Nothing is more remarkable than the great variety of geometrical shapes which the crystals of the same substance, derived from different localities or produced under different conditions, are observed to display. One of the commonest of minerals, calcite, carbonate of lime, shows this feature admirably; the beautiful large rhombohedra from Iceland, illustrated in Fig. 5, or the hexagonal prisms capped by low rhombohedra from the Bigrigg mine at Egremont in Cumberland, shown in Fig. 6, appear totally different from the “dog-tooth spar” so plentifully found all over the world, a specimen of which from the same mine is illustrated in Fig. 7. No mineral specimens could well appear more dissimilar than these represented on Plate III. in Figs. 6 and 7, when seen side by side in the mineral gallery of the British Museum (Natural History) at South Kensington. But all are composed of similar chemical molecules of calcium carbonate, CaCO₃; and when the three kinds of crystals are investigated they are found to be identical in their crystalline system, the trigonal, and indeed further as to the subdivision or class of that system, which has come to be called the calcite class from the importance of this mineral.

Moreover, many of the same faces, that is, faces having the same relation to the symmetry, are present on all three varieties, the “forms” to which they equally belong being the common heritage of calcite wherever found. A “form” is the technical term for a set of faces having an equal value with respect to the symmetry. Thus the prismatic form in Fig. 6 is the hexagonal prism, a form which is common to the hexagonal and trigonal systems of symmetry, and the form “indices” (numbers^[1] inversely proportional to the intercepts cut off from the crystal axes by the face typifying the form) of which are {2̄1̄1}; the large development of this form confers the elongated prismatic habit on the crystal. The terminations are faces of the flat rhombohedron {110}. The pyramidal form of the dog-tooth spar shown in Fig. 7 is the scalenohedron {20̄1}, and it is this form which confers the tooth-like habit, so different from the hexagonal prism, upon this variety of calcite. But many specimens of dog-tooth spar, notably those from Derbyshire, consist of scalenohedra the middle portion of which is replaced by faces of the hexagonal prism {2̄1̄1}, and the terminations of which are replaced by the characteristic rhombohedron {100} of Iceland spar; indeed, it is quite common to find crystals of calcite exhibiting on the same individual all the forms which have been mentioned, that is, those dominating the three very differently appearing types. The author has quite recently measured such a crystal, which, besides showing all these four forms well developed, also exhibited the faces of two others of the well-known forms of calcite, {3̄1̄1} and {310}, and a reproduction of a drawing of it to scale is given in Fig. 8. Instead of indices the faces of each form bear a distinctive letter; m = {2̄1̄1}, r = {100}, e = {110}, v = {20̄1} (the faces of the scalenohedron are of somewhat small dimensions on this crystal), n = {3̄1̄1}, and t = {310}.

It is obviously then the “habit” which is different in the three types of calcite—Iceland spar, prismatic calc-spar, and dog-tooth spar—doubtless owing to the different local circumstances of growth of the mineral. Habit is simply the expression of the fact that a specific “form,” or possibly two particular forms, is or are much more prominently developed in one variety than in another. Thus the principal rhombohedron r = {100}, parallel to the faces of which calcite cleaves so readily, is the predominating form in Iceland spar, while the scalenohedron v = {20̄1} is the habit-conferring form in dog-tooth spar. Yet on the latter the rhombohedral faces are frequently developed, blunting the sharp terminations of the scalenohedra, especially in dog-tooth spar from Derbyshire or the Hartz mountains; and on the former minute faces of the scalenohedron are often found, provided the rhombohedron consists of the natural exterior faces of the crystal and not of cleavage faces. In the same manner the prismatic crystals from Egremont are characterised by two forms, the hexagonal prism m = {2̄1̄1} and the secondary rhombohedron e = {110}, but both of these forms, as we have seen on the actual crystal represented in Fig. 8, are also found developed on other crystals of mixed habit.

