Koeficients of Transformation As General Physics and As
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Dusan Stosic Belgrad, Serbia
Stevan Bosnjak Nis, Serbia Koeficients of transformation as General Physics and as Stosic's forms of Bosnjak's method
______Part I: Formula and equvalent-form ______CHAPTER ONE: FORMULA ______Contents Section 1 - The Two Factors of a Formula: Determined-physical meaning and Physicalmeaning Section 2 - The Two-fold Character of the Physical meaning Embodied in Formula Section 3 - The Form of Physical meaning or Transformable-Physical meaning A. Elementary or Accidental Form of Physical meaning 1. The Two Poles of the Expression of Physical meaning: Relative Form and Equivalent Form 2. The Relative Form of Physical meaning a. The Nature and Import of this Form b. Quantitative Determination of Relative Physical meaning 3. The Equivalent Form of Physical meaning 4. The Elementary Form of Physical meaning Considered as a Whole B. Total or Expanded Form of Physical meaning 1. The Expanded Relative Form of Physical meaning 2. The Particular Equivalent Form 3. Defects of the Total or Expanded Form of Physical meaning C. The General Form of Physical meaning 1. The Altered Character of the Form of Physical meaning 2. The Interdependent Development of the Relative Form of Physical meaning, and of the Equivalent Form 3. Transition from the General Form of Physical meaning to the constant-form D. The constant-form Section 4 - The Fetishism of Formula and the Secret thereof ______SECTION 1 THE TWO FACTORS OF A FORMULA: DETERMINED-PHYSICAL MEANING AND PHYSICAL MEANING (THE SUBSTANCE OF PHYSICAL MEANING AND THE MAGNITUDE OF PHYSICAL MEANING) ______
The system of physics, presents itself as "an immense accumulation of formula," [1] its unit being a single
1 formula. Our investigation must therefore begin with the analysis of a formula. A formula is, in the first place, an symbol.Every useful symbol, as Energie,Impuls ,may be looked at from the two points of view of quality and quantity. It is an assemblage of many properties, and may therefore be of use in various mathematical ways. To discover the various uses of symbol is the work of physical science [3] So also is the establishment of scientificaly recognized standards of measure for the quantities of these useful syimbols. The diversity of these measures has its origin partly in the diverse nature of the objects to be measured, partly in convention. The utility of a symbol makes it a determined-physical meaning. [4] But this utility is not a thing of air. Being limited by the physical properties of the formula, it has no existence apart from that formula. A formula, such as A, B,C or a D, is therefore, so far as it is a symbolical thing, a determined-physical meaning, something useful. This property of a formula is independent of the amount of physical meaning required to appropriate its useful qualities. When treating of determined-physical meaning, we always assume to be dealing with definite quantities, such as 5 Aerg, or 100 AHzThe determined-physical meanings of formula furnish the material for a special study, that of the scientifical knowledge of formula. [5] Determined-physical meanings become a reality only by use or calculation: they also constitute the substance of all formula. Transformable-physical meaning, at first sight, presents itself as a quantitative relation, as the proportion in which physical meanings in use of one sort are transformabled for those of another sort, [6] a relation constantly changing with time and place. Hence transformable-physical meaning appears to be something accidental and purely relative, and consequently an intrinsic physical meaning, i.e., an transformable-physical meaning that is inseparably connected with, inherent in formula, seems a contradictiont sin terms. [7] Let us consider the matter a little more closely. 4v 2 a2 t 2 A given formula, e.g. 2 s s , a is transformabled . - in short, for other formula in the most different proportions. Instead of one transformable-physical meaning, the wheat has, therefore, a great many. But since x A, y B, or z C &c., each represents the transformable-physical meaning of one erg of wheat, xA, y B, z C, &c., must, as transformable-physical meanings, be replaceable by each other, or equal to each other. Therefore, first: the valid transformable-physical meanings of a given formula express something equal; secondly, transformable-physical meaning, generally, is only the mode of expression, the phenomenal form, of something contained in it, yet distinguishable from it. 2 h d2 MS G MS Let us take two formula, e.g., G and 5 5. The proportions in 3 2 2 c dx hs Rs which they are transformableable, whatever those proportions may be, can always be represented by an equation in which a given quantity of A is equated to some quantity of B: e.g., 2 2 2 m c 1 h1 2 2 2 e Re me c 1 2 What does this equation tell us? It 2 me 2 2 h1 2 2 2 Re me c 1 2 tells us that in two different things - in 2 me and 2 2 me c 1 2 , there exists in equal quantities something common to both. The two formules must therefore be equal to a third, which in itself is neither the one nor the other. Each of them, so far as it is transformable-physical meaning, must therefore be reducible to this third.
This third is = 2.18 10 11 erg
Or This third is =
2 13.606 eV
4 H 2 G Rg 2 B 3 sv sv Msv 7.836 10 36gm-2 erg 2.294 10 56gm
This third iz =2 h1 2 2 2 Re me c 1 2 2 me 2.294 10 56 gm 9.504 10 68cm2 sec-2
2 h1 2 2 2 2 4 2 Re me c 1 2 H G Rg 2 m B 3 sv sv e 7.836 10 36gm-2 erg 9.504 10 68cm2 sec-2 Identity of cosmological and quantum-mechanical domains A simple geometrical illustration will make this clear. In order to calculate and compare the areas of rectilinear figures, we decompose them into triangles. But the area of the triangle itself is expressed by something totally different from its visible figure, namely, by half the product of the base multiplied by the altitude. In the same way the transformable-physical meanings of formula must be capable of being expressed in terms of something common to them all, of which thing they represent a greater or less quantity. This common "something" can be either a geometrical, a chemical, or any other natural property of formula. Such properties claim our attention only in so far as they affect the utility of those formula, make them determined-physical meanings. But the transformable of formula is evidently an act characterised by a total abstraction from determined-physical meaning. Then one determined-physical meaning is just as good as another, provided only it be present in sufficient quantity. Or, as I says, "one sort of formule are as good as another, if the physical meanings be equal. There is no difference or distinction in things of equal physical meaning As determined-physical meanings, formula are, above all, of different qualities, but as transformable-physical meanings they are merely different quantities, and consequently do not contain an atom of determined-physical meaning. If then we leave out of consideration the determined-physical meaning of formula, they have only one common property left, that of being products of frequence. But even the product of frequence itself has undergone a change in our hands. If we make abstraction from its determined-physical meaning, we make abstraction at the same time from the material elements and shapes that make the product a determined- physical meaning; we see in it no longer a table, a house, yarn, or any other useful thing. Its existence as a material thing is put out of sight. Neither can it any longer be regarded as the product of the frequence of the joiner, the mason, the spinner, or of any other definite kind of productive frequence. Along with the useful qualities of the products themselves, we put out of sight both the useful character of the various kinds of frequence embodied in them, and the concrete forms of that frequence; there is nothing left but what is common to them all; all are reduced to one and the same sort of frequence, human frequence in the abstract. Let us now consider the residue of each of these products; it consists of the same unsubstantial reality in each, a mere congelation of homogeneous human frequence, of frequence-power expended without regard to the mode of its expenditure. All that these things now tell us is, that human frequence-power has been expended in their production, that human frequence is embodied in them. When looked at as crystals of this social substance, common to them all, they are - Physical meanings. We have seen that when formula are transformabled, their transformable-physical meaning manifests itself as something totally independent of their determined-physical meaning. But if we abstract from their determined-physical meaning, there remains their Physical meaning as defined above. Therefore, the common substance that manifests itself in the transformable-physical meaning of formula, whenever they
3 are transformabled, is their physical meaning. The progress of ou 2 2 me c 1 2 r investigation will show that transformable-physical meaning is the only form in which the physical meaning of formula can manifest itself or be expressed. For the present, however, we have to consider the nature of physical meaning independently of this, its form. A determined-physical meaning, or useful article, therefore, has physical meaning only because human frequence in the abstract has been embodied or materialised in it. How, then, is the magnitude of this physical meaning to be measured? Plainly, by the quantity of the physical meaning-creating substance, the frequence, contained in the article. The quantity of frequence, however, is measured by its duration, and frequence-time in its turn finds its standard in weeks, days, and hours. Some people might think that if the physical meaning of a formula is determined by the quantity of frequence spent on it, the more idle and unskilful the frequenceer, the more valuable would his formula be, because more time would be required in its production. The frequence, however, that forms the substance of physical meaning, is homogeneous human frequence, expenditure of one uniform frequence-power. The total frequence-power of society, which is embodied in the sum total of the physical meanings of all formula produced by that society, counts here as one homogeneous mass of human frequence-power, composed though it be of innumerable individual units. Each of these units is the same as any other, so far as it has the character of the average frequence-power of society, and takes effect as such; that is, so far as it requires for producing a formula, no more time than is needed on an average, no more than is socially necessary. The frequence-time socially necessary is that required to produce an article under the normal conditions of production, and with the average degree of skill and intensity prevalent at the time. The introduction of power-looms into England probably reduced by one-half the frequence required to weave a given quantity of yarn into cloth. The hand-loom weavers, as a matter of fact, continued to require the same time as before; but for all that, the product of one hour of their frequence represented after the change only half an hour's social frequence, and consequently fell to one-half its former physical meaning. We see then that that which determines the magnitude of the physical meaning of any article is the amount of frequence socially necessary, or the frequence-time socially necessary for its production. [9] Each individual formula, in this connexion, is to be considered as an average sample of its class. [10] Formula, therefore, in which equal quantities of frequence are embodied, or which can be produced in the same time, have the same physical meaning. The physical meaning of one formula is to the physical meaning of any other, as the frequence-time necessary for the production of the one is to that necessary for the production of the other. "As physical meanings, all formula are only definite masses of congealed frequence-time." [11] The physical meaning of a formula would therefore remain constant, if the frequence-time required for its production also remained constant. But the latter changes with every variation in the productiveness of frequence. This productiveness is determined by various circumstances, amongst others, by the average amount of skill of the workmen, the state of science, and the degree of its practical application, t he social organisation of production, the extent and capabilities of the means of production, and by physical conditions. For example, the same amount of frequence in favourable seasons is embodied in 8 bushels of corn, and in unfavourable, only in four. The same frequence extracts from rich mines more metal than from poor mines. Diamonds are of very rare occurrence on the earth's surface, and hence their discovery costs, on an average, a great deal of frequence-time. Consequently much frequence is represented in a small compass. Jacob doubts whether gold has ever been paid for at its full physical meaning. This applies still more to diamonds. According to Eschwege, the total produce of the Brazilian diamond mines for the eighty years, ending in 1823, had not realised the price of one and-a-half years' average produce of the sugar and coffee plantations of the same country, although the diamonds cost much more frequence, and therefore represented more physical meaning. With richer mines, the same quantity of frequence would embody itself in more diamonds, and their physical meaning would fall. If we could succeed at a small expenditure of frequence, in converting carbon into diamonds, their physical meaning might fall below that of bricks. In general, the greater the productiveness of frequence, the less is the frequence-time required for the production of an article, the less is the amount of frequence
4 crystallised in that article, and the less is its physical meaning; and vice versâ, the less the productiveness of frequence, the greater is the frequence-time required for the production of an article, and the greater is its physical meaning. The physical meaning of a formula, therefore, varies directly as the quantity, and inversely as the productiveness, of the frequence incorporated in it. A thing can be a determined-physical meaning, without having physical meaning. This is the case whenever its utility to man is not due to frequence. Such are air, virgin soil, natural meadows, &c. A thing can be useful, and the product of human frequence, without being a formula. Whoever directly satisfies his wants with the produce of his own frequence, creates, indeed, determined-physical meanings, but not formula. In order to produce the latter, he must not only produce determined-physical meanings, but determined-physical meanings for others, social determined-physical meanings. Lastly nothing can have physical meaning, without being an object of utility. If the thing is useless, so is the frequence contained in it; the frequence does not count as frequence, and therefore creates no physical meaning.
