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crystalline mixtures can be experimentally verified, this method is a numerical and measurable one, and in no sense arbitrary.

with them; they therefore belong to the class of pseulomorphs, or false crystals. There is, however, no doubt of the existence of a whole series of natural and artificial homeomorphs, which differ from each other by atomic amounts of water, silica, and some other component parts. Thus, Thomsen (1874) showed a very striking instance. The metallic chlorides, RC1,, often crystallise with water, and they do not then contain less than one molecule of water per atom of chlorine. The most familiar representative of the order RC1.,,21,0 is BaCl2,2H1.,0, which crystallises in the rhombic system. Barium bromide, BaBr.), 2H.,O, and copper chloride, CuCl.,,2H.,0, have nearly the same forms potassium iodate, K104; potassium chlorate, KC104; potassium permanganate, KMnO4; barium sulphate, BaSO4; calcium sulphate, CaSO4; sodium sulphate, Na S04; barium formate, BaC.H.,04, and others have almost the same crystalline form (of the rhombic system). Parallel with this series is that of the metallic chlorides containing RC1.,,4H,O, of the sulphates of the composition RS04,21.,0, and the formates RC,H,O4,2H,O. These compounds belong to the monoclinic system, have a close resemblance of form, and differ from the first series by containing two more molecules of water. The addition of two more molecules of water in all the above series also gives forms of the monoclinic system closely resembling each other; for example, NiCl2,6H.,0 and MnSO4,4H.,0. Hence we see that not only is RC1,,2HO analogous in form to RSO, and RC,H,O4, but that their compounds with 2H20 and with 4H, also exhibit closely analogous forms. From these examples it is evident that the conditions which determine a given form may be repeated not only in the presence of an isomorphous exchange--that is, with an equal number of atoms in the molecule-but also in the presence of an unequal number when there are peculiar and as yet ungeneralised relations in composition. Thus ZnO and Al,05 exhibit a close analogy of form. Both oxides belong to the rhombohedral system, and the angle between the pyramid and the terminal plane of the first is 118° 7', and of the second 118° 49'. Alumina, Al2O3, is also analogous in form to SiO2, and we shall see that these analogies of form are conjoined with a certain analogy in properties. It is not surprising, therefore, that in the complex molecule of a siliceous compound it is sometimes possible to replace Si0, by means of Al2O3, as Scheerer admits. The oxides Cu,0, MgO, Nio, Fe304, CeO2, crystallise in the regular system, although they are of very different atomic structure. Marignac demonstrated the perfect analogy of the forms of K ZrFand CaCO3, and the former is even dimorphous, like the calcium carbonate. The same salt is isomorphous with R.,NbOF; and R,WO.F4, where R is an alkali metal. There is an equivalency between CaCO3 and K. ZrF6, because K2 is equivalent to Ca, C to Zr, and Foto 03, and with the isomorphism of the other two salts we find besides an equal contents of the alkali metal—an equal number of atoms on the one hand and an analogy to the properties of K.,ZrFe on the other. The longknown isomorphism of the corresponding compounds of potassium and ammonium, KX and NH X, may be taken as the simplest example of the fact that an analogy of form shows itself with an analogy of chemical reaction even without an equality in atomic composition. Therefore the ultimate progress of the entire doctrine of the correlation of composition and crystalline forms will only be arrived at with the accumulation of a sufficient number of facts collected on a plan corresponding with the problems which here present themselves. The first steps have already been made. The researches of the Geneva savant, Marignac, on the crystalline form and composition of many of the double fluorides, and the work of Wyruboff on the ferricyanides and other compounds, are particularly important in this respect. It is already evident that, with a definite change of composition, certain angles remain constant, notwithstanding that others are subject to alteration. Such an instance of the relation of forms was observed by Laurent, and named by him hemimorphism (an anomalous term) when the analogy is limited to certain angles, and paramorphism when the forms in general approach each other, but belong to different systems. So, for example, the angle of the planes of a

