Chapter Viii., and of Others Which Are Still Less Intimately Connected.

Unfortunately, the equivalence parameters do not make clear the relationships in an isomorphous series, as do the molecular distance ratios; for they are, from their very nature and mode of derivation, almost identical for all the members of an isomorphous series, the valencies of the interchangeable elements being the same. The molecular distance ratios have also the great advantage of being derived from the three measurements which have now been brought to the highest pitch of experimental accuracy, namely, atomic weight determinations, density determinations by the Retgers immersion method, and goniometrical and physical measurements (optical and thermal) with instruments now available of the utmost refinement. Structural constants thus derived are obviously of especial value. It would thus appear that the theory requires modification so as to take account of the experimentally proved regular increase in volume and in the directional dimensions of the structural unit cell of the crystal space-lattice, when one element of the same family group and of the same valency is interchanged for another. Indeed, as the theory stands at present it entirely ignores and fails to offer any explanation of the highly important physical property of density, specific gravity. That this physical constant, and the equally important constant molecular volume, derived by dividing the molecular weight by the density, possess a real and significant meaning in isomorphous series, formed by the interchange of elements of the same family group, has been clearly proved in Chapter X. This fact is, indeed, so obvious that any further development of the theory must of necessity take account of it.

A precise statement of their conception has recently been made by Prof. Pope in an excellent Report on the Progress of Crystallography, issued by the Chemical Society early in the year 1909. He states that they (Pope and Barlow) “regard the whole of the volume occupied by a crystalline structure as partitioned out into polyhedra, which lie packed together in such a manner as to fill the whole of that volume without interstices. The polyhedra can be so selected that each represents the habitat of one component atom of the material, and are termed the spheres of atomic influence of the constituent atoms. Up to this point no assumption is made other than that clearly indicated by the result of crystallographic measurements, namely, that each atom present in a crystalline structure exerts a distinct morphological effect—or, what is the same thing, appropriates a certain definite volume. The assumption is next made that the crystalline structure, which is resolvable into individual molecules and ultimately into individual atoms, exists as such by reason of equilibrium set up between opposing attractive and repulsive forces operating between the component atoms, and that this equilibrium results in the polyhedra representing the spheres of atomic influence assuming shapes which are as nearly as possible spherical.... The polyhedra thus arrived at may be regarded as derived by compression of a close-packed assemblage of deformable, incompressible elastic spheres, the compression sufficing for the practical extinction of the interstitial space. When such an assemblage is released from pressure it is evident that in place of polyhedra, the shapes of which approximate as closely as possible to the spherical, closely packed spheres are presented; the distances between the sphere centres can be substantially in the same ratios as the distances between the centres of the corresponding polyhedra in the unexpanded mass, and the equilibrium condition of maximum sphericity of the polyhedra will be presented in the expanded mass of spheres by the existence of the maximum number of contacts between spheres. The whole method of treating the primary assumption thus resolves itself into finding close-packed assemblages of spheres of various sizes representing by their relative volumes the spheres of influence of the component atoms of any particular crystalline structure.”

Some very interesting evidence of the validity of their fundamental assumption of spheres of influence of the component atoms as the ultimate structural units is brought forward. They show that there are two modes of closely packing equal spheres, which give rise respectively to a cubic and a hexagonal crystal structure, the latter having a specific axial ratio of the vertical to the three equal equatorial horizontal axes; and that the chemical elements which are solids and crystallise, and the structural units of which can naturally be assumed to be equal spheres, being those of the similar atoms of the same chemical element, do practically all crystallise either in the cubic system or in the hexagonal system with the specific axial ratio indicated by them. The theory as it concerns chemical valency is obviously not affected by these interesting facts, as the spheres of influence present are those of the identically similar atoms of the same element. But the theory has received considerable support from the results of the investigation of a number of carbon compounds, chiefly derivatives of benzene.

