by sulphuric acid from solutions of baryta-salts; silver as precipitated by proto-sulphate of iron from nitrate of silver.-Granular; coarsely pulve rulent masses having a more distinct crystalline character: sulphate of potash as precipitated by sulphuric acid from aqueous solution of carbonate of potash.-Arborescent; the union of a great number of individual crystals into larger ramified masses: metallic trees.

V. Magnitude or Strengh of Affinity.

There must exist a relation inexpressible in numbers between the magnitude of chemical affinities and those of other natural forces, such as gravitation, adhesion, or cohesion.

Absolute strength of affinity.--A solution of nitre saturated while warm deposits part of the nitre at 0° on account of increasing cohesion. Now supposing we were to determine what suspended weight would be required to break a crystal of nitre of a given thickness at 0°; then this weight would express the affinity of the water saturated with nitre at 0° for more nitre: for after the crystallization at 0° has ceased, this affinity is in equilibrio with the cohesion. A similar process might be adopted with other bodies soluble in water, the cohesion being always determined with reference to a crystal of given thickness. On the same principle Lavoisier and Laplace proposed to bring an acid of various degrees of strength into contact with ice at different temperatures below 0°, and to enquire at what degree of cold and at what dilution the acid ceased to exert any solvent power on the ice, and consequently its affinity for the ice became exactly equal in force to the cohesion of that substance-and thus to reduce the affinity of the acid for the ice, at different states of concentration, to degrees of the thermometer. A similar method might he adopted with various salts and ice: since for example common salt ceases to act on ice at -20° C., but chloride of calcium not till -60°, the affinity of the latter for water must be much greater than that of the former. But these methods only enable us to determine the weights or degrees of temperature by which the weakest and least important affinities may be expressed. All affinities which have any considerable value exceed the force of cohesion to such a degree, that comparison between the two powers becomes impossible.

For the present we must content ourselves with an approximate determination of relative strength of affinity, i. e., of the proportion which individual magnitudes of affinity bear to one another without reference to other natural forces. Perhaps we shall some day be able to affix a certain relative number to each particular magnitude of affinity; at present, however, we are contented if we can determine, with some degree of certainty, in what order the affinities of different bodies for a given body succeed one another with regard to their strength.

Is the affinity between two bodies different at different temperatures? Just as heat weakens cohesion by striving to increase the distance between homogeneous atoms, so likewise it may diminish the strength of affinity by increasing the difference between heterogeneous atoms. It appears, however, that as long as the action of heat does not go so far as to form a gaseous compound with one of the bodies, -in which case it would act like a third ponderable body in undoing the combination,-it does not weaken chemical attraction, probably because in a combination of two ponderable bodies, it tends to increase the distance of the compound atoms only, not of the simple ones by whose

union the compound atoms are formed. On the other hand, it might be inferred, from the phenomena mentioned on page 36 D, that elevation of temperature increases the strength of affinity. When, for example, sulphur combines with carbon at a red heat, we might suppose that the affinity between the two bodies is called into action by this temperature, or at least heightened in such a degree as to be able to overcome the cohesion of carbon; but in that case the sulphuret of carbon ought, on cooling, when the affinity is again diminished or annihilated and the cohesion of the carbon increased, to be again resolved into its elements. Such, however, is not the case either with this or with any other of the more intimate compounds, and therefore the affinity between such bodies exists even in the cold,—and heat does not develope affinity in the first instance, but favours the exertion of it in a manner not hitherto explained. At present, therefore, there is no ground for supposing that the affinity between two bodies is different at different temperatures. If, indeed, we would explain Berthollet's law of double affinity, not by the influence of cohesion, but on the supposition that out of a number of possible compounds those actually formed are always the most intimate, and have likewise the smallest relative solubility (page 125), it might, perhaps, be necessary to assume, with reference to the reciprocal affinity between common salt and sulphate of magnesia, for example (page 127), that the magnitudes of the affinities are different at different temperatures.

The following are the principal methods which have been adopted for the determination of relative magnitudes of affinity.

A. Difference of magnitude or strength of affinity is determined by the results of conflict or opposition of affinities, on the principle that the decomposing must be stronger than the existing or quiescent affinities. a. Decompositions in which the Affinity of Heat contributes to the Result.

Many combinations of ponderable substances are decomposed by elevation of temperature, one of the ponderable elements combining with heat and forming a gaseous compound. The affinity of heat for ponderable bodies must be supposed to increase with the quantity in which it is accumulated, and therefore with the temperature; consequently, the temperature required to decompose a compound of a less volatile with a more volatile body will increase with the affinity between the two. According to this, the strength or magnitude of the affinity may perhaps be found from the temperature required to effect the decomposition ;-the boiling point of the more volatile element must, however, be likewise taken into consideration.

