I.3.2. Real Measure

Measure is determined as a Relation of Measures which constitute the Quality of different stable Somethings, or, more familiarly, Things. The Measure-Relations which we have just considered belong to abstract Qualities like space and time: specific gravity, and further the chemical properties, are examples (which are determinations of material existences) of those which still remain to be considered. Space and time are also moments of such Measures; but now, subordinated to further determinations, they are no longer related only in accordance with their peculiar conceptual determination. In sound, for instance, the time in which a certain number of vibrations occurs, and the spatial elements of length and thickness of the vibrating body, are among the determining moments; but the magnitudes of these ideal moments are determined externally: they manifest themselves no longer in a ratio of powers, but in ordinary direct ratio; and harmony reduces itself to the wholly external simplicity of numbers the ratios of which are most easily apprehended, and therefore afford a satisfaction which belongs entirely to sensation, since the spirit finds no image, phantasy, thought, nor anything of this kind, to fill it. The sides which now constitute the Measure-Relation are Measures themselves, but are also real Somethings; and thus their Measures are, first, immediate Measures and, as Relations, direct Relations. The relation to each other of such relations must now be considered in its progressive determination.

Measure is now real Measure, and thus first, it is the stable Measure of a corporeality which is in a relation to others, and in this attitude specifies them and also, thereby, specifies stable materiality. This specification, as an external relating to many others in general, is the production of other Relations and therefore of other Measures; and specific stability does not continue to consist in one direct Relation, but passes over into specific determinateness, which is a Series of Measures.

Secondly, the direct Relations which thus result are Measures determinate and exclusive in themselves (Elective Affinities); but their difference is also only quantitative, and thus there is a progress of Relations, which partly is merely externally quantitative, but also is interrupted by qualitative Relations, and forms a nodal line of specific stable entities.

Thirdly, however, in this progress measurelessness in general and, more determinately, the infinity of Measure, enter into play for Measure: here the mutually exclusive stabilities are One with one another, and the stable entity enters into a negative relation to itself.

Measures must now be called not merely immediate, but stable, since they in themselves now become Relations of Measures which are specified; they are thus first, in this Being-for-Self, physical somethings, material things. Now the whole which is a Relation of such Measures is (a) first, itself immediate; thus the two sides, which are determined as being such Stable Measures, severally subsist in separate things; their connexion is effected from without.

(b) The stable materialities are, however, what they are qualitatively, only by virtue of the quantitative determination which they have as Measures; that is, they are determined by virtue of a relation to others which is itself quantitative, and are determined as themselves different from these (this is so-called Affinity) and as members of a series of such quantitative attitude.

(c) This indifferent manifold attitude also rounds itself off into exclusive Being-for-Self,—into so-called Elective Affinity.

In itself, Something is determined as a Measure-relation of Quanta, which, further, have Qualities; and the Something is the relation of these Qualities. One of them is its Being-in-Self, which makes it a Being-for-Self—a material (like weight, taken intensively; or extensively, multitude, that is of material parts). The other is the externality of this Being-in-Self (the abstract or ideal, or space). These Qualities are determined quantitatively, and their relation constitutes the qualitative nature of the material Something;—the relation between weight and volume, determinate specific gravity. The volume (that which is of ideal nature) must be taken as Unit, and that which is intensive (which appears in quantitative determinateness and, in comparison with the former, as extensive magnitude, a multitude of Ones of which each is for self) as Amount.—The purely qualitative attitude between one magnitudinal determinateness and the other according to a ratio of powers has vanished in the fact that, in the stability of Being-for-Self (or material Being), immediacy has returned; and here the magnitudinal determinateness is determined as a Quantum as such, and the ratio of such a Quantum to the other side is also determined in the ordinary exponent of a direct ratio.

This exponent is the specific Quantum of a Something, but it is immediate Quantum; and this (and therefore the specific nature of such a Something) is determined only in comparison with other exponents of such ratios. It constitutes the specific determinateness-in-self, the inner peculiar Measure of something. But this its Measure is based upon Quantum, and therefore it is only external and indifferent determinateness; and hence such a Something is variable, in spite of the internal measure-determination. The Other towards which it can be variable is not a material multitude, a Quantum in general (for its specific determinateness-in-self can withstand this), but a Quantum which is also exponent of such a specific ratio. Two things having different internal Measures are related and enter into union,—like two metals of different specific gravities;—and what kind of homogeneity of nature (since it is not the case that the union of a metal, for instance, with water, is here in question) is further required to make possible such a union need not here be considered.—On the one hand now each of the two Measures preserves itself in the variation, which might reach it through the externality of Quantum, because it is Measure; on the other hand this self-preservation itself is a negative attitude to this Quantum, a specification of it; and, since the Quantum is exponent of the Measure-relation, it is a change in Measure itself—a reciprocal specification.

According to the merely quantitative determination, Union is a mere summation of the two magnitudes of the one Quality and of the two magnitudes of the other; for instance, the sum of the two weights and the two volumes in the union of two bits of matter of different specific gravity, with the condition that not only the weight of the compound remains equal to that sum, but also the space which it occupies equal to the sum of those spaces. But in fact only the weight is equal to the sum of the weights which were found before the union: that side is summed up which, because it is for itself, has become fixed Determinate Being and therefore has permanent immediate Quantum, and this is the weight of matter, or (which is the same from the point of view of quantitative determinateness) the multitude of material parts. It is into the exponents that the change falls, for as Measure-relations they are the expression of qualitative determinateness, of Being-for-Self, which also manifests itself as negative towards this externality, since Quantum as such undergoes the contingent and external change by accretion which is summed up. This immanent determining of the quantitative cannot appear in weight (as has been shown), and therefore manifests itself in the other Quality, which is that side of the relation which is of ideal nature. It may be remarkable to sensuous perception that, after the mixture of two specifically different bits of matter, a change,—and usually a diminution,—of the volume which is summed up should appear: space itself constitutes the persistence of material things existing externally to one another. But this persistence as against negativity (which contains Being-for-Self) is that which is not in itself, or is the variable; in this manner space is posited as that which in truth it is—that which is of ideal nature.

