When the operation is arranged to occur during the night, as will

usually be the case, the solution being set out to crystallise in a

quiet and protected place on the previous afternoon or evening, the

slight fall of temperature during the night gently assists the process

and almost ensures a good crop of a few well-formed crystals large

enough for goniometrical purposes next morning. They should be removed

before the temperature begins to rise again with the advent of the sun,

dried with blotting paper and by air exposure for a short time, and

stored in a miniature bottle labelled with the name or formula of the

substance and the date of collection of the crop. In such cases the

labile state is never reached, and the course of the crystallisation is

represented by the curve BE. The whole conditions for the curve ABE,

however, would correspond to much lower temperatures, such as those

given at the foot of the diagram below the word “temperature,” rather

than to the upper row of temperature abscissæ suitable for the other

purposes of the diagram already referred to. Crystallisation might well

begin about 13° or 14°, as shown at B, and the liquid would cool a

couple of degrees or more during the night while crystallisation was

steadily proceeding, until equilibrium was reached at E on the

solubility curve.

The diagram does not represent any substance in particular, but is a

perfectly general one, corresponding to the facts observed with most of

the very varied salts worked with by Miers and those of which the author

has had experience. The exact temperatures and concentrations will, of

course, differ for each substance.

A beautiful experimental demonstration of crystallisation from the

metastable and labile conditions of solution respectively is afforded by

potassium bichromate, K_{2}Cr_{2}O_{7}. When deposited slowly from a

metastable solution under conditions of quietude, this salt is slowly

deposited in bright orange coloured and excellently formed crystals,

often of considerable size, belonging to the triclinic system of

symmetry; they are bounded by good pinakoidal (pairs of parallel) faces

intersecting in sharp edges. But when the crystallisation occurs from a

labile solution, being much more rapid, it takes the form of feathery or

arborescent branching skeletal growths, there being inadequate time for

the formation of well-developed crystals.

Fig. 99, Plate XXI., is a photographic reproduction of well-formed

crystals of potassium bichromate, grown from a solution in the

metastable condition on a microscope slip, just as they are seen through

the microscope in the slow act of formation, employing a 1½ inch

objective. The crystallisation had been started by germ crystals of the

salt falling in from the air, after which the drop, placed within the

ring of hardened gold size on the slide, had been covered with a

cover-glass, under which the crystallisation had proceeded with

sufficient slowness to enable a successful photograph to be taken, when

the camera was subsequently attached above the vertically arranged

microscope. An upright micrographic apparatus had been designed by the

author specially for this photography of growing crystals, many of the

results of which are reproduced in this book.

[Illustration:

_PLATE XXI._

FIG. 99.—Potassium Bichromate slowly crystallising from a Metastable

Solution.

]

[Illustration:

FIG. 100.—Potassium Bichromate rapidly crystallised from a Labile

Solution.

CHARACTERISTIC DIFFERENCE IN THE CRYSTALS DEPOSITED FROM METASTABLE

AND LABILE SOLUTIONS.

]

Fig. 100 is the reproduction of another photograph taken under similar

conditions, but employing a hot and somewhat more concentrated solution

of potassium bichromate, and making the exposure at the moment when, in

the particular field chosen, a rapid labile crystallisation was just

completing itself, the rapidity of growth of the feathery skeletal

crystals having just become arrested. Indeed, the branches are

frequently terminated by small well-formed crystals, the rapid growth

having been succeeded by a final slow crystallisation where the solution

had discharged its labile excess and attained once more the metastable

condition.

This experiment with potassium bichromate lends itself admirably to

lantern demonstration with the projection microscope. When the drop of

hot concentrated solution is first placed on the warmed microscope slip,

and the latter laid on the stage, nothing visible on the screen happens

for a minute or two, the solution becoming, however, more or less

rapidly cooled. But suddenly, the drop having cooled sufficiently to

bring the solution to the labile condition of supersaturation

corresponding to the conditions for spontaneous crystallisation

indicated by the supersolubility curve, arborescent or feathery growths

begin to shoot out from various points in the field, often near the

margin, and traverse the screen so rapidly that in a moment or two it is

filled with them. The crystallisation then slows down once more, the

labile shower of excess having become exhausted, and the terminations of

the branches and ramifications begin to develop into good little

crystals, which thus hang like fruit on a tree. The experiment is

rendered the more brilliant and beautiful by the bright orange colour of

the crystals.

In Fig. 101, Plate XI., facing page 88, a reproduction of a photograph

of a similar crystallisation from a labile solution of ammonium chloride

is given. This salt is also particularly suitable for screen

demonstrations. The beautiful skeletal ramifications follow the axial

directions of the cubic axes, ammonium chloride crystallising in the

pentagonal-icositetrahedral class of the cubic system. Good crystals

may, however, be very slowly grown from metastable solutions, and they

usually exhibit as the principal forms the icositetrahedron

(predominating), cube, octahedron, rhombic dodecahedron, and the

class-distinguishing pentagonal icositetrahedron. The rapid growths by

spontaneous crystallisation of labile solutions, however, invariably

take the form of the rectangularly branching feathery crystals shown in

Fig. 101.

Further light has been thrown on the act of crystallisation by another

most interesting research of Miers concerning “vicinal faces,”[21] such

as the three very low pyramid faces (forming a very flat triakis

octahedron) which often replace each octahedron face on a crystal of

alum which has been grown somewhat rapidly. The author has frequently

observed this phenomenon in the course of the numerous crystallisations

required for the investigation of the sulphates and selenates. It may be

described in general terms as the replacement of primary faces

possessing the simplest rational indices by faces having such high

indices that it is doubtful whether they ought really to be represented

by indices at all. The number of such vicinal faces which replace the

simple face depends on the symmetry of the crystal, to which, of course,

they conform. Thus, while three such vicinal faces replace an octahedral

face, and two replace the face of a tetragonal prism, the simple primary

prism face of a rhombic or monoclinic crystal would only be replaced by

one, which may have a deformation of as much as even 30′ from the

correct position of the prism face, and on either side of it. Indeed it

is possible for a whole succession of such vicinal faces to be developed

within the degree of arc which may in extreme cases separate the

limiting values on each side of the prism face, and such are often seen

and make up the well-known bundle of images afforded on the goniometer

by a bad face, a face which would cause the author at once to reject the

whole crystal for measurement purposes. One of the faces, even in cases

such as alum or a tetragonal crystal, where three or two might have

equal values as regards the symmetry, generally predominates, and

affords a very much more brilliant image of the goniometer signal than

the others in the bundle, so that an unwary observer might easily come

to the conclusion that this was the really valid image corresponding to

the octahedron face or to the simple primary prism face, or whatever

particular face was expected in the neighbourhood indicated by the

bundle of images. Obviously, however, it might only be one of three or

two equally valid faces of a vicinal form, which had grown

predominatingly during the last period of growth previous to removal

from the mother liquor.