The regularity and simplicity expressed by the exact laws of crystalline forın repeat themselves in the aggregation of the atoms to form molecules. Here, as there, there are but few forms which are essentially different, and their apparent diversity reduces itself to a few fundamental differences of type. There the molecules aggregate themselves into crystalline forms ; here, the atoms aggregate themselves into molecular forms or into the types of compounds. In both cases the fundamental crystalline or molecular forms are liable to variations, conjunctions, and combinations. If we know that potassium gives compounds of the fundamental type KX, where X is a univalent element (which combines with one atom of hydrogen, and is, according to the law of substitution, able to replace it), then we know the composition of its compounds : K,O, KHO, KCI, NH,K, KNO3, K,SO 4, KHSO4, K,Mg (SO4)2,6H,O, &c. All the possible derivative crystalline forms are not known. So also all the atomic combinations are not known for every element. Thus in the case of potassium, KCH3, K3P,

rhombohedron may be greater or less than 90%, and therefore such acute and obtuse rhombohedra may closely approximate to the cube. Hausmannite, Mn304, belongs to the tetragonal system, and the planes of its pyramid are inclined at an angle of about 118°, whilst magnetic iron ore, Fe30,, which resembles hausmannite in many respects, appears in regular octahedra---that is, the pyramidal planes are inclined at an angle of 109° 28'. This is an example of paramorphism; the systems are different, the compositions are analogous, and there is a certain resemblance in form. Hemimorphism has been found in many instances of saline and other substitutions. Thus, Laurent demonstrated, and Hintze confirmed (1873), that naphthalene derivatives of analogous composition are hemimorphous. Nicklès (1849) showed that in ethylene sulphate the angle of the prism is 125' 26', and in the nitrate of the same radicle 126 95'. The angle of the prism of methylamine oxalate is 131° 20', and of fluoride, which is very different in composition from the former, the angle is 132° Groth (1870) endeavoured to indicate in general what kinds of change of form proceed with the substitution of hydrogen by various other elements and groups, and he observed a regularity which he termed morphotropy. The following examples show that morphotropy recalls the hemimorphism of Laurent. Benzene, C6H,, rhombic system, ratio of the axes 0:891 : 1 : 0·799. Phenol, CH(OH), and resorcinol, C.H (OH), also rhombic system, but the ratio of one axis is changed--thus, in resorcinol, 0:910 : 1 : 0:540; that is, a portion of the crystalline structure in one direction is the same, but in the other direction it is changed, whilst in the rhombic system dinitrophenol, CoH;(NO)2OH) = 0·833 :1: 0753; trinitrophenol (picric acid), C&H, NO)-(OH) = 0.937 : 1 :0.974; and the potassium salt – 0.942 : 1 : 1354. Here the ratio of the first axis is preserved—that is, certain angles remain constant, and the chemical proximity of the composition of these bodies is undoubted. Laurent compares hemimorphism with architectural style. Thus, Gothic cathedrals differ in many respects, but there is an analogy expressed both in the sum total of their common relations and in certain details--for example, in the windows. It is evident that we may expect many fruitful results for molecular mechanics (which forms a problem common to many provinces of natural science) from the further elaboration of the data concerning those variations which take place in crystalline form when the composition of a substance is subjected to a known change, and therefore I consider it useful to point out to the student of science seeking for matter for independent scientific research this vast field for work which is presented by the correlation of form and composition. Thegeometrical regularity and varied beauty of crystalline forms offer no small attraction to research of this kind.

K,Pt, and other like compounds which exist for hydrogen or chlorine, are unknown.