But thus not only is one of the qualitative sides posited as variable, but Measure itself and the qualitative determinateness of the Something, which is based on it, has shown itself not to be in itself fixed, but to have its determinateness (like Quantum in general) in other Measure-relations.

1. If something which enters into union with another, and this other too, were determined only by simple Quality and were what it is only for this reason, then they would only cancel each other in this union. But something which is a Measure-relation in itself is stable, and therefore it can enter into union with another such; and being cancelled in this union it preserves itself by virtue of its indifferent and quantitative persistence, and at the same time functions as specifying moment in a new Measure-relation. Its Quality is enveloped in the quantitative; thus it is also indifferent to the other Measure, and continues itself into it and into the newly-formed Measure; the exponent of the new Measure is itself only an indifferent Quantum, external determinateness, and manifests its indifference when the specifically determinate Something enters upon similar neutralizations of pairs of Measure-relations with similar Measures; its specific peculiarity fails to express itself when it and another form One only.

2. This union with a plurality of others which also are Measures in themselves yields different ratios, which accordingly have different exponents. What is stable has the exponent of its determinateness-in-self only in the comparison with others: now the neutrality with others constitutes its real comparison with them; it is its comparison with them through itself. But the exponents of these ratios are different, and thus it exhibits its qualitative exponent as the series of these different Amounts to which it is related as Unit,—or as a series of specific attitudes to others. The qualitative exponent as one immediate Quantum expresses one single relation. In truth the differentia of what is stable is the peculiar series of exponents which, if taken as Unit, are formed by it together with other such stable entities, one Other of them being similarly brought into relation with these and (taken as Unit) forming another series.—Now the relation of such a series within itself constitutes the qualitative element of that which is stable.

Now such a stable entity forms a series of exponents with a series of stable entities, so that at first it appears to be differentiated from an Other (outside this series) with which it is compared, by the fact that this latter forms another series of exponents with the same opposed entities. In this way, however, these two stable entities would be incommensurable, for here each is regarded as Unit to its exponents, and the two series which arise from this relation are other, but indeterminate else. The two entities which are to be compared as stable are so far different from each other only as Quanta; and in order that their relation may be determined, a common Unit which is for itself is required. And this determinate Unit must be looked for there only where the entities which are to be compared have the specific Determinate Being (as has been shown) of their Measure: that is, in the ratio which subsists between the ratio-exponents of the series. But this ratio of the exponents themselves is a Unit which is in fact determinate and for itself only in so far as the terms of the series have it to both as a constant relation among themselves; and then it can be their common Unit. Here alone then we have the commensurability of the two stable entities which are assumed to be indifferent to, and not neutralizing, each other. Each severally and apart from comparison is the Unit of the relations with the terms which stand opposed: the terms are Amounts as opposed to this Unit, and thus represent the series of exponents. But conversely this series is Unit for those two which, when compared with each other, are Quanta each to the other; as such they are themselves different Amounts of their lately demonstrated Unit.

But further those entities which, together with the pair (or rather the many in general) opposed to and compared with one another, produce the series of the exponents of their behaviour, are, in themselves, stable too, each being a specific Something of a Measure-relation which in itself belongs to it. And so each can in this regard be taken as Unit; so that they have a series of exponents in the first-mentioned and merely internally compared pair or rather indeterminate plurality; which exponents are the numbers resulting from comparison among themselves of the entities just mentioned; and conversely, if the entities are now severally taken as stable, then their numbers of comparison, among themselves, are the series of exponents for the terms of the first series. Thus both sides are series; in them, each number, firstly, is Unit in general to the series which opposes it, and in this latter it has its determinateness-in-self as a series of exponents; secondly, it is itself one of the exponents for each term of the opposite series; and thirdly, it is number of comparison for the other numbers of its series, and as being such an Amount (which belongs to it also as exponent) it has its Unit which is determinate in itself, in the opposite series.

3. In this attitude the manner has recurred in which Quantum as existing for self, that is as Degree, is posited as simple, but also as having magnitudinal determinateness in a Quantum which exists outside it and is a circle of Quanta. But in Measure, this external field is not merely a Quantum and a circle of Quanta but a series of ratio-numbers; and the determinateness-for-self of Measure lies in their totality. It is here as in the Being-for-Self of Quantum as Degree: the nature of Stable Measure has converted itself into this externality of itself. Its self-relation is, so far, immediate relation; and hereby, immediately, its indifference to an Other consists only in the Quantum. Its qualitative side therefore falls within this externality, and its attitude to Other becomes what constitutes the specific determination of this stable entity. Thus it consists, absolutely, in the quantitative character of this attitude, and this character is determined by the Other as much as by itself, and this Other is a series of Quanta, and itself is reciprocally a Quantum. But this relation, where two specific entities specify themselves to something, to some third element (the exponent), contains this too, that one has not here passed over into the other, so that not one negation in general has been posited, but both are posited here as negative; and, each preserving itself indifferent, its negation itself is negated. This their qualitative unity is thus self-existent exclusive unity. The exponents, which at first are numbers of comparison among themselves, have their true specific determinateness relatively to one another only in the moment of exclusion, and thus at the same time their difference becomes qualitative. But it is based upon the quantitative element: the stable element is in a relation to a plurality of its qualitatively different side, firstly, only because it is also indifferent in this attitude; secondly, this neutral relation, by virtue of the quantitativity which it contains, is not only change, but is posited as negation of negation and as exclusive unity. And so the Affinity of a stable entity to the plurality of the other side is no longer an indifferent relation, but an Elective Affinity.

