# Transactions of the Geological Society, 1st series, vol. 4/On the Angles of the Primitive Crystals of Quartz, and the Sulphate of Barytes

By WILLIAM PHILLIPS, Esq.
member of the geological society.
The primitive crystal of quartz is considered to be an obtuse rhomboid, of which the angles are given by Haüy in his “Tableau comparatif,” &c. as being 94° 24′ and 85° S6′: that of the sulphate of barytes is a quadrangular prism with rhombic terminations, the angles of which according to the same authority are 101° 32′ 13″ and 78° 27′ 47″. The results of some attempts to verify these admeasurements by subjecting the natural planes of the crystals of both these substances, as well as some regular fragments of the latter, to the reflecting goniometer, form the particular object of the present communication.
The first attempts to ascertain by this means the angles of the rhomboid of quartz, were made upon some minute primitive crystals from Bristol: seven of these gave incidences on the one angle varying from 94° 12′ to 94° 17′, and on the other from 85° 44′ to 85° 52′; not more than two or three agreed. But the reflections ​afforded by these crystals were not perfectly clear, probably owing to their enclosing a multitude of very minute diverging fibres, perhaps of the oxide of iron. Numerous attempts were afterwards made upon some crystals obtained under the name of Bornholm diamonds; many of which exhibit, on the primitive crystal, the planes of the modifications producing the pyramids and the prism, not in a very advanced state; the measurements they afforded were much the same as, and by no means more regular than, those obtained from the primitive crystals from Bristol.
I next carefully examined about 300 very small, brilliant, and colourless crystals of which I became possessed under the name of Gibraltar diamonds, and selected a large number presenting the I most perfect reflections. These crystals generally shew both pyramids, separated by a very short intervening prism. But even those that were found to reflect the best, did not all present similar results.
Several of these however afforded perfect co-incidences of 94°. 15′ on the one angle, and 85°. 45′ on the other. Two of the seven crystals from Bristol, and two or three from Cornwall, with brilliant reductions, gave exactly the same admeasurements: and since these are the only incidences that were found to agree, I am induced to suppose that they approach, if not actually constitute, the true value of the angles of the primitive rhomboid of quartz. It will be observed that the former of these differs from that given by Haüy, in being 9′ less; the latter, in being 9′ more. It seems requisite to add, that among the very numerous crystals that I have attempted to measure by means of the reflecting goniometer, not one has afforded results agreeing with Haüy.
From among several hundreds of detached crystals of the sulphate of barytes, eight were selected, which afforded reductions ​so perfect, that the expectation of actual agreement in the admeasurement to be obtained from them, naturally arose; but in this I was disappointed on finding them to vary on the one angle from 101°. 25′ to 101°. 51′; and on the other, from 78°. 10′ to 78°. 28′.
This want of co-incidence in the admeasurements obtained from crystals which, on account of their brilliancy, seemed unexceptionable, induced me to submit to the reflecting goniometer some cleavages made in the direction of the primitive planes, and selected with the utmost care. Six of these agreed perfectly in affording on each of the acute angles of each fragment the incidence of 70°. 18′, and on each of the obtuse angles that of 101°. 42′; the former being 9′. 47″ less, and the latter, in being 9′. 47″ more, than the value assigned to these angles by Haüy.
This remarkable agreement afforded by the cleavages of the sulphate of barytes, induces regret that it is not in like manner practicable to obtain regular fractures of quartz. The evidence above cited in regard to the difficulties attending the measurement of that substance, by means of the reflections afforded by the natural planes of its crystals, tend, it must be owned, to render it somewhat uncertain whether the only co-incidences obtained, viz. those 94°. 15′ 85°. 45′, are the true angles of its primitive rhomboid; but the co-incidences given by the fracture of the sulphate of barytes, seem to authorize the conclusion that the true value of the angles of its primitive crystals are 78°. 18′ and 101°. 42′.
It would not perhaps be reasonable to draw, from evidence relating only to two substances, the inference that the actual value of the angles of mineral substances in the general cannot by any means be obtained by admeasurements attempted upon the natural planes of their crystals. The difficulties attendant on many of them will be found to be very great; in regard to some they seem insurmountable. ​Of a very large number of crystals of the red oxide of copper in my possession, some hundreds of which were selected on account of their extraordinary brilliancy, solely with the view of subjecting them to the reflecting goniometer, I have not been able to find a single crystal of which the primitive planes are adapted to its use.
The attempt to measure the angles formed by the meeting of the primitive planes of the red oxide of copper, may reasonably be supposed to have been made only for the sake of corroborating the results of calculation. These results cannot perhaps be doubted, when it is considered that the primitive crystal of this substance is the regular octahedron, which is often found to pass into the cube; for the angles of the one being known with certainty, it follows that those of the other may be calculated with precision. This observation will apply to all those substances which have for their primitive crystals, either of those solids, or the rhomboidal dodecahedron, the regular tetrahedron, or the hexahedral prism.
But there are many forms of primitive crystals, included under the term parallelepiped (amongst which are those of quartz and the sulphate of barytes,) as well as several varieties of the octahedron, both acute and obtuse, which do not, with the same case, seem susceptible of equal certainty in the determination of the value of their angles. I am induced to believe that many, if not most, of these, which have already been given by Haüy, will be found to demand revision.