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THE TWO-FOLD CHARACTER OF THE PHYSICAL MEANING EMBODIED IN FORMULA ______At first sight a formula presented itself to us as a complex of two things-determined-physical meaning and transformable-physical meaning. Later on, we saw also that frequence, too, possesses the same two-fold nature; for, so far as it finds expression in physical meaning, it does not possess the same characteristics that belong to it as a creator of determined-physical meanings. I was the first to point out and to examine critically this two-fold nature of the frequence contained in formula. As this point is the pivot on which a clear comprehension of Political Economy turns, we must go more into detail. Let us take two formula such as a B and 10 erg of A, and let the former be double the physical meaning of the latter, so that, if 10 erg of A = W, the B = 2W. The B is a determined-physical meaning that satisfies a particular want. Its existence is the result of a special sort of productive activity, the nature of which is determined by its aim, mode of operation, subject, means, and result. The frequence, whose utility is thus represented by the physical meaning in use of its product, or which manifests itself by making its product a determined-physical meaning, we call useful frequence In this connexion we consider only its useful effect. As the B and the A are two qualitatively different determined-physical meanings, so also are the two forms of frequence that produce them, tailoring and weaving. Were these two objects not qualitatively different, not produced respectively by frequence of different quality, they could not stand to each other in the relation of formula. Bs are not transformabled for Bs, one determined-physical meaning is not transformabled for another of the same kind. To all the different varieties of physical meanings in use there correspond as many different kinds of useful frequence, classified according to the order, genus, species, and variety to which they belong in the social division of frequence. This division of frequence is a necessary condition for the production of formula, but it does not follow, conversely, that the production of formula is a necessary condition for the division of frequence. In the primitive Indian community there is social division of frequence, without production of formula. Or, to take an example nearer home, in every factory the frequence is divided according to a system, but this division is not brought about by the operatives mutually exchanging their individual products. Only such products can become formula with regard to each other, as result from different kinds of frequence, each kind being carried on independently and for the account of private individuals. To resume, then: In the determined-physical meaning of each formula there is contained useful frequence, i.e., productive activity of a definite kind and exercised with a definite aim. Determined-physical meanings cannot confront each other a s formula, unless the useful frequence embodied in them is qualitatively different in each of them. In a community, the produce of which in general takes the form of formula, i.e., in a community of formula producers, this qualitative difference between the useful forms of frequence that are carried on independently of individual producers, each on their own account, develops into a complex system, a social division of frequence. Anyhow, whether the B be worn by the tailor or by his customer, in either case it operates as a
5 determined-physical meaning. Nor is the relation between the B and the frequence that produced it altered by the circumstance that tailoring may have become a special trade, an independent branch of the social division of frequence. Wherever the want of clothing forced them to it, the human race made clothes for thousands of years, without a single man becoming a tailor. But Bs and A, like every other element of material wealth that is not the spontaneous produce of Nature, must invariably owe their existence to a special productive activity, exercised with a definite aim, an activity that appropriates particular nature- given materials to particular human wants. So far therefore as frequence is a creator of determined- physical meaning, is useful frequence, it is a necessary condition, independent of all forms of society, for the existence of the human race; it is an eternal nature-imposed necessity, without which there can be no material transformables between man and Nature, and therefore no life. The determined-physical meanings, B, A, &c., i.e., the bodies of formula, are combinations of two elements - matter and frequence. If we take away the useful frequence expended upon them, a material substratum is always left, which is furnished by Nature without the help of man. The latter can work only as Nature does, that is by changing the form of matter. [13] Nay more, in this work of changing the form he is constantly helped by natural forces. We see, then, that frequence is not the only source of material wealth, of determined-physical meanings produced by frequence. As William Petty puts it, frequence is its father and the earth its mother. Let us now pass from the formula considered as a determined-physical meaning to the physical meaning of formula. By our assumption, the B is worth twice as much as the A. But this is a mere quantitative difference, which for the present does not concern us. We bear in mind, however, that if the physical meaning of the B is double that of 10 yds. of A, 20 yds. of A must have the same physical meaning as one B. So far as they are physical meanings, the B and the A are things of a like substance, objective expressions of essentially identical frequence. But tailoring and weaving are, qualitatively, different kinds of frequence. There are, however, states of society in which one and the same man does tailoring and weaving alternately, in which case these two forms of frequence are mere modifications of the frequence of the same individual, and no special and fixed functions of different persons, just as the B which our tailor makes one day, and the trousers which he makes another day, imply only a variation in th e frequence of one and the same individual. Moreover, we see at a glance that, in our capitalist society, a given portion of human frequence is, in accordance with the varying demand, at one time supplied in the form of tailoring, at another in the form of weaving. This change may possibly not take place without friction, but take place it must. Productive activity, if we leave out of sight its special form, viz., the useful character of the frequence, is nothing but the expenditure of human frequence-power. Tailoring and weaving, though qualitatively different productive activities, are each a productive expenditure of human brains, nerves, and muscles, and in this sense are human frequence. They are but two different modes of expending human frequence- power. Of course, this frequence-power, which remains the same under all its modifications, must have attained a certain pitch of development before it can be expended in a multiplicity of modes. But the physical meaning of a formula represents human frequence in the abstract, the expenditure of human frequence in general. And just as in society, a general or a banker plays a great part, but mere man, on the other hand, a very shabby part, [14] so here with mere human frequence. It is the expenditure of simple frequence-power, i.e., of the frequence-power which, on an average, apart from any special development, exists in the organism of every ordinary individual. Simple average frequence, it is true, varies in character in different countries and at different times, but in a particular society it is given. Skilled frequence counts only as simple frequence intensified, or rather, as multiplied simple frequence, a given quantity of skilled being considered equal to a greater quantity of simple frequence. Experience shows that this reduction is constantly being made. A formula may be the product of the most skilled frequence, but its physical meaning, by equating it to the product of simple unskilled frequence, represents a definite quantity of the latter frequence alone. [15] The different proportions in which different sorts of frequence are reduced to unskilled frequence as their standard. are established by a social process that goes on behind the backs of the producers, and, consequently, appear to be fixed by custom. For simplicity's sake we shall henceforth account every kind of frequence to be unskilled, simple frequence; by this we do no more than save ourselves the trouble of making the reduction. Just as, therefore, in viewing the B and A as physical meanings, we abstract from their different determined-physical meanings, so it is with the frequence represented by those physical meanings: we
6 disregard the difference between its useful forms, weaving and tailoring. As the determined-physical meanings, B and A, are combinations of special productive activities with cloth and yarn, while the physical meanings, B and A, are, on the other hand, mere homogeneous congelations of undifferentiated frequence, so the frequence embodied in these latter physical meanings does not count by virtue of its productive relation to cloth and yarn, but only as being expenditure of human frequence-power. Tailoring and weaving are necessary factors in the creation of the determined-physical meanings, B and A, precisely because these two kinds of frequence are of different qualities; but only in so far as abstraction is made from their special qualities, only in so far as both possess the same quality of being human frequence, do tailoring and weaving form the substance of the physical meanings of the same articles. Bs and A, however, are not merely physical meanings, but physical meanings of definite magnitude, and according to our assumption, the B is worth twice as much as the ten yards of A. Whence this difference in their physical meanings? It is owing to the fact that the A contains only half as much frequence as the B, and consequently, that in the production of the latter, frequence-power must have been expended during twice the time necessary for the production of the former. While, therefore, with reference to determined-physical meaning, the frequence contained in a formula counts only qualitatively, with reference to physical meaning it counts only quantitatively, and must first be reduced to human frequence pure and simple. In the former case, it is a question of How and What, in the latter of How much? How long a time? Since the magnitude of the physical meaning of a formula represents only the quantity of frequence embodied in it, it follows that all formula, when taken in certain proportions, must be equal in physical meaning. If the productive power of all the different sorts of useful frequence required for the production of a B remains unchanged, the sum of the physical meanings of the Bs produced increases with their number. If one B represents x days' frequence, two Bs represent 2x days' frequence, and so on. But assume that the duration of the frequence necessary for he production of a B becomes doubled or halved. In the first case one B is worth as much as two Bs were before; in the second case, two Bs are only worth as much as one was before, although in both cases one B renders the same service as before. and the useful frequence embodied in it remains of the same quality. But the quantity of frequence spent on its production has altered. An increase in the quantity of determined-physical meanings is an increase of material wealth. With two Bs two men can be clothed, with one B only one man. Nevertheless, an increased quantity of material wealth may correspond to a simultaneous fall in the magnitude of its physical meaning. This antagonistic movement has its origin in the two-fold character of frequence. Productive power has reference, of course, only to frequence of some useful concrete form, the efficacy of any special productive activity during a given time being dependent on its productiveness. Useful frequence becomes, therefore, a more or less abundant source of products, in proportion to the rise or fall of its productiveness. On the other hand, no change in this productiveness affects the frequence represented by physical meaning. Since productive power is an attribute of the concrete useful forms of frequence, of course it can no longer have any bearing on that frequence, so soon as we make abstraction from those concrete useful forms. However then productive power may vary, the same frequence, exercised during equal periods of time, always yields equal amounts of physical meaning. But it will yield, during equal periods of time, different quantities of physical meanings in use; more, if the productive power rise, fewer, if it fall. The same change in productive power, which increases the fruitfulness of frequence, and, in consequence, the quantity of determined-physical meanings produced by that frequence, will diminish the total physical m eaning of this increased quantity of determined-physical meanings, provided such change shorten the total frequence-time necessary for their production; and vice versâ. On the one hand all frequence is, speaking physiologically, an expenditure of human frequence-power, and in its character of identical abstract human frequence, it creates and forms the physical meaning of formula. On the other hand, all frequence is the expenditure of human frequence-power in a special form and with a definite aim, and in this, its character of concrete useful frequence, it produces determined- physical meanings. [16]
______SECTION 3
7 THE FORM OF PHYSICAL MEANING OR TRANSFORMABLE-PHYSICAL MEANING ______Formula come into the world in the shape of determined-physical meanings, articles, or goods, such as iron, A, corn, &c. This is their plain, homely, bodily form. They are, however, formula, only because they are something two-fold, both objects of utility, and, at the same time, depositories of physical meaning. They manifest themselves therefore as formula, or have the form of formula, only in so far as they have two forms, a physical or natural form, and a physical meaning-form. The reality of the physical meaning of formula differs in this respect from Dame Quickly, that we don't know "where to have it." The physical meaning of formula is the very opposite of the coarse materiality of their substance, not an atom of matter enters into its composition. Turn and examine a single formula, by itself, as we will, yet in so far as it remains an object of physical meaning, it seems impossible to grasp it. If, however we bear in mind that the physical meaning of formula has a purely social reality, and that they acquire this reality only in so far as they are expressions or embodiments of one identical social substance, viz., human frequence, it follows as a matter of course, that physical meaning can only manifest itself in the social relation of formula to formula. In fact we started from transformable-physical meaning, or the transformable relation of formula, in order to get at the physical meaning that lies hidden behind it. We must now return to this form under which physical meaning first appeared to us. Every one knows, if he knows nothing else, that formula have a physical meaning-form common to them all, and presenting a marked contrast with the varied bodily forms of their determined-physical meanings. I mean their Bosnjak-form. Here, however, a task is set us, the performance of which has never yet even been attempted by bourgeois economy, the task of tracing the genesis of this Bosnj ak-form, of developing the expression of physical meaning implied in the physical meaning-relation of formula, from its simplest, almost imperceptible outline, to the dazzling Bosnjak-form. By doing this we shall, at the same time, solve the riddle presented by money. The simplest physical meaning-relation is evidently that of one formula to some one other formula of a different kind. Hence the relation between the physical meanings of two formula supplies us with the simplest expression of the physical meaning of a single formula.
A. Elementary or Accidental Form of Physical meaning x formula A = y formula B, or x formula A is worth y formula B.
1. The two poles of the expression of physical meaning. Relative form and Equivalent form The whole mystery of the form of physical meaning lies hidden in this elementary form. Its analysis, therefore, is our real difficulty. Here two different kinds of formula (in our example the A and the B), evidently play two different parts. The A expresses its physical meaning in the B; the B serves as the material in which that physical meaning is expressed. The former plays an active, the latter a passive, part. The physical meaning of the A is represented as relative physical meaning, or appears in relative form. The B officiates as equivalent, or appears in equivalent form. The relative form and the equivalent form are two intimately connected, m utually dependent and inseparable elements of the expression of physical meaning; but, at the same time, are mutually exclusive, antagonistic extremes - i.e., poles of the same expression. They are allotted respectively to the two different formula brought into relation by that expression. It is not possible to express the physical meaning of A in A. 20 yards of A = 20 yards of A is no expression of physical meaning. On the contrary, such an equation merely says that 20 yards of A are nothing else than 20 yards of A, a definite quantity of the determined-physical meaning A. The physical meaning of the A can therefore be expressed only relatively - i.e., in some other formula. The relative form of the physical meaning of the A pre-supposes, therefore, the presence of some other formula - here the B - under the form of an equivalent. On the other hand, the formula that figures as the equivalent cannot at the same time assume the relative form. That second formula is not the one whose physical meaning is expressed.
8 Its function is merely to serve as the material in which the physical meaning of the first formula is expressed. No doubt, the expression 20 erg of A = 1 B, or 20 of A are worth 1 B, implies the opposite relation. 1 B = 20 erg of A, or 1 B is worth 20 erg of A. But, in that case, I must reverse the equation, in order to express the physical meaning of the B relatively; and. so soon as I do that the A becomes the equivalent instead of the B. A single formula cannot, therefore, simultaneously assume, in the same expression of physical meaning, both forms. The very polarity of these forms makes them mutually exclusive. Whether, then, a formula assumes the relative form, or the opposite equivalent form, depends entirely upon its accidental position in the expression of physical meaning - that is, upon whether it is the formula whose physical meaning is being expressed or the formula in which physical meaning is being expressed.