The expression Elective Affinity has here been used as above “Neutrality” and “Affinity” were used,—expressions which refer to the chemical relation. For in the chemical sphere the material essentially has its specific determinateness in the relation to its Other: as this difference only does it exist. Further, this specific relation is tied to Quantity, and at the same time is not only the relation to one single Other, but to a series of such entities, different from and opposed to it; its combinations with this series are based upon a so-called Affinity with each of its members; but, while indifferent, each is also exclusive of others,-—which relation of opposite determinations remains still to be considered.—But it is not only in the chemical sphere that the specific manifests itself in a circle of combinations: a single note too has meaning only in the attitude to and combination with another and with a series of others; the harmony or disharmony in such a circle of combinations constitutes its qualitative nature, which at the same time is based upon quantitative ratios that form a series of exponents and are the ratios between the two specific ratios which each of the notes that are combined is in itself. A single note is the key-note of a system; but also it is a single member in the system of any other key-note. The harmonies are exclusive Elective Affinities; but their qualitative peculiarity equally resolves itself again into the externality of merely quantitative progress.—As for the question as to where the principle of a Measure resides for these Affinities, which (be they chemical or musical or other) are Elective Affinities among and to one another, an observation remains to be made with regard to chemical affinity in the sequel; but this higher question is connected in the closest manner with the Specific of the properly Qualitative, and belongs to the separate parts of concrete Natural Science.

Inasmuch as the member of a series has its qualitative unity in its attitude to the totality of an opposed series, the members of which are differentiated from one another only by the Quantum according to which they neutralize themselves with the former, in so far the more special determinateness in this multiple affinity too is only quantitative. In Elective Affinity—as exclusive and qualitative relation—the attitude avoids this quantitative difference. The next determination which presents itself is this, that upon the distinction of multitude (that is, of extensive magnitude) which subsists between the members of the one side for the neutralization of a member of the other side should depend the Elective Affinity-of this member to the members of the other series (to all of which it has affinity). Exclusion—as a firmer coherence against other possible combinations—which would be justified by this, would appear, when thus transformed, in a proportionately greater intensity according to the identity of the forms of intensive and extensive magnitude (which was proved above), since in these two forms magnitudinal determinateness is one and the same. But this transformation of the one-sided form of extensive magnitude into its other, the intensive form, makes no difference in the nature of the fundamental determination, which is one and the same Quantum: in fact, then, no exclusion would be posited here, but indifferently either only one combination, or, equally, one combination of an indeterminate number of members, could take place, if only the portions of these which came into play corresponded with the Quantum asked for in accordance with their relations to one another.

However, the combination which we have also called neutralization, is not only the form of intensity: the exponent essentially is measure-determination, and hence is exclusive; and the numbers, in this side of exclusive attitude, have lost their continuity and fluid power of mingling; the “more” or “less” acquires a negative character, and the advantage which one exponent has over others is not confined to magnitudinal determinateness. But equally there is present this other side, in which it is indifferent to a moment if it receive the neutralizing Quantum from several opposed moments, and from each according to its specific determinateness against the other; the exclusive negative attitude at the same time undergoes this infringement from the quantitative side.—Thus here there is posited a transformation of indifferent and merely quantitative attitude into qualitative, and conversely a transition of specific determinateness into merely external relation,—a series of relations which sometimes are of merely quantitative nature, and sometimes are Measures, and specific.

Chemical substances are the properest examples of such Measures as, being Measure-moments, have that which constitutes their determination only in their attitude to others. Acids and alkalis or bases appear as things immediately determinate in themselves, but still more as incomplete elements of bodies, as constituent parts which do not really exist for themselves, but have this existence only, that they transcend their isolated persistence and combine with an other. Further, the distinctness which makes them stable does not consist in this immediate quality, but in the quantitative character of the attitude. For this is not confined to the chemical opposition of acid and alkali or base in general, but is specified to be a measure of saturation, and consists in the specific determinateness of the quantity of the substances which neutralize one another. This quantity-determination in respect of saturation constitutes the qualitative nature of a substance: it makes it what it is for itself, and the number which expresses this is essentially one of several exponents for an opposed unit.—Such a substance has a so-called Affinity for another; in so far as this relation were purely qualitative, the one determinateness—like the relation of the magnetic poles or of the two kinds of electricity—would be merely related as negative to the other, and the two sides would not also manifest themselves as indifferent to each other. But the relation is also quantitative, and therefore each of these substances is capable of neutralizing itself with more than one; it is not confined to the one only to which it is opposed. It is not only the acid and the alkali or base which are in relation, but acids and alkalis or bases are related to one another. First they are characterized as against one another according as one acid requires (for example) more of an alkali than another in order to become saturated by it. But the stability (which is for itself) manifests itself in the fact that the Affinities remain exclusive of one another, and one remains superior to the others, since one acid can, by itself, combine with all the alkalis, and conversely. Thus the capital difference as between two acids consists in the closer affinity of one to a base,—that is, in its so-called Elective Affinity.

