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Le diagramme suivant illustre la mdthode : 1 2 3 1 8 S » 6 /7 Crystal Formation of the Elements AND THEIR Allotropic Modifications With a Deduction of the Atomic Forms therefrom I ..BY.. i :!■ 1 1 I i -WM. L. T. ADDISON, B.A., i M.B. J 1 i " ■ ' 1 t •j' 1 i %" i a: C ^ (^ © 1 TORONTO : The Mail Job Printing Co'v, Limited. 1898. 1 1 — . . 1 ■•■"■"• ^--^"- „^- '*'• ON Crystal Formation of the Elements AND THEIR Allotropic Modifications With a Deduction of the Atomic Forms therefrom ..BY.. WM. L. T. ADDISON, 13.A., M.B. TORONTO : The Mail Jon Printing Co'v, Limit i:d. 1898. PREFACE. An outline of the research of which this monogram treats was given before Section B of the Toronto meeting of the British Association for the Advancement of Science. The paper after all possible condensation proved too long for the time allotted to its reading. Its length and character renders it inconvenient as a scientific magazine article. In response to' a number of requests that the paper be published, the Author, after revising the MS. and add- ing where he deemed it advisable, issues the paper in its present form. Wm. L. T. Addison. April 27, 1898, Byng Inlet P.O. Ontario, Canada. CHAPTER I. Molecular form and arrangement. CHAPTER H. The form of the atoms of the elements of group IV. of Mendeljeff's table. CHAPTER HI. The forms of the atoms of the elements of group V. of Mendeljeff's table. CHAPTER IV. The atom forms of the elements of group VI. of Mendeljeff's table. CHAPTER V. The atom form of iodine, and the phe- nomena of crystallization of iodine from solutions. CHAPTER 'VI. The atom forms of the elements of groups III., II. and I. of Mendeljeff's table, and the influence of atomic form upon malleability. CHAPTER I. Molecular Form and Arrang^ement. As a preface to the research presented before you, a short outline of the history of the progress of the study of Crystals, is interesting. Nicolas Steno, a Dane, in 1669, gives, as a result of his observations of crystals, thr,' law, "in piano axis laterum et numerum et longitudinem varie mutari non mutatis angulae." In 1707 Robert Hoyle observed bismuth to crystallize from its molten state. In 1768 Linnaeus classified crystals as cubes, prisms, and pyramids. In 1772, Bergman drew attention to the planes of cleavage in the rhombohedron of calcite, and made a study of cleavage, internal forms, and arrangements of crystals. In 1783, Rome Delisle formulated his law of constant angles, that the angles formed by corresponding faces of crystals of the same compound are equal. This law under more modern knowledge has been modified to the following ; " the angles formed by corresjjonding faces of crystals of the same compound are under the same temperature eijual." l-oUowing and as a later contemporary of Rome Delisle lived Hany. From observation of the planes of cleavage of calcite, Hany built the following theory of the structure of crystals : — "In each mineral there exists integrant molecules, solid bodies incapable of further division and of invariable form, with faces parallel to the natural joints indicated by mechanical division of the crystals, and with angles and dimensions given by calculation and observation combined. These molecules are marked in different species, by distinct and determinate forms, except in a few regular bodies as the cube, which do not admit of variations. From these integrant or primitive molecules, all the crystals found in each species are built up according to definite laws and thus secondary crystals are produced. " Of these primitive forms six only were known from observation, the parallelopiped, the octahedron, the tetrahedron, the hexagonal prism, the dodecahedron of triangular face^ ^nd composed of two six-sided pyramids base to base, and the rhombic dodecahedron. In order to produce secondary crystals which cover the primitive form, so as to disguise it in so many different ways, he supposed the enveloping matter, "to be made up of a series of laminae, each decreasing ecjually in extent either in all directions, or at certain points. This decrease takes place by the regular substraction. of one or several ranges of integrant molecules in each success- ive layer, and the theory (determined by calculation of the number of these ranges), can represent all known results of crystallization, and even anticipate discoveries, discover hypothetical forms, which may some day reward the research of the naturalist." He also discovered the modification of the angles, edges and faces accord- ing to the laws of symmetry : and, that the variations of form in ai)parently similar compounds, indicate in reality, a difference in t'ne ( omposition. hater Mitscherlich discovered the replacement of one compound in a crystal, by other compounds of similar chemical grouping. This he discussed as vicarious displacement. If the experiment of fracture of calc or Iceland spar be followed, the inference is of a fission into integrant molecules, and that these molecules are definitely and regularly arranged, which arrangement accounts for its gross form. If the calc-spar be ground, and the particles (which microscopi- cally are rhombohedra) be placed in mechanical contact, the result is not a gross rhombohedron 'such as has been destroyed, but still a powder. At some time in its history, there has been some agency, not now present, at work to cause this arrangement. If, however, some c.-ystals of potassium ferrocyanide (which show an equally marked cleavage) be crushed, as was the calc-spar, and placed in water, a new condition is brought about. The powder is dissolved, and the result is a yellow solution. If the water be evaporated from this solution, there are left crystals of similar angles to those destroyed by grinding, showing that though the connection of some parts of the crystal have l)een severed, yet it has with., itself, a [selective power for some particular and chosen arrangement. The molecules have been set (juite free in the solution, and have been given the opportunity of selection, as determined by some power within themselves. Were there no attraction the one molecule for the other, as the solution became overloaded the particles would drop down, one by one, to form an amf)ri)hous powder. The particles or molecules are, however, thrown out as aggregates of crystals of definite proportions and angles, and of the same angles and projjortions as those of the cry tal destroyed. This shores an attraction of some sort, in definite directions. The form might arise as suggested by Hany, " from integrant molecules, solid bodies incapable of further division^ and of invariable form, with faces parallel to the natural joints indicated by the mechanical division of the crystal, and with angles and dimensions, given by calculation and observation, or both combined " ; or from such forms, as are suggested by 1 ).alton's diagrams, roundish or irregular atoms but of indefinite form ; or from definite masses, projected in definite directions, to a definite extent in space, so that if these points be joined, they would, in outline, enclose a definite space of a definite form, such as are found in crystals. The gross or resultant form need not be the same as the integrant form, but is a result of the arrange- ment of such forms. Hany's theory is an inj^cnious one, l)ut one founded before the estabUsh- ing of Dalton's atomic theory, and before the discovery of tlie dimorphic forms of calcium carbonate. Such a theory would require two sorts of integrant molecules of calcium carbonate, one for calcite, and one for aragonite. The regular and rhombohedral forms of carbon and phosphorous would thus recjuire different integrant forms of the same element. Were this theory correct, it would reciuire a plastic atom (jr molecule, and one in which the form of lighter specific gravity occupies more space than the one of heavier specific gravity. This controverts his theory of invariable molecules. Were his theory applied to the 'molecules of compounds, it involves a molecule of faces, which again necessitates either: (i) a fusion of the atoms within a molecule to form a homogeneous mass of geomerrii- form, or (2) within this geometric molecule a definite sjjace filled by each atom, be this as a whole face, a portion of any or several faces, or be it within the space enclosed by these faces. 'I'he individuality of the form of the atoms within a compound, and theiv varied arrangements, account too fully and distinctly, for isomeric compounds and stereo forms of the same compound, to accept the first alternative. Potassium iodide exists in cube form, and by Hany's theory its molecules are cubical in form. Potassium as an element exists in quadratic octahedra, iodine as an element exists in rhombic plates. Neither of these may make a cubical face by arrangements of their own forms, or l)y any combination of their face forms, so that the second alternative cannot be accepted. I )alton's diagrams show the atoms as round forms of matter, attached to each other. His hypothetical forms do not indicate any special areas of valence, and ir them it is supposed that an atom might be attached to another at any part. An arrangement of similar atoms would thus be as shot in a pile, and result in regular forms only, and could not account for such allotropic modifications, as those of carbon and phosphorous, so we must dispense with this theory. Were a number of atoms grouped about another (as they are), it would produce a grouping of prominences about the central atom. These outlying points give the molecule its form, and such form must determine the gross form. The form of the same compound is constant, and so it follows, that the grouping of the atoms about the central atom, is constant and fixed. It is found that analogous compounds crystallize in similar forms, often replacing each other in the same crystal, and in so doing modify the crystal but slightly by their presence. Mitscheilich, the observer of this phenome- non, says "substances which are analogous chemical compounds have the same crystalline form and replace each other." Thus