Thus, in spite of the very wise decision of Barlow at the time of developing his theory of the homogeneous partitioning of space, to keep quite clear of attributing shape to the structural unit atoms or molecules, and to consider them as points, he, in common with the other contributors to that splendid geometrical work, appears driven to consider the question of shape when, in collaboration with his chemical colleague, he endeavours to apply his geometrical results to the practical problems of chemistry. It may be inevitable that we cannot get away from the idea of shape of the fundamental structural units. Yet the moment we do admit the idea, and begin to talk of polyhedra, or even of spheres, in close or any other packing, we enter the debatable land, concerning which the experimental evidence is as yet but shadowy and liable to many interpretations. Hence it is that we have the parallelohedra of Von Fedorow, having volumes proportional to the molecular volumes, the more general plane-faced cell of fourteen faces, the tetrakaidecahedron of Lord Kelvin and its deformed derivatives, and now the polyhedra of Pope and Barlow. The more indefinite “Fundamentalbereich” of Schönflies appears to be left behind, and we have embarked on a definite course of attributing shape to the component atoms or their regions of influence in the crystal structure. Von Fedorow has developed his particular theory in a very masterly manner, and with the aid of it professes, and with very considerable success in many cases, to determine the correct mode of setting up a crystal for truly comparative descriptive purposes, and has derived therefrom a remarkable method of crystallochemical analysis.

Moreover, there is yet another view, that of Sollas, that the packing of the molecules is a more open one altogether, a view to which he has been guided by consideration of the molecular volume. Sollas has offered some remarkable explanations of crystal structure, notably in the case of the dimorphous forms of silver iodide. The abnormal contraction which occurs on heating this interesting substance, and its sudden transformation at 146° from the ordinary hexagonal into a cubic modification as discovered by Lehmann, appear capable of very clear explanation on the basis of his theory. According to this theory of Sollas the volumes of the spheres of influence of the atoms of the different elements of the same family group, such as those of the group of alkali metals or those of the halogens, chlorine, bromine, and iodine, vary progressively in a manner which is dependent on the atomic volumes of the elements, which have a real comparative significance when the elements belong to the same family group.

It is probable that there is a considerable substratum of truth behind these various apparently conflicting views, and what is now required is that the germ of real fact shall be winnowed from the husk of fallacious speculation, just as occurred in the happy recent settlement of the old issue between Haüy and Mitscherlich. As in that case, moreover, it will be experimental work of superlative accuracy which can alone offer the desirable evidence on which a satisfactory arbitration can be founded.

It is thus obvious that we have now arrived at a stage in the history of crystallography when more experimental data, and many more measurements of the most carefully conducted character, on pure materials and excellently developed crystals, are most urgently needed, in order to decide these important, indeed fundamental, questions, the present state of which the author has endeavoured to present with judicial impartiality. When one looks around, and sees the almost complete lack of opportunities for the training of investigators in this rapidly growing branch of science, the importance of which to chemistry and physics is increasing every day, while the field is ripe for the harvesters, one is inclined to feel depressed with the thought of the opportunities which are being lost. Our country has, in this science at any rate, a fine record, having with few breaks led the van of progress from the time of Wollaston, the inventor in the year 1809 of the reflecting goniometer, and of Miller, the originator of our method of describing crystals and the pioneer of accurate experimental work, down to the present day. It may be, also, that our country’s reputation is safe at this moment. But it is in the hands of a band of investigators so small, and often of the private and not professional nature, carrying on the work for sheer love of it and deep interest in it, that the wonder is that so much has been done, and it is the provision for carrying on our national tradition of leadership in crystallography in the future that is a matter for the deepest concern.

If the perusal of this book should have awakened sufficient interest in the minds of some of its readers to prompt them to offer themselves as recruits to this small band of investigators, and especially if it should have inspired the zeal and enthusiasm of a few young students looking around for a promising and fascinating field of work, and, finally, if it should prove to be of assistance in obtaining the means of training such recruits with the help of the best and most accurate experimental apparatus which can be obtained, the author’s main objects in writing it will have been attained.