Iron pyrites, Fe S2, when raised to a moderate red heat, which may be estimated at about 500° C., gives off vapour of sulphur, and is converted into Fe S; at a stronger red heat (perhaps = 800°), a still greater quantity of sulphur sublimes, and Fe S remains behind. Taking Dumas' determination of the boiling point of sulphur, viz., 440°, and supposing the higher degrees of temperature (a more accurate determination of which would, however, be desirable) to be correct, the affinity of Fe S for the quantity of sulphur required to produce Fe S, may be expressed by 800 440 360, and that of Fe S for as much sulphur as will produce Fe S2, by 500 440 60. Sulphuret of gold, Au S3, parts with all its sulphur, perhaps at about 450°; if so, the affinity of gold for sulphur will be expressed by 450 440 = 10. But few of the other metallic sulphurets are decomposed by heat; whence we may conclude that the number which would express the affinity of these metals for sulphur is

greater than the number of degrees of temperature which the sulphurets can bear without decomposition, minus 440°. In a similar manner might be determined the affinity of iodine, bromine, and chlorine for the few metals from which they can be separated by heat, provided the temperatures at which the decompositions take place could be more accurately determined: so likewise might be estimated the affinity of mercury and arsenic for certain other metals, that of ammonia for the more fixed acids, such as the boracic and phosphoric acids, and that of carbonic acid for most salifiable bases. The greater number of bases part with their combined carbonic acid at a low red heat, lime at a somewhat higher temperature, strontia at a still higher, baryta only in the strongest wind-furnace, potash and soda not at all. Accordingly, the last two bases must have the strongest affinity for carbonic acid; and the fact of lime, baryta, and strontia taking carbonic acid from them when a considerable quantity of water is present, must be explained by the greater affinity of water for caustic potash and soda (page 128). Nitrate of copper is decomposed at a lower heat than nitrate of silver, whence it follows that the latter oxide has the greater affinity for nitric acid. Lastly, since many oxidized compounds, such as peroxide of manganese, chromic acid, antimonic acid, and arsenie acid give up part of their oxygen at a high temperature, and the noble metals give up the whole of it, and since the compounds of hydrogen with carbon, phosphorus, and sulphur, and those of nitrogen with chlorine and iodine are decomposed at various temperatures, the affinities by which these compounds are held together may be at least comparatively determined; but no exact numbers can be assigned to them, because the boiling points of oxygen, hydrogen, and nitrogen are unknown. This method of determining magnitudes of affinity deserves closer examination.

b. Decompositions in which Ponderable Bodies are alone concerned.

a. By Simple Affinity. If we find that the compound A B is decomposed by C with formation of A C, and that similarly the compound A C is decomposed by D with formation of A D, &c., we conclude that A has the greatest affinity for D, the next for C, and the smallest for B. In this manner, A may be tested with respect to all the substances with which it can combine. If, then, we place A at the head, and below it all the substances capable of uniting with it, in the order in which their affinity for A diminishes, we obtain the Column of Affinity of A. And if we proceed in the same manner with other bodies, simple and compound, assigning a column to each, and collecting all these columns into a general table, we shall obtain a Table of Affinity, Tabula Affinitatum.

The first table, which was very imperfect, was drawn up by Geoffroy; he was followed by Gellert, Rüdiger, Limbourg, Marherr, De Fourcy, Demachy, Erxleben, Weigel, Wiegler, and Bergman.

A few examples will suffice to illustrate this method. Carbonate of lime treated with hydrochloric acid yields hydrochlorate of lime and carbonic acid; hydrochlorate of lime is resolved by sulphuric acid into sulphate of lime and free hydrochloric acid; and when oxalic acid is added to a solution of sulphate of lime in water, oxalate of lime is thrown down, while free sulphuric acid remains in the water. Hence in the column headed Lime, the four acids above mentioned succeed one another in the following order: oxalic, sulphuric, hydrochloric, carbonic. From an aqueous solution of sulphate of alumina ammonia precipitates the alumina, producing sulphate of ammonia; this salt is converted by lime into sul

phate of lime and free ammonia; the sulphate of lime treated with solution of potash is resolved into sulphate of potash and free lime; and, lastly, the aqueous solution of sulphate of potash gives with baryta-water a precipitate of sulphate of baryta, while free potash remains in solution. Consequently in the sulphuric acid column, the four bases here considered would stand in the order: baryta, potash, lime, ammonia, alumina.