crystallizing in rhom bohedra may be found. CAl.C-SrAR. DOI.OMITE. MAC.NKS.CARH MANO. CARK. FERROUS CARB. ZINC CARB. o / 105 5 106" 15' 107° 29' 109° 51' 107° 0' 107' 40' These might better be spoken of as similar forms, for while their angles a[)proximate each other, they all vary slightly. Then close approximation of form, together with their analogous chem ical composition, and the tendency for the one to replace the other in well- defined crystals, show a marked similarity of gross and molecular form. There is in each a common factor, the group CO,.,, which may be cred- ited as the basis of the common form. The valence of CO;, being common, there must be a similar placing of the valence areas of calcium, magnesium, manganese, iron and zinc. There must also be some difference in each element, which shall increase the molecule of the compound in a definite direction, and so vary the form resulting from the arrangement of these out- lying points in space. This difference must be in the displacement, arising from the difference of size and form of the atoms of the above-named basic elements. Calcium carbonate occurs as calcite in rhombohedral forms of spec. gr. 2.9, and aragonite in rhombic forms of spec. gr. 2.7. Aragonite if heated breaks down to a powder, which under the microscope is seen to be of small rhombobedra, and is of spec. gr. 2.9, or in other words, breaks down to cal- cite. This must result from a different arrangement in the two forms of a common sort of lecule. In aragonite the molecule occupies more space than in calcite, and hence, in aragonite at least, there must be some unfilled space between the molecules. So far the substances dealt with have been principally compounds, and so are more complicated. The next chapter will deal with the less complicated substances or elements. CHAPTER IL The Above Forms the Elements of Group IV. of Mendeljeff's Table. Carbon, as an element, occurs in two crystalline modifications, diamond and graphite. As the diamond it crystallizes in regular tetrahedra, octahedra, rhombic dodecahedra, and trisoctahedra. Its spec, gr- is 3 • 5 to 3 . 55, see Von Buchka's tables; or 3.5 to 3.6, see Zirkel's " Mineralogie." 8 That its cleavage is in regular octahedra, shows a tendency to that form, and that the atoms are arranged in series giving rise to fission in the octahedral planes. It might mean that the atoms are of octahedral form, and it means that the lines of union of the atoms lie in octahedral planes. If six regular octahedra be placed edge to edge, with a solid angle of each about the same point, a larger octahedron will be obtained. These octahedra do not fill space, but are separated by regular tetrahedral spaces. Suppose regular tetrahedra be placed in these spaces, and the regular octa- hedra withdrawn, the lines of union and cleavage will still remain the same, that is of regular octahedral cleavage. One of these two forms is necessary to produce such a cleavage. It has been seen, that the form of the molecules is dependent upon the outlying points, and these are caused by the atoms attached to the central atom. The form of these molecules are, therefore, due to the attachments of the atoms, or to the areas of valence of the central atom to which the outer atoms are attached. Such a relationship would show valence, and the form of the atom, or its differentiated and attractive portions, to be intimately connected. If the solid angles of the two solid forms, which would account for the diamond, were areas of valence, then the octahedron would be hexavalent, and the tetrahedron tetravalent. AVere the attraction of valence and of crystallization the same, then on the above supposition, the tetrahedra would fulfill the reciuirements. So far the atoms have been discussed as solid bodies. Of this there is no proof, yet in the discussion of the hypothesis of atomic forms, a solid, for convenience in nomenclature, will be assumed. If eight tetrahedra about a point, be attached by their edges, they will give a form with eight exposed surfaces, which if produced would give an octahedron. If eight tetrahedra be attached by their edges, and so arranged as to enclose an octahedron, they will give rise to a form, corresponding in its outlying angles to a cube. If either of these forms be cut through one of its principal axes, it would be divided at the line of attachment, and if each half be reversed and reattached, the form resulting would be found to be the other one of the two forms just described. If the number of tetrahedra attached edge to edge be increased, then the gross form is merely one of fission. If an addition of regular tetrahedra be made about the octahedral-faced form, until there be thirty-two, about this model by fission, or by building out certain series may be produced, the regular tetrahedron, cube, octahedron, and rhombic dodecahedron. Assuming the octahedral form as demonstrated by fission, on each face is seen a series of three points projecting into space, the satisfaction of which tends toward the trisoctahedral form. In the model of 32 tetrahedra, all the outlying points lie in a sphere, the full satisfaction of which would tend to a sphere and so the curved faces of diamond crystals. \VL'rL' the octahedral spaces filled in by octahedra and the tetrahedra withdrawn, there would then he no tendency to the trisoctahedrai form. Thus the evidence is in hwor of the atomic form of carbon being tetraliedral, and of the same number of solid angles as it has areas of valence. A regular tetrahedron is a four-sided figure, and as such, is the simplest isometric form that may enclose si)ace; If two regular tetrahedra be placed base to base, they give a bipyramidal hexahedron, and one with five solid angles. The sides are of e(iuilateral triangles, and the angles over the com- bined bases or the zonal edges of the hexahedron are 141'' 3' 18". The angles over the remaining edges are 70" 31' 47". The solid angles are of two sorts, two apiceal and three zonal. This form is of interest, in that it is referred to in the discussion of phos- phorous. If an infinite number of regular tetrahedra were arranged edge to edge to give octahedral spaces, the different proportion of the outer layers might be ignored. The inner portion of the model would have a homogeneous arrangement It is found that in it the tetraliedral faces form the faces of the octahedral spaces, so that for each octahedral fiice there is a tetrahedral face. The proportion of the tetrahedra to octahedra then, is inversely to the num- ber of their faces or as four to eight or one to two. It may be well while the proportions are fresh in mind to work out some calculations, which will be of use in further study. Tiie space of the regular tetrahedron may be foui\d as follows : The octahedron consists ,- =3.7712 cubic inches. An oitahedron four inches in edge would be composed of six octahedra and eight tetrahedra of two inches edge. The area would then be 2 ('*'" x -r-) = -':r-'- '!''">« six octahedra of two inches edge would be 6 {^p) ■= i^^^^, therefore the remaining eight tetrahedra woukl occupy ('--;J-^ - -Tr~) = -V"-> and one tetrahedron would be '-->.(''-, or -^ of that of an octahedron. The octahedron of two-inch sitle has an area of 3.7712 cubic inches, therefore the tetrahedron of two-inch edge has an area of .9428 cubic inches. In the diamond model the tetrahedra are to the octahedra, as two to one, and the space filled, is as two to four, or one-third the entire space filled. The length of the bipyramidal hexahedron, as described, may be esti- mated as follows : — If the angles at the base of a regular tetrahedron be bisected, and the bisecting lines be produced, they will be at right angles to and bisect the opposite sides, and will intersect at the centre of the base, to divide the base into six ecjual triangles. The angles about the common point 10 of intersection are 60° each, and the half of the bisected angle is 30", so that each triangle is half of an eciuilateral triangle of sides e'- -?^>/-^= 1.63 inches. Twice the line from the apex to the centre of the base -the length of a hexahedron of 2 inches edge = 3. 26 inches. If instead of sectioning the octahedral-faced group of eight regular tetrahedra in the principal axes, it be sectioned in one of the diagonal axes of synuiietry, the arrangement will then be in layers, which, if produced, are of triangu'ar and hexagonal arrangement. Each layer is comi)osed of two series, one of which has the apices of its tetrahedra ])()inting downwards, and the other with the aj)ices of its tetrahedra pointing upwards. Such a series has its outer surfaces in a symmetric condition, in that they each are of the same sort, and would tend to ecjual di-velop- ment on each side. Suppose one of these series to be removed, then that s\ nmietry is removed, and the free areas of attraction are all upon one side, and tend to develop on that side only. Since the apc\ does not lie over the edge of the tetrahedron, there is a recession from the edge of the base, at the angle of that edge or 70° 31' 47", fvnd the result would be a hexagonal column receding from its base at angles of 70 31' 47 ". Were the ba>^c, as it might be rhombic, then the column arising from it would form a rhombohedron. Such an arrangement of tetrahetlra would gi\e rise to a rhombohedral form, or a hexagonal form, the long axis of which was oblicjue to the three zonal axes. This last form might be <:lassified as a monoclinic form, the long axis being oblique, and the three zonal axes be reduced to the rhombic two axes at right angles. Such a form will prove of use in the study of carbon as graphite. Such a form has half the number of atoms to the space as the diamond form has, and so would be of half the specific gravity of the diamond. II Carbon as graphite occurs in the hexagonal and rhombohedral forms. It has a basal cleavage, and the base shows triangular striations. It is a soft, flexible mineral, and in its pure state has a smooth frictionless feeling. For form see Dana's Text-book of Mineralogy, p. 230. Von Huchka's 'I'ables. p. 12. Zirkel's Mineralogie, p. 301. Concerning the data of