A law has been discovered with regard to the chemical affinities of acids and alkalis, which states that, if two neutral solutions are mixed, so that there results a separation and hence two new combinations, these products likewise are neutral. It follows that the amounts of two alkaline bases required to saturate an acid must be in the same ratio in order to saturate another acid; and generally, if for one alkali (which is taken as unit) the series of ratio-numbers has been determined in which the various acids saturate it, then the series is the same for any other alkali; only the different alkalis must be taken in different amounts relatively to one another,—amounts which again on their part form a similar fixed series of exponents for any of the opposite acids, for they are related to each acid in the same ratio as to any other.—Fischer first extracted these series in their simplicity from the works of Richter: see his observations on the translation of Berthollet’s treatise on the Law of Affinity in Chemistry, p. 232, and Berthollet, Statique Chimique, I. Part. p. 134 sqq.—Our knowledge of the ratio-numbers of mixtures of chemical elements has grown more perfect in every respect since that was written: to take it into consideration here would be a digression, because (among other reasons) this extension, which is empirical and partly only hypothetical, remains confined within the same conceptual determinations. But we may add a few observations on the categories used, and further on views about chemical Elective Affinity and its relation to the quantitative, and likewise on the attempt to base this upon determinate physical qualities.

It is well known that Berthollet modified the common idea of Elective Affinity by the concept of the activity of a chemical mass. It must be clearly distinguished that this modification has no influence upon the quantitative ratios of the laws of chemical saturation themselves; but the qualitative moment of exclusive Elective Affinity as such is not merely weakened but transcended. If two acids act upon an alkali, and that acid, of which it is said that it has the closer affinity to the alkali, is present also in that Quantum which is sufficient to saturate the Quantum of the base, then, according to the earlier idea of Elective Affinity, only this saturation takes place: the other acid remains quite inactive and is excluded from the neutral combination. But according to this other concept of the activity of a chemical mass, each of the two is active in a ratio which is composed of the amount in which they are present and of their saturation-capacity or so-called Affinity. Berthollet’s investigations have indicated in greater detail the circumstances in which the activity of the chemical mass is suspended, and one acid (the more powerfully allied) appears to cast out the other (the weaker) and exclude its activity, that is, to be active within the meaning of the earlier Elective Affinity. He has shown that the circumstances in which this exclusion takes place are such as cohesive force or the insolubility in water of the salts formed, and not the qualitative nature of the agents as such;—circumstances which can be suspended in their activity by other circumstances in turn—by temperature, for example. These obstacles removed, the chemical mass enters into activity uncrippled, and that which appeared as a purely qualitative exclusion, as Elective Affinity, shows itself as consisting only in external modifications.

Berzelius is the next writer who best deserves to be heard on this matter. But in his Manual of Chemistry he brings forward nothing peculiar or more definite on the subject. Berthollet’s views have been incorporated and repeated word for word, tricked out only with the peculiar metaphysics of an uncritical reflection; the categories of this alone therefore offer themselves for further consideration. The theory goes beyond experience, and partly invents sensuous images of a kind which experience does not offer of itself, partly it employs determinations of thought: in each way it makes itself the object of logical criticism. We will therefore scrutinize what we are told about the theory in the Manual itself (Vol. III., Part I., transl. by Wöhler, pp. 82 sqq,). Now here we read that we must imagine that in a fluid uniformly mixed each atom of the dissolved body is surrounded by an equal number of atoms of the solvent: “when several substances are dissolved together, they must share among themselves the interstices between the atoms of the solvent, so that, when the fluid is mixed uniformly, a symmetry arises in the arrangement of the atoms such that all the atoms of the individual bodies are in a uniform position relatively to the atoms of the other bodies; one could therefore say that the solution is characterized by symmetry in the position of the atoms, and the combination by the fixed proportions”—Berzelius proceeds to exemplify this by means of the combinations which result when sulphuric acid is added to a solution of copper chloride: unfortunately the example demonstrates neither that atoms exist, nor that a number of atoms of the bodies which are dissolved surround atoms of the fluid, nor that free atoms of the two acids arrange themselves around those which remain combined (with the copper oxide), nor that there is any symmetry in position and arrangement, nor that there are interstices between the atoms,—and least of all that the dissolved substances share among themselves the interstices between the atoms of the solvent. This would mean that the atoms of the dissolved substance take up their position where the solvent is not,—for the interstices between its atoms are spaces empty of it,—and hence that the dissolved substances are not in the solvent but outside it (although they surround and are ranged around it, or conversely), and therefore certainly are not dissolved by it. Consequently it is not clear why we must form such images, which are not exhibited in experience, essentially contradict themselves immediately, and are not corroborated in any other manner. This could be effected only by a consideration of these images themselves, that is, through Metaphysics, which is Logic; but this confirms them as little as experience—quite the contrary.—For the rest, Berzelius admits (what also was said above) that Berthollet’s propositions are not opposed to the theory of determinate proportions; although he adds that they also do not oppose the views of the corpuscular philosophy, that is, the images, cited above, of the atoms and of a solvent fluid which fills the interstices with the atoms of the undissolved bodies, and so on;—but this latter and baseless metaphysic has essentially nothing to do with the proportions of saturation itself.