As it may be expected that reasonable cause should be shewn for doubting authority so eminent, I shall briefly subjoin the reasons that have principally led me to adopt this opinion.
The first step towards ascertaining the value of the several angles at which the numerous planes of crystals meet each other, is altogether ​a mechanical operation dependent on the skilful use of the goniometer; and for this purpose doubtless brilliant and well defined crystals have been selected. Having arrived at the admeasurement of some one prominent angle, by means of the goniometer in common use, it can scarcely be doubted that its value has been assumed as a basis on which to calculate the rest. This, there is reason to believe, was the process adopted by Haüy in regard to his determination of the angles of the primitive crystal of the sulphate of barytes, which he has given to seconds, and which the common goniometer will not indicate. It must be obvious that the perfect fidelity of this preliminary mechanical determination is most essential.
It is no trivial argument against the accuracy of this practice, that those who are the most skilful in the use of the common goniometer, have differed in the results obtained from the same substances. But, even were it possible to depend upon the accuracy of the instrument, and upon the skill of the hand using it, there seems much reason for doubting whether the planes of such crystals as are best adapted to its use can be relied on. I allude of course to such as are of considerable dimension. These, when submitted to the reflecting goniometer, rarely agree with each other; and the measurements they afford almost always differ very considerably from those obtained upon small crystals; which much more frequently give similar results, but which are too minute, as it seems to me, for the accurate use of the common goniometer.
The difficulties already described as having attended my numerous attempts to verify the admeasurements of Haüy. in regard to the primitive crystals of quartz and the sulphate of barytes, belong not to the crystals of these two substances only. I have found these difficulties to exist in different degrees in respect to more than ​twenty others, of each of which I possess very numerous isolated crystals. Amongst these, the red oxide of copper already mentioned is one, though of comparatively little importance; because, as the real value of the angles of the cube, which it occasionally assumes, are known, the rest may be calculated with precision.
But there is still another circumstance which forcibly shews the great difficulties attending the accurate admeasurement of the angles formed by the meeting of the natural surfaces of crystals, by subjecting those surfaces to either goniometer. It is not often found that the best selected afford incidences corresponding with the results obtained by calculation, even where we must be assured that calculation may be relied on; as is the case in respect of all those substances which assume the cube, the regular octahedron, the rhomboidal dodecahedron, or the hexahedral prism. The angles formed by the meeting of the planes of these solids are known, yet rarely do the best selected crystals accurately afford the admeasurements which belong to them in their perfect state. It is not sufficient that they approximate; they should be precise.
The foregoing are my principal reasons for adopting the belief that many of the determinations of Haüy in regard to the admeasurements given by him of the primitive crystals comprehended in the term parallelepiped, and of the numerous varieties of the octahedron, will be found inaccurate. It is probable that the reflecting goniometer will render service to science by detecting some of the inaccuracies incident to the use of the common goniometer.
The accuracy of which the reflecting goniometer is capable, requires, for the reasons above assigned, great patience and perseverance in measuring the angles of crystals on their natural planes; and the chief, if not the only, difficulty attending its use, ​is the finding of crystals that are adapted to it. It is requisite not only that their planes should be brilliant, but also that the image of the line or bar reflected upon them should be perfectly defined; its, edges should be seen with an exactness which they who have not given attention to the subject will scarcely believe to exist on surfaces so small. No reliance can be placed upon a solitary admeasurement taken upon the natural planes of one crystal, however brilliant and perfect they may appear; it is essential that several should be found to exhibit a perfect agreement, before it can be assumed that the actual value of any angle has been obtained. From one crystal of quartz, nearly perfect at both terminations and affording pretty clear reductions, I obtained six admeasurements of the same angle from its various planes. One of 94° 9′, another of 94° 12′, a third of 94° 16′, and three of 94° 11′. I did not discover one crystal whose planes were sufficiently perfect to enable me to obtain corresponding measurements from plane to plane, around it.
It cannot however, be doubted, that much of the labour attendant on the use of the reflecting goniometer in the measuring of the angles of crystals on their natural planes, will be spared, and that the results will be much more satisfactory, because more accurate, whenever cleavages can be obtained sufficiently brilliant for its use. In almost every instance in which I have tried it upon the planes produced by good fractures, the success has been complete. The great value of this instrument, which may be used with readiness and case, demands the attention of every one who has the slightest pretension to crystallographical research. I feel much pleasure in adding an instance of the accuracy of which it is susceptible. Having seen in some periodical publication, a notice that Dr. Wollaston had discovered differences in the value of the angles of the primitive ​rhomboids of the carbonate of lime, the bitter-spar, and the brown-spar, which had previously been considered to be alike, and conceiving them to be erroneously quoted, as in fact they were, I submitted to the reflecting goniometer some cleavages of the two former, not having a portion of the latter adapted to its use. I afterwards called on my friend Arthur Aikin, Esq. who shewed me an account of the exact admeasurements obtained by Dr. Wollaston, and had the satisfaction of convincing him that those obtained by me perfectly coincided therewith.
I possess thirty-eight varieties of crystals of quartz, resulting from the combinations of eleven modifications on the primitive rhomboid; and of the sulphate of barytes I have one hundred and thirteen varieties, the result of eighteen modifications of the primitive crystal; the former are principally foreign, the latter chiefly from the north of England.