graphite many ditificulties arise. It is usually very impure, containing (juartZ; iron, calcium carbonate, etc., with a specific gravity varying from 2.26 to r.8oi8. This last figure is from an observation by I. owe, and is given as of a jjcrfectly pure preparation (des ganz reinen preparirteni, and as such should be accepted as the most nearly correct esti- mation. The softness, together with the impurity, would naturally bring about a variation of angles, and this does occur. The effect of a soft, pliable character in the crystal form of an element is well shown by jjotassium, sodium and gallium, all of which crystallize in long, regular and short octa- hedra. In such crystals the law of constant angles does not hold. Clark, Suckow and Nordenskiold found crystals of graphite to occur in the monoclinic system, in which the angle of the base on the oblique axis is 71" 16' and the angle of the faces as P. 122' 24', which angles approximate very closely 70° 31' 17 " and 120, the angles shown for arrangement of tetrahedra, as described on page 11. Craphite has been 01- erved by ecjually accurate observers to be in the hexagonal system. Were this not so the variations to which its angles are subject, together with the close approximation of the observed angles to those of the theoretic form, and the intermobility of the theoretic form, would make it proper to still regard it as hexagonal in form. In addition to its form being accounted for, its specific gravity is accounted for by the theory of a regular tetrahedral primal form, in that the specific gravity of the diamond is 3.5 to 3.6 and that of pure graphite is 1.8018. Its pliability is accounted for by its extreme opportunity of inter- mobility, and the triangular striations on the base, may be accounted for by the prominent unsupplied angles of the tetrahedra which are exposed upon the base, and that certain series of these atoms are built up above the others. Suppose a series of six regular tetrahedra be placed about a point with their bases in the same i)lane, and with the body of every other one placed respectively above and below this plane, the result will be six hy])othetical carbon atoms, each bound to the others with three of its bonds of valence, and in union with all the others, though specially bound to the two more adjacent ones. Thus a ring with free bonds of valence so that i, 3 and 5 and 2, 4 and 6 are ^milarly arranged to the base, and with i to 4, 2 to 5 and 3 to 6 in symmetric positions towards the centre, is formed. 12 This arrangement, and this alone, accounts for the peculiarities of the benzene ring, and were this the only proof of the regular tetrahedral form of the atom of carbon, the hypothesis might be regarded as a working one. Assuming valence to be a function of form, it follows that the remaining elements must have their valence accounted for by their form, and vice versa. A tetrahedral form must be assumed for all the elements of group IV. of Mendeljeffs table, and by its arrangements account for its ?;ross form and physical properties. Silicon, germanium, lead and thorium all occur in regular octahedra, and may be accounted for as in carbon. There remain unaccounted for titanium, zirconium, tin and cerium. Tlie gross forms of titanium and cerium are not yet known. Zirconium has been observed in microscopic monoclinic leaf- lets, that is in leaflets of a less symmetry than oilhorhombic. Were the other axis known it might be found oblicjue. Tin was observed by Franken- heim to be in the regular system, but later observers have found it in (luad- ratic octahedra. These (luadratic octahedra may be formed of (juadratic tetrahedra, whose faces are of equal isosceles triangles. A section through the oblique lines of symmetry of these octahedral groups, would give series which appear monoclinic. These series would account for the monoclinic leaflets of zirconium. It may be, however, due to a laying of the ([uadratic tetrahedra down, as in the regular tetrahedra to form a rhombohedron, and that zirconium may be capable of allotropic modifications. Titanium, tin and zirconium dioxides, are not only in the same form, but are isomorphous ; showing that the one molecule is of such a form as to replace a molecule of the other compound, in the same crystal, that is of the same form. The oJcygen is common to both, hence the atoms of which the oxides are compounds are of the same form. This would con- firm the view that the atoms of zirconium are of a (|uadratic tetrahedral form. CHAPTER IIL The Atom Forms of the Elements of Group V. of Mendeljeffs Table. In pursuance of the hypothesis of form being coincident with the func- tion of valence, the atoms of group V. must have a form of five solid angles, and the gross forms must be such as arise from this atomic form. The specific gravity must be inversely in proportion to the space occu- pied per atom. Phosphorous is found in a rhombohedral form of specific gravity 2 . 34, and in a regular octahedral and rhombic dodecahedral form of specific gravity 1 .957 or 1 .826 to 2.098. See Von Huchka's tables. Arsenic and antimony are also found in rhombohedra, and in the regu- lar forms. (See Zirkel's Mineralogie.) There has not as yet been discovered 13 a regular form of bismuth. JJismuth exists in the rhombohedral form, as does phosphorous, arsenic, and antimony, and isisomorphous with arsenic and antimony. That there is a regular form in phosphorous is a very significant fiict, and tends to show that its primal form is of a regular form, or a combination of regular forms. This is merely a guiding fact. In carbon there is a rhombohedral form and a regular form, the specific gravities being as one to two. In phosphorous there are rhombohedral and regular forms, of specific gravities three to two. This shows a different arrangement, and arrangement being consequent on form, would tend to show a difference of form. 'I'he bipyramidal hexahedron as described on page lo, has five solid angles, two ai)ical and three zonal, and as such would satisfy our hypothesis, and would at the same time have some features of the regular system. If these hexahedra be arranged edge to edge, so that about a point two apical and three zonal solid angles meet in such a way that the apical angles are opposite, and the zonal ones arranged synmietrically about the point of union, the arrangement if continued will have its lines ol iission and series, in rhombohedral planes, and each series will interlock with the ones above and below it. I'hus any series will be incomplete, and will tend to irregular development, and this is well marked in both antimony and bisnuith. The arrangement as described, consists of a series of columns of atoms separated by columns of unlilled space. These columns of space are of unfilled octahedral spaces face to face. Two of the faces of octaliedral spaces are in apposition wuh other octahedral s|)aces, and thus each octa- hedral space has six remaining sides, which are in apposition with the Oices of the hexahedra. l<:ach hexahedron has six faces, and so the hexahedra and the octahedral are as one to one, or there are two tetrahedra to one octahe- dron, and one-third of the space filled, or each hexahedron of two inch edge occupies 5 .6561' cubic inches of sjjace. Suppose eight hexahedra to be arranged edge to edge, so that eight apical angles are about the same point, the arrangement of the inner half of these atoms is the same as that of the carbon atoms in the diamond mode!, and the whole form may be regarded as the octahedral form, made by eight regular tetrahedral atoms with eight other tetrahedra upon the faces, the out- lying solid angles of which if joined would form the edges of a cube. The question arises do these groups act as a unit, or do the individual atoms go on adding themselves to the form already within the group ? If one outlying solid angle be built about by individual atoms, the others must be built about to retain the symmetry. To do this it is necessary either to have an apical solid angle in apposition with a zonal one, or to have the atoms reverting into the model, and into an insufficient space. 14 The arrangement of apical and zonal angles together is a rhombo- hedral arrangement, and so the atoms do not act in this form separately, but in groups. In connection with the hypothesis of an eight atom group, it may be ohserv^'d that there is a potential line of fission in the principal axes of the cube form. The cubical arrange.nent results in eight apical angles meeting at the same point, and the distance between the two apical angles of the atom is the distance from the centre of the cube to its angle. This has been shown to be in a two-inch edge hexahedron 3. 26 inches. The line from the centre to the angle of the cube is one-half the line joining the opposite angles of the cube. If a- -= the side of the cube, then the diagonal mentioned ^=.v ^'3, and the line from the centre to the angle of the cube = ^'^^ = 3.26 inches ; X = «;:V'- ; .x" - contents of cube = ('>Jt^)'' = 53- 34' cubic inches. Eight hexahedra occupy 53.341 cubic inches; one hexahedra occupies 6 . 668. The specific gravity of the rhombohedral form is 2 . 