The explanation of this interesting phenomenon of the production of

vicinal faces is one intimately connected with the structure of

crystals, and it forms one of the strongest confirmations of the

correctness of the theory of crystal structure the basis of which is the

molecular space-lattice. Miers is in full agreement with the author in

emphasising the importance of the space-lattice formed by the “points”

representative of the molecules, and analogously chosen in the

molecules. He says: “Whatever structures may be necessary to account for

other features of crystals, there is little doubt that we are justified

in regarding their faces as the planes of a space-lattice.”[22] Now

Wulff,[23] who has contributed very considerably to our knowledge of the

nature of the act of crystallisation, has proved, from his own

investigations and those of Weyberg, carried out at his suggestion in

his laboratory at Warsaw,[24] that faces of greatest reticular density,

that is, those along which the points of the space-lattice are most

thickly strewn, are those which grow the most slowly, and therefore are

the best developed. This latter will be obvious on a little

consideration, for the faces of less reticular density which grow more,

tend in doing so to extend the boundaries of the faces of greatest

reticular density, and thus to enlarge those faces. Hence the usual

planes on a crystal must be those of high reticular density; and these

are such as are represented by the simplest indices, the faces most

dense of all in points being the primary ones.

But it has been shown from the researches of Miers that vicinal faces

are often produced in preference to these simple index planes of high

density, and such vicinal faces, although the nearest (in angular

position) of all possible faces to those simple index planes, are

themselves of excessively low reticular density, so much so that if

represented by indices at all they can only be indicated by very high

numbers, not such as we are accustomed to consider as in keeping with

the simple spirit of the law of rational indices. Taking the example

worked out most fully by Miers, the octahedral crystals of alum, it is a

fact that the cubic faces of highest reticular density are those of the

cube itself, then come in order those of the rhombic dodecahedron and

those of the octahedron. Hence, the density of octahedral faces is very

high. But those of the very low triakis octahedron, which Miers finds to

replace the octahedron faces so frequently as vicinal faces, are of

excessively low reticular density.

Miers explains the appearance of the latter instead of octahedral faces

by assuming that the supersaturated liquid in contact with the growing

crystal consists of the particles (molecules) of salt uniformly mingled

with those of water, the solvent, and that the act of crystallisation

consists of the escape of the water and solidification of the salt.

Consequently, the salt particles just before crystallisation cannot be

so dense as they are along primary planes of the crystal, as they are

separated by the water particles, which are presumably much more

numerous. Hence it is that they are not deposited along the planes of

high reticular density, but along vicinal planes of low density of

points. For instance, he shows that the shower of salt particles upon a

cube face would have to be so dense that there would be insufficient

room for the water particles. The density in a cube face is 114 times as

great as that in one of the vicinal planes observed. Now, 100 cubic

centimetres of solid alum weigh 172 grammes, and 100 c.c. of the

solution depositing crystals contain 9·74 grammes of alum. Thus the

density of the growing crystal of alum is nearly 18 times that of the

alum in the adjacent saturated solution.

Consequently the deposition of the salt particles, in a moderately quick

crystallisation, when insufficient time is afforded for the deliberate

escape of the water particles and for the orderly rearrangement of the

salt particles, occurs along vicinal planes instead of along the primary

planes. For it must not be forgotten that whenever it has the

opportunity of coming into operation there is a directive molecular

force of some kind, which controls the operation of crystallisation, and

which undoubtedly attempts to cause, and given adequate time and scope

succeeds in causing, the production of faces of high reticular density,

the fundamentally important primary faces of lowest indices, and which

are often those along which cleavage occurs. Wulff emphasises this in

saying (_loc. cit._, p. 461): “Bei der Krystallisation orientiren sich

die Molekeln auf den Flächen des Krystalles ganz gleichförmig durch den

Einfluss der Richtkraft der Krystallisation.” The more rapidly the

crystallisation occurs, however, the less chance is there for this force

to attain its ultimate object. More will be said about this directive

force in the next chapter, after we have studied the remarkable “liquid

crystals” discovered by Lehmann.

This highly interesting explanation of Miers, supported as it is by the

work of Wulff, and confirmed also in many respects by the observations

of the author, whose great aim throughout his investigations has been to

avoid the production of such vicinal faces, throws an important light on

the nature of the act of crystallisation. It renders the reason clear

why crystals which are very slowly grown from solutions only feebly

supersaturated and under conditions of absolute rest, protected from

either air currents or preventable earth tremors—conditions which the

author has taken quite exceptional pains to procure for the preparation

of the crystals used in the investigation of the sulphates and selenates

of the rhombic simple salt series and monoclinic double salt series—are

occasionally obtained quite free from any sign of such vicinal faces.

They are small perfect individuals exhibiting primarily the faces of

high reticular density, that is, the faces of the simple forms of low

rational indices; and these faces are absolutely plane, affording one

single brilliant image of the goniometer signal, which can be adjusted

with great precision to the cross-wires of the telescope. For the slower

the growth, the more time is afforded for the escape of the water

molecules, and for the salt molecules to deposit themselves as directed

by the molecular guiding force of crystallisation, along the planes of

high reticular density. In many of his experiments Miers expressly

stirred the solution, to prevent concentration currents, which had been

considered by Wulff of importance in the process, from coming into play

and causing unknown effects. Hence his experiments in which vicinal

faces were produced are not comparable with the author’s slow growths.

The work of Miers assists in the proof that the constancy of angle to

within one or two minutes of arc is a real property of the crystals of a

substance. For previously the frequent presence of vicinal faces rather

than the simple forms of high reticular density, and which had been

mistaken for the latter, had caused Pfaff in 1878[25] and others to

conclude that variations from the true crystal angle amounting to as

much as 30′ were of common occurrence as the result of strain during

deposition.

Brauns[26] in 1887 made a careful series of measurements of very good

octahedral crystals of lead nitrate, and found 13′ 20″ the largest

deviation of a good image from the theoretical position. He imputed it

to the action of gravity as a disturbing cause during deposition. The

researches of Miers have cleared away all this misconception, in proving

that the bright images referred to, taken for those of the simple

primary form, are not such at all, but vicinal faces of very low

reticular density.

CHAPTER XVI

LIQUID CRYSTALS.

