Transactions of the Geological Society, 1st series, vol. 4/On the Measurement and Cleavage of certain Primitive Crystals

XIII. On the measurements, by the reflecting Goniometer, of certain primitive Crystals; with observations on the methods of obtaining them by mechanical division along the natural joints of Crystals.

By WILLIAM PHILLIPS, Esq.

member of the geological society.

IN a communication read before the Society about the middle of last year, I detailed some reasons for concluding that the angles of some primitive crystals included in the terms parallelepiped, as well as some varieties of the octahedron, had not been accurately ascertained. Since that time, further attention to the subject has confirmed those observations. I proceed to lay before the Society the results of investigations in regard to ten other substances, two or three of which have been measured by the assistance of the reflecting goniometer only upon their natural planes, on account either of their not yielding to mechanical division with sufficient freedom, or not yielding to it at all. The rest have been fractured with exactness enough to allow the use of that instrument; and for that reason, the results allow of more complete confidence, than if there had been a necessity for relying on their natural planes.

It would have spared me much time and difficulty, if to the other labours of the Abbé Haüy and the Count de Bournon, they had added some account of the means by which the mechanical division of each substance may be most readily attained. Concluding that the same difficulties are felt by others, I shall add some remarks on that subject, in regard to such of the substances as I have been able to cleave with regularity, presuming that it may tend to render the way more easy for those who may desire to attain the same object. It must be obvious that very different means have been resorted to; for no one will imagine the same to be applicable to the sulphate of barytes and the sapphire: one of them soft, and yielding to mechanical division with the utmost ease; the other, the hardest of all the earthy minerals, and splitting only by the application of great force, and even then, not without much difficulty and perseverance in more than one direction. Still further remarks will be needful in regard to one of the substances, the sulphate of lead, since the mechanical division it affords has necessarily led me to differ from the Abbé Haüy and the Count de Bournon, as to the form of its primitive crystal.

The following pages would not have been offered to the notice of the Geological Society, but for such reasons as belong to the importance of determining with precision not only the forms, but the measurements of the angles of primitive crystals. If it should be thought that it is assuming too much, to differ from authors so distinguished as the Abbé Haüy and the Count de Bournon, I beg to offer the same apology as was offered by the latter for differing from the former in the same respects. “The attainment of truth is the great object that every man 'ought to propose to himself, who has any pretension to science.”[1]

Such of the figures in the accompanying drawing [2] as suited my purpose were copied from those of Haüy, and when compelled to alter the form, the letter by which he designates each plane, has been studiously retained for the more ready reference to his works.

Nothing having been said in my papers on the oxide of tin, and the sulphate of barytes and quartz, on the mode of cleaving them, they are now placed in the following table at the head of the ten substances forming the particular objects of this communication, chiefly to allow the opportunity of saying a few words on the subject of splitting them.