Only a few fundamental types exist for the building up of atoms into molecules, and the majority of them are already known to us. If X stand for a univalent element, and R for an element combined with it, then eight atomic types may be observed :

RX, RX,, RX3, RX4, RX;, RX., RX,, RX,. Let X be chlorine or hydrogen. Then as examples of the first type we have : H.,, Cl, HCI, KCl, NaCl, &c. The compounds of oxygen or calcium may serve as examples of the type RX, : OH,, OC12, OHCI, CaO, Ca(OH)2, CaCl2, &c. For the third type RX, we know the representative NH, and the corresponding compounds N2O3, NO(OH), NO(OK), PC13, P,03, PH3, SbH3, Sb,O3, B,0 3, BCl3, A1,03, &c. The type RX, is known among the hydrogen compounds. Marsh gas, CH4, and its corresponding saturated hydrocarbons, C,H2u + 2, are the best representatives. Also CH3C1, CCI,, Sici,, SnCl, SnO2, CO2, SiO.,, and a whole series of other compounds come under this class. The type RX, is also already familiar to us, but there are no purely hydrogen compounds among its representatives. Sal-ammoniac, NH,CI, and the corresponding NH (OH), NO,(OH), CIO,(OK), as well as PC15, POC13, &c., are representatives of this type. In the higher types also there are no hydrogen compounds, but in the type RX, there is the chlorine compound WCle. However, there are many oxygen compounds, and among them SO, is the best known representative. To this class also belong SO2(OH)2, SO,C1,, SO,(OH)CI, CrO2, &c., all of an acid character. Of the higher types there are in general only oxygen and acid representatives. The type RX, we know in perchloric acid, CIO3(OH), and potassium permanganate, MnO(OK), is also a member. The type RX, in a free state is very rare ; osmic anhydride, Os(, is the best known representative of it.6

6 The still more complex combinations which are so clearly expressed in the crystallo-hydrates, double salts, and similar compounds-although they may be regarded as independent, are, however, most easily understood with our present knowledge as aggregations of whole molecules to which there are no corresponding double compounds, containing one atom of an element R and many atoms of other elements RXn. The above types embrace all cases of direct combinations of atoms, and the formula MgSO4,7H,0 cannot, without violating known facts, be directly deduced from the types MgXn or SX", whilst the formula MgSO4 corresponds both with the type of the magnesium compounds MgX, and with the type of the sulphur compounds S0,X2, or in general SX6, where X, is replaced by (OH)2, with the substitution in this case of H., by the atom Mg, which always replaces H... However, it must be remarked that the sodium crystallo-hydrates often contain 101,0, the magnesium crystallo-hydrates 6 and 71,0, and that the type Pt M,X, is proper to the double salts of platinum, &c. With the further development of our knowledge concerning crystallo-hydrates, double salts, alloys, solutions, &c., in the chemical sense of feeble compounds (that is, such as are easily destroyed by feeble chemical influences) it will probably be possible to arrive at a perfect generalisation for them. For a long time these subjects were only studied by the way or by chance; our knowledge of them is accidental and destitute of system, and therefore it is impossible to expect as yet any generalisation as to their nature. The days of Gerhardt are not long past when only three types were recognised : RX, RX,, and RX;; the type RX4 was afterwards added (by Cooper, Kekulé, Butleroff, and others), mainly for the purpose of generalising the data respecting the carbon compounds. And indeed many are still satisfied with these types, and derive the higher types from them; for instance, RX, from RX;-as, for example, POCI, from PC13, considering the oxygen to be bound both to the chlorine (as in HCIO) and to the phosphorus. But the time has now arrived when it is clearly seen that the forms RX, RX.,, RX3, and RX, do not exhaust the whole variety of phenomena. The revolution became evident when Wiirtz showed that PCI; is not a compound of PC13 + Cl, (although it may decompose into them), but a whole molecule capable of passing into vapour, PCl, like PF, and SiF4. The time for the recognition of types even higher than RX, is in my opinion in the future; that it will come, we can already see in the fact that oxalic acid, C.,H204, gives a crystallohydrate with 2H20; but it may be referred to the type CH, or rather to the type of ethane, C2H6, in which all the atoms of hydrogen are replaced by hydroxyl, C,H,021,0 = C(OH)6 (see Chapter XXII., Note 35).