Thus that specific nature which is expressed in the laws of saturation applies only to the multitude of units of a body which are themselves quantitative (and not atoms), with which multitude the quantitative unit (which equally is no atom) of another body chemically different from the first, neutralizes itself; the difference consists solely of these different proportions. And if Berzelius, in spite of the fact that his theory of proportions is wholly a determination of multitudes, speaks (for instance, p. 86) also of degrees of affinity, when he explains Berthollet’s chemical mass, as the sum of the degree of affinity, from the given quantity of the active body, then he himself falls here into the form of intensive magnitude. Berthollet here more consistently uses “capacity de saturation.” But this form constitutes the peculiar element of the so-called dynamic philosophy which above (p. 29, loc. cit.) he calls “the speculative philosophy of certain German schools,” and expressly rejects in favour of the excellent “Corpuscular Philosophy.” He there states of this dynamic philosophy that it assumes that the elements interpenetrate one another in their chemical combination, and that neutralization consists in this mutual interpenetration: this merely means that the chemically different particles, which are in the relation one to another of multitudes, collapse into the simplicity of an intensive magnitude,—a fact which also manifests itself as a diminution of volume. In the corpuscular theory, on the other hand, the atoms, even when chemically combined, are supposed to remain outside one another in the interstices (juxtaposition); and in such an attitude, as being a merely extensive magnitude and persisting multitude, degree of affinity has no meaning. If it is stated in the same place that the appearances of determinate proportions came quite unexpectedly for the dynamic view, then this would be a merely external historical circumstance, apart from the fact that Richter’s stoechiometric series (in Fischer’s arrangement) were already known to Berthollet and are quoted in the first edition of this Logic, which demonstrates the invalidity of the categories upon which are based the corpuscular theories—the old and that which strives to be new. But Berzelius’s judgment is wrong when he says that, under the dominion of “the dynamic view,” the appearances of determinate proportions would have been “for ever” unknown,—meaning that this view is incompatible with the determinateness of proportions. In any case this determinateness is only a magnitudinal determinateness, and it is indifferent whether it is in extensive or intensive form; so that even Berzelius, however much he is attached to the first form (multitude), himself uses the idea of degrees of affinity.

Affinity hereby is traced back to the quantitative difference, and therefore is transcended as Elective Affinity; while the exclusive element which occurs in it is traced back to circumstances, that is to determinations which appear as something external to the affinity—to cohesion, insolubility of the combinations reached, and so forth. With this idea, in a measure, the procedure adopted in considering the effect of gravity may be compared: what in itself belongs to gravity (the fact that the moving pendulum, through its operation, necessarily passes into a state of rest) is there taken only as a concomitant fact due to the external resistance of air, of the thread, and so on, and is attributed to friction alone instead of to gravity.—Here it makes no difference to the nature of the qualitative which is contained in Elective Affinity, whether it appears in the form of these circumstances (these being taken as its conditions) and is so conceived. With the qualitative as such a new order begins, of which the specification no longer is quantitative difference only.

Accordingly the difference of chemical affinity is exactly fixed in a series of quantitative ratios as against Elective Affinity: it is fixed as a difference of qualitative determinateness which begins to function, the behaviour of which by no means coincides with that order; but this difference is wholly confused by the manner in which electricity has recently been coupled with chemical behaviour; and the hope to reach a clue about the most important principle, namely, Measure-relation, from this, which professes greater profundity, is entirely disappointed. In this theory the phenomena of electricity and of chemism are completely identified in so far as it refers to physical properties and not to Measure-relations only; here the theory need not further be considered, and need be noticed only in so far as it contributes to confuse the differentiation of Measure-determinations. It may be called shallow in itself, for shallowness is the identification of things which differ, the differentia being omitted. As for affinity, chemical processes being thus identified with electrical, as well as with phenomena of light and fire, this is reduced “to neutralization of opposite electricities.” It is almost funny to see the identification of electricity and chemism put into the following words (p. 63, loc. cit.): “it is true that electrical phenomena explain the action of bodies at a greater or less distance, their attraction before they are united (that is, behaviour which is not yet chemical), and the fire (?) caused by this union; but they offer us no explanation for the combination of the bodies which powerfully persists even after the opposite electrical condition has been destroyed;” that is, the theory tells us that electricity is the cause of chemical behaviour, but electricity cannot tell us what is chemical in the chemical process.—By the fact that chemical difference in general is traced back to the opposition of positive and negative electricity, the difference in affinity of the agents which belong to either side is determined between them as the order of two series of electro-positive and electro-negative bodies. When electricity and chemism are identified according to their general determination, it is overlooked already that the former in itself and in its neutralization is transient and remains external to the Quality of bodies, while chemism in its action, and especially in neutralization, occupies and alters the whole qualitative nature of the bodies. And within electricity the opposition of positive and negative is equally transient; it is so unstable that it depends upon the smallest external circumstances, and cannot even be compared with the determinateness and fixity of the opposition of acids (for instance) and metals, and so on. The variability which can have place in this chemical behaviour through exceedingly violent activity (for instance of a raised temperature and the like) cannot be compared with the superficiality of the electrical opposition. Finally the further difference, within the series of each of the two sides, between more or less positively electrical or more or less negatively electrical nature is entirely uncertain and undemonstrated. But from these series of bodies (Berzelius, loc. cit., p. 84 sq.) “the electrochemical system is to be evolved according to their electrical dispositions,—a system fittest of all to give an idea of chemistry”: these series are next indicated; and of their actual nature, this is added (p. 67): “this, roughly, is the order of these bodies; but this matter has been so little investigated that nothing quite certain can yet be determined of this relative order.”—The ratio-numbers of these series of affinity (first made by Richter), as well as the exceedingly interesting reduction of the combinations of two bodies into the simplicity of a few quantitative ratios (first made by Berzelius), are wholly independent of this would-be electrochemical brew. It may be that in these proportions and in their universal extension, made since Richter, the experimental method was the true guiding star; if so, the mixture of these great discoveries with the so-called corpuscular theory, a wilderness lying apart from the road of experience, contrasts with it all the more; and only this beginning (by deserting the principle of experience) could cause that idea once more to be taken up after it had already been commenced upon earlier (especially by Ritter), namely, to set up fixed orders of electro-positive and electro-negative bodies which were also to have chemical significance.