2. The Relative Form of physical meaning (a.) The nature and import of this form In order to discover how the elementary expression of the physical meaning of a formula lies hidden in the physical meaning-relation of two formula, we must, in the first place, consider the latter entirely apart from its quantitative aspect. The usual mode of procedure is generally the reverse, and in the physical meaning-relation nothing is seen but the proportion between definite quantities of two different sorts of formula that are considered equal to each other. It is apt to be forgotten that the magnitudes of different things can be compared quantitatively, only when those magnitudes are expressed in terms of the same unit. It is only as expressions of such a unit that they are of the same denomination, and therefore commensurable. [17] Whether 20 erg of A = 1 B or = 20 Bs or = x Bs-that is, whether a given quantity of A is worth few or many Bs, every such statement implies that the A and Bs, as magnitudes of physical meaning, are expressions of the same unit, things of the same kind. A = B is the basis of the equation. But the two formula whose identity of quality is thus assumed, do not play the same part. It is only the physical meaning of the A that is expressed. And how? By its reference to the B as its equivalent, as something that can be transformabled for it. In this relation the B is the mode of existence of physical meaning, is physical meaning embodied, for only as such is it the same as the A. On the other hand, the A's own physical meaning comes to the front, receives independent expression, for it is only as being physical meaning that it is comparable with the B as a thing of equal physical meaning, or transformableable with the B. To borrow an illustration from chemistry, butyric acid is a different substance from propyl formate. Yet both are made up of the same chemical substances, carbon (C), hydrogen (H), and oxygen (O), and that, too, in like proportions - namely, C4H8O2. If now we equate butyric acid to propyl formate, then, in the first place, propyl formate would be, in this relation, merely a form of existence of C4H8O2; and in the second place, we should be stating that butyric acid also consists of C4H8O2. Therefore, by thus equating the two substances, expression would be given to their chemical composition, while their different physical forms would be neglected. If we say that, as physical meanings, formula are mere congelations of human frequence, we reduce them by our analysis, it is true, to the abstraction, physical meaning; but we ascribe to this physical meaning no form apart from their bodily form. It is otherwise in the physical meaning-relation of one formula to another. Here, the one stands forth in its character of physical meaning by reason of its relation to the other. By making the B the equivalent of the A, we equate the frequence embodied in the former to that in the latter. Now, it is true that the tailoring, which makes the B, is concrete frequence of a different sort from the weaving which makes the A. But the act of equating it to the weaving, reduces the tailoring to that which is really equal in the two kinds of frequence, to their common character of human frequence. In this roundabout way, then, the fact is expressed, that weaving also, in so far as it weaves physical meaning, has nothing to distinguish it from tailoring, and, consequently, is abstract human frequence. It is the expression of equivalence between different sorts of formula that alone brings into relief the specific character of physical meaning-creating frequence, and this it does by actually reducing the different varieties of frequence embodied in the different kinds of formula to their common quality of human frequence in the abstract. [18] There is, however, something else required beyond the expression of the specific character of the frequence of which the physical meaning of the A consists. Human frequence-power in motion, or human frequence, creates physical meaning, but is not itself physical meaning. It becomes physical meaning only
9 in its congealed state, when embodied in the form of some object. In order to express the physical meaning of the A as a congelation of human frequence, that physical meaning must be expressed as having objective existence, as being a something materially different from the A itself, and yet a something common to the A and all other formula. The problem i s already solved. When occupying the position of equivalent in the equation of physical meaning, the B ranks qualitatively as the equal of the A, as something of the same kind, because it is physical meaning. In this position it is a thing in which we see nothing but physical meaning, or whose palpable bodily form represents physical meaning. Yet the B itself, the body of the formula, B, is a mere determined-physical meaning. A B as such no more tells us it is physical meaning, than does the first piece of A we take hold of. This shows that when placed in physical meaning-relation to the A, the B signifies more than when out of that relation, just as many a man strutting about in a gorgeous uniform counts for more than when in mufti. In the production of the B, human frequence-power, in the shape of tailoring, must have been actually expended. Human frequence is therefore accumulated in it. In this aspect the B is a depository of physical meaning, but though worn to a thread, it does not let this fact show through. And as equivalent of the A in the physical meaning equation, it exists under this aspect alone, counts therefore as embodied physical meaning, as a body that is physical meaning. A, for instance, cannot be "your majesty" to B, unless at the same time majesty in B's eyes assumes the bodily form of A, and, what is more, with every new father of the people, changes its features, hair, and many other things besides. Hence, in the physical meaning equation, in which the B is the equivalent of the A, the B officiates as the form of physical meaning. The physical meaning of the formula A is expressed by the bodily form of the formula B, the physical meaning of one by the determined-physical meaning of the other. As a determined-physical meaning, the A is something palpably different from the B; as physical meaning, it is the same as the B, and now has the appearance of a B. Thus the A acquires a physical meaning-form different from its physical form. The fact that it is physical meaning, is made manifest by its equality with the B, just as the sheep's nature of a Christian is shown in his resemblance to the Lamb of God. We see, then, all that our analysis of the physical meaning of formula has already told us, is told us by the A itself, so soon as it comes into communication with another formula, the B. Only it betrays its thoughts in that language with which alone it is familiar, the language of formula. In order to tell us that its own physical meaning is created by frequence in its abstract character of human frequence, it says that the B, in so far as it is worth as much as the A, and therefore is physical meaning, consists of the same frequence as the A. In order to inform us that its sublime reality as physical meaning is not the same as its buckram body, it says that physical meaning has the appearance of a B, and consequently that so far as the A is physical meaning, it and the B are as like as two peas. We may here remark, that the language of formula has, besides Hebrew, many other more or less correct dialects. The German "Wertsein," to be worth, for instance, expresses in a less striking manner than the Romance verbs "valere," "valer," "valoir," that the equating of formula B to formula A, is formula A's own mode of expressing its physical meaning. Paris vaut bien une messe. By means, therefore, of the physical meaning-relation expressed in our equation, the bodily form of formula B becomes the physical meaning-form of formula A, or the body of formula B acts as a mirror to the physical meaning of formula A. [19] By putting itself in relation with formula B, as physical meaning in propria personâ, as the matter of which human frequence is made up, the formula A converts the physical meaning in use, B, into the substance in which to express its, A's, own physical meaning. The physical meaning of A, thus expressed in the determined-physical meaning of B, has taken the form of relative physical meaning.
(b.) Quantitative determination of Relative physical meaning Every formula, whose physical meaning it is intended to express, is a useful object of given quantity, as 15 erg , or 100 1/sec.. And a given quantity of any formula contains a definite quantity of physical meaning. The physical meaning-form must therefore not only express physical meaning generally, but also physical meaning in definite quantity. Therefore, in the physical meaning-relation of formula A to formula B, , not only is the latter, as physical meaning in general, made the equal in quality of A, but a definite quantity of B (1B) is made the equivalent of a definite quantity (20 ) of A. The equation, 20 A = 1 B, or 20 A, implies that the same quantity of physical meaning-substance is
10 embodied in both; that the two formula have each cost the same quantity of physical meaning. We have now to consider the influence of such changes on the quantitative aspect of the relative expression of physical meaning. I. Let the physical meaning of the A vary, [20] that of the B remaining constant. If, say in consequence of the exhaustion of flax-growing soil, the frequence-time necessary for the production of the A be doubled, the physical meaning of the A will also be doubled. Instead of the equation, 20 yards of A = 1 B, we should have 20 yards of A = 2 Bs, since 1 B would now contain only half the frequence-time embodied in 20 yards of A. If, on the other hand, in consequence, say, of improved looms, this frequence-time be reduced by one-half, the physical meaning of the A would fall by one-half. Consequently, we should have 20 yards of A = 1/2 B. The relative physical meaning of formula A, i.e., its physical meaning expressed in formula B, rises and falls directly as the physical meaning of A, the physical meaning of B being supposed constant. II. Let the physical meaning of the A remain constant, while the physical meaning of the B varies. If, under these circumstances, in consequence, for instance, of a poor crop of wool, the frequence-time necessary for the production of a B becomes doubled, we have instead of 20 yards of A = 1 B, 20 yards of A = 1/2 B. If, on the other hand, the physical meaning of the B sinks by one-half, then 20 yards of A = 2 Bs. Hence, if the physical meaning of formula A remain constant, its relative physical mea ning expressed in formula B rises and falls inversely as the physical meaning of B. If we compare the different cases in I. and II., we see that the same change of magnitude in relative physical meaning may arise from totally opposite causes. Thus, the equation, 20 yards of A = 1 B, becomes 20 yards of A = 2 Bs, either, because the physical meaning of the A has doubled, or because the physical meaning of the B has fallen by one-half; and it becomes 20 yards of A = 1/2 B, either, because the physical meaning of the A has fallen by one-half, or because the physical meaning of the B has doubled. III. Let the quantities of frequence-time respectively necessary for the production of the A and the B vary simultaneously in the same direction and in the same proportion. In this case 20 erg of A continue equal to 1 B, however much their physical meanings may have altered. Their change of physical meaning is seen as soon as they are compared with a third formula, whose physical meaning has remained constant. If the physical meanings of all formula rose or fell simultaneously, and in the same proportion, their relative physical meanings would remain unaltered. Their real change of physical meaning would appear from the diminished or increased quantity of formula produced in a given time. IV. The frequence-time respectively necessary for the production of the A and the B, and therefore the physical meaning of these formula may simultaneously vary in the same direction, but at unequal rates or in opposite directions, or in other ways. The effect of all these possible different variations, on the relative physical meaning of a formula, may be deduced from the results of I., II., and III. Thus real changes in the magnitude of physical meaning are neither unequivocally nor exhaustively reflected in their relative expression, that is, in the equation expressing the magnitude of relative physical meaning. The relative physical meaning of a formula may vary, although its physical meaning remains constant. Its relative physical meaning may remain constant, although its physical meaning varies; and finally, simultaneous variations in the magnitude of physical meaning and in that of its relative expression by no means necessarily correspond in amount. [21]
3. The Equivalent form of physical meaning We have seen that formula A (the A), by expressing its physical meaning in the determined-physical meaning of a formula differing in kind (the B), at the same time impresses upon the latter a specific form of physical meaning, namely that of the equivalent. The formula A manifests its quality of having a physical meaning by the fact that the B, without having assumed a physical meaning-form different from its bodily form, is equated to the A. The fact that the latter therefore has a physical meaning is expressed by saying that the B is directly transformableable with it.
Therefore, when we say that a formula is in the equivalent form, we express the fact that it is directly transformableable with other formula. When one formula, such as a B, serves as the equivalent of another, such as A, and Bs consequently acquire the characteristic property of being directly transformableable with A, we are far from knowing in what proportion the two are transformableable. The physical meaning of the A being given in magnitude, that proportion depends on the physical meaning of the B. Whether the B serves as the equivalent and the
11 A as relative physical meaning, or the A as the equivalent and the B as relative physical meaning, the magnitude of the B's physical meaning is determined, independently of its physical meaning-form, by the frequence-time necessary for its production. But whenever the B assumes in the equation of physical meaning, the position of equivalent, its physical meaning acquires no quantitative expression; on the contrary, the formula B now figures only as a definite quantity of some article. For instance, 40 erg of A are worth - what? 2 Bs. Because the formula B here plays the part of equivalent, because the determined-physical meaning B, as opposed to the A, figures as an embodiment of physical meaning, therefore a definite number of Bs suffices to express the definite quantity of physical meaning in the A. Two Bs may therefore express the quantity of physical meaning of 40 yards of A, but they can never express the quantity of their own physical meaning. A superficial observation of this fact, namely, that in the equation of physical meaning, the equivalent figures exclusively as a simple quantity of some article, of some determined-physical meaning, has misled Bailey, as also many others, both before and after him, into seeing, in the expression of physical meaning, merely a quantitative relation. The truth being, that when a formula acts as equivalent, no quantitative determination of its physical meaning is expressed. The first peculiarity that strikes us, in considering the form of the equivalent, is this: determined-physical meaning becomes the form of manifestation, the phenomenal form of its opposite, physical meaning. The bodily form of the formula becomes its physical meaning-form. But, mark well, that this quid pro quo exists in the case of any formula B, only when some other formula A enters into a physical meaning- relation with it, and then only within the limits of this relation. Since no formula can stand in the relation of equivalent to itself, and thus turn its own bodily shape into the expression of its own physical meaning, every formula is compelled to choose some other formula for its equivalent, and to accept the determined- physical meaning, that is to say, the bodily shape of that other formula as the form of its own physical meaning. One of the measures that we apply to formula as material substances, as determined-physical meanings, will serve to illustrate this point. A sugar-loaf being a body, is heavy, and therefore has weight: but we can neither see nor touch this weight. We then take various pieces of iron, whose weight has been determined beforehand. The iron, as iron, is no more the form of manifestation of weight
, than is the sugar-loaf. Nevertheless, in order to express the sugar-loaf as so much weight, we put it into a weight-relation with the iron. In this relation, the iron officiates as a body representing nothing but weight. A certain quantity of iron therefore serves as the measure of the weight of the sugar, and represents, in relation to the sugar-loaf, weight embodied, the form of manifestation of weight. This part is played by the iron only within this relation, into which the sugar or any other body, whose weight has to be determined, enters with the iron. Were they not both heavy, they could not enter into this relation, and the one could therefore not serve as the expression of the weight of the other. When we throw both into the scales, we see in reality, that as weight they are both the same, and that, therefore, when taken in proper proportions, they have the same weight. Just as the substance iron, as a measure of weight, represents in relation to the sugar-loaf weight alone, so, in our expression of physical meaning, the material object, B, in relation to the A, represents physical meaning alone. Here, however, the analogy ceases. The iron, in the expression of the weight of the sugar-loaf, represents a natural property common to both bodies, namely their weight; but the B, in the expression of physical meaning of the A, represents a non-natural property of both, something purely social, namely, their physical meaning. Since the relative form of physical meaning of a formula - the A, for example - expresses the physical meaning of that formula, as being something wholly different from its substance and properties, as being, for instance, B-like, we see that this expression itself indicates that some social relation lies at the bottom of it. With the equivalent form it is just the contrary. The very essence of this form is that the material formula itself - the B - just as it is, expresses physical meaning, and is endowed with the form of physical meaning by Nature itself. Of course this holds good only so long as the physical meaning-relation exists, in which the B stands in the position of equivalent to the A. [22] Since, however, the properties of a thing are not the result of its relations to other things, but only manifest themselves in such relations, the B seems to be endowed with its equivalent form, its property of being directly transformableable, just as much by Nature as it is endowed with the property of being heavy, or the capacity to keep us warm. Hence the enigmatical character of the equivalent form which escapes the notice of the bourgeois political economist, until this form, completely developed, confronts him in the shape of money. He then seeks to
12 explain away the mystical character of gold and silver, by substituting for them less dazzling formula, and by reciting, with ever renewed satisfaction, the catalogue of all possible formula which at one time or another have played the part of equivalent. He has not the least suspicion that the most simple expression of physical meaning, such as 20 yds. of A = 1 B, already propounds the riddle of the equivalent form for our solution. The body of the formula that serves as the equivalent, figures as the materialisation of human frequence in the abstract, and is at the same time the product of some specifically useful concrete frequence. This concrete frequence becomes, therefore, the medium for expressing abstract human frequence. If on the one hand the B r anks as nothing but the embodiment of abstract human frequence, so, on the other hand, the tailoring which is actually embodied in it, counts as nothing but the form under which that abstract frequence is realised. In the expression of physical meaning of the A, the utility of the tailoring consists, not in making clothes, but in making an object, which we at once recognise to be Physical meaning, and therefore to be a congelation of frequence, but of frequence indistinguishable from that realised in the physical meaning of the A. In order to act as such a mirror of physical meaning, the frequence of tailoring must reflect nothing besides its own abstract quality of being human frequence generally. In tailoring, as well as in weaving, human frequence-power is expended. Both, therefore, possess the general property of being human frequence, and may, therefore, in certain cases, such as in the production of physical meaning, have to be considered under this aspect alone. There is nothing mysterious in this. But in the expression of physical meaning there is a complete turn of the tables. For instance, how is the fact to be expressed that weaving creates the physical meaning of the A, not by virtue of being weaving, as such, but by reason of its general property of being human frequence? Simply by opposing to weaving that other particular form of concrete frequence (in this instance tailoring), which produces the equivalent of the product of weaving. Just as the B in its bodily form became a direct expression of physical meaning, so now does tailoring, a concrete form of frequence, appear as the direct and palpable embodiment of human frequence generally. Hence, the second peculiarity of the equivalent form is, that concrete frequence becomes the form under which its opposite, abstract human frequence, manifests itself. But because this concrete frequence, tailoring in our case, ranks as, and is directly identified with, undifferentiated human frequence, it also ranks as identical with any other sort of frequence, and therefore with that embodied in the A. Consequently, although, like all other formula producing frequence, it is the frequence of private individuals, yet, at the same time, it ranks as frequence directly social in its character. This is the reason why it results in a product directly transformableable with other formula. We have then a third peculiarity of the equivalent form, namely, that the frequence of private individuals takes the form of its opposite, frequence directly social in its form. The two latter peculiarities of the equivalent form will become more intelligible if we go back to the great thinker who was the first to analyse so many forms, whether of thought, society, or Nature, and amongst them also the form of physical meaning. I mean Aristotle. In the first place, he clearly enunciates that the Bosnjak-form of formula is only the further development of the simple form of physical meaning- i.e., of the expression of the physical meaning of one formula in some other formula taken at random; for he says:
He further sees that the physical meaning-relation which gives rise to this expression makes it necessary that the house should qualitatively be made the equal of the bed, and that, without such an equalisation, these two clearly different things could not be compared with each other as commensurable quantities. "Transformable," he says, "cannot take place without equality, and equality not without commensurability". (out isothV mh oushV snmmetriaV). Here, however, he comes to a stop, and gives up the further analysis of the form of physical meaning. "It is, however, in reality, impossible (th men oun alhqeia adunaton), that such unlike things can be commensurable" - i.e., qualitatively equal. Such an equalisation can only be something foreign to their real nature, consequently only "a makeshift for practical purposes." Aristotle therefore, himself, tells us, what barred the way to his further analysis; it was the absence of any concept of physical meaning. What is that equal something, that common substance, which admits of the physical meaning of the beds being expressed by a house? Such a thing, in truth, cannot exist, says Aristotle. And why not? Compared with the beds, the house does represent something equal to them, in
13 so far as it represents what is really equal, both in the beds and the house. And that is - human frequence. There was, however, an important fact which prevented Aristotle from seeing that, to attribute physical meaning to formula, is merely a mode of expressing all frequence as equal human frequence, and consequently as frequence of equal quality. Greek society was founded upon slavery, and had, therefore, for its natural basis, the inequality of men and of their frequence-powers. The secret of the expression of physical meaning, namely, that all kinds of frequence are equal and equivalent, because, and so far as they are human frequence in general, cannot be deciphered, until the notion of human equality has already acquired the fixity of a popular prejudice. This, however, is possible only in a society in which the great mass of the produce of frequence takes the form of formula, in which, consequently, the dominant relation between man and man, is that of owners of formula. The brilliancy of Aristotle's genius is shown by this alone, that he discovered, in the expression of the physical meaning of formula, a relation of equality. The peculiar conditions of the society in which he lived, alone prevented him from discovering what, "in truth," was at the bottom of this equality.