This illustration from the naturally occurring minerals might readily be supplemented by almost any common artificial chemical preparation, sulphate of potash for instance, K₂SO₄, the orthorhombic crystals of which take the form of elongated prisms, even needles, on the one hand, or of tabular plate-like crystals on the other hand, according as the salt crystallises by the cooling of a supersaturated solution, or by the slow evaporation of a solution which at first is not quite saturated. In both cases, and in all such cases, whether of minerals or chemical preparations, the same planes are present on the crystals of the same substance, although all may not be developed on the same individual except in a few cases of crystals particularly rich in faces; and these same planes are inclined at the same angles. But their relative development may be so very unlike on different crystals as to confer habits so very dissimilar that the fact of the identity of the substance is entirely concealed.

A further example may perhaps be given, that of a substance, hydrated sulphate of lime, CaSO₄.2H₂O, which occurs in nature as the beautiful transparent mineral gypsum or selenite—illustrated in Fig. 9, and which is found in monoclinic crystals often of very large size—and which may also be chemically prepared by adding a dilute solution of sulphuric acid to a very dilute solution of calcium chloride. The radiating groups of needles shown in Fig. 10 (Plate II.) slowly crystallise out when a drop of the mixed solution is placed on a microscope slip and examined under the microscope, using the one-inch objective. These needles, so absolutely different in appearance from a crystal of selenite, are yet similar monoclinic prisms, but in which the prismatic form is enormously elongated compared with the other (terminating) form.

This difference of facial development, rendering the crystals of one and the same substance from different sources so very unlike each other, was apparently responsible for the very tardy discovery of the fundamental law of crystallography, the constancy of the crystal angles of the same substance. Gessner, sometime between the years 1560 and 1568, went so far as to assert that not only are different crystals of the same substance of different sizes, but that also the mutual inclinations of their faces and their whole external form are dissimilar.

What was much more obvious to the early students of crystals, and which is, in fact, the most striking thing about a crystal after its regular geometric exterior shape, was the obviously homogeneous character of its internal structure. So many crystals are transparent, and so clear and limpid, that it was evident to the earliest observers that they were at least as homogeneous throughout as glass, and yet that at the same time they must be endowed with an internal structure the nature of which is the cause of both the exterior geometric regularity of form, so different from the irregular shape of a lump of glass, and of the peculiar effect on the rays of light which are transmitted through them. From the earliest ages of former civilisations the behaviour of crystals with regard to light has been known to be different for the different varieties of gem-stones.

About the year 1600 Cæsalpinus observed that sugar, saltpetre, and alum, and also the sulphates of copper, zinc and iron, known then as blue, white and green vitriol respectively, separate from their solutions in characteristic forms. Had he not attributed this to the operation of an organic force, in conformity with the curious opinion of the times concerning crystals, he might have had the credit of being the pioneer of crystallographers. The first two real steps in crystallography, however, with which in our own historic times we are acquainted, were taken in the seventeenth century within four years of each other, one from the interior structural and the other from the exterior geometrical point of view. For in 1665 Robert Hooke in this country made a study of alum, which he appears to have obtained in good crystals, although he was unacquainted with its true chemical composition. He describes in his “Micrographia” how he was able to imitate the varying habits of the octahedral forms of alum crystals by building piles of spherical musket bullets, and states that all the various figures which he observed in the many crystals which he examined could be produced from two or three arrangements of globular particles. It is clear that the homogeneous partitioning of space in a crystal structure by similar particles building up the crystal substance was in Hooke’s mind, affording another testimony to the remarkably prescient insight of our great countryman.

Four years later, in 1669, Nicolaus Steno carried out in Florence some remarkable measurements, considering the absence of proper instruments, of the angles between the corresponding faces of different specimens of rock-crystal (quartz, the naturally occurring dioxide of silicon, concerning which there will be much to say later in this book), obtained from different localities, and published a dissertation announcing that he found these analogous angles all precisely the same.

In the year 1688 the subject was taken up systematically by Guglielmini, and in two memoirs of this date and 1705 he extended Steno’s conclusions as to the constancy of crystal angles in the case of rock-crystal into a general law of nature. Moreover, he began to speculate about the interior structure of crystals, and, like Hooke, he took alum as his text, and suggested that the ultimate particles possessed plane faces, and were, in short, miniature crystals. He further announced the constancy of the cleavage directions, so that to Guglielmini must be awarded the credit for having, at a time when experimental methods of crystallographic investigation were practically nil, discovered the fundamental principles of crystallography.