34, and since the specific gravity is inversely to the space occupied per atom, the specific gravity of the regular form should be ---^, ,',;&-"- = i -^^S- The average of the extreme estimations at the ordinary temperatures as given in Von Buchka's tables is '_«^ool until it begins to crust over, then the crucible is broken, the fluid sulphur drained off, and a network of brilliant yellow crystals left. These if examined within an hour, and while they retam their brilliancy, show a marked and constant cleavage in different crystals, so that the base is at 79 + to the long axis of the column. The cross section or basal face has angles 118 - and 62 + , a condition which might once in a great number of cases have a rhombic proportion but does not tend to assume proportions which when apparently conjplete are rhombic. The forms are columnar and most freiiuently ending abruptly. By beating a solution of sulphur in carbon disulphide to loo'C under pressure, the monoclinic form is given. Its specific gravity is 1.96. This form, as has been stated, reverts in a few hours to the rhombic variety, showing a rhombic cleavage and specific gravity. This action takes place with the evolution of heat, thus indicating that the rhombic form is the most stable one, and the monoclinic modification is in a condition of strain. Of whatever primal form the sulphur atom is, it must be of such a sort that it will give rise to, ist, a gross rhombic form which is stable; jnd, a gross mono- clinic form which is in a condition of strain, and which tends to give a rhombic form when this strain is effective; 3id, a slight change of specific gravity in the transition, so that this change is inversely to the space occupied per atom ; 4th, an arrangement in which there is a free space through which the atoms may rotate in their change from the monoclinic form to the rhombic form. If six octahedra be arranged about a point with their similar edges together, they will reproduce their own proportions. Sulphur occurs in rhombic octahedra of axes i, 1.23 and 2.34, so that its atomic form is of these proportions. If a form be built with its shortest axis S inches, the remaining axes will be 9.84, and 8.752 inches, and the edges of the primal form will be 12-*^^^, 20'-^'^'-, and 2i^-Yr\- inches. The edges of the face therefore are unequal. The two long edges, however, are very nearly of the same length. In the octahedral grouping, or that edge to edge, the same sort of angles are diametrically opposite, and six meet about a point. If the octahedra were placed face to face, so that similar edges were together, the two apical angles are not opposite, but adjacent ; they, however, have an open space above and below, through which they might rotate. The zonal solid angles are arranged in such a way, that the diametrically opposite angles are cf different sorts, and the angle above and below the line of union in the same series, are of the same sort, but differ from the angles of the series in approximation. '7 A rotation to adopt tlic ilionihic airan,L;cmLiu has no space facilities, and requires a great molecular disarrangement to a(('om|)iish such a change. ir the model lie \]\)(m its face the zonal ])'ane leans to one side, tlnis If another model be placed upon this niodi'l in the way descrihed al)o\e, the lean of the underlying model is I'orrecled, and the base of the column is at right angles to the columnar axis. The base is made v.]) of a series with two axes, a short and a long, Mhich are ol)li(|ue to oiH' another. The colunmar axis is at right angles to both the basal axes. Tlu' unfilled spaces in the octahedral arrrangement ori' of single tetrahedra of the same edges as those upon the octahedra. In this arrangement the unfilled spaces are in i)airs of tetrahedra of the same proi)orli()n, as in the octahedral arrangement, and are in the .same proportion of single tetrahedra as in the octahedral arrangement, and the octahedra in the monoclinic arrangement (xcujiy the same space per atom as in the octahedral arrangement. 'i'he arrangement may be spoken of as a monoclinic one of the first sort. It is, how. ver, an impossible one for sulphur in that it does not account for the monoclinic colunui with an obli'|ue base, its sjjace per atom and so s|)ecific gravity does not \ary from that of the octahedral arrangement, and it does not offer the s])ace opportunity to re\ert to the rhombic form. The long edges of the model are nearly of the same length, so that if the opposite sorts of zonal angles be brought together, the faces will nearly coimid' , but yet l)e slightly divergent at the apical angles. K series be set alongsitle eacii other, there are about the divergent apical angles unfilled sjiaces to ])erniil of rotation above, below, and laterally. In the vicinity cf the divergent apical angles, are four zonal angles to which the apical angles would be powerfully attracted. 'I'he apical angles would differ widely from the z )nal ones in electro condition, if the angles as in phosphorous have their electro ipiality according to the distance from the centre, and so be power- fu ly attra':te(l to the shorter or zonal angles. The two atoms which would tend to rotate would have their zonal angles thrust apart. The zonal angles are very similar, and so would not have the same powerful attraction I'fi/er se as the ajiiceal angles have for their neighboring angles, and in addition to greater attraction of the apical angles, they have a very decided leverage over the zonal ones, and their attraction would prove effective. Did this attraction not prove effective, continued form would be impos- sible under this arrangement. This arrangement perpetuates the slant of the first series to the base, and the slant occurs in the direction of the small axes of the l)ase, and the a.xes of the base are not only oblique to themselves but the short axis of the base is oblique to the columnar axis, and the long axis of the base is at right angles to the columnar axis. This arrangement might be called a diclinic arrangement, or, as it is classed, a monoclinic arrangement of a different sort from the first. I I I I I I i In the unrotaled SL-rics (jf atom-, tht; /dm.iI c-J^'j is (^hliciue to tlic liiK^ dI series, thus ^. ; in rotatiwti it hecomes less ohIii|ue and the series is tiiickened. To estimate this widening, a model triangular face of sides 12.28, 20 3S7 and 21.177 inches respectively was made. The triangle was then placed upon a sheet of paper and the outline muked. The triangle was then reversed, so that the zonal edge and the opposite sorts of angles are in apposition. A pin was passed through the c.irdboard at the centre of the zonal or short edge, and the triangle rotated through the divergence of the a[)ical angles, and the position of the two zonal angles marked. One of the long sides of the triangle is produced both ways. A line is dropjied from the angle apical to this line, and at right angles to it. This line represents the thickness of the single layer m its ordinary position, 'i'he distance of the Hew points brought about by rotation are measured from this line, and the sum of these measurements is the thick- ness of the rotated series. 'I'he lengths of these two lines are in\ersely according to the specific gravities of their arrangements. The line dropped from the zonal angle at right angles to the o[)posite and produced line, was 1 I }. inches, and after rotation the t'ombined distance of the zonal angles from this line is 12,',, inches. The <\orrection of the divergence caused a thickening of ,'',, of an inch, or ,",, i 1 .^i J„ .. of the entire thickness of the series. J,, .; more space is filled than in the divergent arrangement, ff)r then the zonal planes are as in the octahedral arrangement, and the divergent portions are in the unfilled space. In this arrangement six solid angles meet about a point in such a way that the two a[)ical angles are not diametrically opposite but in apposition, while the other four are arranged as in the octahedral arrangement, with the similar angles diametrically opposite. The apical angles are free to move in space both up and down, and laterally. If they diverge until the long axes of the models are parallel, the arrangement then becomes octahedral. Thus the primal form assumed accounts for, ist, a gross octahedral arrangement of axes i, 1.23 and 2.344 ; 2nd, a gross so-called monoclinic (really diclinic) arrangement of a base obliciue to its columnar axis : 3rd, a condition of strain in thediclinicarrangement due to slight divergence of the solid zonal angles, the satisfaction of which strain sets free energy as heat; 4th, a rotation of the primal form in the diclinic arrangemei t in such a way that the series is thickened o\, .) more than in the octahedral series, and that this approximates inversely the increase in space, as shown by the specific gravities observed in the two modifications of sulphur, thus, '^'-\. },-{-" ~ :,\ ^ ; 5th, free spaces through which the divergent apical angles may con- verge, and through which they may rotate above and below, to assume the octahedral form, and JJi'ce versa : (nh, tliut ihc dicliiiic modificution is in t /oiul grouping liku the octa- hedral arrangement, and rotation need occur in hut one and an easy way, to assume the octahedral form. Mr. Joseph I'-aston drew my attention to a most significant fact, viz., that in the molei ulur gr()U|)s of tlie gas, the atoms are in the same proportions as they are in the smallest groups which give the lompleie outlines of the two crystal modifications of sulphur. The relationshi]) goes even farther, and it is seen that the six-atom group, or octahedral group, is lower in temperature, both as a gas and solid, than the two-atom or didinic group. There are three modifications of selenium as of sulpluir. 'i'hese may be compared as follows ; — sn.l'lll'K. ! SKI.KNirM. .