^{page 317 note *} My first experiments on Apophyllite are published in the Edinburgh Philosophical Journal, vol. i. p. 1.

^{page 318 note *} Haüy makes this angle 117° 48ʹ.

^{page 318 note †} Ichthyoplithalmite, or Fish-Eye Stone. These pearly tints occur only in one variety of the Tesselite.

^{page 319 note *} More recent observations have proved this to be the case, as will be seen in a subsequent part of this paper.

^{page 320 note *} See Edinburgh Philosophical Journal, vol. i. p. 5.

^{page 320 note †} In an ingenious memoir, ‘On certain remarkable instances of deviation from ‘Newton's scale, in the tints developed by crystals with one axis of double refrac-‘tion, on exposure to polarised light,’ published in the Transactions of the Cambridge Philosophical Society, vol. i.; and reprinted in the Edinburgh Philosophical Journal, vol. iv. p. 334; and vol. v. p. 334, Mr Herschel has, I think, misconceived the full import of this experiment. ‘This alternation,’ says he, ‘or superposition of laminæ of different polarising powers, is no hypothetical case. I have observed its occurrence not only in the instance before us, but in other crystals of perfect regularity in their external forms. Dr Brewster has also observed phenomena referable to this principle in his paper on the Apophyllite.’ Upon reexamining the passage in my paper, Mr Herschel will, I am sure, agree with me in thinking, that the phenomena which I observed are not merely referable to that principle, but are a complete demonstration of it, and distinctly prove, that in several crystals there were as many ‘laminæ of different polarising ‘powers,’ as there were ‘successions of coloured bands at the same thick-‘ness.’ The crystals, indeed, of the specimen which I employed, were the upper portions of those represented in Plate XXI. Fig. 1. The bending and inequalities of the fringes, too, which I have described, and represented in Fig. 7. of my former paper, establish in the clearest manner the alternation, as well as the existence, of different polarising powers in the planes parallel to the faces of the pyramid.

^{page 322 note *} See Edinburgh Philosophical Journal, vol. i. p. 4., and Plate I. Fig. 7.

^{page 325 note *} In comparing the polarising forces of different crystals of this variety of Apophyllite, I have been surprised to observe the great diversity which exists among them; some of the prisms, which are only th of an inch, thick, having a greater polarising force than others which are th of an inch thick.

^{page 325 note †} In some crystals the two smaller green segments have a different tint from the two larger segments, and the same tint as the central square.

^{page 325 note ‡} Owing to the feeble polarising power of the apophyllite, these superficial irregularities produce a less degree of derangement in the tints than might have been expected.

^{page 328 note *} See this Volume, p. 270.

^{page 328 note †} There are many examples of Apophyllite having been deposited upon groups of Needlestone; but in these cases, the crystal is not penetrated by them, but merely rests upon their filaments.

^{page 329 note *} The mechanical structure of the cleavage planes resembles the optical figure even after the planes are ground.

^{page 329 note †} Published in their Transactions, vol. i.; and in the Edinburgh Philosophical Journal, vol. iv. p. 334.; and vol. v. p. 334.

^{page 330 note *} Proceedings of the Cambridge Philosophical Society, in the Edinburgh Philosophical Journal, vol. v. p. 213.

^{page 331 note *} I must refer the reader to my paper ‘On the Laws of Polarisation and Double Refraction,’ in the Phil. Trans. Lond. for 1818, p. 231, and p. 245,—254. for the grounds upon which this resolution of axes is made. In the case of Apophyllite, there are reasons of a peculiar kind for supposing the existence of three axes.

^{page 332 note *} For an illustration of these views, the reader is referred to my letter to Mr Herschel, published at the end of his paper in the Phil. Trans. 1820, p. 94.; and to Mr Herschel's paper in the Transactions of the Cambridge Philosophical Society, vol. i.; or in the Edin. Phil. Journal, vol. iv. p. 335.; and vol. v. p. 340.

^{page 332 note †} This partial equilibrium of polarising forces is analogous to the paradoxical phenomena of a compound lens, which, as I have elsewhere shewn, may be constructed so as to converge the Blue rays, diverge the Red rays, and exercise no action at all upon the Yellow ones. That is, the same compound lens is a Plane lens in yellow light, a convex one in blue light, and a concave one in red light.

^{page 333 note *} Among the various residual spectra which I have examined in the course of my experiments ‘on the Action of Transparent Bodies upon, the differently coloured Rays of Light,’ there are, many among the polarised rings which have exactly the same tint; and there are some, which, resemble as nearly as possible those in Apophyllite. See Edinburgh Transactions, vol. viii. p. 1.

^{page 333 note †} The preceding explanation may be presented in, a more brief form, by stating that the specimen of Apophyllite in question had three positive rectangular axes, which were in equilibrium only for the yellow rays of the spectrum. See Phil. Trans. 1818, p. 256.