The opposition between electro-positive and electro-negative bodies is not in fact as true as it is assumed to be; and when this is made the basis of chemical affinity, then the vanity of this basis soon shows itself even in experiment, and leads to further inconsistencies. It is admitted (p. 73, loc. cit.) that two so-called electro-negative bodies, like sulphur and oxygen, combine in a far more intimate manner than, for example, oxygen and copper, although the latter is electro-positive. Thus the basis of affinity founded upon the general opposition of positive and negative electricity must come second to a mere more or less within one and the same series of electrical determinateness. From this it is concluded that the degree of affinity between bodies does not only depend upon their specific unipolarity (it is here irrelevant with what hypothesis this determination is connected: here it means only the alternative determinations of positive and negative), and that the degree of affinity must chiefly be derived from the intensity of their polarity in general. Thus here the consideration of affinity passes over to the relation of Elective Affinity, which is our chief concern; and we must consider what now results for this subject. It is forthwith admitted (ibid. p. 73) that the degree of this polarity, unless it exists merely in our imagination, seems to be no constant quality, but greatly depends on temperature; so that after all this the result announced is not only that every chemical effect is ultimately an electrical phenomenon, but also that what appears to be effect of so-called Elective Affinity is really brought about only by an electrical polarity which is stronger in some bodies than in others. At the end of our meanderings in hypothetical images we remain at the category of greater intensity, which is the same formality as Elective Affinity in general; and the latter, after it has been founded on greater intensity of electrical polarity, is no nearer to being on a physical basis than before. But even that which is here supposed to be determined as greater specific intensity is later traced back only to the modifications demonstrated by Berthollet, which have already been cited.

The merit and fame which were won for Berzelius by his doctrine of proportions, which has been extended to all chemical relations, are in themselves no reason why the deficiencies of this theory should not be set forth; and there is a further reason in the fact that such merit in one branch of Science (as with Newton) tends to become the authority for a baseless fabric of invalid categories which is connected with it, and that it is just this kind of metaphysic which is proclaimed and echoed with the greatest pretension.

Apart from the forms of Measure-relation which refer to chemical and to Elective Affinity, others too may be considered with respect to quantities which qualify themselves into a system. Chemical bodies form a system of relations in regard to saturation: saturation itself depends on the determinate proportion in which combine the two aggregates which are opposed to each other as having separate material existence. But there are also Measure-relations of which the moments are inseparable and cannot be represented in a private and independent existence. These are what before were called immediate Stable Measures’, they are represented in the specific gravity of bodies.—Within the bodies they are a ratio of weight to volume; the ratio-exponent which expresses the determinateness of a specific weight and thus differentiates it from others, is a determinate Quantum of comparison only, a ratio external to them in an external reflection, not based upon its own qualitative attitude to an opposite existence. The task would be this,—from a rule, to understand the ratio-exponents of the series of specific gravities to be a system,—the rule specifying a merely arithmetical plurality to be a series of harmonic knots.—And the same demand would be applied to the understanding of the chemical affinity-series which have been mentioned. But Science has far to go before it will reach this point,—as far as it must go before it can comprehend in one Measure-system the numbers relating to the distances between the planets of the solar system.

Although at first specific gravities appear to be in no qualitative relation, they too do become qualitatively related. When bodies are chemically combined, or even only amalgamated or synsomatized, a neutralization of specific gravities also appears. The phenomenon has been mentioned above, that the volume, even of a mixture of substances which really remain chemically indifferent to one another, is not equal to the sum of their volumes before they were mixed. In the mixture they reciprocally modify the Quantum of the determinateness with which they enter into the relation; and in this manner they show that the relation subsisting between them is qualitative. Here the Quantum of specific gravity manifests itself not merely as a fixed number of comparison, but as a ratio-number, which is variable; and the exponents of the mixtures furnish series of Measures whose progress is determined by a principle other than the ratio-numbers of the specific gravities which are combined. The exponents of these ratios are not exclusive Measure-determinations: their progress is continuous, but contains a specifying law that is different from the ratios (which progress formally) in which the amounts are combined. The two progresses thus are made incommensurable.

The last determination of Measure-Relation was that, being specific, it is exclusive”, exclusiveness is proper to neutrality as negative unity of the differentiated moments. This unity is for self”, it is Elective Affinity: with regard to its relation to the other neutralities no further principle of specification has shown itself; the latter resides only in the quantitative determination of Affinity in general, according to which the amounts which neutralize one another, and thereby stand opposed to other relative Elective Affinities of their moments, are determinate. But further, by virtue of its fundamentally quantitative determination, exclusive Elective Affinity also continues itself into neutralities other to it; and this continuity is not only external relation of the various relations of neutrality as a comparison, but, besides, neutrality as such contains a separability, since the entities whose unity produced it enter into relation, as stable Somethings and each as indifferent as to whether it combines with one or with other of the opposing series, although they do so in different and specifically determinate amounts. Thus this Measure, being in itself based upon such a relation, is in itself infected with indifference: it is external in itself, and in its relation to itself is variable.

The relation to itself of the Measure-Relation is a different matter from its externality and variability as its quantitative side: as relation to itself as against these it is an existent and qualitative foundation,—an enduring and material substratum which ought to contain in its Quality this principle of the specification of this externality together with the continuity of Measure in its externality with itself.