\morphous, spec. gr. i.yj. Von , Amorphous, spec. gr. 4.28 to 4.3. Huchka. , \'on Buchka. Diclinic or (monoclinic), spec. gr. 1 Monoclinic, spec. gr. 4.5. Von 1.96. Von Buchka. | Buchka. These monoclinic forms are said by Kichter to be isomorphous. Rhombic octahedra : | (Iray metallic lustre of form un- Spec. gr. 2.06, Von. Buchka. j known ; " 2 05, Richter. I Spec. gr. 4.8, Von Buchka. i.9-2.i,Zirkel. | " 4.8, Richter. The most stable form, to which the 'i'he most statMe and insoluble de- or monoclinic form slowly reverts ; modification to which the monoclinic at ordinary temperatures, with the form, if heated to 97 ^C, reverts rising evolution of a small amount of heat, rapidly to over 2oo"C. in the transi- ', tion. Ri.se of the spec. gr. in transi- Rise of spec. gr. in transition from tion from 1.96 to 2.o^ = r}j^^ 4.46 to 4.8. Von Buchka. ^•*^-i^. From 4.3 to 4.8. Richter. The difference between the two crystal forms of sulphur is less, and the change easier, than between the two crystal forms of selenium, that is there must be a wider difference between the zonal axes. If selenium be isomorphous with sulphur, it follows that an absolute coincidence of form is not necessary to isomorphism. That both sulphur and selenium occur in forms which are under a strain, and have a mobility within their arrangement, is in itself an enunciation of the principle of pos- sible non-apposition of the axes, and unstable equilibrium. II 20 Tellurium is found in both hexagonal and rhombohedral forms. Von Huchka hexagonal. Kichter rhombohedral. y . . ( rhombohedral, by Rose. I hexagonal, by Rose. I >ana hexagonal. In rhombohedral forms according to Rose the angle R ^86 57', and in the hexagonal form with "mit pole Kante of R 71.54." The angle «6' 57' is very much akin to angle of bismuth 87 40', and could intercrystalli/e with bismuth. The angle 71" 54' is very much like the angle 70' 31' 47" of the regular tetrahedron, and is really the complement of the angle of the regular octahedron. If regular octahedra be placed face to face, their outlying points are in a hexagonal series, and are capable of a rhombohedral series of angles R 82' 18', or of in the hexagonal system 70' 31' 47". Close observation of numbers of crystals may show these angles. As a coincidence supporting a view of the atom of tellurium approximating the regular octa- hedral form, may be cpioted the fact of its isomorphism with gold, which is distinctly regular in form, There remain undiscussed in this group chromium, molybdenum, tungs- tenum and uranium. Of chromium alone the crystal form is known, and that with no cer- tainty. Von Buchka says it occrs in "mikroskopische fast zinnweisse rhombohiieder, oder ({uadratische Pyramiden." Remsen says "in lustrous rhombohedra of tin-white color." Were the chromium atoms joined face to face, they would have three areas of valence unsupplied, and the chemical valence would be three, with the result of formula Cr.^ CI ,1 and Cr .^ O3. There are unstable compounds, chromium dechloride and chromium bi-hydroxide. From the hydroxide an oxide of the formula Cr ._, O ,, is obtained, and not one of the formula Cr (). The valence of molybdemum, tungstenum and uranium will be studied later. A iiuestion arises as to why sulphur, which has four angles of valence near its centre, and so four electro-negative areas of valence, should form a dihydride instead of a tetrahydride. Facts furnished in the study of chlorine and the chlorides, show that if one angle of valence be satisfied, the diametrically opposite angle is to a greater or less extent satisfied. This question is fully discussed in connec- tion with chlorine. 21 CtL\PTER V. The Atom Form of Iodine and the Phenomena of Crystallization ci Iodine From Solutions. In group VII. of Mendeljeff's table there are five elements to study, fluorine, chlorine, bromine, iodine and manganese. Of these elements fluorine and chlorine are gases at ordinary temperatures, and bromine a liquid, so that their crystal forms are imi)ra(-ticab!e for present study. Iodine occurs as a distinctly crystalline solid at ordinary temperatures. From the molten state it is found to solidify in distinctly foliated plates and leaflets. Cleavage is shown in one direction, and in this direction there must be a special regularity of arrangement. The cleavage shows ease of fission, that is less tenacity in the plane of fission, and hence less attraction. This plane is very smooth and glistening, that is tliere is no roughness of the plane or perceptible intrusion, or in other words there is a continuous arrangement along the plane of fission. A group of atoms closely bound together and passing into both planes, would make fission more difficult, to the extent of the greater amount of energy reciuired to dismember the group than the layer, or the increase of energy retjuired to displace the group througli a series of continuously arranged atoms, which have an inter attraction. Upon the leaflets are often observed striations, and even raised minute ridges which meet each other at angles 36", 72°, 108" and 144°. When these ridges are more developed they become developments in the third dimension. This circumstance is of interest in further study. It has been noticed that the rhombic plates have an easy and natural fission in planes parallel to the surface of the plate. These plates are, however, flexible and show consider- able tenacity in the two dimensions in which the leaflet lies. Fission, when forced, tends toward assuming lines at 36°, 72°, 108' and 144' to each other, but is indistinct and is most frequently irregular. This indicates a greater attraction in this plane, a continued arrangement to produce plate firms of angles 36°, 73', etc., and that there are other lines of fission, and that the lines of fission pass through the series which cause the grouping in angles 36° and 72°. The strife arranged one behind the other would show rows or series of rows as mentioned by Hany. Iodine is soluble in ether and in chloroform, and more soluble in the former than in the latter. If a saturated solution of iodine in ether be slowly evaporated, the result is a casting down of rhombic octahedra, of roughly formed rhombic plates, the angles of which are represented by a meeting of octahedral faces P, and of a crystalline aggregate about the sides ot the 22 evaporating disk, in which the crystals are elongated and striated, the stria: being at angles 72", 36°, lOcS' and 1 44'' to each other. From a saturated solution of chloroform, in which the evaporation is si )wer, there is a special tendency to the formation of octahedra. There are also needle-shaped crystal forms, which grow, by addition from the evaporating solution, to rods with octahedral ends. These crystals are too smo.ll for measurement with a contact goniometer, and so were measured under 125 I) enlargement, the arms of the goniometer being placed parallel to the edge of the image, as seen through the microscope. To place the crystals a cardboard was roughened, and the crystal laid in the fuzz, and so moved that the outer edges are in the same focus, or by cut- ting a slit in a piece of cardboard into which the crystal is placed, and may be made to show its edges in the same focus. In placing the crystals, a graphite pencil point was used, in that it was not corroded as a metal point would be. The measurements taken were of the angles which like edges make upon each other. The same crystal was measured upon both sets of edges : B II ^^' ABC 72" < E 13 0=34" ; I' ^ ii A " 72" < " ==54'': " 72^' < " =54^': 72" < " --=54" : " 72" < •' =54°; 72^' < " =54" ; 7th 'Y / I < K B F=^54^ ^' K A ,. < F Don EB = 27^^; Of the first six the regularity is very striking, and specially so since they are from different batches of crystals. Number 7 gives two series of measurements, one at each end. The angle 72 ' is constant, and is in the broader plane of the crystal. At the one end, the 27' is that part between the outer edge, and the I'ne which bisects the angle between the usual sides of 54^ or the angle between the outer edge and the edge, which were the crystal rotated 90° would form an outer edge. This crystal was a little point by itself; the main point was at 54°. The other end of the crystal shows over its point an angle of 54". From one of its sides goes another line which lies at 27" to the opposite edge. The angle of 54" has a line bisecting it, and the new line or edge is parallel to this bisecting line or edge. If a saturated solution of iodine in ether be placed upon a glass slide under a microscope of I > 125, and be permitted to evaporate slowly, the result will be a multitude of octahedra. 23 ISt < A' .. . ^•c I) .•>nd < 3rd < 4tn < 5th < 6th < These are thrown down as soon as evaporation commences, and the octahedra are drawn towards that part at which there is most fluid. A rapid evaporation leads to octahedra, to needle forms with octahedral points, to a series of parallel needles, which may be rnited by bars to give a coarse retiform form. In saturated chloroform solutions of iodine, slowly evaporated, are seen more perfect octahedra, and more perfect rhombic plates. These plates show a selection of obtuse for acute angles and vice versa, and one may see formed from two, three, or four smaller plates, a complete oblong plate, an incomplete one of three, thus /9^ , or even a complete i)late by four, thus /—^ . Evaporation is slowest in chloroform, hence the more perfect octahedra. 1 )iagonally across the plate between the two angles of 72", is seen a line, thus ^. If the iodine be permitted to volatili/e, the edges and this median line remain, till towards the end. The portion between them is most frecjuently the first to assume vapor form. The edges of all crystals of the iodine, show by refracted light, a violet fringe of color similar to that of the vapor, or the chloroform solution. A rapid evaporation of the solvent, gives a series of small plates, an. small octahedra, a series of coarse needles, and sometimes a very beautiful series of fine needles, or a fine retiform conformation which, under 450 1 ), still appears very fine. The outline of such a retiform mass, is roughly rhombic. Iodine is a volatile element, and as a result of the -.mmense exposed surface in a retiform arrangement, the evaporation is very rapid. If a retiform crystal be allowed to evaporate on a slide, under a microscope of 1)450, one little bar disappears, and then another, till some outlying portion would tend to be isolated. Were there no attraction, the isolated portion would remain where it was deposited. This is not the case. The minute particles, so soon as they are not held off by intervening solid jjarticles, immediately spring, with great rapidity, to the nearest portion of the crystal, showing a very active attraction. In the slow evaporation of a concentrated solution of iodine in chloro- form, the crystal is seen to grow at the expense of the color within the solution. The color keeps going faster, and faster, till suddenly the color disappears, and the iodine has all been drawn to the crystal, even while there yet remains some of the solvent about a crystal. This phenomenon shows an attraction of the crystal of iodine, for the iodine in solution. II there can be an attraction of the crystal of iodine for the iodine in solution, and the iodine still remains in solution, it follows that there is some counter attraction of the solvent for the iodine, and the solution is dei)endent upon this attraction. Thus solutions are a series of eciuasions of forces of attraction, and the effect of a crystal in a saturated .solution is felt throughout the entire solution, as will be seen later. 