Simple and sure as this method may appear, and well as it may be adapted to furnish available materials for the determination of relative magnitudes of affinity, it is still far from being unexceptionable, and demands the greatest caution in its application. The influence of cohesion, elasticity, and the affinity of the solvent, are especially deserving of the most careful attention. For example, that oxalic acid added to an aqueous solution of sulphate of lime precipitates oxalate of lime, might be explained on the hypothesis that the cohesion of the latter salt is greater than that of the former; and that at the same time the affinity of water for sulphuric acid is greater than for oxalic acid; if such be the case, the affinity of sulphuric acid for lime may still be greater than that of oxalic acid. It has also been suggested that hydrochloric acid may expel carbonic acid from carbonate of lime, not in consequence of greater affinity, but because carbonic acid is more elastic i. e., has greater affinity for heat than hydrochloric acid has; but this supposition is negatived by the experiment described on page 130, in which the decomposition was found to take place under a pressure sufficient to liquify the carbonic acid set free. Again it has been shown (p. 129) that e. g., boracic acid decomposes sulphate of soda at a red heat, whilst the opposite effect takes place in the cold. Generally, the various cases of reciprocal affinity (page 125 .... 133) show that it is important to examine the action of bodies under variously altered circumstances, and in drawing conclusions respecting magnitude of affinity from decompositions which result from simple affinity, never to neglect the circumstances which, as was shown in discussing the theory of reciprocal affinity, may invert the result and enable the weaker affinity to gain the victory. One of these circumstances, viz., difference of temperature, was long ago noticed by Bergman. In his table, the Affinitates electivæ via humida are distinguished from those via sicca, accordingly as the decompositions take place at ordinary temperatures or at a red heat. This mode of distinction is not indeed unexceptionable, since opposite results often take place at different degrees of incandescence: thus, for example, at a red heat potassium takes oxygen from iron, while at a white heat iron takes oxygen from potassium. At the same time such distinctions oblige us to admit that tables of affinity do not always give the relative magnitudes of that force, but merely the results of decomposition under certain circumstances: hence these tables are by many chemists called Tables of Precipitation, or more correctly, Tables of Decomposition.

It must also not be forgotten that a body C sometimes takes from the body B only a part of the body A. When soda precipitates oxide of lead from a solution of chloride of lead in water-which may be regarded as hydrochlorate of oxide of lead-this does not exactly prove that the affinity of soda for hydrochloric acid is greater than that of oxide of lead; for the precipitate is a compound of 4 atoms of oxide of lead with one atom of hydrochloric acid; and the same compound is on the other hand produced, with separation of soda, when oxide of lead in excess is digested with a solution of hydrochlorate of soda. From this it follows that 4 atoms of oxide of lead have a greater affinity for 1 atom of hydro

chloric acid than 1 atom of soda has; but that 1 atom of soda has a greater affinity for hydrochloric acid than 1 atom of oxide of lead, and consequently abstracts from the latter of the acid with which it is combined. Hence, in precipitations of this kind, it must be carefully examined whether the precipitate contains the substance B in a state of purity or still in combination with part of the body A.

Lastly, on bringing together A B and C, we very often obtain, not A C and B, but A C and BC. If, for example, in order to determine whether arsenic or sulphur has the greater affinity for oxygen, we heat together arsenious acid and sulphur, we obtain indeed sulphurous acid, but the separated arsenic combines with another portion of the sulphur and forms sulphuret of arsenic (Sch. 100). In this case we cannot conclude that oxygen has a greater affinity for sulphur than for arsenic, but only that the affinity of sulphur for oxygen that of sulphur for arsenic is greater than that of arsenic for oxygen;-the affinity of heat for sulphurous acid must likewise be taken into account.

B. By Double Affinity. Guyton-Morveau supposed that when two salts decompose one another, the sum of the two decomposing affinities must be greater than that of the two quiescent affinities. According to the decompositions which the salts of certain acids and bases exhibit one with another, he endeavoured to assign such magnitudes to their affinities that calculation should agree with observed results. He thus found by trial the following numbers:

According to this table, sulphate of soda and hydrochlorate of baryta must decompose each other, because 66 +31 (97) is greater than 58 +36 (=94); similarly with carbonate of potash and acetate of lime, since 12+26> 19+ 9, and so on. But in many cases in which decomposition takes place the sums are equal; e. g., with sulphate of potash and nitrate of baryta (6262 66 + 58); and with sulphate of potash and hydrochlorate of baryta (62+36 66 + 32). In others the sum of the latent is even greater than that of the separating affinities, so that the calculation directly contradicts the experimental result; e. g., in the case of nitrate of baryta and sulphate of soda (62 + 58 > 50 + 66); so likewise nitrate of baryta is decomposed by sulphate of ammonia, sulphate of lime, sulphate of magnesia or carbonate of soda, and sulphate of magnesia by carbonate of ammonia, although calculation would lead to the contrary result. Moreover, Guyton-Morveau assigns to the affinity of nitric and hydrochloric acid for baryta larger numbers than to the affinities of the same acids for potash, although potash separates baryta both from the nitrate and hydrochlorate of that base. Generally, it is easy to see that it would be useless trouble to attempt to rectify the preceding numbers and adapt them to all decompositions of these salts by