We have seen in the foregoing pages that a crystal is usually a solid,

highly organised in a homogeneous manner, and, unless the symmetry be

developed to its highest extent, the crystal then belonging to the cubic

system, it is also in general anisotropic, that is, it exhibits double

refraction. Section-plates of it, more or less thin according to the

strength of the double refraction, exhibit colours in parallel polarised

light, and show the phenomenon of a single optic axis, or of two optic

axes, in convergent polarised light. Every variety of hardness, however,

is displayed, from that of the diamond down to that of a crystal as soft

as gypsum, and even softer. Moreover, many of the softer crystallised

substances develop the property of permitting one layer to glide over

another by gentle side pressure with a knife blade, when inserted in an

edge or face in an attempt to cut the crystal. Calcite and ice, for

instance, both possess such planes of gliding of the structural units

over one another in layers. There are also the border line cases of

crystals so soft as to be readily bent, and many well-known viscous

substances crystallisable only with great difficulty, some of which form

pliable crystals.

But in the year 1876 Lehmann discovered a new property in an already

remarkable substance, iodide of silver, AgI, namely, that at

temperatures superior to 146° C. it can flow like a viscous liquid,

while exhibiting several of the properties which are characteristic of

crystals. Silver iodide is dimorphous, exhibiting a hexagonal form at

the ordinary temperature, which persists up to 146°. But during the

heating to the latter temperature a regularly accelerating diminution of

volume occurs, the feeble expansion in directions perpendicular to the

axis being overbalanced by a considerable contraction along the axis,

both quantities having been accurately measured so long ago as the year

1867 by Fizeau, by means of his delicate interference dilatometer. This

contraction, so unusual an occurrence with increase of temperature,

culminates at 146°, according to Mallard and Le Chatelier, in a sudden

change of condition into a cubic modification, accompanied by absorption

of heat. Now Lehmann, studying this cubic modification of silver iodide

under a microscope which he had devised—specially adapted for

observations at temperatures higher than the ordinary, by being supplied

with the means of heating the object under observation—found that it was

not only plastic, but actually a liquid.

[Illustration:

FIG. 102.—Lehmann’s Crystallisation Microscope.

]

The form of Lehmann’s “Crystallisation Microscope,” as now constructed

by Zeiss, is shown in Fig. 102. Its essential features are that the

glass object-plate, which is somewhat wider than the usual microscope 3

by 1 inches slip, is supported by little metallic columns at a height an

inch or more above the ordinary stage, and may be heated from below by a

miniature Bunsen burner, which is provided with a delicate graduated

gas-tap and is adjustable for its position, swinging in or out as

desired. The small Bunsen flame may be converted into a blowpipe flame

if necessary, an air-blast attachment to a mixing reservoir being

provided, to which the arm of the burner is hinged. Two cooling blasts,

connected with a gas-holder of air, are also provided, and are

adjustable to the most suitable symmetrical positions above the slide

for directing the cooling air on the part of the latter where the liquid

is situated. These arrangements enable the substance on the slide to be

rapidly or slowly heated or cooled at will. Electric connections are

also provided, in the event of the observer desiring to study the

behaviour of the liquid crystals under the influence of the electric

current.

Considerably later, in the year 1889, the attention of Lehmann was

called by Reinitzer to another similarly singular substance, cholesteryl

benzoate, which appeared to consist of an aggregate of minute crystals

which flow as readily as oil, while preserving many of the characters of

crystals.

In the next year, 1890, the substance para-azoxyphenetol, then recently

discovered by Gattermann, was observed by Lehmann to form a turbid

“melt” on fusion, which consisted of an aggregate of crystals flowing

with a mobility equal to that of water, and which take the form of

spherical drops showing a dark kernel inside, as shown at _a_ in Fig.

103, quite unlike a drop of ordinary liquid. The kernel disappears on

shaking, but reappears on coming to rest again. In polarised light the

drops show dichroism, that is two different colours in different parts

or directions, being divided into white and yellow parts, the yellow as

a pair of opposite approximately 60°-sectors, as indicated at _c_ in

Fig. 103. Under crossed Nicols they show a black cross, as represented

at _d_ in Fig. 103.

Now obviously these drops are doubly refractive, and their whole optical

behaviour corresponds to the arrangement of the molecules in concentric

circles, such as that suggested at _b_ in Fig. 103.

[Illustration:

FIG. 103.—Liquid Crystals of Para-azoxy-phenetol arranged in Spherical

Drops.

]

Another substance of like character, para-azoxy-anisol, was subsequently

found to behave similarly, and forms an excellent substance to use for

demonstration purposes. A reproduction of a photograph, kindly sent to

the author by Prof. Lehmann, of a slide of this substance is given in

Fig. 104, Plate XXII. It shows a characteristic field of such drops,

exhibiting white parts and yellow sectorial parts which photograph dark,

of para-azoxy-anisol mixed with a little para-azoxy-phenetol, oil and

resin (colophony), as seen under the polarising microscope with crossed

Nicols.

The next and possibly most interesting step in this remarkable series of

discoveries was made by Lehmann himself in the year 1894. He alighted on

the fact that ammonium oleate, crystallised from solution in alcohol,

affords a splendid example of flowing crystals, which are sufficiently

large to enable their habits to be studied in detail. The individuals

are almost invisible in ordinary light, owing to the refractive index of

the crystals and of the mother liquor being approximately the same. But

in polarised light, using crossed Nicols, they are clearly revealed as

steep double pyramids with more or less rounded edges. Their section is

nearly circular in consequence, and they exhibit optical properties of a

uniaxial character, the optic axis being that of the double cone or

bipyramid. A characteristic individual is shown at _e_ in Fig. 105. When

two of these flowing crystals approach each other, as at _a_ in Fig.

105, they coalesce to form a larger single individual, as is indicated

in stages at _b_, _c_, and _d_ in the illustration.

[Illustration:

FIG. 105.—Liquid Crystals of Ammonium Oleate.

]

When the cover-glass, under which they are growing on a microscope 3 by

1 inch slip, is moved to and fro so as to distort these remarkable

bodies, which we may well hesitate to call crystals, the singular effect

is produced of causing them all to become similarly orientated, for the

extinction directions follow the direction of the pressure. They at once

seek to regain their original form, however, on cessation of the

disturbance. A slide of the bipyramids under pressure is shown in Fig.

