Chapter VII., Note 28. Thus W. G. Burdakoff determined in my

laboratory that the specific gravity at 15°/4° of the solution BeCl_{2} + 200H_{2}O = 1·0138--that is, greater than the corresponding solution KCl + 200H_{2}O (= 1·0121), and less than the solution MgCl_{2} + 200H_{2}O (= 1·0203), as would follow from the magnitude of the molecular weight BeCl_{2} = 80, since KCl = 74·5 and MgCl_{2} = 95.

Dulong and Petit, having determined the specific heat of a number of solid elementary substances, observed that as the atomic weights of the elements increase, their specific heats decrease, and that _the product of the specific heat Q into the atomic weight A is an almost constant quantity_. This means that to bring different elements into a known thermal state an equal amount of work is required if atomic quantities of the elements are taken; that is, the amounts of heat expended in heating equal quantities by weight of the elements are far from equal, but are in inverse proportion to the atomic weights. For thermal changes the atom is a unit; all atoms, notwithstanding the difference of weight and nature, are equal. This is the simplest expression of the fact discovered by Dulong and Petit. The specific heat measures that quantity of heat which is required to raise the temperature of _one unit of weight_ of a substance by one degree. If the magnitude of the specific heat of elements be multiplied by the atomic weight, then we obtain the atomic heat--that is, the amount of heat required to raise the temperature of the atomic weight of an element by one degree. It is these products which for the majority of the elements prove to be approximately, if not quite, identical. A complete identity cannot be expected, because the specific heat of one and the same substance varies with the temperature, with its passage from one state into another, and frequently with even a simple mechanical change of density (for instance by hammering), not to speak of allotropic changes, &c. We will cite several figures[4] proving the truth of the conclusions arrived at by Dulong and Petit with respect to solid elementary bodies.

Li Na Mg P A = 7 23 24 31 Q = 0·9408 0·2934 0·245 0·202 AQ = 6·59 6·75 5·88 6·26

Fe Cu Zn Br A = 56 63 65 80 Q = 0·112 0·093 0·093 0·0843 AQ = 6·27 5·86 6·04 6·74

Pd Ag Sn I A = 106 108 118 127 Q = 0·0592 0·056 0·055 0·541 AQ = 6·28 6·05 6·49 6·87

Pt Au Hg Pb A = 196 198 200 206 Q = 0·0325 0·0324 0·0333 0·0315 AQ = 6·37 6·41 6·66 6·49

[4] The specific heats here given refer to different limits of temperature, but in the majority of cases between 0° and 100°; only in the case of bromine the specific heat is taken (for the solid state) at a temperature below -7°, according to Regnault's determination. _The variation of the specific heat with a change of temperature_ is a very complex phenomenon, the consideration of which I think would here be out of place. I will only cite a few figures as an example. According to Bystrom, the specific heat of iron at 0° = 0·1116, at 100° = 0·1114, at 200° = 0·1188, at 300° = 0·1267, and at 1,400° = 0·4031. Between these last limits of temperature a change takes place in iron (a spontaneous heating, _recalescence_), as we shall see in Chapter XXII. For quartz SiO_{2} Pionchon gives Q = 0·1737 + 394_t_10^{-6}-27_t_^{2}10^{-9} up to 400°, for metallic aluminium (Richards, 1892) at 0° 0·222, at 20° 0·224, at 100° 0·232; consequently, as a rule, the specific heat varies slightly with the temperature. Still more remarkable are H. E. Weber's observations on the great variation of the specific heat of charcoal, the diamond and boron:

0° 100° 200° 600° 900° Wood charcoal 0·15 0·23 0·29 0·44 0·46 Diamond 0·10 0·19 0·22 0·44 0·45 Boron 0·22 0·29 0·35 -- --

These determinations, which have been verified by Dewar, Le Chatelier (Chapter VIII., Note 13), Moissan, and Gauthier, the latter finding for boron AQ = 6 at 400°, are of especial importance as confirming the universality of Dulong and Petit's law, because the elements mentioned above form exceptions to the general rule when the mean specific heat is taken for temperatures between 0° and 100°. Thus in the case of the diamond the product of A × Q at 0° = 1·2, and for boron = 2·4. But if we take the specific heat towards which there is evidently a tendency with a rise of temperature, we obtain a product approaching to 6 as with other elements. Thus with the diamond and charcoal, it is evident that the specific heat tends towards 0·47, which multiplied by 12 gives 5·6, the same as for magnesium and aluminium. I may here direct the reader's attention to the fact that for solid elements having a small atomic weight, the specific heat varies considerably if we take the average figures for temperatures 0° to 100°:

Li = 7 Be = 9 B = 11 C = 12 Q = 0·94 0·42 0·24 0·20 AQ = 6·6 3·8 2·6 2·4

It is therefore clear that the specific heat of beryllium determined at a low temperature cannot serve for establishing its atomicity. On the other hand, the low atomic heat of charcoal, graphite, and the diamond, boron, &c., may perhaps depend on the complexity of the molecules of these elements. The necessity for acknowledging a great complexity of the molecules of carbon was explained in Chapter VIII. In the case of sulphur the molecule contains at least S_{6} and its atomic heat = 32 × 0·163 = 5·22, which is distinctly below the normal. If a large number of atoms of carbon are contained in the molecule of charcoal, this would to a certain extent account for its comparatively small atomic heat. With respect to the specific heat of compounds, it will not be out of place to mention here the conclusion arrived at by Kopp, that the molecular heat (that is, the product of MQ) may be looked on as the sum of the atomic heats of its component elements; but as this rule is not a general one, and can only be applied to give an approximate estimate of the specific heats of substances, I do not think it necessary to go into the details of the conclusions described in Liebig's 'Annalen Supplement-Band,' 1864, which includes a number of determinations made by Kopp.

