ting angles, like A and B, Fig. 1., in the supposed regular sixsided prism. The remainder, ABA', of the terminal face of one of the individuals, is inclined to the similarly situated face of the other at an angle of 179° 10′, to which, on the opposite side, corresponds a re-entering angle of 180° 50'. Both these facts I had observed separately in numerous specimens, but the smallness of well-pronounced crystals, and the impossibility of distinguishing by the eye an angle of 119° 50', from one of 120° 20′, rendered it very difficult to combine these observations into one representation of its forms. The observation, that the plane of the resultant optical axes passes through a line parallel to A'A, Fig. 1., led me to inquire whether the face b, which I had before supposed to be one of the faces of an oblique-angular four-sided prism, might not be parallel to the short diagonal of the prism produced by the enlargement of the faces c, c, &c. The examination of a small, but beautiful, and very regularly formed twin-crystal, in the collection of Mr Allan, carried on upon this supposition, gave at last the results which form the substance of this paper. One of the individuals of that regular composition is represented in Fig. 2.; and Fig. 3. is its projection, on a plane parallel to the face a, the whole of the crystal having been duly completed.

If enlarged to their mutual intersection, P and P' produce the fundamental form of the species, a scalene four-sided pyramid, in which the axis of the form, is inclined to a line perpendicular to the base, at an angle of 0° 29′. In the method of Professor Mohs this angle is called the Inclination of the Axis, and the variable quantities considered are, the line perpendicular to the base of the pyramid, which line is called a, the diagonal b, in the plane of inclination, the other diagonal c, and a fourth line d, which corresponds to, or subtends, the angle of inclination.

The ratio of these lines a: b:c: d, which gives a result agreeing nearest with observation, is that of 120: 95: 54.5:1. Upon this supposition the angles of the fundamental form are the following: Inclination of P upon P over the face ƒ= 72° 36′; of P' upon P', on the opposite side, = 72° 10′; of P upon P/ contiguous to the same apex, = 124° 50′; of P upon P', contiguous to the opposite apex, = 137° 0'.

Inclination of P — (a) upon

The following table contains some of the most important angles, together with the crystallographic signs, referring to the simple forms, according to the method of Professor Mohs.

Angle at the edge contiguous to the

plane of inclination in

The perfectly hemiprismatic appearance of a crystal similar to the given figures, would be alone sufficient for excluding the forms of axotomous lead-baryte from the rhombohedral system, even though the measures of the angles should have been found to approach still nearer to 120° and 90°. But one and the same individual seldom presents more than one or two of its six sides to the observer, being in most cases joined to other individuals, according to the law of regular composition mentioned in the beginning of this paper.

The planes of composition pass through a line nearly perpendicular to two sides of the six-sided tabular crystals, like AB,

Fig. 4. They are parallel to one face of (P + ∞ )3, = 119° 40′, a prism which is likewise found in the crystals of this species. Upon this supposition, the angles are 90° 20', and 89° 40′. Of the individuals AA'BCDE, and AA"BC'D'E, which meet in the plane of composition passing through A B, nothing will remain but the rhomb-like trapezium AA'BA", the angles of which are A=60° 20′; A' and A" each=119° 50′, and B-60o. If a third individual A'A"CGFC' joins the regular composition of the preceding two, being applied to BMA', the remainder of BAA', Fig. 4. in the line A'M, there will also arise a face of composition between A'MA" and BMA', and the angles of the remaining triangular figure AʼA"B, Fig. 5. will be exactly = 60°. In the compound crystals of axotomous lead-baryte, each of the edges A'M, A'M, and BM is 179° 10.

The regular composition of three individuals, if the faces of Př+ 1 ore are considerably increased, while those of

P

2

or P

disappear, assumes very nearly the form of an acute rombohedron, whose apices and lateral solid angles are truncated, as in Fig. 6. The incidence of e upon e' is = 72° 39', almost the same as the angle given by Mr Brooke for the terminal edge of his acute rhombohedron. Even in crystals most perfectly formed, it is very easy to overlook the small salient angle of 179° 10′ upon the faces RST, supposed perpendicular to the axis of the rhombohedron; but this composition is often so intricate, particularly in larger crystals, that it sometimes becomes difficult to point out the direction and extent of each separate individual, though the existence of the composition is indicated by small, salient and reentering angles, and proves, with the highest degree of evidence, that the forms of axotomous lead-baryte are not Rhombohedral but Hemiprismatic.