106. In the black extinguished portions of the field the flowing

crystals are flattened, according to Lehmann, and arranged so that the

optic axis is in all cases perpendicular to the tabular crystals and the

glass plates and parallel to the axis of the microscope. The black parts

are separated by oily strips, as shown in another slide under

considerable pressure, represented in Fig. 107, which are composed of

the tabular crystals standing on end, with their optic axes parallel to

the plates. These strips polarise the more brightly the more truly the

crystals stand perpendicularly to the plates. The two conditions are

shown diagrammatically at _a_ and _b_ in Fig. 108.

[Illustration:

FIG. 106.—Liquid Crystals of Ammonium Oleate under slight pressure.

]

[Illustration:

FIG. 107.—Ammonium Oleate under considerable pressure.

]

[Illustration:

FIG. 108.—Diagrammatic Representation of Arrangement of Molecules.

]

Lehmann believes the explanation of these singular phenomena to be that

the “liquid crystals” of ammonium oleate are composed of piles or layers

of thin plates perpendicular to the optic axis. Disturbance detaches the

plates from their piled positions over one another, and sets them

parallel to the glass plate, except in places, the oily strips, where

the plates stand upright, perpendicularly to the micro-slip and

cover-glass. Lehmann, indeed, goes further, and asserts that the

molecules themselves are anisotropic, and probably take the form of

plates.

[Illustration:

FIG. 109.—A Crystal of Ammonium Oleate A, broken at B, each part

repairing itself at C, perfect again at D.

]

An extremely interesting experimental observation of Lehmann’s with the

bipyramids of ammonium oleate is, that if one of them, for instance A in

Fig. 109, be broken into two parts, as at B, each part grows again and

completely repairs itself, becoming once more a perfect double pyramid,

as indicated in stages at C and D in the figure.

[Illustration:

FIG. 110.

]

[Illustration:

FIG. 111.

Cruciform, Boomerang, and Arrow-head Twins of Ammonium Oleate.

]

[Illustration:

_PLATE XXII._

FIG. 104.

Dichroic Crystal Drops of Para-azoxy-anisol.

]

[Illustration:

FIG. 112.

Rectilinear Liquid Prisms of Para-azoxy-benzoic Acid.

]

[Illustration:

FIG. 115.—Tetragonal Astatic Magnet-system.

]

[Illustration:

FIG. 116.—Cubic Astatic Magnet-system.

]

Twins of ammonium oleate are also shown in Figs. 110 and 111, the former

figure representing a twin of cruciform character, and the latter

exhibiting twins resembling a boomerang and an arrowhead respectively.

This substance, ammonium oleate, thus appears to be one of the most

remarkable and interesting of all the bodies yet observed to afford

liquid crystals. Many other oleates produce liquid crystals also, but

the ammonium salt is by far the most striking, and very convincing as to

the reality of Lehmann’s discovery.

Another substance of a different nature was discovered by Vorländer in

the year 1904, namely, the ethyl ester of para-azoxy-benzoic acid. A

characteristic microscope slide of it in ordinary light is shown in Fig.

112, Plate XXII., which is a reproduction of an actual photograph most

generously sent to the author by Prof. Lehmann.

The individuals are described by Lehmann, who further studied the nature

of the substance, as almost perfectly rectilinear prisms with nearly

sharply defined basal plane end faces. A singular fact about this

substance is, that when two individuals approach each other they arrange

themselves parallel with a jerk, and then flow into each other,

producing a single larger liquid crystal, and often with such rapidity

that the eye can scarcely follow the movements. These coalescences

appear to be occurring all over the field at once, with the production

of larger and larger crystals. Indeed, Lehmann likens it to a struggle

between the innumerable individuals, in which the smaller ones are being

continually eaten up by the larger.

Vorländer also prepared the ethyl ester of para-azoxy-cinnamic acid, and

Lehmann found it to be similarly interesting. The substance separates

from a solution in monobromonaphthalene in uniaxial prisms or

hemimorphic pyramids, the edges and solid angles of which are more or

less rounded, and which appear colourless in the direction of the axis

and yellow in all other directions. When pressed between the cover-glass

and the micro-slip on which the crystallisation is proceeding,

extinction of the light occurs throughout the whole mass when polarised

light is being employed and the Nicols are crossed. For throughout the

entire substance the particles—whether they are the molecules themselves

as Lehmann asserts or aggregations of them in the form of

ultramicroscopic crystals—arrange themselves with their optic axes (the

crystals being uniaxial) perpendicular to the cover-glass and

micro-slip, as in the case of ammonium oleate. Lehmann’s theory is that

the molecules themselves are tabular perpendicular to the axis, as in

the case just referred to, and that they are thus readily coerced by the

pressure of the flat cover-glass to take up positions parallel to it.

Two further reproductions of photographs, taken in polarised light, of a

somewhat remarkable character, which have been placed at the author’s

disposal by the courtesy of Prof. Lehmann, are given in Figs. 113 and

114, Plate XXIII. Fig. 113 represents numerous doubly refractive and

dichroic strips marking the boundaries of elongated individual crystals

of the substance dibenzal benzidine, and affords a graphic idea of the

real character of the double refraction displayed by liquid crystals.

[Illustration:

_PLATE XXIII._

FIG. 113.—Elongated Liquid Crystals of Dibenzal Benzidine, showing

Double Refraction and Dichroism.

]

[Illustration:

FIG. 114.—Spherical Liquid Crystals of Para-azoxy-anisol, showing

Interference Colours under Crossed Nicols as the Effect of

Compression.

]

Fig. 114 represents the effect of compression on para-azoxy-anisol, and

demonstrates very clearly the distribution of the interference colours

due to double refraction.

We are thus face to face in these remarkable experiments with some new

facts concerning the nature of crystals. For we pass here into the

borderland between ordinary liquids—singly refractive and structureless,

in which the molecules are rolling over each other with every possible

orientation—and solid true crystals possessing homogeneous structure,

and the basis of which is a space-lattice arrangement of the chemical

molecules, determinative of the system of symmetry displayed. In this

wonderful borderland we certainly have had revealed to us, by the genius

and persistency of Lehmann, liquids which possess many of the attributes

of crystals, such as definite orientation of the ultimate particles,

double refraction, and optic axes. These are undoubtedly solid facts

which require to be faced.