It is seen from this that the product of the specific heat of the element into the atomic weight is an almost constant quantity, which is nearly 6. Hence it is possible to determine the valency by the specific heats of the metals. Thus, for instance, the specific heats of lithium, sodium, and potassium convince us of the fact that their atomic weights are indeed those which we chose, because by multiplying the specific heats found by experiment by the corresponding atomic weights we obtain the following figures: Li, 6·59, Na, 6·75 and K, 6·47. Of the alkaline earth metals the specific heats have been determined: of magnesium = 0·245 (Regnault and Kopp), of calcium = 0·170 (Bunsen), and of barium = 0·05 (Mendeléeff). If the same composition be ascribed to the compounds of magnesium as to the corresponding compounds of potassium, then the equivalent of magnesium will be equal to 12. On multiplying this atomic weight by the specific heat of magnesium, we obtain a figure 2·94, which is half that which is given by the other solid elements and therefore the atomic weight of magnesium must be taken as equal to 24 and not to 12. Then the atomic heat of magnesium = 24 × 0·245 = 5·9; for calcium, giving its compounds a composition CaX_{2}--for example CaCl_{2}, CaSO_{4}, CaO (Ca = 40)--we obtain an atomic heat = 40 × 0·17 = 6·8, and for barium it is equal to 137 × 0·05 = 6·8; that is, they must be counted as bivalent, or that their atom replaces H_{2}, Na_{2}, or K_{2}. This conclusion may be confirmed by a method of analogy, as we shall afterwards see. The application of the principle of specific heats to the determination of the magnitudes of the atomic weights of those metals, the magnitude of whose atomic weights could not be determined by Avogadro-Gerhardt's law, was made about 1860 by the Italian professor Cannizzaro.

Exactly the same conclusions respecting the bivalence of magnesium and its analogues are obtained by comparing the specific heats of their compounds, especially of the halogen compounds as the most simple, with the specific heats of the corresponding alkali compounds. Thus, for instance, the specific heats of magnesium and calcium chlorides, MgCl_{2} and CaCl_{2}, are 0·194 and 0·164, and of sodium and potassium chlorides, NaCl and KCl, 0·214 and 0·172, and therefore their molecular heats (or the products QM, where M is the weight of the molecule) are 18·4 and 18·2, 12·5 and 12·8, and hence the atomic heats (or the quotient of QM by the number of atoms) are all nearly 6, as with the elements. Whilst if, instead of the actual atomic weights Mg = 24 and Ca = 40, their equivalents 12 and 20 be taken, then the atomic heats of the chlorides of magnesium and calcium would be about 4·6, whilst those of potassium and sodium chlorides are about 6·3.[5] We must remark, however, that as the specific heat or the amount of heat required to raise the temperature of a unit of weight one degree[6] is a complex quantity--including not only the increase of the energy of a substance with its rise in temperature, but also the external work of expansion[7] and the internal work accomplished in the molecules causing them to decompose according to the rise of temperature[8]--therefore it is impossible to expect in the magnitude of the specific heat the great simplicity of relation to composition which we see, for instance, in the density of gaseous substances. Hence, although the specific heat is one of the important means for determining the atomicity of the elements, still the mainstay for a true judgment of atomicity is only given by Avogadro-Gerhardt's law, _i.e._ this other method can only be accessory or preliminary, and when possible recourse should be had to the determination of the vapour density.

[5] It must be remarked that in the case of oxygen (and also hydrogen and carbon) compounds the quotient of MQ/_n_, where _n_ is the number of atoms in the molecule, is always less than 6 for solids; for example, for MgO = 5·0, CuO = 5·1, MnO_{2} = 4·6, ice (Q = 0·504) = 3, SiO_{2} = 3·5, &c. At present it is impossible to say whether this depends on the smaller specific heat of the atom of oxygen in its solid compounds (Kopp, Note 4) or on some other cause; but, nevertheless, taking into account this decrease depending on the presence of oxygen, a reflection of the atomicity of the elements may to a certain extent be seen in the specific heat of the oxides. Thus for alumina, Al_{2}O_{3} (Q = 0·217), MQ = 22·3, and therefore the quotient MQ/_n_ = 4·5, which is nearly that given by magnesium oxide, MgO. But if we ascribe the same composition to alumina, as to magnesia--that is, if aluminium were counted as divalent--we should obtain the figure 3·7, which is much less. In general, in compounds of identical atomic composition and of analogous chemical properties the molecular heats MQ are nearly equal, as many investigators have long remarked. For example, ZnS = 11·7 and HgS = 11·8; MgSO_{4} = 27·0 and ZnSO_{4} = 28·0, &c.