24 It is in a moderately strong solution that the most may be observed. One easy of observation is made by adding to iCC of saturated iodine solution, in ether, 2CC of ether and ethyl alcohol in e(iual parts. The alcohol is slower of evaporation, and lengthens the process of crystal formation. When a drop of such solution is placed on a slide under a microscope, a brown solution is observed. In the field will probably be seen some small particles of dust, such as epithelium scales, cellulose fibre, etc., which have escaped one's s'ide cleaner. I-Vom one of these foreign bodies is seen a small needle to suddenly shoot forth, projecting itself out into the colored solution, and drawing the color from the immediate vicinity. The longer it proceeds the less is its rate of projection, and one may see its growth distinctly. It does not spring immediately into existence, but is an action of very percep- tible duration. These needles project themselves towards the area in which there is the most color. The result is, that small needles come within the inlluence of others. If two be projecting theniselves toward the same point, and nearly in the same line, when they approach, they ceasr; their self-projec- tion and nroceed to draw the iodine from solution, and thicken themselves, showing instead of an attraction a repulsion the one of the other, even though there be a sufficient su|)ply of iodine to permit of a growth to effect a junction. If, however, the point of a needle formed crystal approach the centre of another needle, and there be still iodine in solution, the point will project itself until it touches the ceui e of the needle. If the ap|)roaching needle be free, or if it be of-a later growth, it will attach itself at angles 36° or 72 . .Sometimes a needle may be observed to take a curved course, and to arrive at the centre of another needle. This needle remains in the curved condition, until the iodine is absorbed from the solvent, and but a small amount of the solvent present ; wiien, howe\ er, the solv(;nt is gone, it suddenly straightens itself, freeing either tlie one end or the other of the curved crystal. The fact that the needles forming in the neighborhood of a larger and older needle crystal are at definite' angles, shows an influence on the part of the larger crystal, over the solution in which the crystal was formed. This will i)c discussed later, in connection with more direct evidence. So far the conditions dealt with have been of immobile crystals. There are some interesting phenomena shown by mobile crystals. From a solution described as of moderate saturation, both mobile and immobile crystals are cast down. The fixed ones show the result of laws of attraition acting while they were becoming fixed. The mobile ones are ameiiabie to the various attractions, acting upon it, and occupy such a position as is determined by the present attractions. The crystals are principally of rhombic plates and needle forms. If a mobile rhombic plate comes in the vicinity of another rhombic plate, its obtuse angle is seen to seek the acute angle of the station- 25 ary rhombic plate, and the sides to come cjuickly into apposition, or the crystal is sometimes seen to remain in e(iuilibrium upon the other, thus / / If a current draw a small and mobile plate towards a large and immobile crystal, in such a way that the small one is borne down with its acute angle towards the acute angle of the stationary one, the mobile one will either rotate as it comes near the angle of the stationary one, or be apparently cast aside, and pass down the stationary crystal till the obtuse angle of the mc^bile crystal is in the neighborhood of the acute angle of the stationary one, and approximate their sides. If a rhombic j)late come in the vicinity of a needle formed crystal, the result is most frequently, that the rhombic plate seeks th<^ octahedral end of the needle, towards which it acts as though the end of the needle were the acute angle of a rhombic plate. It may arrange its side parallel to l\vi\. of the necedle, or may arrange itself with its long axis parallel to long axis of the needle, or a series may so arrange th jmselves as to make the [loints, if joined, give a rhombic outline. Suc;h an arrangement shows an attraction about, and at some distance from the needle, and that the area of attraction is present, whether filled or not, so long as there is an elongation of the crystalline substance in one axis, and that the area of attraction is in propor- tion to the elongation. If a current of the solution bear a needle crystal towards the fixed crystal, so that the point of the one approach the point of the other, the point will rotate, and the side or centre of the moving crystal then comes in the vicinity of the fixed one. The needle will be attracted very rapidly, and will be held at an angle to the point of the fixed crystal. The centre of the needle has a very strong attraction for the point of another needle crystal, and there is apparently a similar attraction of the long to the short points, as in the atoms, as these points act not unlike the positive and negative poles of a magnet. If these positions be, as in the atoms, electro-negative and electropositive, and the electro condition be dei)endent on length, then a shorter crystal placed by the side of a longer one, would, if their centres be together, be electro-positive to the longer one, and each part would be of a different electro condition to that at its side. The form would be determined by the proportions of the atoms, and a reason found for the subtraction of series. In a saturated solution about a crystal that is growing may be observed currents from point to point. This may be due to some peculiar capillary action. Whether it be so, or whether it be due to an action of differently electrified molecules, brought about by different conditions at the different poles, it gives an opportunity of an ecjuilibrium of supply. In the field, between two needles, was seen a particle of something oscillating with great rapidity. A first supposition was that it was a very 26 small crystal, for the rapidity of its motion made it impossible to see what it was. The oscillation occurred between the point of one needle and the body of another. It at last became temporarily attracted to one of the needles, and was then seen to be an epithelium scale. There is an anology between such an oscillation and that of an insulated pithball a + iind a- static electrical i)o1ps. If a dilute solution of iodine in ether and alcohol be evaporated upon a glass slide, under 125 I) enlu.gement, the result will be as the last of the solvent is evaporating, very fine needles will l)e deposited, and do not float, but are cast down in the position dictated by the conditions in the solution at the time of their formation. These crystals, if in apposition, are almost invariably at angles of 36" n.nd 72''. In those which are ncjt at angles 36'" and 72"-', there is some larger needle, and a prior one, which predominates the attraction of the other needle. This predominant needle will have its attachment to the needle, varying from the common angle. .Such a regularity of position shows the influence of the needle over the iodine in solution. The needles occur when the supply of the solution is little and the evaporation is hurried ; the octahedra in the presence of much solution and those in which evaporation is slow ; the one under the conditions in which selection is im|)cifect, the other where the selection is more possible ; or the one an imperfect [)artially finished form and the other in a com[)lete form The physical properties of iodine, for which a primal fortn must account, may be recapitulated as, ist, a continued or (-rystalline structure ; 2nd, easy fission in one series of planes ; 3rd, more tenacity in the f)ther two planes ; 4th, groujjing and a tendency to fission in lines of 36^' and 72^^ to each other ; 5th, grouping to give over the other edges of the octahedron an angle 54". In groups I\^, V. and VL of Mendeljeff"s table, it has been found that the forms which have the same number of solid angles as the elements have areas of valence, account not only for its crystal form, but by different arrangements for the various crystalline modifications known of these elements, and the space occupied per atom form, corresponds inversely with the specific gravity of these modifications. In grouj) \'II. the valence is seven, and if iodine be, as the other atoms of a form, of the same number of solid angles as the atom has areas of valence, it must be of one solid angled form. In groups V. and VI. two of these angles are apical and the remainder zonal. If such a division of zonal and apical angles were the case in iodine; the result would, if the zonal angles were at regular intervals, be a regular pentagonal zone. 27 This form, /<■/• se, is not a rhombic form ; but if in combination with another sucli form edge to edge and the /ones in the same plane, the outly- ing edges, if i)roduced, give a rhombic outline. Ihe angle of a regular pentagon is iocs'-' and its supplement is 72", so that the above grouping gives the required angles of one of the planes of iodme. In such an arrangement, two zonal angles of an atom meet two zonal angles of a contiguous atom, while if a layer be placed over another layer, they meet by single apical angles. The atoms are more attached in the zonal plane than by ine a\nca\ solid angles, and hence the tenacity in the zonal plane, and the ease of fission of the ajjical plane of attachments. The grouping of the atoms with their two zonal angles together, is in the proi)ortion of the grouping in the gaseous molecule, and is an interesting one when compared with sulphur. As yet l)Ut a grou|) (jf two atoms has been discussed. It is evident that these double atom