made up of plates indefinitely thin, separated by spaces indefinitely narrow. If, however, we suppose two cleavages existing at right angles to each other, then we must relinquish the notion of plates and substitute that of little parallel bars; for the plates are divided into such by the second cleavage. If we further suppose these bars to be intersected by a cleavage at right angles to their length, then the component crystals will be little cubes, as in the case of rock-salt and others. By thus increasing the cleavages, the original plates may be subdivided indefinitely, the shape of the little component crystal bearing special relation to the position of the planes. It is an inference which follows immediately from our way of viewing the subject, that if the crystal have several planes of cleavage, but all parallel to the same straight line, this line, in the case of magnetic crystals, will stand axial; in the case of diamagnetic, equatorial. It also follows, that in the so-called regular crystals, in rock-salt, for instance, the cleavages annul each other, and, consequently no directive power will be exhibited, which is actually the case.

Everything which tends to destroy the cleavages tends also to destroy the directive power; and here the temperature experiments of Mr. Faraday receive at once their solution. Crystals of bismuth and antimony lose their directive power just as they melt, for at this particular instant the cleavages disappear. Iceland spar and tourmaline, on the contrary, retain their directive power, for in their case the cleavages are unaffected. The deportment of rock crystal, whose weakness of action appears to have taken both Mr. Faraday and M. Plücker by surprise-as here the optic axis force, without assigning any reason, has thought proper to absent itself almost totally follows at once from the homogeneous nature of its mass; it is almost like glass, which possesses no directive power; its cleavages are merely traces of cleavage. If, instead of possessing planes, of cleavage, a crystal be composed of a bundle of fibres, the forces may be expected to act with greater energy along the fibre than across it. Anything, in short, that affects the mechanical arrangement of the particles will affect, in a corresponding degree, the line of elective polarity. There are crystals which are both fibrous and have planes of cleavage,

the latter often perpendicular to the fibre; in this case two opposing arrangements are present, and it is difficult to pronounce beforehand which would predominate.*

The same difficulty extends to crystals possessing several planes of cleavage, oblique to each other, and having no common direction. In many cases, however, the principle may be successfully applied. We shall content ourselves in making use of it to explain the deportment of that class of crystals, of which, as to form, Iceland spar is the type.

For the sake of simplicity, we will commence our demonstration with an exceedingly thin rhombus cloven from this crystal. Looking down upon the flat surface of such a rhombus, what have we before us? It is cleavable parallel to the four sides. Hence our answer must be, an indefinite number of smaller rhombuses held symmetrically together by the force of cohesion.' Let us confine our attention, for a moment, to two rows of these rhombuses; the one ranged along the greater diagonal, the other along the less. A moment's consideration will suffice to show, that whatever be the number of small rhombuses supposed to stand upon the long diagonal, precisely the same number must fit along the short one; but in the latter case they are closer together. The matter may be rendered very plain by drawing a lozenge on paper, with opposite acute angles of 77°, being those of Iceland spar. Draw two lines, a little apart, parallel to opposite sides of the lozenge, and nearly through its centre; and two others, the same distance apart, parallel to the other two sides of the figure. The original rhombus is thus divided into four smaller ones; two of which stand upon the long diagonal, and two upon the short one, each of the four being separated from its neighbour by an interval which may be considered to represent the interval of cleavage in the crystal. The two which stand upon the long diagonal L, have their acute angles opposite; the two which stand upon the short diagonal, S, have their obtuse angles opposite. The distance between the two former, across the interval of cleavage, is to the distance between the two latter, as L is to S, or as the cosine of 38° 30' to its sine, or as 4:3. We may conceive the size of these rhombuses to decrease till they

It is probable that the primitive plates themselves have different arrangements of the molecules along and across them.

become molecular; the above ratio will then appear in the form of a differential quotient, but its value will be unaltered. Here, then, we have along the greater diagonal a row of magnetic or diamagnetic molecules, the distance between each two being represented by the number 4; and along the short diagonal a row of molecules, the distance between each two being represented by the number 3. In the magnetic field, therefore, the short diagonal will be the line of elective polarity; and in magnetic crystals will stand axial, in diamagnetic equatorial, which is precisely the case exhibited by experiment. Thus the apparent anomaly of carbonate of lime setting its long diagonal axial, and carbonate of iron its short diagonal axial, seems to be fully explained; the position of the former line being due, not to any endeavour on its part to stand parallel with the magnetic resultant, but being the simple consequence of the repulsion of the short diagonal.