INDEX

Airy’s spirals, 197

Alpine snow-field, 49

Alum, ammonium iron, 43; cæsium, 42; potash, 5, 16, 17, 77; vicinal faces of potash, 248, 251

Amethyst quartz, 222–229; as example of pseudo-racemism, 231, 232

Ammonium chloride labile crystallisation, 248; iron alum, 43; NH_{4} group, and its isomorphism with alkalies, 82, 83, 131; oleate, liquid crystals of, 259–263; oleate, twins of, 262

Ampère’s researches on ammonia, 83

Anatase, crystal of, 37

Antimony oxide, dimorphism of, 87, 88

Apatite, crystal of, 37

Aragonite, biaxial interference figure of, 189, 190

Armstrong and Pope on sobrerol, 153

Arsenic oxide, crystals of, 5, 88

Astatic systems of molecular magnets of Lehmann, 271, 272

Asymmetric carbon atom, 144, 145

Axes and axial planes of crystals, 51, 55, 56

Axial ratios, 129

Babinet’s double-wedge quartz plate, 219

Bacteria, destruction of one enantiomorphous form by, 149

Barium nitrate, 152

Barker, researches on perchlorates, 123

Barlow, discovery of remainder of 230 point-systems, 118, 119, 140; and Pope’s theory, 285–292

Bartolinus, Erasmus, 17

Benzoic acid, screen experiment on crystallisation of, 229–231

Bergmann and Gahn’s laws of cleavage, 18

Berzelius and Mitscherlich, atomic weights and isomorphism, 80, 82, 83, 85

Beudant’s researches on the vitriols, 75, 76

Biaxial crystals, 60°-prisms and refractive indices of, 162, 163, 184; optic axes of, 185; optic axial angle of, 191

Biot’s researches on tartaric and racemic acids, 143

Biquartze, natural and artificial, 181, 211, 214, 216, 217

Black band of quartz twins, 216–218

Boisbaudran, Lecoq de, 238

Boyle, Robert, 17

Brauns, 254

Bravais, 114; space-lattices, 114

Brookite, 91

Cæsalpinus, 15

Cæsium alum, 42

Calcite, crystals of, 10–13, 38; amount of double refraction of, 174; in rock sections, 177, 178; uniaxial interference figure of, 189, 190; plate perpendicular to axis of, 209; refractive indices of, 174; 60°-prism of, 165, 168

Calcium carbonate, three habits of crystals of, 11

Calcium dextro-glycerate, optical activity and crystal form of, 155–160

Carangeot’s contact goniometer, 18–20

Carbonate, calcium, 11, 87; potassium sodium, 44

Carbonates of alkaline earths, 74

Carbon, dimorphism of, 137

Carbon dioxide, liquid in quartz cavities, 46

Cavendish, 23

Chemical significance of crystallography, 73, 283, 284; valency and crystalline form, 285–291

Cholesteryl benzoate, liquid crystals of, 258; acetate, spherical liquid crystals of, 281, 282

Chromate, potassium, 84

Chromates and manganates, isomorphism with sulphates, 84

Classes, the 32 crystal, 6, 33

Cleavage, 17; and glide-planes, 275, 276

Cobalt sulphate, 78

Conditions for growth of crystals, 240, 244, 245

Constancy of crystal angles, 6, 13, 14, 17, 23, 132

Convergent light experiments, 186, 188

Copper sulphate, 40, 76, 78

Coppet, de, 238

Crookes, Sir William, 138, 208

Crossed-axial-plane dispersion of optic axes, 89, 94, 95; of ethyl triphenyl pyrrholone, 106, 107, 108; of gypsum, 89

Crystal, definition of, 4; germs and their influence on crystallisation, 236, 237

Crystals, modes of formation of, 4, 5

Cube and its perfection of symmetry, 38; axes of, 52

Cubic system, 37

Cyanide, potassium cadmium, crystals of, 42

Dalton, 25

Dark field of polariscope, 188, 202

Davy, Sir Humphry, researches on ammonia, 82, 83

Delafosse and morphotropy, 101

Deville and Troost’s researches on tantalum chloride, 84, 85

Diamond, 8, 137, 138, 207, 208

Dibenzal benzidine, liquid crystals of, 264

Digonal axis of symmetry, 36

Dimensions of structural parallelepipeda, 129

Dimorphism, 79, 87; of antimony oxide, 87, 88; of carbonate of lime, 79, 87; of mercuric iodide, 97; of sodium dihydrogen phosphate, 80, 81; of sulphur, 86; of vitriols, 79

Directive molecular force in crystallisation, 139, 269, 274–277

Dog-tooth spar, 10–12

Double refraction, interference colours due to, 176, 177; measure of, 169, 170; of biaxial crystals, 184; of uniaxial crystals, 183