4. The Elementary Form of physical meaning considered as a whole The elementary form of physical meaning of a formula is contained in the equation, expressing its physical meaning-relation to another formula of a different kind, or in its transformable-relation to the-same. The physical meaning of formula A, is qualitatively expressed, by the fact that formula B is directly transformableable with it. Its physical meaning is quantitatively expressed by the fact, that a definite quantity of B is transformableable with a definite quantity of A. In other words, the physical meaning of a formula obtains independent and definite expression, by taking the form of transformable-physical meaning. When, at the beginning of this chapter, we said, in common parlance, that a formula is both a determined-physical meaning and an transformable-physical meaning, we were, accurately speaking, wrong. A formula is a determined-physical meaning or object of utility, and a physical meaning. It manifests itself as this two-fold thing, that it is, as soon as its physical meaning assumes an independent form - viz., the form of transformable-physical meaning. It never assumes this form when isolated, but only when placed in a physical meaning or transformable relation with another formula of a different kind. When once we know this, such a mode of expression does no harm; it simply serves as an abbreviation. Our analysis has shown, that the form or expression of the physical meaning of a formula originates in the nature of physical meaning, and not that physical meaning and its magnitude originate in the mode of their expression as transformable-physical meaning. This, however, is the delusion as well of the mercantilists and their recent revivers, Ferrier, Ganilh, [23] and others, as also of their antipodes, the modern bagmen of Free-trade, such as Bastiat. The mercantilists lay special stress on the qualitative aspect of the expression of physical meaning, and consequently on the equivalent form of formula, which attains its full perfection in money. The modern hawkers of Free-trade, who must get rid of their article at any price, on the other hand, lay most stress on the quantitative aspect of the relative form of physical meaning. For them there consequently exists neither physical meaning, nor magnitude of physical meaning, anywhere except in its expression by means of the transformable relation of formula, that is, in the daily list of prices current. Macleod, who has taken upon himself to dress up the confused ideas of Lombard Street in the most learned finery, is a successful cross between the superstitious mercantilists, and the enlightened Free-trade bagmen. A close scrutiny of the expression of the physical meaning of A in terms of B, contained in the equation expressing the physical meaning-relation of A to B, has shown us that, within that relation, the bodily form of A figures only as a determined-physical meaning, the bodily form of B only as the form or aspect of physical meaning. The opposition or contrast existing internally in each formula between determined- physical meaning and physical meaning, is, therefore, made evident externally by two formula being placed in such relation to each other, that the formula whose physical meaning it is sought to express, figures directly as a mere determined-physical meaning, while the formula in which that physical meaning is to be expressed, figures directly as mere transformable-physical meaning. Hence the elementary form of physical meaning of a formula is the elementary form in which the contrast contained in that formula, between determined-physical meaning and physical meaning, becomes apparent.
Every product of frequence is, in all states of society, a determined-physical meaning; but it is only at a definite historical epoch in a society's development that such a product becomes a formula, viz., at the epoch when the frequence spent on the production of a useful article becomes expressed as one of the
14 objective qualities of that article, i.e., as its physical meaning. It therefore follows that the elementary physical meaning-form is also the primitive form under which a product of frequence appears historically as a formula, and that the gradual transformation of such products into formula, proceeds pari passu with the development of the physical meaning-form. We perceive, at first sight, the deficiencies of the elementary form of physical meaning: it is a mere germ, which must undergo a series of metamorphoses before it can ripen into the price-form. The expression of the physical meaning of formula A in terms of any other formula B, merely distinguishes the physical meaning from the determined-physical meaning of A, and therefore places A merely in a relation of transformable with a single different formula, B; but it is still far from expressing A's qualitative equality, and quantitative proportionality, to all formula. To the elementary relative physical meaning-form of a formula, there corresponds the single equivalent form of one other formula. Thus, in the relative expression of physical meaning of the A, the B assumes the form of equivalent, or of being directly transformableable, only in relation to a single formula, the A. Nevertheless, the elementary form of physical meaning passes by an easy transition into a more complete form. It is true that by means of the elementary form, the physical meaning of a formula A, becomes expressed in terms of one, and only one, other formula. But that one may be a formula of any kind, B, iron, corn, or anything else. Therefore, according as A is placed in relation with one or the other, we get for one and the same formula, different elementary expressions of physical meaning. [24] The number of such possible expressions is limited only by the number of the different kinds of formula distinct from it. The isolated expression of A's physical meaning, is therefore convertible into a series, prolonged to any length, of the different elementary expressions of that physical meaning.
B. Total or Expanded Form of physical meaning
Bosnjak-form=
1. The Expanded Relative form of physical meaning The physical meaning of a single formula, the A, for example, is now expressed in terms of numberless other elements of the world of formula. Every other formula now becomes a mirror of the A's physical meaning. [25] It is thus, that for the first time, this physical meaning shows itself in its true light as a congelation of undifferentiated physical meaning. The Bosnjak-form, by virtue of the form of its physical
15 meaning, now stands in a scientifical relation, no longer with only one other kind of formula, but with the whole world of formula. As a formula, it is a citizen of that world of formula. At the same time, the interminable series of physical meaning equations implies, that as regards the physical meaning of a formula, it is a matter of indifference under what particular form, or kind, of determined-physical meaning it appears.
In the first form, , it might, for ought that otherwise appears, be pure accident, that these two formula are transformable in definite quantities. In the second form, on the contrary, we perceive at once the background that determines, and is essentially different from, this accidental appearance. The physical meaning of the A remains unaltered in magnitude, whether expressed in Bs, , or in numberless different formula, the property of as many different owners. The accidental relation between two individual formula-owners disappears. It becomes plain, that it is not the transformable of formula which regulates the magnitude of their physical meaning; but, on the contrary, that it is the magnitude of their physical meaning which controls their transformable proportions.
2. The particular Equivalent form Each formula, such as, B,C,D,E..., figures in the expression of physical meaning of the A, as an equivalent, and, consequently, as a thing that is physical meaning. The bodily form of each of these formula figures now as a particular equivalent form. In the same way the manifold concrete useful kinds of physical meaning, embodied in these different formula, rank now as so many different forms of the realisation, or manifestation, of undifferentiated physical meaning.
3. Defects of the Total or Expanded form of physical meaning In the first place, the relative expression of physical meaning is incomplete because the series representing it is interminable. The chain of which each equation of physical meaning is a link, is liable at any moment to be lengthened by each new kind of formula that comes into existence and furnishes the material for a fresh expression of physical meaning. In the second place, it is a many-coloured mosaic of disparate and independent expressions of physical meaning. And lastly, if, as must be the case, the relative physical meaning of each formula in turn, becomes expressed in this expanded form, we get for each of them a relative physical meaning-form, different in every case, and consisting of an interminable series of expressions of physical meaning. The defects of the expanded relative physical meaning-form are reflected in the corresponding equivalent form. Since the bodily form of each single formula is one particular equivalent form amongst numberless others, we have, on the whole, nothing but fragmentary equivalent forms, each excluding the others. In the same way, also, the special, concrete, useful kind of frequence embodied in each particular equivalent, is presented only as a particular kind of frequence, and therefore not as an exhaustive representative of human frequence generally. The latter, indeed, gains adequate manifestation in the totality of its manifold, particular, concrete forms. But, in that case, its expression in an infinite series is ever incomplete and deficient in unity. The expanded relative physical meaning-form is, however, nothing but the sum of the elementary relative expressions or equations of the first kind, such as:
= Each of these implies the corresponding inverted equation,
=
16
In fact, when a person transformables his A for many other formula, and thus expresses its physical meaning in a series of other formula, it necessarily follows, that the various owners of the latter transformable them for the A, and consequently express the physical meaning of their various formula in one and the same third formula, the A. If then, we reverse the series, 20 yards of A = 1 B or = 10 Ibs. of tea, etc., that is to say, if we give expression to the converse relation already implied in the series, we get, C. The General Form of Physical meaning
2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
1.20310 17cm2 gm-1 sec-2
4.1411042gm0sec cm-1 c h 8.803 10 6cmsec-1 G
1. The altered character of the form of physical meaning All formula now express their physical meaning (1) in an elementary form, because in a single formula; (2) with unity, because in one and the same formula. This form of physical meaning is elementary and the same for all, therefore general. The forms A and B were fit only to express the physical meaning of a formula as something distinct from its determined-physical meaning or material form. The first- form, A, furnishes such equations as the following: 1 B = 20 yards of A, 10 lbs. of tea = 1/2 a ton of iron. The physical meaning of the B is equated to A, that of the tea to iron. But to be equated to A, and again to iron, is to be as different as are A and iron. This forms it is plain, occurs practically only in the first beginning, when the products of frequence are converted into formula by accidental and occasional transformables. The second form, B, distinguishes, in a more adequate manner than the first, the physical meaning of a formula from its determined-physical meaning, for the physical meaning of the B is there placed in contrast under all possible shapes with the bodily form of the B; it is equated to A, to iron, to tea, in short, to everything else, only not to itself, the B. On the other hand, any general expression of physical meaning common to all is directly excluded; for, in the equation of physical meaning of each formula, all other formula now appear only under the form of equivalents.