[6] If W be the amount of heat contained in a mass _m_ of a substance at a temperature _t_, and _d_W the amount expended in heating it from _t_ to _t_ + _dt_, then the specific heat Q = _d_W(_m_ × _dt_). The specific heat not only varies with the composition and complexity of the molecules of a substance, but also with the temperature, pressure, and physical state of a substance. Even for gases the variation of Q with _t_ is to be observed. Thus it is seen from the experiments of Regnault and Wiedemann that the specific heat of carbonic anhydride at 0° = 0·19, at 100° = 0·22, and at 200° = 0·24. But the variation of the specific heat of permanent gases with the temperature is, as far as we know, very inconsiderable. According to Mallard and Le Chatelier it is = 0·0006/M per 1°, where M is the molecular weight (for instance, for O_{2}, M = 32). Therefore the specific heat of those permanent gases which contain two atoms in the molecule (H_{2}, O_{2}, N_{2}, CO, and NO) may be, as is shown by experiment, taken as not varying with the temperature. The constancy of the specific heat of perfect gases forms one of the fundamental propositions of the whole theory of heat and on it depends the determination of temperatures by means of gas-thermometers containing hydrogen, nitrogen, or air. Le Chatelier (1887), on the basis of existing determinations, concludes that the molecular heat--that is, the product MQ--of all gases varies in proportion to the temperature, and tends to become equal (= 6·8) at the temperature of absolute zero (that is, at -273°); and therefore MQ = 6·8 + _a_(273 + _t_), where _a_ is a constant quantity which increases with the complexity of the gaseous molecule and Q is the specific heat of the gas under a constant pressure. For permanent gases _a_ almost = 0, and therefore MQ = 6·8--that is, the atomic heat (if the molecule contains two atoms) = 3·4, as it is in fact (Chapter IX., Note 17 bis). As regards liquids (as well as the vapours formed by them), the specific heat always rises with the temperature. Thus for benzene it equals 0·38 + 0·0014_t_. R. Schiff (1887) showed that the variation of the specific heat of many organic liquids is proportional to the change of temperature (as in the case of gases, according to Le Chatelier), and reduced these variations into dependence with their composition and absolute boiling point. It is very probable that the theory of liquids will make use of these simple relations which recall the simplicity of the variation of the specific gravity (Chapter II., Note 34), cohesion, and other properties of liquids with the temperature. They are all expressed by the linear function of the temperature, _a_ + _bt_, with the same degree of proximity as the property of gases is expressed by the equation _pv_ = _Rt_.

As regards the relation between the specific heats of liquids (or of solids) and of their vapours, the specific heat of the vapour (and also of the solid) is always less than that of the liquid. For example, benzene vapour 0·22, liquid 0·38; chloroform vapour 0·13, liquid 0·23; steam 0·475, liquid water 1·0. But the complexity of the relations existing in specific heat is seen from the fact that the specific heat of ice = 0·502 is less than that of liquid water. According to Regnault, in the case of bromine the specific heat of the vapour = 0·055 at (150°), of the liquid = 0·107 (at 30°), and of solid bromine = 0·084 (at -15°). The specific heat of solid benzoic acid (according to experiment and calculation, Hess, 1888) between 0° and 100° is 0·31, and of liquid benzoic acid 0·50. One of the problems of the present day is the explanation of those complex relations which exist between the composition and such properties as specific heat, latent heat, expansion by heat, compression, internal friction, cohesion, and so forth. They can only be connected by a complete theory of liquids, which may now soon be expected, more especially as many sides of the subject have already been partially explained.

[7] According to the above reasons the quantity of heat, Q, required to raise the temperature of one part by weight of a substance by one degree may be expressed by the sum Q = K + B + D, where K is the heat actually expended in heating the substance, or what is termed the absolute specific heat, B the amount of heat expended in the internal work accomplished with the rise of temperature, and D the amount of heat expended in external work. In the case of gases the last quantity may be easily determined, knowing their coefficient of expansion, which is approximately = 0·00368. By applying to this case the same argument given at the end of Note 11, Chapter I., we find that one cubic metre of a gas heated 1° produces an external work of 10333 × 0·00368, or 38·02 kilogrammetres, on which 38·02/424 or 0·0897 heat units are expended. This is the heat expended for the external work produced by one cubic metre of a gas, but the specific heat refers to units of weight, and therefore it is necessary in order to know D to reduce the above quantity to a unit of weight. One cubic metre of hydrogen at 0° and 760 mm. pressure weighs 0·0896 kilo, a gas of molecular weight M has a density M/2, consequently a cubic metre weighs (at 0° and 760 mm.) 0·0448M kilo, and therefore 1 kilogram of the gas occupies a volume 1/0·0448M cubic metres, and hence the external work D in the heating of 1 kilo of the given gas through 1° = 0·0896/0·0448M, or D = 2/M.

Taking the magnitude of the internal work B for gases as negligible if permanent gases are taken, and therefore supposing B = 0, we find the specific heat of gases at a constant pressure Q = K + 2 M, where K is the specific heat at a constant volume, or the true specific heat, and M the molecular weight. Hence K = Q-2/M. The magnitude of the specific heat Q is given by direct experiment. According to Regnault's experiments, for oxygen it = 0·2175, for hydrogen 3·405, for nitrogen 0·2438; the molecular weights of these gases are 32, 2, and 28, and therefore for oxygen K = 0·2175-0·0625 = 0·1550, for hydrogen K = 3·4050-1·000 = 2·4050, and for nitrogen K = 0·2438-0·0714 = 0·1724. These true specific heats of elements are in inverse proportion to their atomic weights--that is, their product by the atomic weight is a constant quantity. In fact, for oxygen this product = 0·155 × 16 = 2·48, for hydrogen 2·40, for nitrogen 0·7724 × 14 = 2·414, and therefore if A stand for the atomic weight we obtain the expression K × A = a constant, which may be taken as 2·45. This is the true expression of Dulong and Petit's law, because K is the true specific heat and A the weight of the atom. It should be remarked, moreover, that the product of the observed specific heat Q into A is also a constant quantity (for oxygen = 3·48, for hydrogen = 3·40), because the external work D is also inversely proportional to the atomic weight.