Double sulphates and selenates, 35, 79, 121, 127, 128, 132

Dulong and Petit’s law, 84

Electronic corpuscles, constituents of atoms, 113, 124

Elements of a crystal, 68, 69

Enantiomorphism and optical activity, 140; 11 classes showing, 150

Epsom salts, 76, 78

Ethyl triphenyl pyrrholone, 105, 106

Eutropic series, definition of, 132

External molecular compensation, 134, 234

Extinction directions, 204, 205

Fedorow, von, discovery of remainder of 230 point-systems, 118, 119, 140; theory of, 291, 292

Ferricyanide, potassium, 44

Ferrocyanide, potassium, 43

Ferrous sulphate, 76, 78

Fletcher, indicatrix of, 184

Fluorspar, single refraction of, 206

Form, definition of a, 11, 60, 61

Frankenheim on morphotropy, 101; discovery of space-lattices, 114

Frankland and Frew, 155

Fuchs, von, researches on sulphates of barium, strontium, and lead, 75, 77

Fuess reflecting goniometer, 64–66

Fundamentalbereich of Schönflies, 112, 113

Gattermann, 258

Gay-Lussac on alums, 77; on ammonia, 83; on racemic acid, 142

Gernez, 238

Gessner, 14

Gmelin, researches on racemic acid, 142

Goniometer, contact, 19, 20; reflecting, 64–66

Graphite, 137

Groth, von, morphotropic researches, 98, 102–104

Growth of a crystal, 1; from solution, 237–254

Guglielmini, researches on crystal structure, 17

Gypsum (selenite), cleavage of, 203; crystals of, 14; extinction directions of, 204; 60°-prism, experiment with, 163, 168; twins of in polarised light, 205, 206

Habit of crystals, 12, 13

Hardness of crystals, 255, 274

Hatchett’s discovery of columbium, 85

Haüy, 22; and Mitscherlich, 70, 75, 77, 88, 132; fundamental forms, 22, 23; law of constancy of form, 23; lattices, 29; law of rational indices, 24, 29, 30; modernisation of theories of, 30–32; molécules intégrantes, soustractives, and élémentaires, 25–28; structural units, 24

Hemihedral classes of crystals, 34

Hexagonal axes of symmetry, 36; prism, 11; system, 36, 53

Hexakis octahedron, 39; indices of, 61

Hjortdahl and morphotropy, 101

Holohedral classes of crystals, 34

Homogeneity, 6, 16; definition of, 114

Homogeneous structures, the 230 types of, 6, 111

Hooke, Robert, 16

Huyghens, 17; discovery of laws of double refraction, 17; investigation of calcite, 17

Ice, crystalline form of, 47

Iceland spar, discovery of, 17; rhombohedron of, 10–12

Inactive tartaric acid, 144

Inactivity, true optical, 235

Indicatrix of Fletcher, 184

Indices of crystal faces, 11

Intercepts on crystal axes, 58

Interference colours due to double refraction, 177; figures of biaxial and uniaxial crystals, 189–191

Internal structure of crystals, 15, 111–120

Iodide of mercury, dimorphism of, 97

Isomerism, chemical and physical, 142, 143

Isomorphism, Mitscherlich’s conferment of the term, 81; doctrine of, 81, 82; limitations of, 85; recent clearer definition of, 121–132

Isotropic crystals, 206

John of Berlin’s discovery of racemic acid, 142

Kipping and Pope, definition of racemism and pseudo-racemism, 153, 154

Kopp, 100

Kundt’s powder, 149

Labile solutions, 241

Laurent and Nickle’s organic researches, 99

Lavoisier, 23

Law of rational indices, 24, 50, 57, 59

Le Bel and van t’Hoff’s explanation of optical activity, 151

Le Blanc, researches on alums, 77

Lehmann, researches on liquid crystals, 256–282

Liquid crystals, 255–282; and polymorphism, 138, 139; list of substances forming, 280, 281

Magnesium sulphate, 76, 78

Mallard and Le Chatelier on silver iodide, 256

Manganate, potassium, 96

Manganates, 84, 96

Manganese sulphate, 78

Marignac and isomorphism of tantalum and niobium compounds, 84; and morphotropy, 101