Whether Lehmann’s theory is to be accepted in full can only be decided

after much more investigation by several independent investigators. We

are now becoming familiar with the phenomena, as they have naturally

excited immense interest in all scientific circles, and demonstrations

of many of the experiments of Lehmann have been given in this country by

Dr. Miers, Prof. Pope, and others, and particularly by Messrs Zeiss,

with their new high temperature microscope, a description of the use of

which for the projection of liquid crystals on the screen will presently

be given. Prof. Lehmann himself has described the phenomena so clearly

and fully that it is quite easy for others to repeat his experiments,

and doubtless time would often be much better spent in doing so than in

criticising points of theory without observing the phenomena at first

hand. It frequently happens, in the inevitable march of scientific

progress, that striking new facts, such for instance as the discovery of

the composite nature of the chemical atom, are apt to cause either

alarm, even panic, as to cherished theories, or else unreasoning

scepticism. The happy mean between these two modes of receiving such

facts, the open philosophic mind, ever ready to widen the scope of the

horizon when a novel supposition is indubitably proved to be a real

fact, and to assimilate that truth into the theory, widening

correspondingly the scope of the latter if needful, is obviously the

ideal thing to cultivate, and one which eventually finds itself in

harmony with the authenticated final results of the new discoveries. It

usually happens that too sweeping conclusions are at first drawn from

such new facts, but time, with its further wealth of experience,

especially the accumulation of experimental _data_ which it brings in

its train, soon levels these down and relegates the facts to their

proper positions in the great scheme of natural knowledge.

Lehmann’s view is that the ordinary effect of surface tension to cause

truly liquid particles to assume the spherical “drop” form is resisted

by a special force, which he terms “Gestaltungskraft,” and which we may

perhaps translate “Configuration-determining force.” This force he

considers is not identical with that of elasticity, but is that force by

virtue of which a “flowing crystal” continually seeks, while freely

swimming in the mother liquor or fused liquid, to take up its normal

configuration. Even if a spherical drop could be cut out of it, the

sphere would at once become a rod, prism, or pyramid or whatever the

normal configuration of the flowing crystals of the substance in

question might be.

The much debated term “liquid crystal” has been given by Lehmann to the

normal configuration of each of the now considerable number of

substances which have been discovered to exhibit the phenomena of

flowing crystals. The latter appellation “flowing crystal,” which

Lehmann also uses, appears to the author to be in many ways more

suitable, however, and would avoid much of the criticism which has been

levelled at the term “liquid crystal.”

As already indicated, Lehmann attributes the whole phenomena to a

fundamental cause, namely, anisotropy (optical dissimilarity in

different directions) of the molecules themselves, which he considers

must cause self-restoration of the structure after disturbance, a

process which he terms “spontaneous homœotropy.” He considers that it is

the molecular configuration-producing force, connected with the tabular

form of, and directionally differentiated distribution of energy and

force in, the single chemical molecules, which maintains the inner

structure of the flowing crystal in position. The polyhedral outward

form thus appears to be a necessary consequence of the inner structure,

on this basis that it is a force resident in the molecules themselves

which produces the structure.

Now the revelation of new facts, as startling as those which are now

experimentally fully confirmed concerning flowing crystals, must

inevitably cause searching reflection as to whether the magnificent

geometrical work on the 230 homogeneous structures, and their

development in actual fact in the 32 classes of crystals, is to stand or

to be seriously affected. Again the author ventures to express the

opinion, that just what happened in regard to the historic differences

between the schools of Haüy and Mitscherlich, will in all probability

again occur, namely, both extreme views will be shown to depend more or

less on real facts, and other connecting facts will eventually be

revealed which will completely reconcile the two series with each other.

In the author’s opinion, the geometrical work will stand, as the grand

generalisation it really is. But it will be interpreted in the future

without the somewhat arbitrary assumptions which have more or less

accompanied it. From these it will be freed, and then rise purified and

elevated to its real dominating position in regard to crystal

morphology.

Lehmann, with the natural enthusiasm of the discoverer of one of the

most remarkable facts for which the last few decades have been famous,

may have carried his theory too far, and particularly in that part of

his work, to which the author has not hitherto referred, in which he

describes certain phenomena of flowing crystals as akin to the movement

of living organisms such as bacteria, and thus brought even some of the

sound facts under the criticism of the sceptic more than might otherwise

have been the case. He may also have made his theory far more

revolutionary than is essential. But the one incontrovertible thing

stands out plainly, namely, that the “flowing crystals” with which he

has made us acquainted are an indubitable experimental fact. Flowing

crystals are produced, however, by a relatively few substances of very

complex molecular constitution, involving a large number of atoms in the

molecule; they are mostly compounds of carbon, and in number possibly

not one per cent. of the innumerable substances known to produce

ordinary solid crystals. That the theory of crystal structure can

eventually be made to include these few remarkable substances is highly

probable, when many more facts have been accumulated.

Lehmann would appear to have made one point very clear, which at once

removes an objection long felt by the author to the theory of crystal

structure as it stands at present, namely, that the chemical molecule is

endowed with a directive orientative force, which is certainly concerned

in crystallisation. To assume, as has been done, just because it is not

necessary from the point of view of the geometrician in developing his

possible homogeneous structures, that no directive force is operative in

crystallisation, and that all is a mere question of the most convenient

mechanical packing of the molecules, is, in the author’s opinion, going

beyond what the experimental facts justify. If Lehmann’s discovery of

flowing crystals does nothing more than return to the molecule the

property always hitherto attributed to it, of possessing in itself some

directive force by reason of which it arranges itself homogeneously by

mutual accommodation with its similarly endowed fellow molecules, when

its motion in the liquid state has been sufficiently arrested by its

approach to its fellows within the range of molecular action (four or

five molecular diameters), either by cooling or the falling out of

previously separating solvent molecules, it will have achieved a notable

thing.

What does occur at the moment of crystallisation is at the present time

one of the most interesting unsolved questions in crystallography, and

one calling most urgently for solution. Attention was directed to the

problem in the last chapter, in connection with the suggestive work of

Miers on vicinal faces. It was shown that it was only when the directive

force had time to come properly into operation that the primary faces of

fundamental importance were produced, and that when the crystallisation

was rapid vicinal faces formed instead. Lehmann believes that a single

kind of chemical molecule is only capable of producing a single specific

space-lattice, and that polymorphism is due to alteration of the

molecules themselves at the critical temperature of transformation. He

showed so far back as 1872 that this limit could be actually observed

under the microscope, as a definite line of demarcation between the two

varieties as the temperature fell, one side of the field attaining the

critical temperature slightly before the other, and the defining line

between the two kinds thus travelling over the field. Internal friction

did not appear to Lehmann to enter into the question at all, as he

considered it would have done if a rearrangement of the molecules were

the sole cause of the change. The molecules themselves, he states, must

have been undergoing change, and such rearrangement of them as occurred

must have been due to that fact.