 Measurements. Substances Primitive Crystal. Reference to Plate 12 According to Haüy According to Bournon By the Reflecting Goniometer Oxide of Tine An obtuse octohedron of which the common base of the pyramids is square ${\displaystyle \left.{\begin{matrix}\ \\\ \end{matrix}}\right\}}$ Fig.1 P on P 67° 42′ 67° 50′ Haüy P on the opposed plane over the apex 112° 50′ Sulphate of Barytes A right prism, with rhombic bases. ${\displaystyle \left.{\begin{matrix}\ \ \end{matrix}}\right\}}$ Fig. 2. M on M 101° 32′ 13 101° 42′ Haüy M on the adjacent plane, over the edge A 78° 27′ 47 78° 18′ Quartz A slightly obtuse rhomboïd ${\displaystyle \left.{\begin{matrix}\ \ \end{matrix}}\right\}}$ Fig. 5. P on P 94° 24′ 94° 15′ Haüy P on P' 85° 36′ 85° 45′ Zircone An obtuse octohedron; the common base of the pyramid is square. ${\displaystyle \left.{\begin{matrix}\ \\\ \end{matrix}}\right\}}$ Fig. 1. P on P 82° 50′ 84° 20′ Haüy P on the opposed plane over the apex 95° 40′ Staurotide A right rhomboidal prism Fig. 2. M on M 129° 30′ 129° 20′ Haüy M on the adjacent plane over the edge A 50° 40′ Anatase An acute octohedron; the common base of the pyramid is square. ${\displaystyle \left.{\begin{matrix}\ \\\ \end{matrix}}\right\}}$ Fig. 4. P on P 137° 10′ 136° 47′ Specular Iron A slightly acute rhomboid. Haüy ${\displaystyle \left.{\begin{matrix}\ \ \end{matrix}}\right\}}$ Fig. 3. P on P 87° 9′ 86° 10′ 92° 51′ 93° 50′ Diopside An oblique rhomboidal prism. Haüy ${\displaystyle \left.{\begin{matrix}\ \ \end{matrix}}\right\}}$ Fig. 6. M on M 87° 42′ 87° 5′ M on the adjacent plane, over the edge A 92° 55′
 Measurements. Substances Primitive Crystal. Reference to Plate 12 According to Haüy According to Bournon By the Reflecting Goniometer Cyanite An oblique prism of which the plane P is very nearly a rhomb ${\displaystyle \left.{\begin{matrix}\ \\\ \end{matrix}}\right\}}$ Fig. 7. M on T 106° 6′ 106° 15′ Haüy M or T on the adjacent plane, over the edge A 73° 45′ Corundum A slightly acute rhomboid. ${\displaystyle \left.{\begin{matrix}\ \ \end{matrix}}\right\}}$ Fig. 3. P on P 86° 38′ 86° 86° 4′ Haüy & Bournon P on P' 93° 32′ 94° 93° 56′ Sulphate of Strontian A right prism with rhombic bases. ${\displaystyle \left.{\begin{matrix}\ \ \end{matrix}}\right\}}$ Fig. 2. M on M 104° 48′ 104° Haüy M on the adjacent plane, over the edge A 75° 12′ 76° Carbonate of Lead An octoheron, of which the common base of the pyramid is rectangular ${\displaystyle \left.{\begin{matrix}\ \\\ \end{matrix}}\right\}}$ Fig. 2. M on the opposed plane over the apex 70° 30′ 71° 40′ Haüy M on M 108° 20′ P on its opposed plane over the apex 62° 56′ 62° 42′ P on P 117° 18′ A rectangular tetrahedral prism with square bases. Bournon. Sulphate of Lead A rectangular octohedron. Haüy. ${\displaystyle \left.{\begin{matrix}\ \ \end{matrix}}\right\}}$ Fig.2 P' on P' P on P 72° 28′ 109° 18′ A right tetrahedral rhomboidal prism with rhombic bases. Bournon. ${\displaystyle \left.{\begin{matrix}\ \\\ \end{matrix}}\right\}}$ Fig. 11. P on P 101° 30′ P on the adjacent plane over the edge a 78° 30′ A right prism with rhombic bases. W.P. Fig. 13. P' on P' 76° 18′ P on the adjacent plane over the edge a 103° 42′
Oxide of Tine

Pl. 12. Fig. 1.

The crystals of this substance admit of cleavage parallel with all the sides of the common prism, and of its diagonals, as well as the faces of the primitive octohedron, which is obtuse. The first is more readily obtained than the second, but it is extremely difficult to effect it parallel with the primitive planes. Yet having sacrificed very many crystals in the pursuit of this object, I possess several fragments in each direction, having brilliant surfaces. The hardness, and at the same time, the brittleness of the substance were obstacles to the discovery of its natural joints, which it was difficult to find the means of overcoming; but, after resorting to various expedients, I found the employment of a pair of steel pincers the most certain mode of effecting it. Being sharp, with edges about an inch long, they seize on the square prism, equally throughout its whole length; and, if the edges be carefully placed along the center of the prism, or parallel thereto, it splits, by considerable pressure, shewing planes parallel to two of the four sides of the prism. By the same means, it may again be split at right angles. In the endeavour to obtain cleavages in the directions of the diagonals of the prism, I found it impossible to lay hold of the sharp edges lengthwise, because the edges of the instrument were also sharp; and therefore took of the pyramid as nearly at right angles with the prism as possible, producing a plane, parallel to which it was requisite to procure another at the other end of the prism: applying then the pincers to these parallel planes, and in the direction of the diagonal, the prism sometimes yielded in that direction. But the crystals of tin are most readily split according to their natural joints, by placing them for some time in a common fire or a smith's forge; a slight blow with a hammer afterwards reduces them into numerous small pieces, and amongst such, I have found fragments in all the directions above mentioned; indeed this was the only means I could devise for obtaining them parallel with the faces of the primitive octohedron. The subjecting of the crystals to the action of heat, has however some disadvantages: not only are the fragments less brilliant than such as are obtained by the pincers, but it appears that the tendency of heat to separate the natural joints has also the effect of cracking the crystal in other directions in which there, is no regular cleavage; so that, if the blow of the hammer be not gentle, the consequence commonly is that the crystal is reduced almost to powder.