In the case of gases we distinguish the specific heat at a constant pressure _c´_ (we designated this quantity above by Q), and at a constant volume _c_. It is evident that _the relation between the two specific heats, k_, judging from the above, is the ratio of Q to K, or equal to the ratio of 2·45_n_ + 2 to 2·45_n_. When _n_ = 1 this ratio _k_ = 1·8; when _n_ = 2, _k_ = 1·4, when _n_ = 3, _k_ = 1·3, and with an exceedingly large number _n_, of atoms in the molecule, _k_ = 1. That is, the ratio between the specific heats decreases from 1·8 to 1·0 as the number of atoms, _n_, contained in the molecule increases. This deduction is verified to a certain extent by direct experiment. For such gases as hydrogen, oxygen, nitrogen, carbonic oxide, air, and others in which _n_ = 2, the magnitude of _k_ is determined by methods described in works on physics (for example, by the change of temperature with an alteration of pressure, by the velocity of sound, &c.) and is found in reality to be nearly 1·4, and for such gases as carbonic anhydride, nitric dioxide, and others it is nearly 1·3. Kundt and Warburg (1875), by means of the approximate method mentioned in Note 29, Chapter VII., determined _k_ for mercury vapour when _n_ = 1, and found it to be = 1·67--that is, a larger quantity than for air, as would be expected from the above.

It may be admitted that the true atomic heat of gases = 2·43, only under the condition that they are distant from a liquid state, and do not undergo a chemical change when heated--that is, when no internal work is produced in them (B = 0). Therefore this work may to a certain extent be judged by the observed specific heat. Thus, for instance, for chlorine (Q = 0·12, Regnault; _k_ = 1·33, according to Straker and Martin, and therefore K = 0·09, MK = 6·4), the atomic heat (3·2) is much greater than for other gases containing two atoms in a molecule, and it must be assumed, therefore, that when it is heated some great internal work is accomplished.

In order to generalise the facts concerning the specific heat of gases and solids, it appears to me possible to accept the following general proposition: _the atomic heat_ (that is, AQ or QM/_n_, where M is the molecular weight and _n_ the number of molecules) is _smaller_ (in solids it attains its highest value 6·8 and in gases 3·4), _the more complex the molecule_ (i.e. _the greater the number (n) of atoms forming it_) _and so much smaller, up to a certain point_ (in similar physical states) _the smaller the mean atomic weight M/n_.

[8] As an example, it will be sufficient to refer to the specific heat of nitrogen tetroxide, N_{2}O_{4}, which, when heated, gradually passes into NO_{2}--that is, chemical work of decomposition proceeds, which consumes heat. Speaking generally, specific heat is a complex quantity, in which it is clear that thermal data (for instance, the heat of reaction) alone cannot give an idea either of chemical or of physical changes individually, but always depend on an association of the one and the other. If a substance be heated from _t__{0} to _t__{1} it cannot but suffer a chemical change (that is, the state of the atoms in the molecules changes more or less in one way or another) if dissociation sets in at a temperature _t__{1}. Even in the case of the elements whose molecules contain only one atom, a true chemical change is possible with a rise of temperature, because more heat is evolved in chemical reactions than that quantity which participates in purely physical changes. One gram of hydrogen (specific heat = 3·4 at a constant pressure) cooled to the temperature of absolute zero will evolve altogether about one thousand units of heat, 8 grams of oxygen half this amount, whilst in combining together they evolve in the formation of 9 grams of water more than thirty times as much heat. Hence the store of chemical energy (that is, of the motion of the atoms, vortex, or other) is much greater than the physical store proper to the molecules, but it is the change accomplished by the former that is the cause of chemical transformations. Here we evidently touch on those limits of existing knowledge beyond which the teaching of science does not yet allow us to pass. Many new scientific discoveries have still to be made before this is possible.

Among the bivalent metals the first place, with respect to their distribution in nature, is occupied by _magnesium_ and _calcium_, just as sodium and potassium stand first amongst the univalent metals. The relation which exists between the atomic weights of these four metals confirms the above comparison. In fact, the combining weight of magnesium is equal to 24, and of calcium 40; whilst the combining weights of sodium and potassium are 23 and 39--that is, the latter are one unit less than the former.[9] They all belong to the number of _light metals_, as they have but a small specific gravity, in which respect they differ from the ordinary, generally known heavy, or ore, metals (for instance, iron, copper, silver, and lead), which are distinguished by a much greater specific gravity. There is no doubt that their low specific gravity has a significance, not only as a simple point of distinction, but also as a property which determines the fundamental properties of these metals. Indeed, all the light metals have a series of points of resemblance with the metals of the alkalis; thus both magnesium and calcium, like the metals of the alkalis, decompose water (without the addition of acids), although not so easily as the latter metals. The process of the decomposition is essentially one and the same; for example, Ca + 2H_{2}O = CaH_{2}O_{2} + H_{2}--that is, hydrogen is liberated and a hydroxide of the metal formed. These hydroxides are bases which neutralise nearly all acids. However, the hydroxides RH_{2}O_{2} of calcium and magnesium are in no respect so energetic as the hydroxides of the true metals of the alkalis; thus when heated they lose water, are not so soluble, develop less heat with acids, and form various salts, which are less stable and more easily decomposed by heat than the corresponding salts of sodium and potassium. Thus calcium and magnesium carbonates easily part with carbonic anhydride when ignited; the nitrates are also very easily decomposed by heat, calcium and magnesium oxides, CaO and MgO, being left behind. The chlorides of magnesium and calcium, when heated with water, evolve hydrogen chloride, forming the corresponding hydroxides, and when ignited the oxides themselves. All these points are evidence of a weakening of the alkaline properties.