[Illustration:

_PLATE XXIV._

FIG. 117.—Arrangement of Astatic Magnet-systems in a Plane.

]

[Illustration:

FIG. 118.—Arrangement of Astatic Magnet-systems in Space.

]

Lehmann suggests a very interesting explanation of the molecular

orientative force of configuration, namely, that it is due to the action

of the electronic corpuscles (forming the elementary atoms) rotating in

the molecule. For the molecules of flowing crystals behave like freely

suspended astatic systems of magnets, which are constantly setting

themselves, even while moving about, in a crystalline space-lattice. He

suggests that the molecules are really magnets the poles of which

mutually attract and repel one another; that two equal magnetic

molecules are arranged alongside with opposite poles against each other,

thus mutually binding each other, or that four horse-shoe magnets may be

arranged with opposite poles together, in a tetragonal astatic system,

as shown in Fig. 115, Plate XXII. The latter may be grouped in space in

a cubic astatic system, as represented in Fig. 116 on the same Plate;

while Figs. 117 and 118, Plate XXIV., are further suggestive of how a

homogeneous structure of such astatically distributed molecules can be

built up, Fig. 117 representing a single plane of them, and Fig. 118 the

complete arrangement in space.

An astatic system of molecules of this nature would have lost all power

of attraction by a magnet, and the fact would thus be accounted for that

no striking crystallographic results have ever attended experiments on

crystallisation in a magnetic field. Astatic systems, however, such as

that shown in Fig. 115, would certainly arrange themselves in

space-lattices. For such parallel arrangements would, in general,

involve differences in different directions, with regard both to

internal friction and to the power of thermal expansion and of such

regular dilatational or other deformational changes as we know are

provoked by different physical conditions of environment. These

differences would naturally, in turn, give rise to external polyhedral

form.

Lehmann then goes on to point out that either electric currents or

mechanically moved quantities of electricity, such as moving negative

electronic corpuscles, can give rise to just such magnetic effects, and

he suggests that these corpuscles are the true cause. He supposes that

the directive forces result in astatic combinations which find their

equilibrium when the latter have taken up their positions at the eight

corners of a cube or other elementary parallelepipedon of one of the

fourteen possible space-lattices, the positive atoms being encircled

spiral-wise by the negative electronic corpuscles in alternately

opposite directions. Such parallelepipeda would seek homogeneous

repetition by virtue of the fact of the corners exhibiting alternating

polarity.

These theoretical ideas of Lehmann have naturally called forth much

discussion, criticism, and scepticism. But, so far, his experimental

facts have been fully substantiated by further investigation. Much more

practical work is urgently required, however, before the subject can be

considered as laid on a secure foundation. So much may be said, however,

that it is clear that we must concede the existence of a directive force

of crystallisation, and not be led by the pure geometry of the subject

of crystal structure to ignore facts of such interest and undoubted

importance as have been brought into prominence by the remarkable work

of Lehmann.

A further interesting contribution has recently been made by

Vorländer[27] to the facts regarding the relationship between chemical

constitution and the formation of liquid crystals. It must have already

struck the reader that most of the substances which exhibit liquid

crystals are composed of a large number of chemical atoms, being either

long-chain compounds of the fatty acids or complex derivatives of the

hydrocarbon benzene, C_{6}H_{6}; also that many of the latter are “para”

compounds, that is, derivatives in which the substitution groups are

inserted in the benzene ring of six carbon atoms in the “para” position,

which is that at the opposite corner of the hexagon to the carbon atom

to which a substitution group has already been attached. This renders

the para compounds the most extended in a straight line of all the

benzene derivatives. Now Vorländer finds that a particularly favourable

condition for the production of liquid crystals is a linear structure of

the molecule. As the para substitution products of benzene derivatives

possess this elongated structure, many of them exhibit the development

of liquid crystals. The more linearly extended the structure becomes,

that is, the longer the straight chain of atoms is, the more favourable

become the conditions. The advent of a third substitution group,

however, which would have the effect of producing a kink in the chain,

or of bending it, appears to destroy the possibility of the production

of liquid crystals. This interesting observation may afford the key to

many of the extraordinary phenomena of liquid crystals which have been

described, and is undoubtedly one of prime importance. Further

favourable conditions for the formation of liquid crystals, according to

Vorländer,[28] are the aromatic character, and the presence of the

doubly-linked carbon and nitrogen groups C:C, C:N, and N:N, which are

usually so rich in energy.

The idea of the formation of a specific crystalline homogeneous

structure, merely because the mechanical fitting-in of the molecules

occurs with the minimum of trouble or maximum of ease for this

particular type of all the 230 possible types, is certainly not

applicable to the case of Lehmann’s liquid crystals. With this,

moreover, is also connected the question of softness or hardness of

crystals, which was referred to at the opening of this chapter. For the

so-called liquid crystals are extreme cases of softness, and yet in

these cases the molecules must still be arranged in accordance with the

internal structure of a crystal, either parallel or enantiomorphously

definitely orientated with respect to each other, for otherwise it is

not possible to account for the optical properties resembling the

orientated ones of a crystal. Yet the condition being that of a liquid,

the molecules must be able readily to pass and roll over each other, and

hence cannot be at the close quarters where mere “fitting-in” comes into

play.

Again, as has been pointed out earlier, many soft crystals, even such as

calcite, which are only relatively soft, attaining the position of as

much as four in the scale of hardness, readily exhibit the property of

being deformable upon glide-planes. The molecules in these cases have

been shown to undergo a movement which has two components, a

transference and a rotation, a fact which has been thoroughly

substantiated by optical investigations of the parts of the crystal

concerned before and after gliding. There cannot, therefore, have been

merely “fitting-in” of the molecules, but their orientated positions

must have been determined and maintained by the organising force, which

is probably purely physical and not chemical, but is nevertheless the

cause of crystallisation; it draws the molecules within a certain range

of each other, corresponding to and dependent upon the temperature,

causes or enables them to arrange themselves in the marshalled order of

the particular type among the 230 possible arrangements, and keeps them

at the same time from approaching nearer to each other than within these

prescribed limits corresponding to the temperature. It is doubtless

within these limits that gliding can occur parallel to such planes as

leave the molecules most room for the purpose, and which are directions

of least resistance.

[Illustration:

FIG. 119.—Lehmann’s Crystallisation Microscope arranged for

Projection.