Exclusive Measure in this closer determination is external to itself in its Being-for-Self; it repels itself from itself and posits itself as another—both as quantitatively other, and also as another such relation as also is another Measure; it is determined as unity specifying in itself and producing Measure-Relations as against it. Such relations are different from the previous kind of affinities, in which one stable entity is related to stable entities of a different Quality, and to a series of such: they take place against one and the same substratum within the same moments of neutrality; Measure determines itself as repelling itself towards other relations which are only quantitatively different and also form Affinities and Measures, alternating with such as remain merely quantitative differences. They form in this way a Nodal Line of Measures along a scale of more and less.. We have here a Measure-Relation, an independent reality, qualitatively different from others. Such a Being-for-Self is also essentially a relation of Quanta, and therefore open to externality and variation of Quantum: it has some play, within which it remains indifferent to this change and does not alter its Quality. But there comes a point in this quantitative change at which Quality changes and Quantum shows itself as specifying; so that the altered quantitative relation is turned under our hands into a Measure and thereby into a new Quality and a new Something. The relation which has taken the place of the first is determined by this, partly according to the qualitative identity of the moments which have affinity to one another, and partly according to quantitative continuity. But, since the difference falls within this quantitative part, the new Something is indifferent to its predecessor: their difference is one of Quantum, and hence external. It has therefore appeared, not out of the former, but, immediately, out of itself, that is, out of internal specifying unity which has not yet entered into existence.—The new Quality or the new Something is subject to the same progress of change, and so on to infinity.

In so far as the progress of one Quality is in steady continuity of Quantity, the relations which approach to one qualifying point are differentiated, quantitatively considered, only by more and less. In this regard change is gradual. But this gradual nature affects only the external part of change, not its qualitative part; the preceding quantitative relation, which is infinitely near to that which follows, is still a different qualitative existence. Hence the merely quantitative progress of gradualness, which is no limit in itself, is broken short absolutely on its qualitative side; the new emerging Quality in its merely quantitative relation is, relatively to the disappearing one, an indeterminate other, is indifferent, and so far the transition is per saltum: both are posited as wholly external to each other.—Men like to try to make a change conceivable by means of the gradualness of transition; but rather gradualness is precisely the merely indifferent change, the opposite of qualitative change. Rather, in gradualness the connexion of the two realities—whether taken as states or as independent things—is suspended; it is posited that neither is limit of the other, but that one is just external to the other; and hereby, precisely, that which is needful in order that change may be understood is eliminated, however little may be required to this end.

Already the natural numerical system exemplifies such a Nodal line of qualitative moments, which manifest themselves in the merely external progression. There is, partly, a merely quantitative oscillation, a persistent addition or subtraction, so that each number has the same arithmetical relation to its predecessor and successor as either of these had to its predecessor and successor, and so on. But the numbers which thus result have also a specific relation to other numbers that precede or follow, which makes them either such a multiple of one of them as is expressed by a whole number, or else power and root.—In musical relations a harmonic relation in the scale of quantitative progression is introduced by a Quantum, while yet this Quantum for itself has no other relation in the scale to its predecessor and successor than these in turn to their predecessors and successors. While succeeding notes appear progressively to move further from the key-note, and numbers through arithmetical progression to become more and more other, suddenly a return or surprising concord emerges, which was not qualitatively led up to by what immediately preceded, but appears as an actio in distans, as a relation to a distant entity. The progression along merely indifferent relations which do not change the preceding specific reality (or do not even form one) suddenly interrupts itself, and, while it continues in the same manner quantitatively, a specific relation breaks in per saltum.

Among chemical combinations, when mixture-proportions are progressively altered, certain qualitative nodes and jumps occur, such that two materials form products at particular points of the scale of mixture, which then show particular qualities. These products are differentiated not only by more and less, nor are they already given (in a weaker degree, for instance) in the relations which are akin to these nodal relations, but are actually bound to such points. The combinations of oxygen and nitrogen, for instance, produce the various oxides of nitrogen and nitric acids, which appear only in definite quantity-relations of the mixture and have essentially different qualities, so that in intermediate mixture-relations no combinations of specific existences take place.—Metal oxides (for instance, lead oxides) are formed at certain quantitative points of oxidation, and differ in colour and in other qualities. They do not gradually merge in one another; the relations which lie between those nodes produce no neutral and no specific Determinate Being. A specific combination appears which has not passed through these intermediate steps, but is based on a Measure-Relation and has qualities of its own.—Again, water, when it changes its temperature, not merely becomes less hot, but passes through conditions of hardness, of drop-forming liquidity, and of elastic liquidity; these different conditions do not appear gradually; but the merely gradual progress of change of temperature is suddenly interrupted and checked by these points, and the appearance of such a new condition is a jump.—All birth and death, instead of being a continued graduality, are rather an interruption of this and are the jump from quantitative into qualitative change.

It is said, natura non facit saltum\ and ordinary imagination, when it has to conceive an arising or passing away, thinks it has conceived them (as was mentioned) when it imagines them as a gradual emergence or disappearance. But we saw that the changes of Being were in general not only a transition of one magnitude into another, but a transition from the qualitative into the quantitative, and conversely: a process of becoming other which breaks off graduality and is qualitatively other as against the preceding Determinate Being. Water on being cooled does not little by little become hard, gradually reaching the consistency of ice after having passed through the consistency of a paste, but is suddenly hard; when it already has quite attained freezing-point it may (if it stands still) be wholly liquid, and a slight shake brings it into the condition of hardness.

The gradualness of arising is based upon the ideas that that which arises is already, sensibly or otherwise, actually there, and is imperceptible only on account of its smallness; and the gradualness of vanishing on the idea that Not-being or the Other which is assuming its place equally is there, only is not yet noticeable;—there, not in the sense that the Other is contained in the Other which is there in itself, but that it is there as Determinate Being, only unnoticeable. This altogether cancels arising and passing away; or the In-itself, that inner somewhat in which something is before it attains Determinate Being, is transmuted into a smallness of external Determinate Being, and the essential or conceptual distinction into a difference external and merely magnitudinal.—The procedure which makes arising and passing away conceivable from the gradualness of change is boring in the manner peculiar to tautology; that which arises or passes away is prepared beforehand, and the change is turned into the mere changing of an external distinction; and now it is indeed a mere tautology. The difficulty for such Understanding which attempts to conceive consists in the qualitative transition of something into its Other in general and into its opposite; Understanding prefers to fancy identity and change to be of that indifferent and external kind which applies to the quantitative.