[9] As if NaH = Mg and KH = Ca, which is in accordance with their valency. KH includes two monovalent elements, and is a bivalent group like Ca.

These metals have been termed _the metals of the alkaline earths_, because they, like the alkali metals, form energetic bases. They are called alkaline _earths_ because they are met with in nature in a state of combination, forming the insoluble mass of the earth, and because as oxides, RO, they themselves have an earthy appearance. Not a few salts of these metals are known which are insoluble in water, whilst the corresponding salts of the alkali metals are generally soluble--for example, the carbonates, phosphates, borates, and other salts of the alkaline earth metals are nearly insoluble. This enables us to separate the metals of the alkaline earths from the metals of the alkalis. For this purpose a solution of ammonium carbonate is added to a mixed solution of salts of both kinds of metals, when by a double decomposition the insoluble carbonates of the metals of the alkaline earths are formed and fall as a precipitate, whilst the metals of the alkalis remain in solution: RX_{2} + Na_{2}CO_{3} = RCO_{3} + 2NaX.

We may here remark that the oxides of the metals of the alkaline earths are frequently called by special names: MgO is called magnesia or bitter earth; CaO, lime; SrO, strontia; and BaO, baryta.

In the primary rocks the oxides of calcium and magnesium are combined with silica, sometimes in variable quantities, so that in some cases the lime predominates and in other cases the magnesium. The two oxides, being analogous to each other, replace each other in equivalent quantities. The various forms of _augite_, _hornblende_, or _amphibole_, and of similar minerals, which enter into the composition of nearly all rocks, contain lime and magnesia and silica. The majority of the primary rocks also contain alumina, potash, and soda. These rocks, under the action of water (containing carbonic acid) and air, give up lime and magnesia to the water, and therefore they are contained in all kinds of water, and especially in sea-water. The _carbonates_ CaCO_{3} and MgCO_{3}, frequently met with in nature, _are soluble in an excess of water saturated with carbonic anhydride_,[10] and therefore many natural waters contain these salts, and are able to yield them when evaporated. However, one kilogram of water saturated with carbonic anhydride does not dissolve more than three grams of calcium carbonate. By gradually expelling the carbonic anhydride from such water, an insoluble precipitate of calcium carbonate separates out. It may confidently be stated that the formation of the very widely distributed strata of calcium and magnesium carbonates was of this nature, because these strata are of a sedimentary character--that is, such as would be exhibited by a gradually accumulating deposit on the bottom of the sea, and, moreover, frequently containing the remains of marine plants, and animals, shells, &c. It is very probable that the presence of these organisms in the sea has played the chief part in the precipitation of the carbonates from the sea water, because the plants absorb CO_{2}, and many of the organisms CaCO_{3}, and after death give deposits of carbonate of lime; for instance, chalk, which is almost entirely composed of the minute remains of the calcareous shields of such organisms. These deposits of calcium and magnesium carbonates are the most important sources of these metals. Lime generally predominates, because it is present in rocks and running water in greater quantity than magnesia, and in this case these sedimentary rocks are termed _limestone_. Some common flagstones used for paving, &c., and chalk may be taken as examples of this kind of formation. Those limestones in which a considerable portion of the calcium is replaced by magnesium are termed _dolomites_. The dolomites are distinguished by their hardness, and by their not parting with the whole of their carbonic anhydride so easily as the limestones under the action of acids. Dolomites[11] sometimes contain an equal number of molecules of calcium carbonate and magnesium carbonate, and they also sometimes appear in a crystalline form, which is easily intelligible, because calcium carbonate itself is exceedingly common in this form in nature, and is then known as _calc spar_, whilst natural crystalline magnesium carbonate is termed _magnesite_. The formation of the crystalline varieties of the insoluble carbonates is explained by the possibility of a slow deposition from solutions containing carbonic acid. Besides which (Chapter X.) calcium and magnesium sulphates are obtained from sea water, and therefore they are met with both as deposits and in springs. It must be observed that magnesium is held in considerable quantities in sea water, because the sulphate and chloride of magnesium are very soluble in water, whilst calcium sulphate is but little soluble, and is used in the formation of shells; and therefore if the occurrence of considerable deposits of magnesium sulphate cannot be expected in nature, still, on the other hand, one would expect (and they do actually occur) large masses of calcium sulphate or _gypsum_, CaSO_{4},2H_{2}O. Gypsum sometimes forms strata of immense size, which extend over many hectometres--for example, in Russia on the Volga, and in the Donetz and Baltic provinces.

[10] Sodium carbonate and other carbonates of the alkalis give acid salts which are less soluble than the normal; here, on the contrary, with an excess of carbonic anhydride, a salt is formed which is more soluble than the normal, but this acid salt is more unstable than sodium hydrogen carbonate, NaHCO_{3}.