The four lower types RX, RX, RX3, and RX, are met with in compounds of the elements R with chlorine and oxygen, and also in their compounds with hydrogen, whilst the four higher types only appear for such acid compounds as are formed by chlorine, oxygen, and similar elements.

Among the oxygen compounds the saline oxides which are capable of forming salts either through the function of a base or through the function of an acid anhydride attract the greatest interest in every respect. Certain elements, like calcium and magnesium, only give one saline oxide--for example, MgO, corresponding with the type MgX.,. But the majority of the elements appear in several such forms. Thus copper gives CuX and CuX,, or Cu,0 and CuO. If an element R gives a higher type RX, then there often also exist, as if by symmetry, lower types, RX.-2, RX,-4, and in general such types as differ from RX, by an even number of X. Thus in the case of sulphur the types SX2, SX4, and SX, are known-for example SH2, SO2, and SO3. The last type is the highest, SX. The types SX, and SX, do not exist. But even and uneven types sometimes appear for one and the same element. Thus the types RX and RX, are known for copper and mercury.

Among the saline oxides only the eight types enumerated below are known to exist. They determine the possible formula of the compounds of the elements, if it be taken into consideration that an element which gives a certain type of combination may also give lower types. For this reason the rare type of the suboxides or quaternary oxides R,0 (for instance, Ag,O, Ag2Cl) is not characteristic; it is always accompanied by one of the higher grades of oxidation, and the compounds of this type are distinguished by their great chemical instability, and split up into an element and the higher compound (for instance, Ag,0=2 Ag+ Ag2O). Many elements, moreover, form transition oxides whose composition is intermediate, which are able, like N.04, to split up into the lower and higher oxides. Thus iron gives magnetic oxide, Fe3O4, which is in all respects (by its reactions) a compound of the suboxide Feo with the oxide Fe.,Oz. The independent and more or less stable saline compounds correspond with the following eight types :R,0; salts RX, hydroxides ROH. Generally basic like K,O, Na,O,

Hg,0, Ag,0, Cu,0; if there are acid oxides of this composition they are very rare, are only formed by distinctly acid elements, and even

then have only feeble acid properties ; for example, C1,0 and N,0. R20, or RO; salts RX.,, hydroxides R(OH)2. The most simple basic

salts R,OX, orR(OH)X ; for instance, the chloride Zn,OCI, ; also an almost exclusively basic type ; but the basic properties are more feebly developed than in the preceding type. For example, Cao

Mg0, BaO, Pb), FeO, Mn0, đc. R.,03 ; salts RX,, hydroxides R(OH)3, RO(OH), the most simple basic

salts ROX, R(OH)X,. The bases are feeble, like Al,O3, Fe,03, T1,03, Sb,Og. The acid properties are also feebly developed ; for instance, in B,03 ; but with the non-metals the properties of acids

are already clear ; for instance, P,03, P(OH)3. R,O, or RO2; salts RX, or ROX,, hydroxides R(OH), RO(OH),.

Rarely bases (feeble), like ZrO2, PtO2 ; more often acid oxides ; but the acid properties are in general feeble, as in CO2, SO2, Sn02. Many intermediate oxides appear in this and the preceding

and following types. R,05; salts principally of the types ROX,, RO,X, RO(OH)3,

ROZ(OH), rarely RX;. The basic character (X, a halogen, simple or complex ; for instance, NO3, CI, &c.) is feeble ; the acid character predominates, as is seen in N,05, P,05, C1,03 ; then

X=OH, OK, &c., for example NO,(OK). R,06 or RO3 ; salts and hydroxides generally of the type RO,X.,,

RO,(OH). Oxides of an acid character, as SO3, Cr03, MnO,.

Basic properties rare and feebly developed as in U(z. R20,; salts of the form RO,X, RO (OH), acid oxides ; for instance,

C1,07, Mn,O, Basic properties as feebly developed as the acid

properties in the oxides R20. R20, or RO . A very rare type, and only known in OsO, and

RuO.

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