Mercury iodide, dimorphism of, 97

Metastable solutions, 240

Methyl triphenyl pyrrholone, 105, 106

Mica-sectors plate for testing sign of optical rotation, 212, 213

Microscope, Lehmann’s crystallisation, 256, 257, 276–280

Miers, H. A., researches on crystallisation, 238–243; on red silver ores, 109; on vicinal faces, 248–254

Millerian indices, 57

Mirror-image symmetry, 118, 119, 134, 135; illustrated by quartz, 231

Mitscherlich, experiment with gypsum, 90–94; work of, 70–97

Mixed crystals, 77, 86

Molecular compound, racemic acid a, 150

Molecular volume and distance ratios, 129, 130

Molecule, individuality and directive force of, 139, 269

Monochromatic illuminator, 192, 193

Monoclinic system, 39; axes and axial planes of, 53, 54

Morphotropy, 98–104

Muthmann, researches on permanganates, 123

Naphthalene tetrachloride, 99

Newton’s seven orders of spectra, 177

Nickel sulphate, 76, 78

Nicol prism, 174, 175, 187

Nitrobenzenes, von Groth’s researches on, 104

Noble, Sir Andrew, experiments on liquefaction of carbon, 138

Optical activity and mirror-image symmetry, 141; antipodes, characters of, 152; characters of crystals, 7

Optically active classes of crystals, 150, 151

Optic axes of biaxial crystals, 185; axis of uniaxial crystals, 165; axial angle, 191; axial angle of ethyl triphenyl pyrrholone for different wave-lengths, 107, 191; axial angle of gypsum at different temperatures, 90–94, 191

Ostwald’s predictions of crystallisation phenomena, 238, 240

Oxides of arsenic and antimony, isodimorphism of, 88

Para-azoxy-anisol, liquid crystals of, 259, 265; -benzoic acid, 263; -cinnamic acid, 263; -phenetol, 258, 259

Parametral form, 56

Pasteur’s law, 155; research on morphotropy of tartrates, 100; research on tartaric and racemic acids, 142–150

Penfield’s diagram of spherical projection, 61, 62

Penicillium glaucum, destruction of dextro component of racemic acid, 148

Perchlorates and permanganates, isomorphism of, 84, 96

Pfaff, 254

Phases, different solid, 137

Phenol and resorcinol, von Groth’s researches on, 103

Phosphate, ammonium magnesium, 43; sodium dihydrogen, dimorphism of, 80, 81

Phosphates and arsenates, isomorphism of, 73, 74

Phosphorus, dimorphism of, 138

Photomicrographs of growing crystals, mode of obtaining, 41

Pistor’s goniometer, 89

Planeness of crystal faces, 6, 7

Polarisation colours due to optical activity, 179

Polarisation, rectangular, of spectra from doubly refractive prisms, 164

Polariscope, the, 187, 188

Polymorphism, 133–137

Pope and Barlow, theory of, 285–291

Positive and negative uniaxial and biaxial crystals, 166

Potassium bichromate, metastable and labile crystallisation of, 246, 247; manganate, 96; nickel sulphate, 35; selenate, 96; sulphate, 13

Priestley, 23

Primitive form of Romé de l’Isle, 20, 27

Projection polariscope, for convergent light, 92, 186, 188, 189; for parallel light, 201, 202

Progressive change of crystal angles in isomorphous series, 125; of double refraction, 126; of molecular distance ratios, 130, 131; of position of optical ellipsoid, 128

Propyl triphenyl pyrrholone, 106, 108

Proustite, 109, 110

Pseudo-racemism, 153, 154

Pyrargyrite, 109, 110

Pyroelectrical properties of crystals, 149

Quartz, 170; crystalline form of, 171, 172; crystals in rock sections, polarisation colours of, 175–178; crystals, liquid cavities in, 45; crystals on sand grains, 2, 3; double refraction of, 174; interference figure in convergent polarised light, 194–196; optical activity of, 173, 179–181, 210; plates, preparation of for polariscope, 181; polarisation colours of due to optical activity, 209, 210; refractive indices of, 174; screw point-systems of, 151; 60°-prism experiment with, 165, 168; Steno’s research on, 16; twinning of, 215, 216, 219–221, 225; two varieties of as examples of mirror-image symmetry, 171