]

Connected with this important question is the principle enunciated by

Bravais, as a result of his discovery of the space-lattice, that

cleavage occurs most readily parallel to those net-planes of the

space-lattice which are most densely strewn with points. The force just

referred to, whether we term it cohesion or otherwise, is obviously at a

maximum within such a plane, and at a minimum in the perpendicular

direction where the points are further off from each other. Moreover, it

has been fairly well proved also, from the experiments of Wulff,

described in the last chapter, that the direction or directions of

maximum cohesion are those of slowest growth of the crystal; so that

faces parallel to those directions become relatively more extended owing

to the more rapid growth of other faces on their boundaries, and thus

become the most largely developed and confer the “habit” on the crystal.

All these are facts so important as evidences of a controlling force at

work in crystallisation, that a _purely_ geometrical theory of the

formation of crystals which would make “facility of fitting-in” of the

molecular particles its chief tenet, obviously does not tell us the

complete story. Hence the author desires to utter a warning against

going too far with the pure geometry of the subject. The geometricians

have done a grand work in providing us with the thoroughly well

established 230 types of homogeneous structures, as a full and final

explanation of the 32 classes of crystals, and so far their results are

wholly and unreservedly acceptable.

The phenomena of “liquid crystals” lend themselves admirably to screen

demonstration, for which purpose an excellent improved form of the

crystallisation microscope of Lehmann, shown in Fig. 119, is constructed

by Zeiss, and its actual use in the projection, with the aid of the

well-known Zeiss electric lantern, but specially fitted for the purpose,

is shown in Fig. 120.

A magnification of 600–700 diameters on the screen is very suitable,

employing a Zeiss 8–millimetre objective without eyepiece. This

objective affords directly a magnification of 30 diameters. For ordinary

eye observation an eyepiece magnifying 6–8 times is added, thus

affording to the eye a magnification of about 200 diameters.

[Illustration:

FIG. 120.—Zeiss Apparatus for the Projection of Liquid Crystals.

]

The lantern is supplied with a self-feeding electric arc lamp, ensuring

a steady light. A collective lens of extra light-gathering power is

fitted in front as condenser, and from it proceeds a light-tight tube

provided with a water cell to filter out most of the heat rays which

accompany the light. The electric lantern with Brockie-Pell or Oliver

self-feeding arc lamp, shown in Figs. 71 and 79 (pages 186 and 202), is

also equally suitable, and with the water cell, and parallelising

concave lens removed from the large Nicol polariser, affords a parallel

beam of the same character as the Zeiss apparatus. The microscope stands

on a sole plate provided with levelling screws, and is naturally

employed in the vertical position for such work with fused substances. A

mirror inclined at 45° at the foot of the microscope directs the

parallelised rays from the optical lantern through the microscope, and

another above the optical tube reflects them to the screen.

The heating apparatus consists of a form of miniature Bunsen burner

fitted with blowpipe blast, the respective pressures of gas and air

being regulated by means of two taps with graduated arcs for obtaining

greater delicacy of adjustment. The tabular plate seen to the left in

Fig. 119 is the graduated semi-circle of the two taps; below it is seen

the cylindrical mixing chamber for gas and air, in the event of the

necessity for using the Bunsen as a blowpipe. There are two separate

attachments for indiarubber tubes to this cylinder, conveying

respectively gas and air. Above the object stage a double air-blast is

fitted, each tube of which is hinged with a universal joint, so that it

can be readily adjusted to any desired position on either side of and

above the glass plate (supported on little metallic uprights) on which

the experiment is being conducted. A polarising Nicol prism and an

analysing Nicol, both constructed in a manner which protects them from

the effects of heat more effectually than is the case with the usual

form, are provided for obtaining the projections in polarised light. The

objective and analysing Nicol, as well as the substage condenser, are

also specially protected from injury by heat, by being surrounded with a

water jacket, supplied with running water, and a disc-like screen just

above the objective assists in deflecting the heat rays from the optical

tube and its Bertrand lens and other usual fittings. The miniature

Bunsen flame is usually brought about an inch below the object-plate,

and the size of the flame can be regulated with the utmost precision, so

that a fairly constant temperature can be obtained for a considerable

time. With the aid of the blowpipe air-blast temperatures up to 700° C.

can be safely employed.

The microscope shown in position on the projection apparatus in Fig. 120

is a still more recent form introduced by Zeiss, embodying several

further conveniences and improvements.

The following substances lend themselves particularly well to projection

purposes. Para-azoxy-anisol with resin, which exhibits the phenomenon of

rotating drops; cholesteryl acetate, which affords a fine example of

spherical liquid crystals; paraazoxy-phenetol with resin, which gives

beautiful interference colours; and the acetyl ester of

para-azoxy-benzoic acid with resin, which shows the uniting of crystals

to form larger and larger individuals.

Perhaps the most interesting and beautiful of all is cholesteryl

acetate, a characteristic field of which is shown in Fig. 121 on Plate

XVI., facing page 208. It is interesting that on this Plate XVI. there

are represented the very hardest and the softest of crystals, namely,

diamonds and liquid crystals. In order to obtain the finest effect the

heating and cooling should be carried out very slowly. The little Bunsen

burner, with a very minute flame, is first placed under the slide, and

allowed to act until the substance melts and forms a clear liquid. The

gas jet is then removed and the air-blasts, both of which are

simultaneously actuated when the tap controlling them is turned, are

very gently brought into operation, one on each side of the centre of

the slide, there being a good working distance of a quarter of an inch

or more between the slide and the objective. The cooling is thus brought

about very slowly. The Nicols should be crossed, and at this time the

field is quite dark, the liquid substance being at this temperature

(well above 114.5° the ordinary melting point) an ordinary singly

refractive liquid.

As soon as the temperature has become reduced to that at which the

particular modification of cholesteryl acetate is produced which forms

liquid crystals, spots of light make their appearance at various points

in the field, and each expands into a beautiful circular and more or

less coloured disc marked by a rectangular sectorial black cross, which

latter is well shown in the illustration (Fig. 121). These beautiful

apparitions continue to occur, and each to expand to a certain size,

which is rarely exceeded, until the whole field becomes filled with the

wheels or crossed discs, the general effect very much in some respects

resembling that afforded by a slide of the well-known polarising

substance salicine. These discs, however, are liquid, being spherical

drops, of the structure already described and illustrated in Fig. 103,

and that this is so is at once made apparent on touching the cover-glass

with a pen-knife or other hard pointed substance, which immediately

causes them to become distorted. They recover instantly their shape

again when the pressure is removed. When the cooling, moreover, has

proceeded still further, there is a sudden change, and acicular solid

crystals shoot over the screen, tinted with all the colours of the

spectrum, until the field is full of them, the ordinary solid

modification of the substance having then been produced. The experiment

may be repeated with the same specimen of the substance, mounted on the

same slide, covered with the usual thin cover-glass, time after time for

months, at reasonable intervals.