Although the observation of the optical properties of minerals can never supersede the study of their regular forms, yet the preceding examination of the forms of axotomous lead-baryte, affords an ample proof that they may be highly useful in guiding us through the latter, particularly if these regular forms nearly coincide with certain limits. The crystallographic researches relative to this species are attended with considerable difficulties,

since the angles approach in every instance within one degree to the limits of 120° and 90°, and the regular composition very often hinders the crystals from being observed on all sides, while the inclination of the optical axes of no polarisation upon each other is very considerable, and easily ascertained.

The inferences drawn from Dr Brewster's general law, respecting the existence of two polarising axes in crystallised substances, had excluded the forms of axotomous lead-baryte from the rhombohedral system, previous to their correct determination, and even in contradiction to the opinions entertained by crystallographers. The preceding demonstration, that they are hemiprismatic, reconciles the results of both sciences.

ART. XVI.—Notice respecting the genus Caligus of Leach. By GEORGE JOHNSTON, M. D., Extraordinary Member of the Royal Medical, and Corresponding Member of the Medico-Chirurgical Societies of Edinburgh.

SIR,

I AM not aware that any naturalist has heretofore suspected,

that there exists a considerable difference in the external structure of the sexes, of at least one species of the curious genus Caligus. My observations have led me, however, to believe, that this is the case; and should they appear to you as new as they are to me, this notice may, perhaps, be deemed not unworthy a place in the Edinburgh Philosophical Journal.

In the autumn of 1822 I found, on the common cod-fish, what I considered at the time a non-descript species of Caligus. A few weeks since, I met with the same animal, but intermixed on the body of the fish, with the Caligus Mulleri of Leach; and on a comparative examination, their resemblance in general form, and more particularly in the form of the clypeus, antennæ, and legs, was so close as to suggest, that they might be but the male and female of the same species. I felt more confirmed in the accuracy of this conjecture, on finding in the only three perfect specimens of the C. Mulleri I had procured, two little packets of eggs, attached beneath to the lower end of the large segment of

the abdomen, which none of the others, and of them I had a considerable number, possessed.

Fig. 12. Pl. VII. is an outline of what I consider as the female, considerably magnified, and Fig. 13. represents the male. Be tween all the parts of the thorax, in both there is a strict agreement, with the exception of the fourth pair of legs, (uncinuli? Müller,) which in the male are very large, in proportion to the others, strongly toothed on the inner margin, and armed with a stout claw; while in the female these legs are small, and without teeth. The pectinated membranaceous laminæ affixed to the inferior angle of the clypeus, are also somewhat larger in the former than in the latter. But the chief difference is in the abdomen. In the female, it consists of three very disproportionate segments, which, however, are not separated by any distinct lines from one another. The first is very small. The se cond is large, narrowed above and truncate behind, where, on each side, is attached a cylindrical jointed process, (filamenta ovipara of Müller), in length exceeding the whole body. The third segment might, aptly enough, be termed the caudal. It is a very small process, projecting between the filaments, terminated behind by two papillæ, which again have on their extreme points three short transparent setæ. In the male there are no filamenta ovipara. The abdomen is smaller in proportion to the thorax, and its segments are more distinctly marked. The first is small, angulated, and bears the seventh pair of legs, which are in every thing similar to those of the female; the second is broader, considerably larger, rounded before, truncate behind, with two small spines at each external angle; the third segment is considerably less than the second, cordate, terminated behind by two papillæ, whence, as it were, issue from each, three acuminated spines, (of which the mid-one is the longest), finely ciliated an each side, and in length nearly equalling that of the abdomen, (Fig. 14.) These particulars are well enough expressed in the figures, which will give a more correct idea of them, than any description can convey, though they are neither so accurate nor so finished as I could have wished.

Should these observations be verified, they will necessarily introduce a material alteration not only into the specific, but generic characters. These, however, can be formed by him only