Sulphate of Barytes.

Fig. 2.

In almost every flattish crystal of considerable dimension its natural joints are apparent when holding it between the eye and the light. If not, a slight blow will cause them to appear; and if by design or accident, the crystal fall flat upon the floor, it immediately breaks parallel with some of the planes of the primitive form and frequently even into the form itself, which is, a right prism with rhombic bases. It follows that a substance whose laminæ are held together by so slight a crystalline polarity, may be cleaved or split by various means; the same may be observed of the fluate and carbonate of lime, the crystals of which likewise generally present indications of their natural joints. But the most certain and least injurious mode of cleaving these substances is, by placing the crystal, if it be large, on a table; when, if the edge of a sharp and strait knife be placed in the direction of the natural joints, a slight blow with a hammer on the back of the knife readily separates the crystal along them. If on the contrary the crystal be small, the object is perhaps more easily attained by the assistance of a sharp penknife, while holding the crystal between the finger and thumb, more especially if it be very flat and thin; in which case, a slight blow with the hammer, even if the edge of the knife be precisely along the natural joints, is apt to have the effect of splitting it in various directions.

Quartz.

Fig. 5.

Since the time of presenting to the notice of the Geological Society, the memoir on the measurements of the angles of the primitive crystals of quartz and the sulphate of barytes, several other crystals of quartz with perfectly reflecting planes have corroborated the opinion therein stated, that the angles of the primitive rhomboid, which is slightly obtuse, are 94° 15′ & 85° 45′; which have also been further strengthened, and I may say confirmed to be their true value by co-incidences obtained by means of the reflecting goniometer from some fragments, exhibiting brilliant planes parallel with those of the rhomboid.

Crystals of quartz do not often present clear indications of their natural joints. By consulting Haüy, Traité Pl. XL. fig. 3. it will be observed that the primitive rhomboid is so situated in a dodecahedral crystal, that six of the twelve planes of the latter figure are alternately parallel with the primitive planes; the other six being the result of a modification explained by fig. 2 of the same plate. If therefore we would cleave a prismatic crystal of quartz, we are by the above circumstance assured, that by striking the prism diagonally and parallel with any plane of the upper or lower pyramid, it will be parallel with one or other of the planes of the primitive rhomboid, and, of course, in the direction of its natural joints. It will be well to attend to this observation, if if we would methodically seek to obtain the nucleus. By following this plan, I have occasionally succeeded by the assistance of the pincers, or by sharply striking a piece of steel long enough to extend across the surface, with its edge placed on the quartz in the direction of its laminæ. That neither of these plans often succeeds, and I know of none more effectual, is to be attributed to the great brittleness of the substance, which renders it liable, even when struck in the direction of its natural joints, to present fragments wholly irregular, or in various degrees approaching the conchoidal form. Quartz may however, though with still greater difficulty, be split in two or three directions which are not parallel with the planes of the primitive rhomboid.

Zircone.

Fig. 1.

Several substances, not essentially differing in composition or in their crystalline form, are by Haüy arranged under the general term zircone. Their primitive crystal is described in the Tableau Comparatif as an obtuse octahedron with square bases admitting of regular fracture parallel with sections passing through the apices, and through the centers of the edges D. D. The jargoon of Ceylon does not admit of being split with the same ease as the hyacinth of France, of which I have obtained and possess regular cleavages in the directions mentioned by Haüy, and also parallel with sections that would divide the octahedron into four parts by passing along all the edges of both pyramids.