groups must themselves be arranged. This may be clone in two ways : 1st, as in fig. I., in which the atoms are (except within the group) attached by one point only : 2nd, as in fig. II., in which the atoms are attached to each other by two angles. The first case may be disposed of in that the lines of fission are at right angles and demand a right angled form. Such a form does not occur in iodine. In such an arrangement the atoms are attached by one point as are the ai)ical angles, and so do not tend toward tenacity. In fig. II. the series are not at right angles, and about the most outlying angle of the double atom group are attached two other angles. In this arrangement in the zonal plane each atom is bound to three other atoms by two areas of attraction, and to two other atoms by one area of attraction. The series of outlying points may be shown to be at 36" to each other. About the point A are three angles of 108", or in all 324^'. All the angles about A = 36o^", therefore the angle E A 6=^360^ - 324^'=36". The angle A I<: F=the angle K F (1, therefore A E is parallel to F G. Similarly A B may be shown parallel to C 1). iherefore F G and C I) are at an angle of 36^ to each other, and these lines being parallel to the outlying angles, the outlying portions of the series are at an angle of 36'-'. In fig. III. two possible arrangements are seen about the double atom group B F H C. If arranged as C H () P, the arrangement is merely another series added to a grouping, as in fig. II., and the series arising from this arrangement are at angles of 36'^. If it be arranged as the double atom group I) S N R, there are two different sets of series lying together, each of which has its internal series at 36". Thus E H is parallel to C; J, i) F is parallel to (} K, and (1 J is at 36^' to (; K, therefore E H is at 36" to I) F. I) F is at 36" 28 to I) L, therefore I) L is at 2 x 36" or 72^ to E H, and I) L is parallel to M N, therefore M N is at 72" to E H, and these two lines are parallel to the outlying angles of the different series, so that the outlying edges of a crystal of this arrangement are at 72^'. The line of union of the series runs dia- gonally across the rhombic plate between the two angles of 72". 'I'he arrangement above described accounts for the proportions and physical properties of the rhombic form of iodine in its plane of tenacity. The properties in the third dimension are accounted for as to its fission. If the second layer of atoms be attached, one row within the first layer, the angle in this dimension at the corner of the rhombic plate will depend on the line from the ape.x of the corner atom of the one layer to apex of the atom upon which rests the corner atom of the second layer, and the thick- ness of the corner atom of the second layer. This angle is one-half that over two oi)p()site edges of an octahedra, and is dependent on the thickness of the atom. If the atom be of a thickness equal to its zonal edge, this angle may be shown to be 27^', or the whole angle over the octahedral point is 54^'. The crystal of iodine has these pro- portions. This is a coincidence rather than a necessary portion of the hypothesis of the bipyramidal decahedral form for iodine. This form has two angles near the centre, so that one would expect the hydride of its analogous element chlorine to be of the formula H., CI. The hydride of chlorme is a mono-hydride. Chlorine acts as a bivalent element towards potassium and silver. This shows there to be two electro-negative valences in chlorine, and that if one be satisfied by hydrogen, the diametrically opposite valence is satisfied. In phosphorous the zonal angles are not oppo- site, and differ in their manne- of satisfaction of the areas of valence by hydrogen. Suppose this peculiar action on opposite angles of valence occur in sulphur. There are two sets of opposite short axes, and so r«^quire two atoms of hydrogen per atom of sulphur, and the sulphide would then be a dihydride. This is the hydride which actually does occur. Manganese has a valence of seven in potassium permanganate. Its crystal form is however unknown. There is a series of elements, the grouping of which according to their valences, would make their places in Mendeljeff's table uncertain, were it not for their atomic weights. Nickel , , « 2, 4, a Iron ,^ ^^ g Chromium ^ (^ Molybdenum 2, 4, 5, r, and 8 U-"^"'""^ (2, 3), 4,5, ^« Osmium , , a « I""'^'"'" 2, 4, 6, 8 29 Molybdenum is classified in the group with sulphur. It has an oxychlo- ride and an oxide of formuhe MO C.'l^, and MO,. These compounds show a hexavalence. 'J'here is a sulphide, molyhdenum tetrasul|)hide. If molyl)denum he of a form similar to sulphur, the zonal angle of the sulphur may he in apposition to tlie apical angle of the molylxlenum, and the a|)i('al angle of the sul[)hur atom, in apposition with the zonal angle of the molybdenum atom. This may ogcur at both ends in such a way as to he balanced and give attachment to the opposite angles of the sulphur atom. This arrangement leaves two diametrically opposite angles of the sulphur atom unsupplied, to which might be added two sulphur atoms. Were these atoms of sulphur added, it would give the tetrasuli)hide, and sulphur would act moncnalently. If sul])hur be of a fonii like nolybdenum, then i)y anal- ogy one would expect sulphur dioxide to have this balanced arrangement. In formation sulphur dioxide gives heat. The action represented by the equasion (2 SO.j + O.^ + 2H.^ () = 2H,^ SO,) gives more heat. 'I'he heat given by the action represented in the e(|aasion (2 SO,, + 2H. ()=--2 H.^ S()4) is less than that represented by the equasion (2 SO .J + 2 H^ O + O.J--2 H._, SO^), so there must be heat given in the action represented by the equasion (2 SO., +0,:=S(),). 'I'o bring about the further oxidation of sulphur ilioxide, some agitation such as heat, or the presence of a very |)0werful strain as water and nacent oxygen together, is necessar) . 'I'hat is, the arrangement of the sulphur diox- ide must be changed before further oxidation ran take i)lac(;. To account for sulphur trioxide, an oxygen atom must occupy an apical and a zonal angle of sulphur, 'i'his occurs at both enr's, and so there remains two zonal angles as yet unsupplied. If one atom su})|)ly both valences then the unoc- cupied i)oints must be contiguous. 'J'his is the conditio . as rearranged, therefore the alternative condition is that in which the diametrically op])osite zonal angles are occupied. It is not improbable that there is an intermediate form like that of the molybdenum. Group VIII. of MendeljefPs Table. Group Vm. consists of three distinct series, each series being of about the same atomic weight. The first series, iron, nickel and cobalt, have chlo- rides of the general formula X.^ CI,,, each atom being bound by one valence to the other, and so is ([uadrivalent, and as such would be tetrahedral in atomic form. Iron and nickel occur in regular octahedra. Cobalt is isomor- phous with both iron and nickel, but its form, />cr se, has not been deter- mined. 'I'he second series, ruthenium, rhodium and palladium, have chlorides similar to those of the first .series, 'i'he crystal furm of ruthenium and rho- dium are unknown. Palladium occurs in regular octahedra. 30 1U.S r The third series consists of osmium, iridium and platinum. Osmium has chlorides of the formulie Os CI,, Os, Cl„ and Os CI „ and oxides of the tormuhv Os O, Os, (),, Os O, and Os O,. With the exception of osmium tetroxide the oxides and chlorides correspond in valence, assuming the val- ence of chlorine one and oxygen two. If oxygen ac:t monovalently, as does Its analogue sulphur in molybdenum tetrasulphide, then the osmium tetroxide would show a tetravalence as it does in its highest chloride. The same may be said for the oxides and chlorides of iridium. Platinum has chlorides of the formuhe Pt CI., and I't CL, and oxides of the formuhe Pt O and Pt O... The crystal form of platinum is of regular octahedra and cubes group Vni. shows, with the exception of iridium and osmium in llid, tetroxKles, a Muadnvalence and the tetroxides may depend on a monovalent action of oxygen. CHAPTER VJ. The Atom Forms of the Elements of Group III., II. and I. of MendeljefPs Table. The elements of group III. have three apparently ecjual valences. If these be equal m ,,uality they will, if like the atoms discussed, be e()ual in position I hree pomts arranged e-iually about a centre, lie in a plane, and if joined give rise to an e-juilateral triangle. The elements of this group, of which infor- mation as to the crystal form may be obtained, are boron, aluminium, gal- lium. Of thallium we know that it is a very soft malleable metal. Poron (see Richter's Chem. Eng. Trans., p. 244) crystallizes from alumi- nium, showing transparent, more or less colored crystals of specific gravity 2.6v "The crystals are not pure but contain carbon and aluminium. In their lustre, refraction of light and hardness they resemble the diamond " \'on Buchka records them as (luadratic, or monoclinic, and Richter as (luad- ratic. It is isomorphous to carbon, which is regular, and to aluminium. In the isomorphous conditions it has a refraction similar to the regular .system That the crystal is impure detracts greatly from the value of the observations upon It. That it is isomorphous with carbon is a most significant fact as to Its form. It must then be able to take a place with carbon, in the formation of grcss forms, and so is of a similar form. If e.juilateral triangles be placed together, they may form a regular tetra- hedron as the simplest solid form, and these together would form the arrange- ment to give octahedral f. rm. Aluminium occurs in octahedra (\'on Puchka), but of what sort is not stated (lallium is found sometimes in lont;, sometimes in sliorl (luadratic octa- hedra, and sometimes in obruiue octahedra, thus showing a mobility of form. The variation of the (iiiadrati(; forms to obhcjue ones, means a variation of the relati\c positions of the atoms, akin to that of graphite, sodium and potassium. A series '){' triangles set edge to edge do not tend to each others sup- port except