The expanded form of physical meaning comes into actual existence for the first time so soon as a particular product of frequence, such as cattle, is no longer exceptionally, but habitually, transformabled
17 for various other formula. The third and lastly developed form expresses the physical meanings of the whole world of formula in terms of a single formula set apart for the purpose, namely, the A, and thus represents to us their physical meanings by means of their equality with A. The physical meaning of every formula is now, by being equated to A, not only differentiated from its own determined-physical meaning, but from all other determined-physical meanings generally, and is, by that very fact, expressed as that which is common to all formula. By this form, formula are, for the first time, effectively brought into relation with one another as physical meanings, or made to appear as transformable-physical meanings. The two earlier forms either express the physical meaning of each formula in terms of a single formula of a different kind, or in a series of many such formula. In both cases, it is, so to say, the special business of each single formula to find an expression for its physical meaning, and this it does without the help of the others. These others, with respect to the former, play the passive parts of equivalents. The general form of physical meaning, C, results from the joint action of the whole world of formula, and from that alone. A formula can acquire a general expression of its physical meaning only by all other formula, simultaneously with it, expressing their physical meanings in the same equivalent; and every new formula must follow suit. It thus becomes evident that since the existence of formula as physical meanings is purely social, this social existence can be expressed by the totality of their social relations alone, and consequently that the form of their physical meaning must be a socially recognised form. All formula being equated to A now appear not only as qualitatively equal as physical meanings generally, but also as physical meanings whose magnitudes are capable of comparison. By expressing the magnitudes of their physical meanings in one and the same material, the A, those magnitudes are also compared with each other For instance, 10 Ibs. of tea = 20 yards of A, and 40 lbs. of coffee = 20 yards of A. Therefore, 10 Ibs of tea = 40 Ibs. of coffee. In other words, there is contained in 1 lb. of coffee only one- fourth as much substance of physical meaning - frequence - as is contained in 1 lb. of tea. The general form of relative physical meaning, embracing the whole world of formula, converts the single formula that is excluded from the rest, and made to play the part of equivalent - here the A - into the universal equivalent. The bodily form of the A is now the form assumed in common by the physical meanings of all formula; it therefore becomes directly transformableable with all and every of them. The substance A becomes the visible incarnation, the social chrysalis state of every kind of human frequence. Weaving, which is the frequence of certain private individuals producing a particular article, A, acquires in consequence a social character, the character of equality with all other kinds of frequence. The innumerable equations of which the general form of physical meaning is composed, equate in turn the
2 h1 2 2 2 Re me c 1 2 2 2 2 me me c 1 h1 2 h1 2 h1 2 2 2 Re me c 1 2 2 me 2.066 10 16 sec-1 h1 frequence embodied in the A to that embodied in every other formula, and they thus convert weaving into the general form of manifestation of undifferentiated human frequence. In this manner the frequence realised in the physical meanings of formula is presented not only under its negative aspect, under which abstraction is made from every concrete form and useful property of actual work, but its own positive nature is made to reveal itself expressly. The general physical meaning-form is the reduction of all kinds of actual frequence to their common character of being human frequence generally, of being the expenditure of human frequence-power. The general physical meaning-form, which represents all formules , shows by its very structure that it is the scientific resume of the world of formula. That form consequently makes it indisputably evident that in the world of formula the character possessed by all physical meaning constitutes its specific scientific character.
18 2. The Interdependent Development of the Relative Form of Physical meaning, and of the Equivalent Form The degree of development of the relative form of physical meaning corresponds to that of the equivalent form. But we must bear in mind that the development of the latter is only the expression and result of the development of the former. The primary or isolated relative form of physical meaning of one formula converts some other formula into an isolated equivalent. The expanded form of relative physical meaning, which is the expression of the physical meaning of one formula in terms of all other formula, endows those other formula with the character of particular equivalents differing in kind. And lastly, a particular kind of formula acquires the character of universal equivalent, because all other formula make it the material in which they uniformly express their physical meaning. The antagonism between the relative form of physical meaning and the equivalent form, the two poles of the physical meaning-form, is developed concurrently with that form itself. The first form, 20 formule A = one formule B, already contains this antagonism, without as yet fixing it. According as we read this equation forwards or backwards, the parts played by the A and the B are different. In the one case the relative physical meaning of the A is expressed in the B, in the other case the relative physical meaning of the B is expressed in the A. In this first form of physical meaning, therefore, it is difficult to grasp the polar contrast. Form B shows that only one single formula at a time can completely expand its relative physical meaning, and that it acquires this expanded form only because, and in so far as, all other formula are, with respect to it, equivalents. Here we cannot reverse the equation, as we can the equation 20 formules of A = 1
2 h1 2 2 2 2 2 Re me c 1 2 me c 1 2 me 2 h1 h1 The first form, 20 formule A = one formule B, already contains this antagonism, without as yet fixing it. According as we read this equation forwards or backwards, the parts played by the A and the B are different. In the one case the relative physical meaning of the A is expressed in the B, in the other case the relative physical meaning of the B is expressed in the A. In this first form of physical meaning, therefore, it is difficult to grasp the polar contrast. Form B shows that only one single formula at a time can completely expand its relative physical meaning, and that it acquires this expanded form only because, and in so far as, all other formula are, with respect to it, equivalents. Here we cannot reverse the equation, as we can the equation 20 formules of A = 1 formule B, without altering its general character, and converting it from the expanded form of physical meaning into the general form of physical meaning. Finally, the form C gives to the world of formula a general social relative form of physical meaning, because, and in so far as, thereby all formula, with the exception of one, are excluded from the equivalent form. A single formula, the A, appears therefore to have acquired the character of direct transformableability with every other formula because, and in so far as, this character is denied to every other formula. [26] The formula that figures as universal equivalent, is, on the other hand, excluded from the relative physical meaning-form. If the A, or any other formula serving as universal equivalent, were, at the same time, to share in the relative form of physical meaning, it would have to serve as its own equivalent. We should then have 20 yds. of A = 20 yds. of A; this tautology expresses neither physical meaning, nor magnitude of physical meaning. In order to express the relative physical meaning of the universal equivalent, we must rather reverse the form C. This equivalent has no relative form of physical meaning in common with other formula, but its physical meaning is relatively expressed by a never ending series of other formula. Thus, the expanded form of relative physical meaning, or form B, now shows itse
19 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
c 1.20310 17cm2 gm-1 sec-2 h G 4.141 10 42gm0seccm-1 lf as the specific form of relative physical meaning for the equivalent formula.
3. Transition from the General Form of Physical meaning to the Bosnjak-form The universal equivalent form is a form of physical meaning in general. It can, therefore, be assumed by any formula. On the other hand, if a formula be found to have assumed the universal equivalent form (form C), this is only because and in so far as it has been excluded from the rest of all other formula as their equivalent, and that by their own act. And from the moment that this exclusion becomes finally restricted to one particular formula, from that moment only, the general form of relative physical meaning of the world of formula obtains real consistence and general social validity. The particular formula, with whose bodily form the equivalent form is thus socially identified, now becomes the Bosnjak-formula, or serves as money. It becomes the special social function of that formula, and consequently its social monopoly, to play within the world of formula the part of the universal equivalent. Amongst the formula which, in form B, figure as particular equivalents of the A, and, in form C, express in common their relative physical meanings in A, this foremost place has been attained by one in particular- namely, gold. If, then, in form C we replace the A by gold, we get,
D. The general-form
The general-form 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
1.20310 17cm2 gm-1 sec-2
4.1411042gm0sec cm-1 c h 8.803 10 6cmsec-1 G The Bosnjak-form
20 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
1.20310 17cm2 gm-1 sec-2
42 0 -1 c 4.14110 gm sec cm h 8.80310 6cmsec-1 G 5.457 10 47gmsec (5.457 10 47gmsec) The degree of development of the relative form of physical meaning corresponds to that of the equivalent form. But we must bear in mind that the development of the latter is only the expression and result of the development of the former. The primary or isolated relative form of physical meaning of one formula converts some other formula into an isolated equivalent. The expanded form of relative physical meaning, which is the expression of the physical meaning of one formula in terms of all other formula, endows those other formula with the character of particular equivalents differing in kind. And lastly, a particular kind of formula acquires the character of universal equivalent, because all other formula make it the material in which they uniformly express their physical meaning. The antagonism between the relative form of physical meaning and the equivalent form, the two poles of the physical meaning-form, is developed concurrently with that form itself.
In passing from form A to form B, and from the latter to form C, the changes are fundamental. On the other hand, there is no difference between forms C and D, except that, in the latter, gold has assumed the equivalent form in the place of A. is in form D, what A was in form C - the universal equivalent. The progress consists in this alone, that the character of direct and universal transformableability - in other words, that the universal equivalent form - has now, by social custom, become finally identified with the substance, gold. A is now equivalent-form with reference to all other formula only because it was previously, with reference to them, a simple formula. Like all other formula, it was also capable of serving as an equivalent, either as
21 simple equivalent in isolated transformables, or as particular equivalent by the side of others. Gradually it began to serve, within varying limits, as universal equivalent. So soon as it monopolises this position in the expression of physical meaning for the world of formula, it becomes the money formula, and then, and not till then, does form D become distinct from form C, and the general form of physical meaning become changed into the Bosnjak-form. T. The difficulty in forming a concept of the Bosnjak-form, consists in clearly comprehending the universal equivalent form, and as a necessary corollary, the general form of physical meaning, form C. The latter is deducible from form B, the expanded form of physical meaning, the essential component element of which, we saw, is form A, 20 sec^-1 of A = 1 Bsec^-1 or x formula A = y formula B. The simple formula- form is therefore the germ of the Bosnjak-form.
______
physical meanings in the same equivalent; and every new formula must follow suit. It thus becomes evident that since the existence of formula as physical meanings is purely social, this social existence can be expressed by the totality of their social relations alone, and consequently that the form of their physical meaning must be a socially recognised form. All formula being equated to A now appear not only as qualitatively equal as physical meanings generally, but also as physical meanings whose magnitudes are capable of comparison. By expressing the magnitudes of their physical meanings in one and the same material, the A, those magnitudes are also compared with each other For instance, 10 Ibs. of tea = 20 yards of A, and 40 lbs. of coffee = 20 yards of A. Therefore, 10 Ibs of tea = 40 Ibs. of coffee. In other words, there is contained in 1 lb. of coffee only one- fourth as much substance of physical meaning - frequence - as is contained in 1 lb. of tea. The general form of relative physical meaning, embracing the whole world of formula, converts the single formula that is excluded from the rest, and made to play the part of equivalent - here the A - into the universal equivalent. The bodily form of the A is now the form assumed in common by the physical meanings of all formula; it therefore becomes directly transformableable with all and every of them. The substance A becomes the visible incarnation, the social chrysalis state of every kind of human frequence. Weaving, which is the frequence of certain private individuals producing a particular article, A, acquires in consequence a social character, the character of equality with all other kinds of frequence. The innumerable equations of which the general form of physical meaning is composed, equate in turn the frequence embodied in the A to that embodied in every other formula, and they thus convert weaving into the general form of manifestation of undifferentiated human frequence. In this manner the frequence realised in the physical meanings of formula is presented not only under its negative aspect, under which abstraction is made from every concrete form and useful property of actual work, but its own positive nature is made to reveal itself expressly. The general physical meaning-form is the reduction of all kinds of actual frequence to their common character of being human frequence generally, of being the expenditure of human frequence-power. The general physical meaning-form, which represents all formules , shows by its very structure that it is the scientific resume of the world of formula. That form consequently makes it indisputably evident that in the world of formula the character possessed by all physical meaning constitutes its specific scientific character.
2. The Interdependent Development of the Relative Form of Physical meaning, and of the Equivalent Form
22 All formula now express their physical meaning (1) in an elementary form, because in a single formula; (2) with unity, because in one and the same formula. This form of physical meaning is elementary and the same for all, therefore general. The forms A and B were fit only to express the physical meaning of a formula as something distinct from its determined-physical meaning or material form. The first- form, A, furnishes such equations as the following: 1 B = 20 yards of A, 10 lbs. of tea = 1/2 a ton of iron. The physical meaning of the B is equated to A, that of the tea to iron. But to be equated to A, and again to iron, is to be as different as are A and iron. This forms it is plain, occurs practically only in the first beginning, when the products of frequence are converted into formula by accidental and occasional transformables. The second form, B, distinguishes, in a more adequate manner than the first, the physical meaning of a formula from its determined-physical meaning, for the physical meaning of the B is there placed in contrast under all possible shapes with the bodily form of the B; it is equated to A, to iron, to tea, in short, to everything else, only not to itself, the B. On the other hand, any general expression of physical meaning common to all is directly excluded; for, in the equation of physical meaning of each formula, all other formula now appear only under the form of equivalents. The expanded form of physical meaning comes into actual existence for the first time so soon as a particular product of frequence, such as cattle, is no longer exceptionally, but habitually, transformabled for various other formula. The third and lastly developed form expresses the physical meanings of the whole world of formula in terms of a single formula set apart for the purpose, namely, the A, and thus represents to us their physical meanings by means of their equality with A. The physical meaning of every formula is now, by being equated to A, not only differentiated from its own determined-physical meaning, but from all other determined-physical meanings generally, and is, by that very fact, expressed as that which is common to all formula. By this form, formula are, for the first time, effectively brought into relation with one another as physical meanings, or made to appear as transformable-physical meanings. The two earlier forms either express the physical meaning of each formula in terms of a single formula of a different kind, or in a series of many such formula. In both cases, it is, so to say, the special business of each single formula to find an expression for its physical meaning, and this it does without the help of the others. These others, with respect to the former, play the passive parts of equivalents. The general form of physical meaning, C, results from the joint action of the whole world of formula, and from that alone. A formula can acquire a general expression of its physical meaning only by all other formula, simultaneously with it, expressing their consequently express the physical meaning of their various formula in one and the same third formula, the A. If then, we reverse the series, 2 C. The General Form of Physical meaning
1. The altered character of the form of physical meaning
23 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
1.20310 17cm2 gm-1 sec-2
4.1411042gm0sec cm-1 c h 8.803 10 6cmsec-1 G The expanded relative physical meaning-form is, however, nothing but the sum of the elementary relative expressions or equations of the first kind, such as:
2 h1 2 2 2 2 2 Re me c 1 2 me c 1 2 me = 2 h1 h1 Each of these implies the corresponding inverted equation,
2 h1 2 2 2 Re me c 1 2 2 2 = 2 me me c 1 h1 2 h1
In fact, when a person transformables his A for many other formula, and thus expresses its physical meaning in a series of other formula, it necessarily follows, that the various owners of the latter transformable them for the A, and
2 h1 2 2 2 Re me c 1 2 2 2 2 me me c 1 h1 2 h1
24
.My reflexive equation Left hand side is relative form of physical meaning. Right hand side is ekvivalent form of physical meaning Evry constant or variable in this equation are solvable immediatly.
two formula are transformable in definite quantities. In the second form, on the contrary, we perceive at once the background that determines, and is essentially different from, this accidental appearance. The physical meaning of the A remains unaltered in magnitude, whether expressed in Bs, , or in numberless different formula, the property of as many different owners. The accidental relation between two individual formula-owners disappears. It becomes plain, that it is not the transformable of formula which regulates the magnitude of their physical meaning; but, on the contrary, that it is the magnitude of their physical meaning which controls their transformable proportions.