The fractures in the direction of the primitive planes were most difficultly obtained, and though numerous, are not sufficiently brilliant for the use of the reflecting goniometer; that instrument therefore, in regard to this substance, has been used only to measure the angles by means of the reductions of the natural planes of the crystals; but as the hyacinth of France is always too much water-worn to present those well defined reflections which alone can be relied on, and which frequently occur on the smallest and most transparent crystals of the jargoon, I first depended on the latter, but have since been enabled by the examination of a large quantity of hyacinths, to find some crystals which, though dull, afford the same results.

These results differ from those obtained by Haüy, no less than one degree and a half, which caused me to measure over again the whole number of crystals, but without discovering any error. The incidence of P on P is given both in the Traité and Tableau Comparatif as 82° 50′, leaving of course the incidence, of P on the opposed plane over the summit 97° 10′, as the complement. But as the crystals of jargoon in my possession, rarely exhibit both pyramids, and never sufficiently brilliant to be relied on, I have been compelled to depend on measurements obtained on the plane P and the opposed plane over the apex. Clear reductions agree in five instances in affording 95° 40′, in two or three 95° 55′, and in one instance 95° 30′; while the only incidence of P on P is 84° 15′, being five minutes short of what I conceive to be the true value of the angle, viz. 84° 20′. Two fragments exhibiting planes parallel with the faces of the primitive octahedron, but not sufficiently bright for the use of the reflecting goniometer, afford by that in common use, an angle of about 95° 40′; two others of about 84° 20′.

I have now stated the reasons which induce me to assume the true measurement of P on P to be one degree and a half greater than that assigned to it by Haüy. However it must be allowed that, on taking into consideration the circumstances that all the brilliant crystals did not agree in yielding the same results, and of my being compelled for want of brilliant fractures, to depend on the natural planes, it is possible that the measurements on which I rely may not be absolutely correct.

Like most other hard and brittle substances, the hyacinth most readily yields to the pincers.

Stauratide.

Fig. 2.

In regard to this substance also I rely on the measurements obtained by means of the reflecting goniometer on the natural planes. The form of the primitive crystal is a right rhomboidal prism (fig. 2) of which the admeasurement of M on M is given by Haüy as 129° 30′. Two of the only three crystals that were submitted to that instrument agree in affording, each two measurements of that angle 129° 20′, and each also two of M on the adjacent plane over the edge A 50° 40′. The other affords one of 129° 20′; only two of its planes give clear reflections; which on the faces of the other two crystals were remarkably clean and well defined. These crystals are from St. Gothard.

Anatase.

Fig. 4.

The form of the primitive crystal of anatase is an elongated octahedron of which the common base is square. Of nine isolated crystals in my possession only two are sufficiently brilliant for the use of the rejecting goniometer; these agree in the incidence of P on P as 136° 47′, given by Haüy as 137° 10′. These crystals are very small, and as they differ from each other, and exhibit the planes of some modifications not hitherto described, I have not found courage to run the hazard of sacrificing them, incidental to the attempt to cleave them in the direction of their natural joints.

Specular Iron.

Fig. 3.

This substance, a variety of the fer oligiste of Haüy, may be split in the direction of its natural joints when held in the hand, by means of the pincers, care being taken to place their edges parallel with the primitive planes, which are generally observable on the edges of the crystals from Elba. In this manner I have procured six fragments, one of them the primitive rhomboid, which is slightly acute, nearly complete, and all of them having two or more planes sufficiently brilliant for the use of the reflecting goniometer, and all afford the measurements of 86° 10′ or 93° 50′, some of them both; the former being 59′ less, the latter 59′ more than the measurements obtained by Haüy on the natural planes by means of the common goniometer. The perfect agreements afforded by the fragments, have so far satisfied me that the results are the true value of the angles of the primitive rhomboid, that I have not attempted to measure its angles by means of the reflections to be observed on the natural planes, which are often very brilliant; for experience has confirmed me in the opinion that as the natural planes do not often yield results agreeing amongst themselves, they cannot be relied on with the same confidence as the planes obtained by cleaving crystals in the direction of their natural joints, which almost always agree; when they do not, the cause may always be discovered by the observer.

Diopside.

Fig. 6.