The fact that a perfect cleavage is exhibited by calcite had already been observed by Erasmus Bartolinus in 1670, and in his “Experimenta Crystalli Islandici” he gives a most interesting account of the great discovery of immense clear crystals of calcite which had just been made at Eskifjördhr in Iceland, minutely describing both their cleavage and their strong double refraction. Huyghens in 1690 followed this up by investigating some of these crystals of calcite still more closely, and elaborated his laws of double refraction as the result of his studies.

There now followed a century which was scarcely productive of any further advance at all in our real knowledge of crystals. It is true that Boyle in 1691 showed that the rapidity with which a solution cools influences the habit of the crystals which are deposited from it. But neither Boyle, with all his well-known ability, so strikingly displayed in his work on the connection between the volume of a gas and the pressure to which it is subjected, nor his lesser contemporaries Lemery and Homberg, who produced and studied the crystals of several series of salts of the same base with different acids, appreciated the truth of the great fact discovered by Guglielmini, that the same substance always possesses the same crystalline form the angles of which are constant. Even with the growth of chemistry in the eighteenth century, the opinion remained quite general that the crystals of the same substance differ in the magnitude of their angles as well as in the size of their faces.

We begin to perceive signs of progress again in the year 1767, when Westfeld made the interesting suggestion that calcite is built up of rhombohedral particles, the miniature faces of which correspond to the cleavage directions. This was followed in 1780 by a treatise “De formis crystallorum” by Bergmann and Gahn of Upsala, in which Guglielmini’s law of the constancy of the cleavage directions was reasserted as a general one, and intimately connected with the crystal structure. It was in this year 1780 that the contact goniometer was invented by Carangeot, assistant to Romé de l’Isle in Paris, and it at once placed at the disposal of his master a weapon of research far superior to any possessed by previous observers.

In his “Crystallographie,” published in Paris in 1783, Romé de l’Isle described a very large number of naturally occurring mineral crystals, and after measuring their angles with Carangeot’s goniometer he constructed models of no less than 500 different forms. Here we have work based upon sound measurement, and consequently of an altogether different and higher value than that which had gone before. It was the knowledge that his master desired to faithfully reproduce the small natural crystals which he was investigating, on the larger scale of a model, that led Carangeot to invent the contact goniometer, and thus to make the first start in the great subject of goniometry. The principle of the contact goniometer remains to-day practically as Carangeot left it, and although replaced for refined work by the reflecting goniometer, it is still useful when large mineral crystals have to be dealt with. An illustration of a duplicate of the original instrument is shown in Fig. 11, by the kindness of Dr H. A. Miers. This duplicate was presented to Prof. Buckland by the Duke of Buckingham in the year 1824, and is now in the Oxford Museum.

From the time that measurement of an accurate description was possible by means of the contact goniometer, progress in crystallography became rapid. Romé de l’Isle laid down the sound principle, as the result of the angular measurements and the comparison of his accurate models with one another, that the various crystal shapes developed by the same substance, artificial or natural, were all intimately related, and derivable from a primitive form, characteristic of the substance. He considered that the great variety of form was due to the development of secondary faces, other than those of the primitive form. He thus connected together the work of previous observers, consolidated the principles laid down by Guglielmini by measurements of real value, and threw out the additional suggestion of a fundamental or primitive form.

About the same time Werner was studying the principal forms of different crystals of the same substance. The idea of a fundamental form appears to have struck him also, and he showed how such a fundamental form may be modified by truncating, bevelling, and replacing its faces by other derived forms. His work, however, cannot possess the value of that of Romé de l’Isle, as it was not based on exact measurement, and most of all because Werner appears to have again admitted the fallacy that the same substance could, in the ordinary way, and not in the sense now termed polymorphism, exhibit several different fundamental forms.

But a master mind was at hand destined definitely to remove these doubts and to place the new science on a firm basis. An account of how this was achieved is well worthy of a separate chapter.