[11] The formation of dolomite may be explained, if only we imagine that a solution of a magnesium salt acts on calcium carbonate. Magnesium carbonate may be formed by double decomposition, and it must be supposed that this process ceases at a certain limit (Chapter XII.), when we shall obtain a mixture of the carbonates of calcium and magnesium. Haitinger heated a mixture of calcium carbonate, CaCO_{3}, with a solution of an equivalent quantity of magnesium sulphate, MgSO_{4}, in a closed tube at 200°, and then a portion of the magnesia actually passed into the state of magnesium carbonate, MgCO_{3}, and a portion of the lime was converted into gypsum, CaSO_{4}. Lubavin (1892) showed that MgCO_{3} is more soluble than CaCO_{3} in salt water, which is of some significance in explaining the composition of sea water.

Lime and magnesia also, but in much smaller quantities (only to the amount of several fractions of a per cent. and rarely more), enter into the composition of every fertile soil, and without these bases the soil is unable to support vegetation. Lime is particularly important in this respect, and its presence in a larger quantity generally improves the harvest, although purely calcareous soils are as a rule infertile. For this reason the soil is fertilised both with lime[12] itself and with marl--that is, with clay mixed with a certain quantity of calcium carbonate, strata of which are found nearly everywhere.

[12] The undoubted action of lime in increasing the fertility of soils--if not in every case, at all events, with ordinary soils which have long been under corn--is based not so much on the need of plants for the lime itself as on those chemical and physical changes which it produces in the soil, as a particularly powerful base which aids the alteration of the mineral and organic elements of the soil.

From the soil the lime and magnesia (in a smaller quantity) pass into the substance of _plants_, where they occur as salts. Certain of these salts separate in the interior of plants in a crystalline form--for example, calcium oxalate. The lime occurring in plants serves as the source for the formation of the various calcareous secretions which are so common in _animals_ of all classes. The bones of the highest animal orders, the shells of mollusca, the covering of the sea-urchin, and similar solid secretions of sea animals, contain calcium salts; namely, the shells mainly calcium carbonate, and the bones mainly calcium phosphate. Certain limestones are almost entirely formed of such deposits. Odessa is situated on a limestone of this kind, composed of shells. Thus magnesium and calcium occur throughout the entire realm of nature, but calcium predominates.

As lime and magnesia form bases which are in many respects analogous, they were not distinguished from each other for a long time. Magnesia was obtained for the first time in the seventeenth century from Italy, and used as a medicine; and it was only in the last century that Black, Bergmann, and others distinguished magnesia from lime.

_Metallic magnesium_ (and calcium also) is not obtained by heating magnesium oxide or the carbonate with charcoal, as the alkali metals are obtained,[13] but is liberated by the action of a galvanic current on fused magnesium chloride (best mixed with potassium chloride); Davy and Bussy obtained metallic magnesium by acting on magnesium chloride with the vapours of potassium. At the present time (Deville's process) magnesium is prepared in rather considerable quantities by a similar process, only the potassium is replaced by sodium. Anhydrous magnesium chloride, together with sodium chloride and calcium fluoride, is fused in a close crucible. The latter substances only serve to facilitate the formation of a fusible mass before and after the reaction, which is indispensable in order to prevent the access and action of air. One part of finely divided sodium to five parts of magnesium chloride is thrown into the strongly heated molten mass, and after stirring the reaction proceeds very quickly, and magnesium separates, MgCl_{2} + Na_{2} = Mg + 2NaCl. In working on a large scale, the powdery metallic magnesium is then subjected to distillation at a white heat. The distillation of the magnesium is necessary, because the undistilled metal is not homogeneous[14] and burns unevenly: the metal is prepared for the purpose of illumination. Magnesium is a white metal, like silver; it is not soft like the alkali metals, but is, on the contrary, hard like the majority of the ordinary metals. This follows from the fact that it melts at a somewhat high temperature--namely, about 500°--and boils at about 1000°. It is malleable and ductile, like the generality of metals, so that it can be drawn into wires and rolled into ribbon; it is most frequently used for lighting purposes in the latter form. Unlike the alkali metals, magnesium does not decompose the atmospheric moisture at the ordinary temperature, so that it is almost unacted on by air; it is not even acted on by water at the ordinary temperature, so that it may be washed to free it from sodium chloride. Magnesium only decomposes water with the evolution of hydrogen at the boiling point of water,[15] and more rapidly at still higher temperatures. This is explained by the fact that in decomposing water magnesium forms an insoluble hydroxide, MgH_{2}O_{2}, which covers the metal and hinders the further action of the water. Magnesium easily displaces hydrogen from acids, forming magnesium salts. When ignited it _burns_, not only in oxygen but in air (and even in carbonic anhydride), forming a white powder of magnesium oxide, or magnesia; in burning it emits a white and exceedingly _brilliant light_. The strength of this light naturally depends on the fact that magnesium (24 parts by weight) in burning evolves about 140 thousand heat units, and that the product of combustion, MgO, is infusible by heat; so that the vapour of the burning magnesium contains an ignited powder of non-volatile and infusible magnesia, and consequently presents all the conditions for the production of a brilliant light. The light emitted by burning magnesium contains many rays which act chemically, and are situated in the violet and ultra-violet parts of the spectrum. For this reason burning magnesium may be employed for producing photographic images.[16]