The crystals of this substance in my collection are not brilliant enough on the natural planes to give perfect rejections. On applying the pincers to one of them parallel with the planes of its prism, I found that it did not yield in that direction, but in that of its diagonals. The only three fragments submitted to the reflecting goniometer agree in affording the measurement of M on M, 87° 5′; being 3′' less than that obtained by Haüy on the natural planes. Two of these fragments also yield the complementary incidence of 92° 55′; being the angle of M on the adjacent plane over the edge A.

The diopside is considered by Haüy to be a variety of the pyroxene. In the attempt to cleave the latter substance, I have not been able to overcome the difficulties it presents. One crystal yielded to the equal pressure of the edges of the pincers, but did not present brilliant surfaces in more than one direction. It may therefore be true of the pyroxene as of many other minerals, that its cleavage is more difficult in one direction than another; but the circumstance just mentioned may perhaps in this instance be attributable to the heat which this crystal had the appearance of having undergone. Two others, of considerable external lustre, fell into powder under the pressure of the pincers. Two crystals presenting clear reflections on the natural planes, gave the incidence of M on M, one 86° 55′, the other 87° 5′. Two others, also brilliant, gave the value of M on the adjacent plane over the edge A, each 93°.

Cyanite.

Fig. 7.

On submitting some brilliant crystals to the reflecting goniometer, it became evident that no reliance could be placed on their natural planes. The form of the primitive crystal is an oblique prism. The incidence of M on T, given by Haüy as 106° 6′, varied very much; 106° 6′, 106° 10′, 106° 20′.

This substance is considerably hard and brittle; but in the attempt to cleave it in the direction of its natural joints, the same means did not succeed that usually does with other substances possessing those characters. The pincers always bruised the laminæ in separating them, which was fatal to precision. The most effectual means to avoid this, I found to be that of placing the crystal on a table, and supporting its under part in such a manner that the laminæ to be separated should be perfectly at right angles with the table. A sharp penknife then being placed in the desired direction, a smart blow with a light hammer usually produced the effect. Several fragments procured in this manner agreed in the incidence of M on T, 106° 15′, and that of T on M on the adjacent plane over the edge A 73° 45′; the former being 9′ more than the measurement obtained by Haüy from the natural planes by means of the goniometer in common use.

A regular fracture in the direction of the terminal planes of the primitive crystal is not so easily obtained as those parallel with the lateral planes. I obtained one considerably brilliant, but not sufficiently so for the use of the reflecting goniometer.

Corundum.

Fig. 3.

The form of the primitive crystal of corundum is a slightly acute rhomboid. From among the numerous fragments in my possession, two were selected, in the form of the primitive crystal, which, from the unusual splendour of some of their planes, gave reason for supposing they might be adapted to the use of the reflecting goniometer; one of these yielded the incidences of 86° 18′ and 93° 45′. The other one incidence of 94° 3′. These angles are given by Haüy 86° 38′ and 93° 22′, and by the Count de Bournon as 86° and 94°.[3]

In searching for the cause of so great difference in fragments of the same substance, it occurred to me that it arose from the nature of the substance itself, or rather from the peculiar aggregation of its laminæ. Though the corundum is one of the hardest substances in nature, it is well known that its laminæ may be separated without the application of any violent mechanical force, and in some specimens, even with ease. Hence it occurred to me that this must be the consequence of some foreign substance being interposed between the layers of the substance itself; and that, if this were the case, it could not be expected to give coinciding measurements, because of the doubt whether the interposed body could be disposed with perfect regularity. There seemed therefore no hope of attaining the desired object, unless the specimen could be reduced into laminæ so extremely thin that there should remain nothing but corundum. Finding that this was not to be expected from the common varieties, I sought, and fortunately found a small fragment, nearly colourless and transparent, and bearing at first sight as much the aspect of quartz as of corundum. From this, I succeeded in obtaining, among others, four very minute portions with brilliant and perfectly reflecting planes. These were procured by the assistance of the pincers; but it must be confessed that, as the directions of the natural joints were not at all visible, it was more by chance than regular design that they were obtained at all. Owing to the extreme hardness of the substance, I found it requisite, after placing the specimen in the pincers, to envelope it and them in a piece of cloth, to prevent the escape of the fragments; as the force which it is requisite to use would otherwise have caused them to fly in various directions. The same mode was for similar reasons pursued in regard to the oriental ruby and the sapphire: the latter may be cleaved with the utmost beauty and regularity in one direction; in the others it is difficult.

