal bar, a certain degree of permanent magnetism is found to be superposed to a temporary magnetism of the opposite direction.

It would therefore be very natural to recur to an old hypothesis, according to which the condition, whatever it may be, which corresponds to the conservation of a certain permanent magnetism, is communicated, in the conversion into steel or in the tempering, only to a certain number of molecules, the others retaining their former properties. If we remark (1) that the laws of the temporary magnetism of steel appear to be identical with those of induced magnetism in soft iron, (2) that the development of permanent magnetism is eminently variable from one sort of iron or steel to another, and for one and the same sort according to sometimes insignificant physical conditions, we shall be led to examine more closely than has been done yet the consequences of this hypothesis. Let us consider a cylinder of elemental dimensions, but of very great length relatively to its diameter. Let us suppose the two kinds of magnetic elements scattered at random, but in a determinate proportion, in all parts of the cylinder, and a magnetic force F acting in the direction of the axis. If the molecules devoid of coercive power existed alone, the cylinder would take a magnetic moment FAv,-Av representing the volume of the cylinder, and k a coefficient which depends on the density of the molecules. In the same way the molecules endowed with coercive power, if they were alone, would take a magnetic moment qFAV.

If we suppose the coefficients of induction k and q constant (which is sensibly true for small values of the inductive forces), and designate by c a coefficient dependent on the grouping of the mag

netic elements of both kinds, we find that the magnetic momert communicated to the cylinder by the force F will be, taking account of the reactions of the two sorts of molecules.

M=

k+q+2ckq FAv;
1–ckq

after the cessation of the force F, they will retain a moment

(1+ck)2 FAv.
m=q 1 - c2kq
1–ckq

This quantity is what is ordinarily called the permanent magnetism. The temporary magnetism, which disappears on the cessation of the force F, is

μ=M-m=kFAv.

It is thus seen that the two coefficients of temporary and permanent magnetism ordinarily determined are not quantities of the same kind. The quantity q, analogous by the part it plays to k, is obtained by dividing the ordinary coefficient of magnetism by (1+ck)2

1-c3kq

It is evident, and verified without difficulty in a particular case, that the total magnetic moment M is intermediate to those which would be produced by the same force F acting on two cylinders equal to the first, each comprising only one sort of molecules, with the same total density. But it is not the same with the residual moment m, which, for a given value of q, is as much greater as the coefficient k of temporary magnetism itself is greater; and as the coefficient k relative to soft iron is enormous, it is seen that the addition of a certain quantity of soft iron to the hardest steel may augment the residual magnetism of the latter. The employment of armatures of soft iron at the extremities of magnetic bundles, in order to increase their power, comes to the support of our assertion. We will also remark that, according to M. Jamin, the varieties of steel the richest in carbon and tempered the hardest do not present the greatest residual magnetic moments-which is what should be if the molecules of soft iron in them are very rare, as we must suppose them to be. We reserve to ourselves to return to this subject subsequently, and to develop the results by calculation and experiment.

The complete theory of the phenomena of breaking, on which we were engaged in a preceding communication, required a rigorous knowledge of the two functions of temporary and permanent magnetism of steel. Let us consider two bodies, A and B, submitted to one and the same inductive force, but united invariably the one to the other. After the cessation of the inductive force the body A remains under the action of B, and conserves, apart from the residual magnetic moment which would remain to it after its separation from B, a moment (of the same or the contrary direction) produced by the influence of B, and which is permanent only so long as the union between A and B subsists. This magnetic excess might be named the subpermanent magnetic moment. In the experiment