Racemate, sodium ammonium, Pasteur’s researches on, 147, 148

Racemic acid, 142–146, 233, 234

Racemic forms and racemism, 150, 153, 233

Rammelsberg and morphotropy, 101

Rational indices, 24, 50, 59, 116

Reflection of light by crystal faces, 8

Refractive index, meaning of, 167

Reinitzer, 258

Reusch’s artificial quartzes, 198, 199

Rhombic system, 39; axes and axial planes of, 52, 54

Rhombohedron and its axes, 10, 11, 54, 55, 172

Rings and brushes, optic axial, 190, 191

Rock-salt, cube of in quartz cavity, 45; 60°-prism experiment with, 162, 168

Romé de l’Isle, 18–20; researches on alums, 77

Roozeboom, 238

Rotation of plane of polarisation by quartz of two varieties and different thickness, 180, 210, 211

Royal Institution experiment with diamonds, 8

Sal-ammoniac, 82, 83

Salol and betol, Miers’ researches on, 242, 243

Sand grains with quartz crystals, 3

Scalenohedron of calcite, 11

Scheele’s discovery of tartaric acid, 142

Schlippe’s salt, 45

Schönflies, discovery of remainder of 230 point-systems, 118, 119, 140

Seebeck, researches on ammonia, 82, 83

Selenates, isomorphous with sulphates, 96; of alkalies, 121

Selenic acid, 95

Selenite, polarisation colours of films of, 203

Selenium, discovery by Berzelius, 96

Sella’s warning against hasty generalisation, 102

Senarmontite, 88

Silver iodide, 256, 292

Single refraction of cubic crystals, 162, 183

Snow crystals, 49

Sobrerol, 153

Sodium chlorate, 151; sulphantimoniate, 45

Sohncke, regular point-systems, 117; mirror-image molecular arrangement, 141; two point-systems of quartz, 151

Sollas, crystal structure, theory of, 292

Solubility and supersolubility, 238–241; curves of, 240

Solutions, optical activity of, 151; metastable and labile, 240, 241

Space-lattices, 50, 114–116; triclinic illustration of, 115

Specific gravity, importance of determinations of, 129

Spheres of influence of atoms, 113

Steno, 16

Stereographic projection, 34, 62, 67; of topaz, 68; of double sulphates, 35

Stereometric arrangement of atoms in molecule, 124, 136

Story Maskelyne, 34

Strain, polarisation colours of glass and diamond due to, 207, 208

Structural units of crystals, 24, 111–113

Sulphantimoniate of sodium, 45

Sulphate, ammonium magnesium, 44

Sulphates of alkalies, 121; of barium, strontium and lead, 74

Sulphur, dimorphism of, 86, 87, 137; monoclinic form of, 4, 86

Symbol of a face or form, 57

Symmetry, axes and planes of, 34, 36, 41, 55; elements of, 34

Systems, the crystal, 6, 7, 33

Tartaric acid, 142–148; dextro, 143, 146–148; lævo, 144, 146–148; pyro-electrical properties of, 149

Tartrate, hydrogen potassium, 43

Tetartohedral classes of crystals, 34

Tetragonal system, 37; axes and planes of, 36, 52

Thallium, relation of to alkali metals, 131

Thénard and Gay-Lussac, research on ammonia, 83

Thomson, J. M., 238

Thomson, Sir J. J., discovery of composition of atoms, 112

Topaz, crystal of, 40; stereographic projection of, 68

Transition tint, 180

Triclinic bipyramid, 56; system, 40; axes and planes of, 53, 54

Trigonal system, 37; axes and planes of, 37, 53, 55

Triphenyl pyrrholone derivatives, 105–108

Triple tartrate of sodium, potassium, and ammonium, 91

Tutton, fixed positions of atoms in crystals, 122–124; law of progression of crystal properties in isomorphous series, 121–123, 129; nature of structural units, 134, 135; research on calcium dextro-glycerate, 157, 160; researches on simple and double sulphates and selenates, 121; researches on triphenyl pyrrholones, 105–108

Uniaxial crystals, optic axis of, 165; 60°-prisms of, 164; two refractive indices of, 166, 183