One of the fragments of corundum yields the measurements o£ 86° 4′ and 93° 56′; the other three, each 86° 4′. Two minute portions of the sapphire give each 86° 4′; another 93° 56′. One fragment of the oriental ruby yields 86° 4′. In the whole seven corresponding measurements of 86° 4′ and two of 98° 56′, which therefore I consider to be the true value of the angles of the primitive rhomboid.

Sulphate of Strontian.

Fig. 2.

The form of the primitive crystal of the sulphate of strontian is considered to be a right prism with rhombic bases. Its angles are, according to Haüy, 75°. 12′. and 104°. 48′. On submitting several crystals with perfectly rejecting planes to the goniometer, I found the measurements of the obtuse angle vary from 103°. 45′. to 104°. 17′, the greater part of them being 31′ less than that obtained by Haüy, as I presume also on the natural planes.

These disagreements induced me to attempt the splitting them parallel with the natural planes of the prism; for which purpose those from the neighbourhood of Bristol, being flat, nearly transparent, and almost always exhibiting the directions of their natural joints, seemed well adapted. But the result was not at first equal to the promise. For though they were readily split, the fragments first obtained yielded results agreeing scarcely better than those procured from the natural planes; the cause of which, not being then able to discover, I was compelled to forego the hope of determining the point by such means. On resuming these fragments sometime afterwards, their examination induced the suspicion, that the differences in their results under the reflecting goniometer, arose from the numerous crevices observable, when a fragment was held between the eye and the light, in almost all the flat crystals from the neighbourhood of Bristol; but which were no doubt increased in the fragments just alluded to by the manner of cleaving them; not having then discovered the best mode of effecting it. I determined therefore to reduce these fragments, until small portions with splendid surfaces should be obtained, nearly or wholly free from any crevice. And as the crystals are at once soft and very brittle, the utmost care was requisite. When laid on a table, with the edge of a sharp penknife placed in the direction of their natural joints, the pressure or slight blow requisite to divide the laminæ, injures the crystal by increasing the crevices. The only way in which I could succeed was by holding the specimen flat between the left forefinger and thumb, and applying without much force a sharp penknife to the thinner edge of the tabular crystal, pressing at the same time the nail of the right thumb in the opposite direction. But if the blade of the knife be not held perfectly level with the direction of the natural joints, it is apt to injure the brilliancy of the plane it produces. The terminations of the crystals being in general most tree from crevices, and most transparent, are therefore best adapted to the purpose I have been describing.[4]

Five very small fragments procured in this manner, yielded by the reflecting goniometer, co-incidences on the obtuse angle of 104°, and one of 76° on the acute angle of the prism; the one being 48 less, the other 48′ more than the measurements obtained by Haüy. A prismatic crystal from Sicily, having the primitive planes brilliant at one end, gave the incidence of 104°. and planes obtained by fracture at the other end, gave the same result.

The primitive crystal of the carbonate of lead is, according to Haüy, a rectangular octahedron, measuring one way over the summit of the same pyramid (P on the opposed plane) 70°. 30′; the other way (M on the opposed plane) 62°. 56′. The Count de Bournon however considers the primitive crystal to be a rectangular tetrahedral prism with square bases. This determination arose on his part from having cleaved in directions parallel with the planes of that solid, some crystals in the form of square laminæ, which are often extremely thin, and which always yielded in those directions. These crystals, he adds, are found in Derbyshire, in the Bannat, and in Siberia.[5]

From an amorphous specimen of this substance I succeeded in extracting a solid in the form of an octahedron almost entire, and having more or less of every plane brilliant enough for the use of the reflecting goniometer. The results of measurements taken in the same directions as those given by Haüy were, for the first 71°. 40′, being 1°. 10′ more; and for the second, 62°. 42′, being 14′ less; and not only did this fragment yield each of these measurements twice, but also the complementary numbers of 108°. 20′ (P on P) and 117° 18′. (M on M), each also twice. Several other fragments gave perfectly coinciding results.