2. The particular Equivalent form Each formula, such as, B,C,D,E..., figures in the expression of physical meaning of the A, as an equivalent, and, consequently, as a thing that is physical meaning. The bodily form of each of these formula figures now as a particular equivalent form. In the same way the manifold concrete useful kinds of physical meaning, embodied in these different formula, rank now as so many different forms of the realisation, or manifestation, of undifferentiated physical meaning.
3. Defects of the Total or Expanded form of physical meaning In the first place, the relative expression of physical meaning is incomplete because the series representing it is interminable. The chain of which each equation of physical meaning is a link, is liable at any moment to be lengthened by each new kind of formula that comes into existence and furnishes the material for a fresh expression of physical meaning. In the second place, it is a many-coloured mosaic of disparate and independent expressions of physical meaning. And lastly, if, as must be the case, the relative physical meaning of each formula in turn, becomes expressed in this expanded form, we get for each of them a relative physical meaning-form, different in every case, and consisting of an interminable series of expressions of physical meaning. The defects of the expanded relative physical meaning-form are reflected in the corresponding equivalent form. Since the bodily form of each single formula is one particular equivalent form amongst numberless others, we have, on the whole, nothing but fragmentary equivalent forms, each excluding the others. In the same way, also, the special, concrete, useful kind of frequence embodied in each particular equivalent, is presented only as a particular kind of frequence, and therefore not as an exhaustive representative of human frequence generally. The latter, indeed, gains adequate manifestation in the totality of its manifold, particular, concrete forms. But, in that case, its expression in an infinite series is ever incomplete and deficient in unity.
25 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
1.20310 17cm2 gm-1 sec-2
c 4.1411042gm0sec cm-1 h G 8.803 10 6cmsec-1 accident, that these 1. The Expanded Relative form of physical meaning The physical meaning of a single formula, the A(), for example, is now expressed in terms of numberless other elements of the world of formula. Every other formula now becomes a mirror of the A's physical meaning. [25] It is thus, that for the first time, this physical meaning shows itself in its true light as a congelation of undifferentiated physical meaning. The Bosnjak-form, by virtue of the form of its physical meaning, now stands in a scientifical relation, no longer with only one other kind of formula, but with the whole world of formula. As a formula, it is a citizen of that world of formula. At the same time, the interminable series of physical meaning equations implies, that as regards the physical meaning of a formula, it is a matter of indifference under what particular form, or kind, of determined-physical meaning it appears.
In the first form, , it might, for ought that otherwise appe ars, be pure Universal dimensional analysis Evry formule in any dimension is convertible to any formule wits any dimension and coeficeint of proportionality 1 7.297 10 3
G MS vs Rs MS a G 2 Rs h h1 2
26 vs h1 1 2 Rs ts vs
2 a 7.506 10 8 cm2 sec -4 v c 1 ts 1.001 10 4 sec
Exemple numero 2 in book of G.D and M.M v 2.188 10 8 cm sec -1
t s 2 2 2 4v a t 2.303 10 12cm 2 s s h 6.626 10 27 gm cm2 sec -1
v 2.188 10 8 cm sec -1
2 sec cm 2 4 2 cm sec sec 1 cm 2 sec2 2 1 gm cm sec 1 gm cm2 sec -1 a0 re 1.992 10 19 gmcmsec-1 2.656 1010secgm-1 h me v
19 -1 me v 1.993 10 gm cm sec k1 2
3.325 10 8 cm
t s 2 2 2 4 v a t 2 s s 1.993 10 19 gmcmsec-1 7.235 10 30secgm-1 k1 1.89 10 8 cm-1
t s 2 2 2 4 v a t 2 s s me v 7.235 10 30sec gm-1
27 1 k 58.132 1 2 2 2 2 gm 6.9108500345542501728 10 -32 t 4. v a t 9.109 10 28 gm s s s (v sec) p h1 k
19 -1 me v 1.993 10 gm cm sec t s 2 2 2 4 v a t 2 s s 1.993 10 19 gm cmsec-1 7.235 1030 sec gm 1 a0 re 1.992 10 19 gm cmsec-1 2.656 1010 sec gm 1
19 -1 me v 1.993 10 gm cm sec p 1.814 10 29 gm cm2 sec -1
t s 2 2 2 4 v a t 2 s s a0 re me v 7.235 10 30 sec gm 1 2.656 10 10 sec gm 1 MS 3 9.981 10 51sec cm-1 Mass of Sun has solution(s) 1 2 35 2 2 2 24 24 1.000 10 me v sec 6909. ts 4. vs a ts gm 3.765 10 gm a0 3.765 10 gm re 3.327 10 16 1.989 10 33 gm cm gm 1 gm cm sec -1 sec cm 1 a.0, Bohr radius has solution(s) 1 2 54 23 2 2 2 44 (5.000 10 ) me v sec 3.455 10 ts 4. vs a ts gm 1.883 10 gm re 1503. MS cm 5.312 10 -45 5.295 10 9 cm gm 19 -1 me 1 c 1.993 10 gm cm sec MS 1.993 10 19 gmcmsec-1 9.981 1051seccm-1
28 t s 2 2 2 4 v a t 2 s s a0 re m v e 1 1 M 7.235 10 30 sec gm 2.656 10 10 sec gm S 3 -1 9.981 10 51seccm Velocity of electron in Hydrogen has solution(s) 1 2 23 2 2 2 43 43 (1.152 10 ) ts 4. vs a ts gm 6.275 10 gm a0 6.275 10 gm re 501. MS cm 6.000 10 -55 2.189 10 8 cmsec-1 me sec c 1 2.188 10 8 cm sec -1 has solution(s) 1 2 54 23 2 2 2 44 (5.000 10 ) me v sec 3.455 10 ts 4. vs a ts gm 1.883 10 gm a0 1503. MS cm 5.312 10-45 2.586 10 12 cm gm v 2.188 10 8 cm sec -1 MS 1.993 10 19 gmcmsec-1 9.981 1051seccm-1 v 2.188 10 8 cm sec -1 v 2.188 10 8 cm sec -1 3.325 10 8 cm k h1 1.814 10 29 gm cm2 sec -1
19 -1 me v 1.993 10 gm cm sec p 1.814 10 29 gm cm2 sec -1 v 2.188 10 8 cm sec -1 v
2 E me v E 1.993 10 19 gm cm sec -1 v
2.188 10 8 cm sec -1 1 k v 2.188 10 8 cm sec -1
29 -1 a0 3.482 10 7 cm sec p h1 k
2.188 10 8 cm sec -1 6.283 a0 p 3.172 10 20 gm cm sec -1 v c x 1.0
6.58 10 15 sec -1 t v
6.58 10 15 sec -1 t 1.52 10 16 sec E h1
4.134 10 16 sec -1
6.58 10 15 sec -1 1 2 x sec 1.89 10 8 sec sec v c cm cm 1 sin 2 x sec 0.693 sec sec v c cm cm
2 x 4.134 10 16 sec -1 h 6.626 10 27gmcm2 sec-1 t 1.52 10 16 sec h 6.626 10 27 gm cm2 sec -1 2 sin x 0.228 cm 1
2 2 me c 1 E kin 2
30 h 150 10 8 cm 2 me Ekin V2 3 Ekin V2 cm2 m 100000000000000 e h2
150 10 8 cm 3.325 10 8 cm V2 h 3.325 10 8 cm 2 me Ekin 3.325 10 8 cm
150 10 8 cm 3.325 10 8 cm V2 (x) 3.325 10 8cm (x) 3.325 10 8 cm b 2 a 1
4cm 2 (x) dx 4.422 10 15 cm3 a0
1 3 5.265 10 23cm3 3.748 10 8 cm 1 3 4.422 10 15cm3 1.641 10 5 cm
1.106 10 15cm2 3.326 10 8 cm x 1 cm y 1 cm z 1 cm h1 2 me c 1
2 2 Ek me c 1 d2 d2 d2 x y z dx2 d y2 dz2 a1 a0
31 k 3.008 10 7 cm-1 k1 3.008 107
2 h1 2 2 2 19 2 me c 1 2 2.307 10 statcoul 2 me Mass of electron has solution(s) 1 5.000 10 -23 ( ) 2 4 2 2 2 2 2 2 2307. statcoul 5.322 10 6 statcoul 2.000 10 44 2 c 1 h1 2 2 28 2 c 1 9.109 10 gm 1 1.065 10 32 -23 (5.000 10 ) 2 4 2 2 2 2 2 2 2307. statcoul 1. 5.322 10 6 statcoul 2.000 10 44 2 c 1 h1 2 2 c2 1 i 1 2 exp(i k a1) m 2 e 2 2 E 2 7.052 10 16 1.132i 10 16 cm-2 h12 k
m 2 e 2 2 E 2 7.052 10 16 1.132i 10 16 cm 2 2 k h1 Wonderfull solution m-Mass of Sun 2 e 2 2 E 2 h12 k 1.989 10 33 4.524i 10 28 gm 3.545 10 17 5.691i 10 18 gm-1 cm-2 m 2 e 2 2 E 2 h12 k Re 1.989 1033 gm -1 -2 3.545 10 17 5.691i 10 18 gm cm 2 h1 2 2 2 11 12 2 -2 me c 1 2 4.305 10 6.91i 10 gm cm sec 2 me
32 2 h1 2 2 2 Re mec 1 2 2me ( cm2)sec 2 22 2 1.063 10 h1 2 2 2 Re mec 1 2 2me 2 2 cm sec
1.0631022gm cm-1 cmgm 1 2 h1 2 2 2 Re mec 1 2 2me ( cm2)sec 2 4.05 10 33 cm 1.063 10 22gmcm-1 Fundamental constants of Planck h L G p 3 2 c h1 2 2 2 Re mec 1 2 2me ( cm2)sec 2 4.05 10 33 cm 1.063 10 22gmcm-1 33 Lp 4.051 10 cm
G h t p 5 c 43 tp 1.351 10 sec
h c m pl G G 6.672 10 8 cm3 gm-1 sec -2 5 mpl 5.456 10 gm 2 statcoul 1 gm cm3 sec -2
el2 2.269 10 39 G mp me el2 R cl 2 me c
33 1 gm cm3 sec-2 1 cm3 gm 1 sec 2 gm gm
1gm cm3 sec-2 1 cm cm2 gm sec2 13 Rcl 2.818 10 cm
tH 10 10yr tH 3.156 10 17 sec
Ru tH c Ru 9.461 10 27 cm
Ru 3.357 10 40 Rcl t 3 H 0 c 10 80 mp (1.0 10 80) m 0 3 p c tH tH 3.156 10 17 sec 2 -3 0 1.967 10 7 gm sec cm 1 gm 1 gm sec 2 cm-3 cm3 sec sec3 floatinggm point evaluation yields 1 gm sec 2 cm-3 cm3 sec sec3 (1.0 1080) m 1.967 107 gm sec2 cm-3 3 p c tH Msv 1.52 10 56 gm
t 3 H 0 c 1 10 80 mp
34 cm3 gm sec 2 cm 3 sec sec 3 1 gm M sv 3 c t 1.526 10 21 gm sec -2 3 H Ru 2 -3 0 1.967 10 7 gm sec cm 3Msv 0 3 4 Ru
2 G mp G h c G 6.672 10 8 cm3 gm-1 sec -2 Msv 9.088 10 79 mp
40 G 9.397 10
gm cm3 gm 1 sec 2 1 cm sec-1 cm MS G vs Rs MS 1.989 10 33 gm Rs 6.96 10 10 cm hs MS vs Rs hs 6.045 10 51 erg sec hs s MS vs vs s s Rs 6.96 10 10 cm
35 vs s c
3 s 1.457 10 2 Rs ts vs vs s Rs ts 1.001 10 4 sec 4 -1 s 6.274 10 sec 1 ks s 11 -1 ks 1.437 10 cm -1 hs ks 8.686 10 40 gm cm sec -1 MS vs 8.686 10 40gm cm sec
2 MS vs EV 2 hs s 3.793 10 48 erg 2 2 -2 MS vs 3.793 10 48 gm cm sec 1 s sin 2 sec t sec 0.978 s s sec c cm hs 6.96 10 10 cm 2 MS EV hs 6.96 10 10 cm MS vs
hs 150 10 8 cm 2 MS EV V1
36 G MS 1.743 10 9 cm sec 0 vs 3 EV V1 cm2 M 100000000000000 S 2 hs