[13] Sodium and potassium only decompose magnesium oxide at a white heat and very feebly, probably for two reasons. In the first place, because the reaction Mg + O develops more heat (about 140 thousand calories) than K_{2} + O or Na_{2} + O (about 100 thousand calories); and, in the second place, because magnesia is not fusible at the heat of a furnace and cannot act on the charcoal, sodium, or potassium--that is, it does not pass into that mobile state which is necessary for reaction. The first reason alone is not sufficient to explain the absence of the reaction between charcoal and magnesia, because iron and charcoal in combining with oxygen evolve less heat than sodium or potassium, yet, nevertheless, they can displace them. With respect to magnesium chloride, it acts on sodium and potassium, not only because their combination with chlorine evolves more heat than the combination of chlorine and magnesium (Mg + Cl_{2} gives 150 and Na_{2} + Cl_{2} about 195 thousand calories), but also because a fusion, both of the magnesium chloride and of the double salt, takes place under the action of heat. It is probable, however, that a reverse reaction will take place. A reverse reaction might probably be expected, and Winkler (1890) showed that Mg reduces the oxides of the alkali metals (Chapter XIII., Note 42).

[14] Commercial magnesium generally contains a certain amount of magnesium nitride (Deville and Caron), Mg_{3}N_{2}--that is, a product of substitution of ammonia which is directly formed (as is easily shown by experiment) when magnesium is heated in nitrogen. It is a yellowish green powder, which gives ammonia and magnesia with water, and cyanogen when heated with carbonic anhydride. Pashkoffsky (1893) showed that Mg_{3}N_{2} is easily formed and is the sole product when Mg is heated to redness in a current of NH_{3}. Perfectly pure magnesium may be obtained by the action of a galvanic current.

[15] Hydrogen peroxide (Weltzien) dissolves magnesium. The reaction has not been investigated.

[16] A special form of apparatus is used for burning magnesium. It is a clockwork arrangement in which a cylinder rotates, round which a ribbon or wire of magnesium is wound. The wire is subjected to a uniform unwinding and burning as the cylinder rotates, and in this manner the combustion may continue uniform for a certain time. The same is attained in special lamps, by causing a mixture of sand and finely divided magnesium to fall from a funnel-shaped reservoir on to the flame. In photography it is best to blow finely divided magnesium into a colourless (spirit or gas) flame, and for instantaneous photography to light a cartridge of a mixture of magnesium and chlorate of potassium by means of a spark from a Ruhmkorff's coil (D. Mendeléeff, 1889).

Owing to its great affinity for oxygen, magnesium _reduces_ many metals (zinc, iron, bismuth, antimony, cadmium, tin, lead, copper, silver, and others) from solutions of their salts at the ordinary temperature,[17] and at a red heat finely divided magnesium takes up the oxygen from silica, alumina, boric anhydride, &c.; so that silicon and similar elements may be obtained by directly heating a mixture of powdered silica and magnesium in an infusible glass tube.[18]

[17] According to the observations of Maack, Comaille, Böttger, and others. The reduction by heat mentioned further on was pointed out by Geuther, Phipson, Parkinson and Gattermann.

[18] This action of metallic magnesium in all probability depends, although only partially (_see_ Note 13), on its volatility, and on the fact that, in combining with a given quantity of oxygen, it evolves more heat than aluminium, silicon, potassium, and other elements.

The affinity of magnesium for the halogens is much more feeble than for oxygen,[19] as is at once evident from the fact that a solution of iodine acts feebly on magnesium; still magnesium burns in the vapours of iodine, bromine, and chlorine. The character of magnesium is also seen in the fact that all its salts, especially in the presence of water, are decomposable at a comparatively moderate temperature, the elements of the acid being evolved, and the magnesium oxide, which is non-volatile and unchangeable by heat, being left. This naturally refers to those acids which are themselves volatilised by heat. Even magnesium sulphate is completely decomposed at the temperature at which iron melts, oxide of magnesium remaining behind. This decomposition of magnesium salts by heat proceeds much more easily than that of calcium salts. For example, magnesium carbonate is totally decomposed at 170°, magnesium oxide being left behind. This _magnesia_, or _magnesium oxide_, is met with both in an anhydrous and hydrated state in nature (the anhydrous magnesia as the mineral _periclase_, MgO, and the hydrated magnesia as _brucite_, MgH_{2}O_{2}). Magnesia is a well-known medicine (calcined magnesia--_magnesia usta_). It is a white, extremely fine, and very voluminous powder, of specific gravity 3·4; it is infusible by heat, and only shrinks or shrivels in an oxyhydrogen flame. After long contact the anhydrous magnesia combines with water, although very slowly, forming the hydroxide Mg(HO)_{2}, which, however, parts with its water with great ease when heated even below a red heat, and again yields anhydrous magnesia. This hydroxide is obtained directly as a gelatinous amorphous substance when a soluble alkali is mixed with a solution of any magnesium salt, MgCl_{2} + 2KHO = Mg(HO)_{2} + 2KCl. This decomposition is complete, and nearly all the magnesium passes into the precipitate; and this clearly shows the almost perfect insolubility of magnesia in water. Water dissolves a scarcely perceptible quantity of magnesium hydroxide--namely, one part is dissolved by 55,000 parts of water. Such a solution, however, has an alkaline reaction, and gives, with a salt of phosphoric acid, a precipitate of magnesium phosphate, which is still more insoluble. Magnesia is not only dissolved by acids, forming salts, but it also displaces certain other bases--for example, ammonia from ammonium salts when boiled; and the hydroxide also absorbs carbonic anhydride from the air. The magnesium salts, like those of calcium, potassium, and sodium, are colourless if they are formed from colourless acids. Those which are soluble have a bitter taste, whence magnesia has been termed _bitter-earth_. In comparison with the alkalis magnesia is a feeble base, inasmuch as it forms somewhat unstable salts, easily gives basic salts, forms acid salts with difficulty, and is able to give double salts with the salts of the alkalis, which facts are characteristic of feeble bases, as we shall see in becoming acquainted with the different metals.