This substance may be split with about equal ease by the assistance of a sharp knife, whether it be held in the hand or placed on a table; provided the blade of the knife be carefully placed in the direction of the laminæ, and the back gently struck by a light hammer. Instead of a table, however, I frequently place the crystals of such substances as may be best divided by a blow, on a slab of steel, polished on one side for the sake of a perfectly level surface, which is advantageous because the resistance given by steel is greater than that of wood. A lighter blow is therefore effectual, and hence there is less danger of cracking the crystal in directions opposed to its natural joints.

Fig. 9, 10, 11, 12, 13.

The form of the primitive crystal of this substance is considered by Haüy to be a rectangular octahedron (fig. 9.) the angle formed by the meeting of one plane of the upper pyramid, with the adjacent plane of the lower, being in one direction (P on P) 109° 18′ and in the other direction (P'on P') 78° 28′; and he says, “Cet octaédre se soudivise sur les arétes contigues”.

The Count de Bournon, for reasons given in his “Catalogue, &c.” (p. 357) considers the primitive crystal to be a right rhomboidal tetrahedral prism, with rhombic bases, of about 78° 30′ and 101° 30′ (fig. 11.) which are about the measurements of P on P, and P over the elongated edge of a crystal represented by fig. 10. He adds that the sulphate of lead is among those substances in which there is no trace of natural joints, no possibility of obtaining a cleavage.[6]

The crystals of the sulphate of lead, as well those from Anglesea as those from Cornwall, have so great a tendency to become prismatic by the lengthening of what Haüy considers to be an octahedron, and the Count de Bournon the primitive prism, that from among several hundred crystals in my possession, I have been able to select only one, having the appearance of an octahedron with pointed apices, and that this elongation always takes place in the same direction is manifest both from the uniform position of the secondary planes in relation to those which are elongated, and by the measurements afforded by numerous crystals; for although in the latter respect there is not a perfect coincidence, the results are sufficiently near to assure us of the fact.

The common base formed by the meeting of the two pyramids of the octahedron described by Haüy as the primitive crystal, (fig. 9.) though rectangular, is not square. The meeting of two adjacent planes on one pyramid, with their continuous planes on the other, will therefore be at different angles, as is the case also in respect of the primitive octahedron of the carbonate of lead. The angle formed by the meeting of P′ with P′ is according to Hairy 78° 28′, and that of P with P 109° 18′. Six or seven crystals submitted to the reflecting goniometer varied in P' on P from 76° 4′ to 76° 20′. Nine crystals affording 16 measurements of P with P varied from 101° 12′ to 101• 28′; and the same crystals gave 17 measurements of P on the opposed plane of the same pyramid, varying from 78° 35′ to 78° 48′. One elongated crystal similar to fig. 10, gave P′ on the opposed plane over the summit 103° 40′. All these crystals reflected with uncommon brilliancy. One of eight crystals, sufficiently bright to afford clear reflections on each of the four elongated planes P P (fig. 10.) and more nearly approaching to agreement than any of the others, gave on the two obtuse angles 101° 12′ and 101° 15′, and on the two acute 78° 40′ and 78° 43′. Another among them gave one incidence of 78° 35′, and another of 78° 48′ on the two acute angles.

I am induced to be thus particular, not only on account of the vast difference between the measurements given by Haüy and those obtained by means of the reflecting goniometer, but also because it is scarcely possible to find another in the whole range of mineral substances, which seems to unite more decidedly the characters of perfect crystallization and brilliant surface. It seemed therefore pre-eminently adapted to the use of the reflecting goniometer. The result however proves that the sulphate of lead is one among many minerals, on even the perfect reflections of whose natural planes no reliance can be placed without numerous coinciding results; if indeed it would be possible to obtain them at all.

In the endeavour to cleave this substance parallel with its natural joints, I was at first greatly foiled by its extreme brittleness, which without great care causes its fracture to assume the conchoidal form. The directions for finding the joints given by Haüy, are quoted in his own words; if I comprehend them they are not accurate, but they are not expressed with his usual perspicuity.