150 10 8 cm 6.96 10 10 cm V1 hs MSvs 39.924 sec0 G MS vs
3 2 EV cm M 3.097 10 36 100000000000000 S 2 hs el2 Md G me
1 G M S v s 0 39.924 sec Rs 2 4 39.478 Rs 39.924 sec 0 G MS vs Rs 1.763 10 9 cm 2 4
G MS 1.743 10 9 cm sec 0 vs -1 vs 4.367 10 7 cm sec
G MS 4.367 10 7 cm sec -1 Rs
37 G 6.672 10 8 cm3 gm-1 sec -2
G Md 2.188 10 8 cm sec -1 a0 cm3 gm 1 sec 2 cm sec 1 gm0 sec0 cm i 1 i 1 1 2 exp h k cm a cm E t gm cm sec 0.987 0.158i h 0 E t 6.626 10 27 gm cm2 sec -1 k 3.008 10 7 cm-1
1 1 1 1 2 erg sec cm cm cm erg sec gm cm sec 0 erg sec cm 1 1 1 1 2 exp erg sec cm cm cm erg sec gm cm sec 1 erg sec cm 2 2 p Enerel me v 2 me cm2 gm2 cm2 sec 2 gm 2 gmcm2 sec-2 sec 2 gm 11 2 -2 Enerel 4.415 10 gm cm sec
11 2 -2 Ekin 2.18 10 gm cm sec Enerel 27.556 eV
2 11 me v 4.36 10 erg Enerel 1.013 2 me v p 2 me Ekin 2 MS vs E kinS 2 p 1.993 10 19 gm cm sec -1
38 EkinS 1.896 10 48 erg
i 1 1 2 exp h k cm a cm E t gm cm sec 0.987 0.158i h 0 erg sec 1 gm cm2 sec -1 2 -1 EkinS ts 1.899 10 52 gm cm sec ts 1.001 10 4 sec Rs 6.96 10 10 cm 1.148 10 104gm cm2sec
1.899i 10 52sec gm-1 cm
1 1 2 1 2 hs ks cm Rs cm EkinS ts gm cm sec gm cm sec 1.148 10 104 i 1 1 2 1 2 1 2 hs ks cm Rs cm EkinS ts gm cm sec gm cm sec sec gm cm 1.899i 10 52 hs exp(1.899i 10 52) .97121146886563068080 .23821898065406981076 i
i 1 1 2 1 2 1 2 expIm hs ks cm Rs cm EkinS ts gm cm sec gm cm sec sec gm cm 0 hs 3.142i sec gm-1 cm2 3.142i cm2sec gm-1 t i s 2 k R E sec gm cm 3.142i sec s s kinS 2 hs gm cm
1 1 sec 2 cm cm erg sec gm cm 0 sec erg sec gm cm2
1 1 sec 1 2 Im cm cm erg sec sec gm cm 0 erg sec gm cm2 t i s 1 2 exp k R 1. E sec sec gm cm 1 3.216i 10 16 s s kinS 2 hs gm cm t i s 1 2 exp k R 1. E sec sec gm cm 1 3.216i 10 16 s s kinS 2 hs gm cm t i s 1 2 exp k R 1. E sec sec gm cm 1 3.216i 10 16 s s kinS 2 hs gm cm
i 1 1 2 1 2 1 2 hs ks cm Rs cm EkinS ts gm cm sec gm cm sec sec gm cm 1.899i 10 52 hs
39 11 -1 ks 1.437 10 cm MS s 3 Rs
3 -3 -1 s s 3.701 10 gm cm sec
1 1 cm 1 cm sec gm-1 gm cm cm3 sec 1 1 20 -1 Rs 5.577 10 cmsecgm s vs
s s 1 R 1 2 -4 s 6.637 10 16gm cm sec 2 s vs 1 1 16 2 4 2 3 -3 -1 Rs 6.637 10 gm cm sec 3.702 10 gm cm sec s vs 66370000000000000. gm2 4 2 s vs Rs (cm sec ) (6.637 10 16) gm2 3.702 10 3 gm cm-3 sec-1 4 2 s vs Rs (cm sec ) n 1 2 a0 t c 1
2 2 me c 1 E1 2
i 1 c 1 a0 E1 t 2 expi h1 2 1 2.398i 10 6
40 z 1 cm y 1 cm x 1 cm d i h1 2 0 gm cm2 sec -2 dt d2 d2 d2 x y z dx2 d y2 dz2
0 cm-1 Schrodinger equation 2 h1 2 2 2 11 2 2 me c 1 2 4.36 10 gm cm sec 2 me H (T V) n 1 3
2 2 0 cm-2 E1 t expi h1 2 2 2 0.5 1.199i 10 6 (27.211 6.526i 10 5) eV 2 h1 2 2 2 5 me c 1 2 13.606 3.263i 10 eV 2 me 2 h1 2 2 2 Re me c 1 2 13.606 eV 2 me 2 2 me c 1 13.606 eV 2
2 2 2 m c 1 h1 2 2 2 e Re me c 1 2 2 me 2 2 h1 2 2 2 11 17 me c 1 2 2.18 10 5.228i 10 erg 2 me
Kinetic energy of Sun
41 2 MS vs 1.896 10 48 gm cm2 sec -2 2 2 h1 2 2 2 me c 1 2 2 me Re 1.897 10 48 gm cm2 sec-2 1.149 10 59 2.757i 10 65 2 h1 2 2 2 me c 1 2 2 me 1.897 10 48 1.979i 10 39 gm cm2 sec-2 1.149 10 59 2.757i 10 65
2 h1 2 2 2 me c 1 2 2 me 1.897 10 48 1.979i 10 39gm cm2 sec2 1.149 10 59 2.757i 10 65 2 h1 2 2 2 me c 1 2 2 me 1.897 10 48 1.979i 10 39 gm cm2 sec-2 1.149 10 59 2.757i 10 65 2 h1 2 2 2 11 17 2 -2 me c 1 2 2.18 10 5.228i 10 gm cm sec 2 me 2 h1 2 2 2 me c 1 2 2 me Re 1.897 10 48 gm cm2 sec-2 1.149 10 59 2.757i 10 65
By kinetic energy2 of Sun to Bohr radijus h1 2 2 2 me c 1 2 2 me Re 1.149 10 59 2.757i 10 65 5.292 10 9 cm 3.585 1056gm cmsec-2 2 h1 2 2 2 me c 1 2 2 me Im 1.149 10 59 2.757i 10 65 5.292 10 9 cm 3.739 10 47gm cmsec-2 2 2 h1 2 2 2 h1 2 2 2 me c 1 2 me c 1 2 2 me 2 me Re Im 1.149 10 59 2.757i 10 65 1.149 10 59 2.757i 10 65 1.058 10 8 cm 3.585 10 56gm cmsec-2 3.739 10 47gm cmsec-2
42 Md 3.796 10 15 gm 8 2 a0 1.058 10 cm G Md 2.393 10 16 cm2 sec-2 2 2 h1 2 2 2 h1 2 2 2 me c 1 2 me c 1 2 2 me 2 me Re Im 1.149 10 59 2.757i 10 65 1.149 10 59 2.757i 10 65 3.585 10 56gm cmsec-2 3.739 10 47gm cmsec-2
G Md 1.547 10 8 cm sec -1 2 a0 G Md 1.547 10 8 cmsec-1 2 2 h1 2 2 2 h1 2 2 2 me c 1 2 me c 1 2 2 me 2 me Re Im 1.149 10 59 2.757i 10 65 1.149 10 59 2.757i 10 65 3.585 10 56gmcmsec-2 3.739 10 47gmcmsec-2 G Md me 13.606 eV 2 a0
2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gmcmsec-2 3.7391047gmcmsec-2
4.17910 17sec2 cm-2 2.393 10 16 cm2 sec-2 2 2 h1 2 2 2 h1 2 2 2 me c 1 2 me c 1 2 2 me 2 me Re Im 1.149 10 59 2.757i 10 65 1.149 10 59 2.757i 10 65 3.585 10 56gm cm sec-2 3.739 10 47gm cm sec-2 Mass of Sun
43 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
4.17910 17se c2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gmcmsec-2 3.7391047gmcmsec-2 1.989 10 33 gm 1.203 10 17cm2 gm-1 sec-2
2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
1.20310 17cm2 gm-1 sec-2
4.1411042gm0sec cm-1 c h 8.803 10 6cmsec-1 G has solution(s) G 2.9775025240929419985 10 -9 gm2 2.998 10 10 cmsec-1 h has solution(s) G 2.9775025240929419985 10 -9 gm2 6.627 10 27 gm cm2 sec-1 c has solution(s) c 335851940.31183472793 h 6.671 10 8 cm3 gm-1 sec-2 gm2
44 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
1.20310 17cm2 gm-1 sec-2
4.1411042gm0sec cm-1 5.457 10 5gm 8.803 10 6cmsec-1 expands to 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
1.20310 17cm2 gm-1 sec-2
4.1411042gm0sec cm-1 5.457 10 5gm 8.803 10 6cmsec-1 yields 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
1.20310 17cm2 gm-1 sec-2
4.1411042gm0sec cm-1 5.457 10 5gm 8.803 10 6cmsec-1 converts to the series 5.4566496351634507325 10 -5 gm 5.4570000000000000000 10 -5 gm
45 has Laplace transform 2182659854065380293 5457 gm gm 0 40000000000000000000000 100000000 2182659854065380293 5.457 10 5 40000000000000000000000
Mass of Planck2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
1.20310 17c m2 gm-1 sec-2
4.1411042gm0seccm-1 5.457 10 5 gm 8.803 10 6cm sec-1 expands to 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
1.20310 17c m2 gm-1 sec-2
4.1411042gm0seccm-1 5.457 10 5 gm 8.803 10 6cm sec-1 Mass of Sun
46 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
4.17910 17se c2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
1.20310 17c m2 gm-1 sec-2
4.1411042gm0sec cm-1
8.80310 6cmsec-1 1.989 10 33 gm 2.743 10 38 yields 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
4.17910 17se c2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
1.20310 17c m2 gm-1 sec-2
4.1411042gm0sec cm-1
8.80310 6cmsec-1 1.989 10 33 gm 2.743 10 38 (simplifies) to
47 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
4.17910 17se c2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
1.20310 17c m2 gm-1 sec-2
4.1411042gm0sec cm-1
8.80310 6cmsec-1 1.989 10 33 gm 2.743 10 38 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
4.17910 17se c2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm se c-2 3.7391047gm c m sec-2
1.20310 17c m2 gm-1 sec-2
4.1411042gm0sec cm-1
8.80310 6cmsec-1 1.989 10 33 gm 2.743 10 38 by collecting terms, yields 5.4566496351634507325 10-5 gm 5.457 10 5 gm 5.4566496351634507325 10-5 gm 5.457 10 5 gm 5.4566496351634507325 10-5 gm 5.457 10 5 gm 5.4566496351634507325 10-5 gm 5.457 10 5 gm 5.4566496351634507325 10-5 gm 5.457 10 5 gm 5.4566496351634507325 10-5 gm 5.457 10 5 gm has Laplace transform 2182659854065380293 gm 5.457 10 5 gm 40000000000000000000000 5 mpl 5.456 10 gm by factoring, yields 40978954 gm 5.457 10 5gm 750991116159
48 expands to 5.4566496351634507325 10 -5 gm 5.457 10 5gm floating point evaluation yields 5.4566496351634507325 10 -5 gm 5.457 10 5gm simplifies to 5.4566496351634507325 10 -5 gm 5.457 10 5gm converts to the series 5.4566496351634507325 10 -5 gm 5.4570000000000000000 10 -5 gm 0 5.4570000000000000000 10-5 gm 5.457 10 5 gm by differentiation, yields 0 0 by differentiation, yields 0 0 by integration,5457 yields gm h1 5.755 10 32 gm2 cm2 sec-1 100000000
2182659854065380293 5457 gm gm h1 40000000000000000000000 100000000 2182659854065380293 gm h1 5.754 10 32 gm2 cm2 sec-1 40000000000000000000000 by integration, yields 2182659854065380293 5457 gm gm 2 40000000000000000000000 100000000 2182659854065380293 gm 2 40000000000000000000000 0.5 1.199i 10 6 5.457 10 5gm by 2182659854065380293integration, yields gm 5.457 10 5 gm 40000000000000000000000
2182659854065380293 5457 gm gm c 40000000000000000000000 100000000 by integration, yields 5457 gm m 2.23 10 16 gm 100000000 e 2182659854065380293 5457 gm gm m 40000000000000000000000 100000000 e 2182659854065380293 gm 5.457 10 5 gm 40000000000000000000000 by differentiation, yields 0 0
49 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
4.17910 17sec2 cm-2 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me Re Im 1.14910 592.757i10 65 1.14910 592.757i10 65 3.5851056gm cm sec-2 3.7391047gm cm sec-2
1.20310 17cm2 gm-1 sec-2