[19] Davy, on heating magnesia in chlorine, concluded that there was a complete substitution, because the volume of the oxygen was half the volume of the chlorine; it is probable, however, that owing to the formation of chlorine oxide (Chapter XI., Note 30) the decomposition is not complete and is limited by a reverse reaction.

The power of magnesium salts to form double and basic salts is very frequently shown in reactions, and is specially marked as regards ammonium salts. If saturated solutions of magnesium and ammonium sulphates are mixed together, a crystalline double salt Mg(NH_{4})_{2}(SO_{4})_{2},6H_{2}O,[20] is immediately precipitated. A strong solution of ordinary ammonium carbonate dissolves magnesium oxide or carbonate, and precipitates crystals of a double salt, Mg(NH_{4})_{2}(CO_{3})_{2},4H_{2}O, from which water extracts the ammonium carbonate. With an excess of an ammonium salt the double salt passes into solution,[21] and therefore if a solution contain a magnesium salt and an excess of an ammonium salt--for instance, sal-ammoniac--then sodium carbonate will no longer precipitate magnesium carbonate. A mixture of solutions of magnesium and ammonium chlorides, on evaporation or refrigeration, gives a double salt, Mg(NH_{4})Cl_{3},6H_{2}O.[22] The salts of potassium, like those of ammonium, are able to enter into combination with the magnesium salts.[23] For instance, the double salt, MgKCl_{3},6H_{2}O, which is known as _carnallite_,[24] and occurs in the salt mines of Stassfurt, may be formed by freezing a saturated solution of potassium chloride with an excess of magnesium chloride. A saturated solution of magnesium sulphate dissolves potassium sulphate, and solid magnesium sulphate is soluble in a saturated solution of potassium sulphate. A double salt, K_{2}Mg(SO_{4})_{2},6H_{2}_O, which closely resembles the above-mentioned ammonium salt, crystallises from these solutions.[25] The nearest analogues of magnesium are able to give exactly similar double salts, both in crystalline form (monoclinic system) and composition; they, like this salt (_see_ Chapter XV.), are easily able (at 140°) to part with all their water of crystallisation, and correspond with the salts of sulphuric acid, whose type may be taken as _magnesium sulphate_, MgSO_{4}.[26] It occurs at Stassfurt as _kieserite_, MgSO_{4},H_{2}O, and generally separates from solutions as a heptahydrated salt, MgSO_{4},7H_{2}O, and from supersaturated solutions as a hexahydrated salt, MgSO_{4},6H_{2}O; at temperatures below 0° it crystallises out as a dodecahydrated salt, MgSO_{4},12H_{2}O, and a solution of the composition MgSO_{4},2H_{2}O solidifies completely at -5°.[27] Thus between water and magnesium sulphate there may exist several definite and more or less stable degrees of equilibrium; the double salt MgSO_{4}K_{2}SO_{4},6H_{2}O may be regarded as one of these equilibrated systems, the more so since it contains 6H_{2}O, whilst MgSO_{4} forms its most stable system with 7H_{2}O, and the double salt may be considered as this crystallo-hydrate in which one molecule of water is replaced by the molecule K_{2}SO_{4}.[28]

[20] Even a solution of ammonium chloride gives this salt with magnesium sulphate. Its sp. gr. is 1·72; 100 parts of water at 0° dissolve 9, at 20° 17·9 parts of the anhydrous salt. At about 130° it loses all its water.

[21] This is an example of equilibrium and of the influence of mass; the double salt is decomposed by water, but if instead of water we take a solution of that soluble part which is formed in the decomposition of the double salt, then the latter dissolves as a whole.

[22] If an excess of ammonia be added to a solution of magnesium chloride, only half the magnesium is thrown down in the precipitate, 2MgCl_{2} + 2NH_{4}.OH = Mg(OH)_{2} + Mg.NH_{4}Cl_{3} + NH_{4}Cl. A solution of ammonium chloride reacts with magnesia, evolving ammonia and forming a solution of the same salt, MgO + 3NH_{4}Cl = MgNH_{4}Cl_{3} + H_{2}O + 2NH_{3}.

Among the double salts of ammonium and magnesium, the phosphate, MgNH_{4}PO_{4},6H_{2}O, is almost insoluble in water (0·07 gram is soluble in a litre), even in the presence of ammonia. Magnesia is very frequently precipitated as this salt from solutions in which it is held by ammonium salts. As lime is not retained in solution by the presence of ammonium salts, but is precipitated nevertheless by sodium carbonate, &c., it is very easy to separate calcium from magnesium by taking advantage of these properties.

[23] In order to see the nature and cause of formation of double salts, it is sufficient (although this does not embrace the whole essence of the matter) to consider that one of the metals of such salts (for instance, potassium) easily gives acid salts, and the other (in this instance, magnesium) basic salts; the properties of distinctly basic elements predominate in the former, whilst in the latter these properties are enfeebled, and the salts formed by them bear the character of acids--for example, the salts of aluminium or magnesium act in many cases like acids. By their mutual combination these two opposite properties of the salts are both satisfied.

[24] Carnallite has been mentioned in Chapter X. (Note 4) and in