When it appeared that the angle of natural or of cleavage faces could be used to determine the differences of minerals, it became important to measure this angle with accuracy. Haüy’s measurements were found very inaccurate by many succeeding crystallographers: Mohs says[26] that they are so generally inaccurate, that no confidence can be placed in them. This was said, of course, according to the more rigorous notions of accuracy to which the establishment of Haüy’s system led. Among the persons who principally labored in ascertaining, with precision, the crystalline angles of minerals, were several Englishmen, especially Wollaston, Phillips, and Brooke. Wollaston, by the invention of his Reflecting Goniometer, placed an entirely new degree of accuracy within the reach of the crystallographer; the angle of two faces being, in this instrument, measured by means of the reflected images of bright objects seen in them, so that the measure is the more accurate the more minute the faces are. In the use of this instrument, no one was more laborious and successful than William Phillips, whose power of apprehending the most complex forms with steadiness and clearness, led Wollaston to say that he had “a geometrical sense.” Phillips published a Treatise on Mineralogy, containing a great collection of such determinations; and Mr. Brooke, a crystallographer of the same exact and careful school, has also published several works of the same kind. The precise measurement of crystalline angles must be the familiar employment of all who study crystallography; and, therefore, any further enumeration of those [326] who have added in this way to the stock of knowledge, would be superfluous.
[26] Marx. p. 153.
Nor need I dwell long on those who added to the knowledge which Haüy left, of derived forms. The most remarkable work of this kind was that of Count Bournon, who published a work on a single mineral (calcspar) in three quarto volumes.[27] He has here given representations of seven hundred forms of crystals, of which, however, only fifty-six are essentially different. From this example the reader may judge what a length of time, and what a number of observers and calculators, were requisite to exhaust the subject.
[27] Traité complet de la Chaux Carbonatée et d’Aragonite, par M. le Comte de Bournon. London, 1808.
If the calculations, thus occasioned, had been conducted upon the basis of Haüy’s system, without any further generalization, they would have belonged to that process, the natural sequel of inductive discoveries, which we call deduction; and would have needed only a very brief notice here. But some additional steps were made in the upward road to scientific truth, and of these we must now give an account.
CHAPTER IV.
Establishment of the Distinction of Systems of Crystallization.—Weiss and Mohs.
IN Haüy’s views, as generally happens in new systems, however true, there was involved something that was arbitrary, something that was false or doubtful, something that was unnecessarily limited. The principal points of this kind were;—his having made the laws of crystalline derivation depend so much upon cleavage;—his having assumed an atomic constitution of bodies as an essential part of his system; and his having taken a set of primary forms, which, being selected by no general view, were partly superfluous, and partly defective.
How far evidence, such as has been referred to by various philosophers, has proved, or can prove, that bodies are constituted of indivisible atoms, will be more fully examined in the work which treats of the Philosophy of this subject. There can be little doubt that the [327] portion of Haüy’s doctrine which most riveted popular attention and applause, was his dissection of crystals, in a manner which was supposed to lead actually to their ultimate material elements. Yet it is clear, that since the solids given by cleavage are, in many cases, such as cannot make up a solid space, the primary conception of a necessary geometrical identity between the results of division and the elements of composition, which is the sole foundation of the supposition that crystallography points out the actual elements, disappears on being scrutinized: and when Haüy, pressed by this difficulty, as in the case of fluor-spar, put his integrant octohedral molecules together, touching by the edges only, his method became an empty geometrical diagram, with no physical meaning.
The real fact, divested of the hypothesis which was contained in the fiction of decrements, was, that when the relation of the derivative to the primary faces is expressed by means of numerical indices, these numbers are integers, and generally very small ones; and this was the form which the law gradually assumed, as the method of derivation was made more general and simple by Weiss and others.