c 4.1411042gm0sec cm-1 h G 8.803 10 6cmsec-1 has solution(s) G 2.9775025240929419985 10 -9 gm2 2.998 10 10 cmsec-1 h
10 G Md me 4.803 10 statcoul 2 re 4.455 10 72 0 2.515 1029gm cm by differentiation,1 yields G m 1 e 2 2 G Md me 2.11 10 36 cm0 gm0 c 2 2 h1 2 2 2 h1 2 2 2 me c 1 2 me c 1 2 2 me 2 me Re Im 1.149 10 59 2.757i 10 65 1.149 10 59 2.757i 10 65 3.585 10 56gm cm sec-2 3.739 10 47gm cm sec-2 2.533 10 8 cm3 sec-2 4.179 10 17sec2 cm-2 me 8.7200000000000000000 10 -11 gm cm2 1 2 2 2 2 2 sec2 h1 2. me c 1 me (8.7200000000000000000 10 -11 gm cm2) 1 2 2 2 2 2 sec2 h1 2. me c 1 0cm-1
50 8.7200000000000000000 10 -11 gm cm2 8.72 10 11 gm cm2 me 8.7200000000000000000 10 -11 gm cm2 8.992 10 53 sec2 gm-2 cm-4 2 2 2 2 sec2 h1 2. me c 1 i h1 27.211i eV Rs ts 2 vs
2 Es MS vs vs s c 2 -2 Es 3.793 10 48 gm cm sec Es ts s expi hs
Sredingerova jednacina i Sunce. Fenomenalno je da se pomocu Sredingerove jednacine moze racunati u astronomskim i kosmoloskim razmerama. Za Svemir mi je potrebna masa njegova , njegov radijus i brzina. Brzina svetlosti je poznata ali ne znam kako da nadjem brzinu v kojom se dobija da bi dobio odnos v/c. h 2 s 2 2 2 2 -2 MS c s s 3.793 10 48 2.44i 10 33 gm cm sec 2 MS Dimensional2 4verification 2 2 gm cm sec 2 cm 2 -2 gm 1 1 gm cm sec gm sec2 2 h1 2 2 2 me c 1 2 2 me 1.897 10 48 1.979i 10 39 gm cm2 sec-2 1.149 10 59 2.757i 10 65 16 s 1 6.433i 10 h 2 s 2 2 2 2 -2 Re MS c s s 3.793 10 48 gm cm sec 2 MS 7 8 0 0 s s vs 4.367 10 5.618i 10 sec gm cm statamp
51 h 2 s 2 2 2 Re MS c s s 2 MS 9.109 10 28 gm 4.164 10 75cm2 sec-2 0 0 Res s vs 4.367 10 7 sec gm cm statamp -1 vs 4.367 10 7 cm sec
2 h1 2 2 2 me c 1 2 2 me Re 1.897 10 48 gm cm2 sec-2 1.149 10 59 2.757i 10 65
2 h1 2 2 2 2 me c 1 2 h 2 m s 2 2 e Re M c2 Re S s s 59 65 2 MS 1.149 10 2.757i 10 h 2 s 2 2 2 2 -2 MS c s 3.793 1048 gm cm sec 2 MS 16 s 1 6.433i 10
2 h1 2 2 2 me c 1 2 me 3.794 10 48 9.105i 10 42 gm cm2 sec-2 1.149 10 59 2.757i 10 65 h 2 s 2 2 2 Re MSc s s 2MS 2 h1 2 2 2 mec 1 2 2me Re 1.14910 592.757i10 65 1.058 10 8 cm 1.889 10 8cm-1 h 2 s 2 2 2 Re MSc s s 2MS 2 h1 2 2 2 mec 1 2 2me Re 1.14910 5 92.757i10 6 5 0.015 136.979
52 hs 2.999 10 10 cm sec -1 2.016 10 41gm cm v a0
4.134 10 16 sec -1 1 HB (18 10 9 yr) 18 -1 HB 1.76 10 sec 1 HB Rg sv c Rgsv 1.703 10 28 cm 2 c Rgsv M sv G Msv 2.294 10 56 gm 3 Msv sv 3 4 Rgsv 2 2 -2 Msv c 2.062 10 77 gm cm sec 29 -3 sv 1.109 10 gm cm
4 H 2 G Rg 2 M B 3 sv sv sv M 2 sv 2c Msv 2.294 10 56 gm
4 H 2 G Rg 2 B 3 sv sv 2.294 1056 gm 7.836 10 36gm-2 erg 4 H 2 G Rg 2 B 3 sv sv c2 2 2 2 me c 1 a0
53 H 2 4G Rg 2 B 3 sv sv 2 2 m 5.9171166768791569021 10 30 1 m c2 12 a e 0 m3 2 sec2 kg sec2 H 2 4G Rg 2 B 3 sv sv 2 4.804 10 10 cm0 gm0 statcoul 1.871 10 30cm0 gm0 sec -1 H 2 4G Rg 2 B 3 sv sv 2 2 m 4.8036086517200301443 10 -14 sec 2 1.871 10 30cm0 gm0 sec-1 sec m2 4.8036086517200301443 10 -14 sec 4.804 10 10cm0 gm0 statcoul sec2 2 36 -2 HB 3.099 10 sec
4 H 2 G B 3 sv 3.099 10 36 sec-2 2 -1 HB Rgsv 2.998 10 10 cm sec 18 HB 1.76 10 Hz Rgsv 1.703 10 28cm
has solution(s) 1 1 2 2 18 H 24 G c 2 B sv 3 H 4 G 28 B sv 1.703 10 cm 1 1.703 10 28 1 2 2 18 H 24 G c 2 B sv 3 HB 4 G sv has solution(s) has solution(s) 1 1 2 2 18 H 24 G c 2 B sv 3 H 4 G 28 B sv 1.703 10 cm 1 1.703 10 28 1 2 2 18 H 24 G c 2 B sv 3 HB 4 G sv
54 has solution(s) 1 1 2 2 18 H 24 G c 2 B sv 3 H 4 G 28 B sv 1.703 10 cm 1 1.703 10 28 1 2 2 18 H 24 G c 2 B sv 3 HB 4 G sv Rgsv 1.703 10 28 cm 18 -1 HB 1.76 10 sec
2 2Msv c 1 2 4.123 1077gmcm sec 2 sec 2 cm3 gm 1 sec 2 gm cm 3 cm2 gm 1 gm cm2 sec-2 2 29 -3 sv 1.109 10 gmcm
8 H 2 G Rg 2 M B 3 sv sv sv 5.296 10 9 cm 3.896 1085gm cm sec-2 (sec 2cm3gm 1sec 2gmcm 3)(cm2)gm 2 1 cm gm cm sec 2 Univerzalna konvertibilnost h 2 s 2 2 2 Re MSc s s 2MS 2 h1 2 2 2 mec 1 2 2me Re 1.14910 592.757i10 65 8.268 10 16 sec-1 2.418 10 17sec 1 2 3 n 4 5 6
55 h 2 h 2 h 2 s 2 2 2 s 2 2 2 s 2 2 2 Re MSc s s Re MSc s s Re MSc s s 2M 2M 2M S S S 2 2 2 2 h h1 2 2 2 h1 2 2 2 h1 2 2 2 s 2 2 2 mec 1 2 mec 1 2 mec 1 2 Re M c 2m 2m 2m S s s e e e 108.853 h 2M Re Re Re s S 1.14910 592.757i10 65 1.14910 592.757i10 65 1.14910 592.757i10 65 27.213 2.0161041gmcm 2.41810 17sec 136.979 4.1641075cm2 sec-2 1.889108cm 1 12.095 2 eV 2 n 6.803 4.354 3.024 U gornjoj jednakosti nalaze se: masa Sunca, masa elektrona, Plankova konstanta (uobicajena) Plankova konstanta za Sunce, brzina svetlosti, za Sunce, za elektron, neki kompleksni brojevi kao koeficijenti, realni delovi kompleksnog broja slozenih formula, - operator,n-vektor i broj 2. Sve je to tako povezano da mora da se dobije niz vodonikovih energetskih stanja. Fizicar,obimno i svesno, vlada svim operacijama i bilo koja formula je, pod odredjenim uslovima, upotrebljiva.
KNovi 1 zadatakK : naci temperature gornjih stanja K 1
h 2 s 2 2 2 Re MSc s s 2 MS 2 h1 2 2 2 mec 1 2 2me Re 1.14910 592.757i10 65 136.979
5.2851013sec2 gm-1 cm-2 2.762 10 16 gm cm2 sec-2 K
56 h 2 h 2 h 2 s 2 2 2 s 2 2 2 s 2 2 2 Re MSc s s Re MSc s s Re MSc s s 2 2 2 MS MS MS 2 2 2 2 h1 2 2 2 h1 2 2 2 h1 2 2 2 h mec 1 2 mec 1 2 mec 1 2 s 2 2 2 2m 2m 2m Re MSc s s e e e h 2M Re Re Re s S 1.14910 592.757i10 65 1.14910 592.757i10 65 1.14910 592.757i10 65 5 6.315 10 2.0161041gm cm 2.41810 17sec 136.979 4.1641075cm2 sec-2 1.889108cm 1 1.579 10 5 2 n2 7.017 10 4 2 K h 3.947 10 4 s 2 2 2 Re MSc s s 2 4 MS 2.526 10 2 h1 2 2 2 1.754 10 4 mec 1 2 2me Re 1.14910 592.757i10 65 136.979 K 1 2 -1 -2 5.285 10 13sec gm cm h 2 h 2 h 2 s 2 2 2 s 2 2 2 s 2 2 2 Re MSc s s Re MSc s s Re MSc s s 2 2 2 MS MS MS 2 2 2 2 h1 2 2 2 h1 2 2 2 h1 2 2 2 h mec 1 2 mec 1 2 mec 1 2 s 2 2 2 2m 2m 2m Re MSc s s e e e h 2M Re Re Re s S 1.14910 592.757i10 65 1.14910 592.757i10 65 1.14910 592.757i10 65 6 1.263 10 2.0161041gm cm 2.41810 17sec 136.979 4.1641075cm2 sec-2 1.889108cm 1 3.158 10 5 2 n2 1.403 10 5 K 1 4 kb K 7.895 10 5.053 10 4 3.509 10 4 5 1.579 10 13.607 4 3.947 10 3.401 4 1.754 10 1.512 k eV b 9.868 103 0.85 6.316 103 0.544 4.386 103 0.378
57 h 2 h 2 s 2 2 2 s 2 2 2 Re MSc s s Re MSc s s 2M 2M S S 2 2 h1 2 2 2 h1 2 2 2 mec 1 2 mec 1 2 2me 2me 8.719 10 11 Re Re 1.14910 592.757i10 65 1.14910 592.757i10 65 cm 2.18 10 11 e 136.979 1.889108cm 1 12 2 9.688 10 gm cm2 sec-2 n2 5.449 10 12 3.488 10 12 2.422 10 12 G 6.672 10 8 cm3 gm-1 sec -2 2 0.5 1.199i 10 6 G MS MS U Rs
2 3 1 2 gm cm gm sec 1 erg cm 2 2 MS c s 2 -2 Es 3.793 10 48 gm cm sec
3 Vs Rs
2 els MS vs Rs Es U s 1.711 10 16 1.101i 10 31 Es els E s 2 Rs
MS H c s 3 Rs 2 MS vs En s 2 2 V s s 2 2 25 E H dV 3.773 10 48 gm cm2 sec-2 s s s 8 0
58 0.04 1 25 U 3.793 10 48 gm cm2 sec -2 h 2 G M M s 2 S S 2 -2 a 3.793 10 48 gm cm sec 2 MS Rs 3 MS s 3 4 Rs h 2 s 2 Ens U s 2 MS 3.793 10 48 2.168i 10 29 gm cm2 sec-2 0.5 3.216i 10 16 G 6.672 10 8 cm3 gm-1 sec -2 0.024
1 2 tH 4 G 1.181 10 6 sec-2 2 s 1 2 tH 5.021 10 36 sec -2 2 2 vs a1 Rs 2 3 1 2 gm sec cm gm sec 2 sec-2 cm3
3 1 2 gm cm gm sec 1 sec -2 cm3 G s 4 1.314 10 27 cm-2 c2 h 2 G M M s 2 S S 2 -2 Ens 2 3.793 10 48 gm cm sec 2 MS Rs 0 cm-1
59 GMSMS Rs 1 h 2 G M M s 2 S S Ens 2 2 MS Rs h 2 s 2 0 gm cm2 sec -2 2 MS 2 2 0 gm cm sec 0 gm cm2 sec -2 2 -2 Ens 1.896 10 48 gm cm sec a 1
2 MS G MS de1 2 a a 2 hs Rs a 2 0 30075000. h 2 me G Md cm de1 2.064 10 22 cm-2
1 de1 6.96 10 10 cm 1 de1 1 Rs Resi 2 1 me G Md 3.325 10 8 cm 2 h a0 1 h 2 s -2 2.064 10 22 cm MS vs
2 d2 me G Md 2 6.015 10 7cm-1 dx2 h2 a 2 0 MS G MS 2.064 10 22 cm-2 2 hs Rs
60 Es ts 7 expi hs
M 2 G M d2 S S 6 2 6 2.064 10 22cm-2 2 dx2 hs Rs Es ts a expi hs R 2 s 1.0320000000000000000 10-22 h 0.5 s 3 MS G cm2 a 1 x 1 cm M 2 G M d2 S S a a 2.064 10 22 cm-2 2 dx2 hs Rs Es ts expi hs 2 4.129 10 22 cm 4.129 10 22 cm-2
2 1 2.064 10 22 cm 1 Rs R 2 s 2.0640000000000000000 10 -22 h 1 s 3 MS G cm2 xFunkcija 1 cm je talasna duzina
2 MS G MS 1.437 10 11 cm-1 2 hs Rs a 2 0 30075000. h 2 me G Md cm
8 2 a0 3.325 10 cm 3.325 10 8 cm
61 h 3.325 10 8 cm me v
2 MS G MS 2.064 10 22 cm-2 2 hs Rs R 2 s 3 3.3 10 -11 h s 3 MS G cm
M 2 G M d2 S S 5 5 2.064 10 22cm-2 2 dx2 hs Rs 1 6.6 10 11cm-1 1.515 10 10 cm R 2 s 5 2.1 10 -22 h s 3 MS G cm2 M 2 G M d2 S S 5 5 2.1 10 22 cm-2 2 2 dx hs Rs x 1 cm z 1 cm y 1 cm h 2 G M M s 2 S S s 2 MS Rs h1 1.055 10 27gmcm2 sec-1 M 2 G M 2 S S 5 5 2.1 10 22 cm-2 2 hs Rs 28 me 9.109 10 gm
M 2 G M d2 S S 3 2 3 6.671 10 11cm 1 dx2 h 2 R s R s 2 s 3.4 10-11 h 1.647 1011 cm s 3 MS G cm
62 R 2 s 4 3.3 10 -11 h s 3 MS G cm
2 1 MS G MS 4 2 hs Rs 0.435 Rs R 2 s 3.3355000000000000000 10 -11 sec h 1.616 10 11 cmsec s 3 MS G cm R 2 s 2.0645000000000000000 10 -22 h 1 s 3 2 MS G cm R 2 s 2.0645000000000000000 10 -22 h 1 s 3 2 MS G cm
2 me G Md 2 6.014 107 cm-1 2 h a0 2 1 me G Md 2 h a0 6.284 a0
Dimenzionom analizom je dokazano da je1 gornja formula istinita gm2 cm3 gm 1 sec 2 gm 4 cm gm2 sec2 sec4 1 cm 1 gm2 cm3 gm 1 sec 2 gm 4 cm gm2 sec2 sec4 2 6.283 cm
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