Valentinite, 88

Vanadium family group of elements, 85

Vauquelin, researches on alums, 77

Vicinal faces, 248–254

Vitriols, the, 15, 76, 78

Von Lang, 23, 34

Vorländer, 263; nature of molecules forming liquid crystals, 273

Water, exceptional thermal dilatation of, 47

Water flowers in ice, 47

Water of crystallisation, 76, 78, 79

Wave-length of most luminous part of spectrum, 179

Werner’s fundamental form, 20

Westfeld, 18

Weyberg, 250

White of higher orders, 178

Wollaston’s reflecting goniometer, 63, 81; work on carbonates and sulphates of barium, strontium and lead, 74, 75

Wulff, 250, 252, 253

Zinc sulphate, 76, 78

Zone of crystal faces, 63; circle, 63

PRINTED BY TURNBULL AND SPEARS, EDINBURGH

-----

Footnote 1:

See page 57 for explanation of indices.

Footnote 2:

Proc. Roy. Soc., 1908, A, 81, 40.

Footnote 3:

Comptes Rendus, 1842, 15, 350, and 1845, 20, 357.

Footnote 4:

Comptes Rendus, 1848, 27, 611, and 1849, 29, 339.

Footnote 5:

Jahresbericht, 1849, 19.

Footnote 6:

Comptes Rendus, 1848, 26, 535.

Footnote 7:

Journ. für Prakt. Chemie., 1865, 94, 286.

Footnote 8:

Mem. R. Accad. di Torino, 2A, 17, 337, and 20, 355.

Footnote 9:

Pogg. Ann., 141, 31.

Footnote 10:

Mineralogical Magazine, 1888, 8, 37.

Footnote 11:

Journ. Chem. Soc., 1896, 69, 507.

Footnote 12:

Ann. de Chim. et Phys., 1848, 24, 28 and 38; also 1850, 28, 56; Comptes Rendus, 1848, 26, 535; also 1849, 29, 297; also 1850, 31, 480; also 1853, 37, 162, and 1858, 46, 615.

Footnote 13:

Journ. Chem. Soc., 1891, 315.

Footnote 14:

Ibid., 1897, 989.

Footnote 15:

Journ. Chem. Soc., 1891, 59, 233.

Footnote 16:

Ibid., 1891, 59, 96.

Footnote 17:

Phil. Trans. Roy. Soc., 1895, A, 185, 913.

Footnote 18:

Mineralogical Magazine, 1892, 10, 123.

Footnote 19:

Journ. Chem. Soc., 1906, 89, 413; Proc. Roy. Soc., A, 1907, 79, 322.

Footnote 20:

“Lehrbuch der Allgemeinen Chemice,” vol. 2, part 2, p. 780.

Footnote 21:

Phil. Trans., 1903, A, 202, 459.

Footnote 22:

Phil. Trans., 1903, A, 202, 519.

Footnote 23:

Zeitschr. für Kryst., 1901, 34, 449.

Footnote 24:

Loc. cit., p. 531.

Footnote 25:

Sitzungsber. d. Physik. Med. Soc., Erlangen, 1878, 10, 59.

Footnote 26:

Neues Jahrbuch, 1887, 138.

Footnote 27:

Ber. der deutsch. Chem. Ges., 1907, 40, 1970.

Footnote 28:

Zeitschr. f. Phys. Chemie., 1907, 57, 357.

Footnote 29:

This apparent contradiction in terms the author takes to mean that, whatever compression is produced by pressure on one part of the sphere, is counterbalanced by a corresponding protuberance produced in the part not confined under pressure, the total volume being incompressible.

Footnote 30:

Proc. Roy. Soc., 1898, 63, 270, 286, and 296; 1901, 67, 493.

------------------------------------------------------------------------

TRANSCRIBER’S NOTES

1. Silently corrected obvious typographical errors and variations in spelling. 2. Retained archaic, non-standard, and uncertain spellings as printed. 3. Re-indexed footnotes using numbers and collected together at the end of the last chapter. 4. Enclosed italics font in underscores. 5. Denoted superscripts by a caret before a single superscript character or a series of superscripted characters enclosed in curly braces, e.g. M^r. or M^{ister}. 6. Denoted subscripts by an underscore before a series of subscripted characters enclosed in curly braces, e.g. H_{2}O.