There is no difficulty in extending the reasoning used above to the case of full crystals. If this be done, it will be seen that the line of closest proximity coincides with the optic axis, which axis, in the magnetic field, will signalise itself accordingly. A remarkable coincidence exists between this view and that expressed by Mitscherlich in his beautiful investigation on the the expansion of crystals by heat.* If,' says this gifted philosopher, we imagine the repulsive force of the particles increased by the accession of heat, then we must conclude that the line of greatest expansion will be that in which the atoms. lie most closely together.' This line of greatest expansion Mitscherlich found, in the case of Iceland spar, to coincide with the optic axis. The same conclusion has thus been arrived at by two modes of reasoning, as different as can well be conceived.

If, then, speculation and experiment concur in pronouncing the line of closest proximity among the particles, to be that in which the magnetic and diamagnetic forces will exhibit themselves with peculiar energy, thus determining the position of the crystalline mass between the poles, we are furnished with a valuable means of ascertaining the relative values of this proximity in different directions through the mass. An order of contact might, perhaps, by this means be established, of great interest in a mineralogical point of view. In the case of a

* Poggendorff's Annalen, vol. x. p. 138.

right rhombic prism, for example, the long diagonal of the base may denote an order of contact very different from that denoted by the short one; and the line at right angles to the diagonals, that is, the axis of the prism, a contact very different from both. We can compare these lines two at a time. By hanging the short diagonal vertical in the magnetic field, its rotatory power is annulled, and we can compare the long diagonal and the axis. By hanging the long diagonal vertical, we can compare the short diagonal and the axis. By hanging the axis vertical, we can compare the two diagonals. From this point of view the deportment of heavy spar and cœlestine, so utterly irreconcilable with the assumption of an optic axis force, presents no difficulty. If we suppose the proximity along the axis of the prism to be intermediate between the proximities along the two diagonals, the action of both crystals follows as a necessary consequence. Suspended from one angle, the axis must stand from pole to pole; from the other angle, it must stand equatorial.

A ball of dough, made from bismuth powder, was placed between two bits of glass and pressed to the thickness of a quarter of an inch. It was then set edgeways between the plates and pressed again, but not so strongly as in the former case. A model of heavy spar was cut from the mass, so that the shorter diagonal of its rhombic base coincided with the line of greatest compression, the axis of the model with the direction of less compression, and the longer diagonal of the base with that direction in which no pressure had been exerted. When this model was dried and suspended in the magnetic field, there was no recognisable difference between its deportment and that of heavy spar.

When a crystal cleaves symmetrically in several planes, all parallel to the same straight line, and, at the same time, in a direction perpendicular to this line, then the latter cleavage, if it be more eminent than the former, may be expected to predominate; but when the cleavages are oblique to each other, the united action of several minor cleavages may be such as to overcome the principal one, or so to modify it that its action is not at all the same as that of a cleavage of the same value unintersected by others. A complex action among the particles of the crystal itself may contribute to this result, and possibly in some cases modify even the influence of proximity. If we hang a magnetic body between the poles, it always shows a pre

DECREASE OF FORCE WITH INCREASE OF DISTANCE. 31

ference for edges and corners, and will spring to a point much more readily than to a surface. Diamagnetic bodies, on the contrary, will recede from edges and corners. A similar action among the crystalline particles may possibly bring about the modification we have hinted at.

During this investigation a great number of crystals have passed through our hands, but it is useless to cumber the reader with a recital of them. The number of natural crystals have amounted to nearly one hundred; while through the accustomed kindness of Professor Bunsen, the entire collection of artificial crystals, which his laboratory contains, has been placed at our disposal.*

We now pass over to a brief examination of the basis on which the second law of M. Plücker rests:-the affirmation, namely, that the magnetic attraction decreases in a quicker ratio than the repulsion of the optic axis.' The ingenuity of this hypothesis, and its apparent sufficiency to account for the phenomena observed by M. Plücker, are evident. It will be seen, however, that this repulsion arises from quite another cause a source of error which has run undetected through the entire series of this philosopher's inquiries.

The following experiment is a type of those which led M. Plücker to the above conclusion. A tourmaline crystal 36 millimeters long and 4 millimeters wide was suspended between a pair of pointed movable poles, so that it could barely swing between them. It set its length axial. On removing the poles to a distance and again exciting the magnet the crystal set equatorial. The same occurred, if the poles were allowed to remain as in the former case, when the crystal was raised above them or sunk beneath them. Thus, as the crystal was withdrawn from the immediate neighbourhood of the poles it turned gradually round and finally set itself equatorial.†

A similar action was observed with staurolite, beryl, idocrase, smaragd, and other crystals.

We have repeated these experiments in the manner described, and obtained the same results. A prism of tourmaline three

We gladly make use of this opportunity to express our obligation to Dr. Debus, the able assistant in the chemical laboratory.

+ Poggendorff's Annalen, vol. lxxii. p. 319.