In Ethics, in so far as it is considered in the sphere of Being, the same transition from quantitative to qualitative takes place, and different qualities appear to base themselves on differences in magnitude. A more or less suffices to transgress the limit of levity, where something quite different, namely, crime, appears; and thus right passes over into wrong, and virtue into vice.—Thus too do States—other things equal—derive a different qualitative character from magnitudinal difference. Laws and constitution become something different when the extent of the State and the number of citizens increases. The State has a certain measure of its magnitude, and if forced beyond this it collapses helplessly under that very same constitution which was its blessing and its strength for as long as its extent alone was different.

In its realized Being-for-Self exclusive Measure still remains infected with the moment of quantitative Determinate Being, and therefore remains capable of oscillation along the scale of Quantum, on which the alteration of relations takes place. A Something or a Quality which rests on such a relation is forced beyond itself into the Measureless, and perishes by the mere alteration of its magnitude. Magnitude is that characteristic wherein, while no harm appears to be intended, a Determinate Being can be seized, and whereby it can be destroyed.

The abstract Measureless is Quantum in general as lacking determination in itself and as merely indifferent determinateness by which the Measure is not changed. In the Nodal Line of Measures determinateness is also posited as specifying; the abstract Measureless transcends itself into qualitative determinateness; the first Measure-Relation passes over into another which is new, and is a Measureless in regard to it, while in itself it is just as much a Quality which is for itself; thus then is posited the alternation of specific existences with one another and also with relations which remain merely quantitative,—and so to infinity. This transition then contains the negation of specific relations as well as the negation of the quantitative progress,—that is, infinity which is for itself.—Qualitative infinity (as in Determinate Being) was the eruption of the infinite in the finite, as immediate transition and disappearance of the Hither in its Beyond. But quantitative infinity is according to its determinateness the continuity of Quantum—a continuity of it beyond itself. The qualitatively finite becomes infinite: the quantitatively finite is its Beyond in itself and points beyond itself. But this infinity of the specification of Measure posits the qualitative as well as the quantitative, each cancelling the other, and thereby also posits their first and immediate unity (which is Measure in general) as having returned upon itself, and therefore as itself posited. The qualitative—a specific existence—passes over into another in such a manner that nothing takes place except a change in the magnitudinal determinateness of a relation: thereby the change of qualitative itself into qualitative is posited as external and indifferent, as a coincidence with itself; and apart from this the quantitative transcends itself as turning into qualitative, as being determinate in itself. This unity which thus continues itself into itself in its alternation of Measures is the stable Matter or Thing which in truth persists.

We have, then, (α) one and the same Thing which is posited as the substratum of its differentiations, and as persisting. This severance of Being from its determinateness begins already in Quantum in general; something has magnitude as indifferent to its determinateness as Being. In Measure the Thing is already in itself the unity of the qualitative and the quantitative—the two moments which constitute the distinction in the general sphere of Being, each being the Beyond of the other; in this manner the persisting substratum, so far, has in itself the determination of infinity which is. (β) This undifferentiatedness of the substratum is posited in the fact that the qualitative stabilities into which the measure-determining unity is broken up consist only in quantitative differences, so that the substratum continues itself into this its differentiating process; (γ) in the infinite process of the nodal series the continuation of the Qualitative into the quantitative progress, as into an indifferent variation, is posited; and in this is posited the negation of the Qualitative and therefore of merely quantitative externality. The quantitative reference beyond itself to an Other, as being another Quantitative, perishes in the emergence of a Relation-measure or Quality, and the qualitative transition transcends itself precisely in the fact that the new Quality itself is only a quantitative relation. This transition of Qualitative and Quantitative into each other takes place upon the foundation of their unity, and the only meaning of this process is the Determinate Being, the demonstration or positing that it is based on such a substratum, which is their unity.

In the series of Stable Measure-Relations, the one-sided members of these series are immediate qualitative Somethings (specific gravities, or chemical substances, basic or alkaline, for instance acids); and next their neutralizations (—by which here must be understood also combinations of substances of different specific gravity—) are stable and even exclusive Measure-Relations; relatively to one another they are indifferent totalities of Determinate Being which is for itself. Now such relations are determined as being only nodes of one and the same substratum. This reduces the Measures and their implied stabilities to states. The change is change only of a state, and that which passes over is posited as remaining the same in the process. We now survey the progress in determination which Measure has covered. The moments of this progress are grouped in such a manner that Measure first is the unity (itself immediate) of Quality and Quantity, since it is an ordinary Quantum, which however is also specific. Here it is a quantitative determinateness referring not to other but to itself; it is, essentially, Relation. And further, therefore, it contains its moments as transcended and unseparated; the differentiation within it—as in every concept—is such that each of its moments is itself unity of the Qualitative and the Quantitative. The differentiation has thus become real, and produces a multitude of Measure-Relations which formally are totalities and as such are stable within themselves. The series which form the sides of these relations are the same constant order for each individual member which, as belonging to one side, is in a relation to the whole opposing series. This unity, as being mere order, is quite external; it shows itself as immanent specifying unity of a Measure which is for itself as distinct from its specification; but the specifying principle is not yet the free concept which alone gives immanent determination to its differentiations: so far the principle is only a substratum or material; and to effect that its differentiations shall be totalities, that is, shall contain the nature of the unchanging substratum, there is only the external quantitative determination, which at the same time manifests itself as differentiation of Quality. In this unity of the substratum with itself the Measure-determination is transcended, and its Quality is a condition determined by the Quantum, and external.—This course is the realizing and progressive determination of Measure, and this determination is also its reduction to the position of a moment.