As the elongated planes present the largest surfaces, it was an inducement to attempt a cleavage parallel with them in the first instance, on the presumption of their being planes of the primitive octahedron; but after destroying a large number of crystals, I was still unsuccessful. In the direction of the lesser planes (P′ P′) and parallel with them, a cleavage is not only practicable, but may readily be obtained by the assistance of a sharp penknife, when the crystal is pressed on the fore finger beneath the thumb nail, which is the most effectual mode I have been able to find. The crystals are also divisible parallel with a section passing along the elongated summit and down the centers of the planes P′ P′ of a crystal formed like fig. 10. The search for natural joints in any other direction was fruitless.

If therefore we divide an elongated crystal (fig. 10.) in the direction of the dotted lines a b c d e and b c d, being parallel sections in the direction of its natural joints, we shall obtain a solid represented by fig. 12, which occurs in nature, and greatly resembles some crystals of the sulphate of barytes. If then this solid be cleaved parallel with the planes P′ P′, we shall obtain a nucleus similar in form to the dotted lines within it, and of course to fig. 13, which, though not in the same position, resembles in form, but not in measurement, the primitive crystal of the sulphate of barytes (fig. 2.); it is a right prism with rhombic terminations. Of these solids obtained from amorphous specimens of the sulphate of lead, I possess several, and am led to the conclusion that if we are to depend on the cleavage of minerals for a knowledge of the forms of their primitive crystals, this solid is that of the sulphate of lead.

In my collection there is an amorphous specimen from the Lead Hills, exhibiting natural joints parallel with all the planes of a right prism with rhombic terminations. It is covered on one of its larger sides by long and nearly flat crystals with diedral terminations, lying on the mass with the terminations parallel with the natural joints observable in it; and there is a still more perfectly characterized specimen in the collection of Mrs. Lowry.

On submitting to the reflecting goniometer several crystals cleaved parallel with the planes P′ P′, they all afforded the result of 76° 18′, coinciding therein with several fragments in the form of the primitive crystal fig. 13, which also gave 103° 42′ as the value of the obtuse angle. I am therefore induced to conclude that the primitive crystal of the sulphate of lead is a right prism with rhombic terminations, whose angles are 76° 18′ and 108° 42′.

1. Catalogue, p. xvii.
2. Pl. 12.
3. Phil. Trans. 1802.
4. Many other substances also possessing the characters of brittleness and softness at the same time, may be likewise split while held in the hand, with the greatest success. Other substances yield best to the same mode, for other reasons. Blende is one of these. It may be cleaved in so many directions, that if attempted to be split by means of a blow on the back of a knife whose edge is placed parallel with the natural joints, it is most probable that a fracture will ensue, which, though in the direction of the laminæ, is not in the desired direction. A specimen of no particular external form, but internally laminated with great regularity, and about an inch and a half square, and half an inch thick, lately yielded me, I believe, all the forms into which blende can be cleaved, and even duplicates of them. Haüy considers its primitive form to be s rhomboidal dodecahedron, its substractive crystal an obtuse rhomboid, and its integrand molecule au irregular tetrahedron. I obtained solids not only in these forms, but also others in the form of an octahedron of 90° over the summit, and of a plane of one pyramid on the adjacent plane of the other, and of 120° of one plane of either pyramid, on the adjacent plane of the same pyramid; I procured also others in the form of an acute rhomboid of 60° and 120° These measurements were obtained by means of the reflecting goniometer, which also gave there of the obtuse rhomboid 60° and 120°, which by Haüy, are said to be 70°, 31′. 44″ and 109°. 28′. 16″. Hence blende may be split into five different solids.
5. Catalogue, p. 389.
6. From the circumstance of the Count de Bournon having attributed to the angles of what he conceives to be the primitive prism, measurements nearly approximating to theme of P on P, and of P on the opposed plane over the elongated edge of a crystal similar to fig. 10, which is common to this substance, it may be assumed that he considers such a crystal to be a rhomboidal prism with diedral terminations. It will appear that I agree with the Count de Bournon in assuming the right rhomboidal prism with rhombic terminations as the primitive form; but differ from him in the manner in which that form lies (if it may so be said) in a crystal represented by fig. 10. He conceives the planes P P, to be primitive: I am on the contrary induced to suppose the planes P′ P′ to be primitive planes; we consequently differ in the angles of the prism.