as they are bound to each other. If the triangle have thickness, and the angles of the triangle be attracted, these angles might be in approxi- mation, and yet have varying jjositions, as on one either side of the triangle. If two points of a triangle be fixed, it still has a power of rotation about these points. Thus if one |)oint only be free, it is mobile in a circle. F"rom a tetrahedral form of atom, a less mobile form might be jjredicted. In tetrabedra any attraction to a free angle would displace another angle to move the atom, or it might even have to rei)la(e two, in other words would have to overcome the e(iuilibrium of a tripod. If there be attached about the angles of these triangular atoms, three of another sort of atoms, the result will be in outline an etjuilateral triangular plate. If these triangular bodies lie placed layer above layer, they will give triangular columns, and if these be placed together, they give a hexagonal arrangement. That such occurs in aluminium oxide, shows aluminium to be of an equilateral triangular form. in group II. there are two somewhat different series of atoms, viz. : — Beryllium, calcium, strontium, barium, and magnesium, zinc cadmiun, and mercury. Of the fust series it is known that beryllium is hexagonal, and that the other elements are soft ductile metals. Magnesium occurs as octahedra, but of what sort i? not stated by \on liuchka. Zinc occurs in hexagonal plates, and in pentagonal dodecahedra ; cadmium occurs in regular octahedra ; mercury occurs in regular octahedra. The forms thus divide themselves between the hexagonal and regular systems, and zinc is capable of both. It is probable that all are <■ liable of both forms, but have not been observed as yet. The theory of the areas of valence representing the prominent portions of the atom, reciuires for this group two prominences, which, if joined, would have more or less of a rod form. An arrangement of these rods must account for a hexagonal and regular form. The arrangement side by side would not give rise to a hexagonal arrange- ment, or a regular arrangement. Three might form a triangle, which would of necessity be eiiuilattral, and which would, if placed angle to angle and in the same plane, give a hexagonal arrangement. The thickness of the rods 32 would give length to the hexagonal column. They might be attached, as are the lines of union in the diamond model, twelve aliout a point. This would give the sjjaces between the atoms an equilateral triangle and the resultant gross form would be in regular octahedra. Such an arrange- ment involves a mobility and ease of arrangement of the atoms. 'l"he elements of group I. have a valence of one and occupy space. The atoms of this group may be a sphere, in which all portions are of the same sort, or may be a sphere in which one |)ortion only is attractive. Hydrogen is of this group. Of it we know that it has at least two atoms per molecule. Were there but two, there would be a full satisfaction of the bonds of valence in the gas molecule. The coincidence of vapor sulphur in molecules of 6 and 2 as full groups of the forms giving rise to the two sure is due to very free intermolecular mobility, and not to absence of definite lines of attraction. In annealed c opper this tenacious condition exists, but in [it there is more tendency to crystal form, and regularity in that form. In silver the crystal- line characteristic is less marked, and it is more ductile and softer than copper. There is more mobility of the atoms ni/er se. These characteristics are more marked in gold than in silver. There are compounds of the formulae Ag CI, Ago CI, Ag O, Cu ( ), Cu. C), CU4 and Au CI, Au Cl.i and Au CI..,. Cuprous and cupric oxides are common, and the bivalence is well marked. As a result of more than one bond of valence, the position arising from these two areas of attraction is more stable than that which would arise from but one area of attraction. jj This may We said of the other two elements, gcM and silver. In the American Journil of Science, June, i88(>, p. 446, an article by Mr. Cary Lea, of rhilade!i)iua, appeared, in wiiicli he demonstrates four forms of silver, three unstable, and one stai)le or the ci^mmon gray silver. 'I'he following is ([uoted froni his descrii)lion cf the unstable modifica- tions : — "A. Soluble, deej) red in solution, mat lila«' blue or green, while moist brilliant bluish green, metallic when dry." " H. insoluble, derived from A, dark reddisii brown while moist, wiien dry resembles .\." •' C. Gold silver, dark brown wliile wet, when dry exactly resend)ling gold in burnished lumps : of this form is a copper colored variety insoluble in water, and with no corresponding soluble form." The steps necessary to build uj) regular formed bodies fri m spherical forn^s are, isc, two spheres together to give a rod form ; ^m\, two rods attach each other and a I(;ng clumsy rod result: . 'i'he dimensions of this double rod might be a cause of the insolubi'ity of modification B ; .3rd, three rods to form a triangle : and 4th, the rc(ls arranged in the places of the lines of union, of the edges of the tetrahedra in the diamond model, to give a regular and stab'c form, 'i here is a coincidence betwem the four arrange- ments of a sphere form, and the four allotropic modifications of silver. Malleal)ility and softness have a coincidence with arrangements of form, to permit intermobility of atoms, 'i'he atoms of group I. of Mendeljeffs table are attached by one area of attraction, and .so are less stable of position and more malleable. The atoms of group II. have high functions of atomic intermobility, for if one area of attnctitJU be wrenchetl free, it may, uidess hindered by some other atom, rotate in a sphere about the fixed area of attraction. 'I'hey are of lower intermobility than those of grou[) i., for their rod form is not jointed in the centre. In group 111. there is a very free intermobility of the atoms permitted by form, though less than in group II., for if one area of attraction of the atom become free, it may, until stojjped by some other atom, rotate in a circle, the centre of which is the middle of a line joining the other two areas of attraction. In group I\'. new conditions arise, from which may be determined some ether factors, in [)roducing softness and hardness of elements. The atoms of the elements of group I\'. are tetrahedral in form, so that each angle or area of attraction is as the a])ex of a tripod to the other three areas of attraction, and so its })osition tends to be a most stable one. 'i'he tetrahedra are of two sorts, regular and ([uadratic. The regular is more couipact, more simulating a sphere so that its rotation causes the least possible displacement. i'he quadratic tetrahedra are not so compact and simulate an ovoid figure, and so in rotation wo ild cause considerable inter-atomic displacement, 'i'in is quadratic and in twisting or bending causes a crying sound, due to this 34 atonuc (l.spIaccn.e.U. Lead is „f a regular form and decs not cnit this soinul. Another factor of intcr-aton.ic- mobility is siiown l,y the followi.m droui conii)arison : — ( Copper ^ (Iroiip I. ■ Silvtr [Increasing malleability, witii increasing atomic I Gold j weight, and decreasing chemical activity. r Magnesium ] I Zinc I Increasing in softness with increase of atomic I Oulmium I weight, and decrease of chemical activity I Mercury J I Diamond as regular tetrahed,al primal form, brittle Group n'. Tin malleable, breaking with crystalline structure. I Lead soft and malleable. f Iron \ Group VIILJ Nickel. A-;- .. brittle as compared with platinum. \ Cobalt j There is an increased malleability and ductility with increased atonuc weight and decreased chemical activit)-. 'Lhere has been shown a concidence of areas of valence, with those of crystal attraction, and that the quality of valence, as instanced in phos- phorous, IS a function of its imsition within the elements. If c-arbon dioxide set free more energy than lead dioxide, the inference IS that carbon has a more powerful chemical attraction for oxygen than lead lias : and if the supposition that chemical and crystal energies are different manifestations of the same energy, be correct, then the attraction of the carbon atoms in/erse is greater than that of the lead atoms vi/cr se. Thus the carbon atoms are held more firmly in position, and as carbon atom in the outer layer is attached to the crystalline mass in the diamond, with greater fixedness than a lead atom on the outside of its crystalline mass. If a diamond be broken the particles are in perfect adherence to the different masses, and so for a coaptation they would need to be brought into absoluve apposition, for the atoms would not be movable, except under extreme pressure. Were the atoms movable, then the prominences would spread themselves out under pressure, and a general apposition of the attractive areas come about. Ihe adhesive power of graphite is an admirable example of easy coaptation, for the atom in its loose arrangement and its requiring merely points m coaptation gives a free opportunity of motion, and the coaptation demanded is easy of .satisfiiction. The malleable character of an element may be attributed to ease of inter-atomic. mobility, and this it has been seen is dependent on form and its 35 arrangement, so that its displacement is but slight in movement, and also to ease of inter-atomic mobility, due to weak inter-atomic attraction. It is probable that we will, at no distant day, be able to determine the causes of the different physical properties of different sorts of matter, and of these causes form of atoms and molecules will bear no insignificant part. In closing I cannot but express my sense of special gratitude to my frier.cb Drs. Smale and D. H. McLaren, and Messrs. Hunter and Easton, for their assistance and kindly encouragement, under diffici-lties which they best appreciate. William L. T. Ahdison. 3'i f 7i' i ^ y ^ N /■ > \ >' / > 1 \ 1 1 ^^ ' \. » 1 / ■ ( y \ / \ 1 \ 1 \ / \ 1 \ 1 \/ 1 ' >. X X V FV G/ I / N.' Figure I. g; ^\ ^^A. / 1 n- ;'E '!^- ic \ I I A'~. 'J? V / \ I \ X M; \ Figure II. Figure III.