In concluding this chapter it may be mentioned that absolute proof of

the double refraction of the liquid crystals of several different

substances, derivatives of cinnamic acid, has been afforded during the

year 1910. For direct measurements have been carried out by two

independent investigators, Dorn and Stumpf, of the two refractive

indices corresponding to the ordinary and extraordinary rays in each

case, the crystals being uniaxial.

CHAPTER XVII

THE CHEMICAL SIGNIFICANCE OF CRYSTALLOGRAPHY. THE THEORY OF POPE AND

BARLOW—CONCLUSION.

Nothing in connection with the subject of crystallography is more

surprising than the neglect and apathy with which it has been for long

treated by the chemical world. That crystalline structure is intimately

related to chemical constitution will have been made abundantly plain

during the course of this book. Yet in spite of the great work of

Mitscherlich, essentially a chemist, and of a large amount of striking

work which has been steadily accumulating during the last thirty years,

with results of vital importance to chemistry, it is only at the

eleventh hour that chemists are really awakening to the vast

significance which crystal structure has for them.

The explanation undoubtedly is, that the long interregnum of conflicting

investigations, doubt, and controversy, which followed the work of Haüy

and Mitscherlich, and preceded the beginning of really accurate and

painstaking investigation of an organised and systematic character, had

caused chemists to regard with more or less of indifference the work of

the crystallographers. Added to this we must remember that the subject

of crystallography has hitherto been taught, when taught at all, merely

as an appanage of mineralogy, although the pure chemical substances

which crystallise well infinitely outnumber the naturally occurring

minerals, and the results afforded by them frequently possess a much

greater value by reason of the purity of the substances and their more

definite chemical constitution. Also the mathematical and geometrical

side has usually been unduly emphasised, and carried on in lectures

without any practical goniometrical work at all. Moreover, the current

text-books have often proved forbiddingly full of calculations and

formulæ, and of the obsolete and unenticing symbols of Naumann.

At last we have come to see that the subject is one of fascinating

interest when its study is commenced in a practical manner from the

beginning, armed from the very first lesson with the goniometer. The

crystal itself is then our main and highly interesting study; its

exterior form unravels itself in a most delightfully simple manner when

we follow the arrangement of its faces in zones on the goniometer

itself; and its symmetry becomes immediately patent to our eyes in all

ordinary simple cases, when we construct for ourselves its plan in a

stereographic projection, drawn at first in freehand while still at the

goniometer. The calculations also become perfectly simple when we have

learnt that only the simplest of the very easy formulæ of spherical

trigonometry are required, and which a knowledge of only elementary

plane trigonometry enables us to apply. Aided by a few very helpful

rules, such as those of Napier for calculating right-angled spherical

triangles, and the rule of the anharmonic ratio of four poles in a

zone—which, when the positions of three crystal faces of the zone are

known, at once enables us to calculate the situation of any fourth face

of the zone—we have at once a stock-in-trade which carries us over all

difficulties in the way of calculation, and relegates this side of the

work to an altogether subordinate position, although accuracy in

carrying it out is, of course, absolutely essential and even vital.

Especial interest has recently been attracted on the part of chemists to

the bearing of crystallography on their science by a remarkable theory

which has been advanced by Pope and Barlow, connecting the internal

structure of crystals with chemical valency, the power which the atom of

a chemical element possesses of combining with the atoms of other

elements, and which is generally expressed by the number of atoms of a

monad element, such as hydrogen or chlorine, with which it is capable of

combining chemically. Thus the electro-positive metal potassium is said

to have monad valency because it is capable of combining with one atom

of the electro-negative element chlorine to form the salt potassium

chloride, KCl; calcium possesses dyad valency because it can unite with

two atoms of chlorine to form calcium chloride, CaCl_{2}; aluminium is

triadic as it can combine with three atoms of chlorine producing

aluminium chloride, AlCl_{3}; carbon is a tetrad because it can take up

four chlorine atoms, forming carbon tetrachloride, CCl_{4}, and

phosphorus a pentad as it can fix five with production of phosphorus

pentachloride, PCl_{5}; while sulphur is a hexad because it can take up

as many as six atoms of chlorine, forming sulphur hexachloride, SCl_{6}.

Occasion has already been taken in Chapter XI. to refer to the able work

of Prof. Pope with regard to optically active carbon compounds, and in

Chapter IX. the important contribution of Mr Barlow to the completion of

the theory of the homogeneous partitioning of space has likewise been

discussed. In collaboration these two investigators have now propounded

a theory which connects the chemical and geometrical sides of

crystallography in a somewhat startling manner, which has naturally

aroused very considerable discussion, and which, whether right or wrong,

cannot fail to have the best results in attracting investigators to the

subject.

Starting from the facts which have now been laid down in this book as

having been firmly established by the most careful measurement and

experimental investigation—notably the constancy of the interfacial

angles of the crystals of the same substance, the fixed positions of the

atoms or their spheres of influence in the molecule and in the crystal,

and the arrangement of the molecules in space-lattices and the atoms in

point-systems—Pope and Barlow assume that valency, the expression of the

relative combining power of the chemical elements, is a question of the

size of the sphere of influence of the atom of an element, and that the

relative sizes of such spheres of influence determine the modes in which

they can be packed, that is, the nature of the homogeneous crystal

structure which they can build up. The theory consequently renders the

chemical phenomenon of valency and the physical phenomenon of

crystalline form mutually interdependent.

It will thus be apparent that the essence of their conception is that

the chemical molecule may be considered as made up of a number of

spheres corresponding to, and representing, the spheres of influence of

the atoms composing it, and that the volume of each sphere is roughly

proportional to the valency of the atom which it represents. They then

assume that the sum of the valencies of the atoms present in the

molecule may be substituted for the molecular volume, and the quantity

thus arrived at is termed by them the “valency volume.” By using the

valency volume instead of the molecular volume in the author’s formulæ

for calculating the molecular distance ratios, which have been shown in

Chapter X. to afford the relative dimensions of the unit cell of the

space-lattice, and the distances of separation of the centres of gravity

of the molecules from each other along the directions of the crystal

axes, Pope and Barlow arrive at new ratios, which they term equivalence

parameters. By the use of these latter they have attempted to account

for the crystalline structure of a number of substances—chiefly organic

compounds, in the investigation of which Prof. Pope has proved so

adept—which are connected morphotropically in the manner described in

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,[29] 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,[30] 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.