Comte - The positive philosophy. Vol. 1

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an inferior place, with the rest.

No other science offers so great a variety of curious and important phenomena; but facts do not constitute science, though they are its foundation and material. Science consists in the systematizing of facts under established general laws: and, regarded in this way, Electrology is the least advanced of all the branches of Physics, imperfect as they all are. In the absence of ascertained laws, arbitrary hypothesis has run riot. The simple confidence with which students have explained all phenomena by endowing imaginary fluids with new properties for every fresh occurrence, reminds us of the old metaphysical explanations,—the ancient entities being merely replaced by supposed fluids. But the delusion is less mischievous here than in Optics, where the arbitrary conjectures are closely connected with real laws, and share their imposing character. In electrology the hypotheses, standing alone, exhibit their barrenness; and everybody can see that they have borne no share in the great discoveries of the last half-century, though the discoveries once made, have been afterwards attached to the hypotheses. Most people regard them now as a sort of mnemonic apparatus, useful for connecting facts in the memory, though originally designed for a very different purpose. They are a bad apparatus for even this object, which would be much better answered by a system of scientific formulas especially adapted to that use. And though less mischievous than in Optics, hypotheses of this order do harm in electrology, as everywhere else, by concealing from most minds the real needs of the science. It should be remembered, moreover, that anti-scientific action like this extends its influence over the succeeding and more complex sciences, which, on account of their greater difficulty, require the severest method, the type of which will naturally be looked for in the antecedent sciences. It is a serious in jury to transmit to them a radically vicious model. While physicists are using these hypotheses as having avowedly no intrinsic reality, their very use leads students of the successive sciences, and especially physiologists, to consider them the very sublimity of physics, and to proceed to take them for the bases of their own labours. We see how the notion of magnetic and electric fluids tends to confirm that of a nervous fluid, and to encourage wild dreams about the nature of what is called animal magnetism, in which even eminent physicists have shared. Such consequences show how a. study which is naturally favourable to the positive development of human intelligence may, by vicious methods of philosophizing, become fatal to our understandings.

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From the complex nature of the phenomena, there can be but little application of mathematics in electrology. It has as yet borne only a small share in the progress of the science: but it is as well to point out the two ways,—the one illusory, the other real,—in which the of mathematics has been attempted.

Those who have occupied themselves with imaginary fluids as the causes of electrical and magnetic phenomena, have transferred the general laws of rational mechanics to the mutual action of their molecules; thus making the body under notice a mere substratum, necessary for the manifestation of the phenomenon, but unconcerned in its production; with which office the fluid is charged. It is clear that mathematical labours so baseless can serve no other purpose than that of analytical exercise, without adding a particle to our knowledge. In the other case,—of a sound application,—the mathematical process has been based on some general and elementary laws, established by experiment, according to which the study of phenomena proper to the bodies themselves has been pursued,—all chimerical hypotheses being discarded. This is the character of the able researches of M. Ampère and his successors, on the mathematical investigation of electro-magnetic phenomena, in which the laws of abstract dynamics have been efficaciously applied to certain cases of mutual action between electric conductors or magnets.

In examining the principal parts of electrology, we must exclude all that belongs to the chemical or physiological influence of electricity, and all connection of electricity with concrete physics; and especially with meteorology.

Thus limited to the physical and abstract, electrology at present comprehends three orders of researches. The first relates to the production, manifestation, and measurement of electrical phenomena: the second, to the comparison of the electric state proper to the different parts of the same mass, or to different contiguous bodies: the third, to the laws of the motions which result from electrization: we may add, as a fourth head, the application of the results under the other three to the special study of magnetic phenomena, which can never henceforth be separated from them.

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Section I

Electric Production

The sum of our observations leads us to regard the electric condition of bodies as being, more or less evidently, an invariable consequence of almost all the modifications they can undergo: but the chief causes of electrization offer themselves, in the order of their power and scientific importance, thus: chemical compositions and decompositions: variations of temperature: friction: pressure: and, finally, simple contact. This distribution differs widely from that first indicated by inquiry,—friction being long supposed the only, and then the most powerful means of producing the electric condition. The comparison of means is very far from being exhausted; but we may be assured that the order specified above will never be radically changed

There is no doubt that chemical actions are the most general sources of electricity, as well as the most abundant; as they are with regard to Heat. In the most powerful electrical apparatus and especially in the Voltaic pile, the chemical action, which at first passed unnoticed, is now recognized, thanks to the labours of Wollaston and others, as the principal source of electrization, which becomes indeed almost insensible when care is taken to exclude chemical action.—After this, the next most powerful cause is thermological action, though, till recently, it was recognized only in the single case of heated tourmalin. We now know that marked differences of temperature between consecutive bars of different kinds, whether homogeneous or otherwise in the particular case, suffice to induce a marked electrical condition, the more intense as the elements are more numerous,—the thermometrical conditions remaining the same.—These two causes are so powerful, and so difficult to exclude, that the estimate of the others becomes a very delicate matter. It is difficult to determine how much influence to ascribe to any cause after these two, while yet they are almost unavoidably present.

Thus, even about friction, which used to be regarded as so powerful a cause, it is now doubtful whether the friction itself has any influence, and whether the electrization is not due to the thermometrical, and even the chemical effects which always accompany friction, but which used to be altogether overlooked in this instance.

The case is nearly the same with Pressure, the electric influence of which however is, if less marked, more unquestionable, from our being able to isolate it more. But the remark is above all applicable to the production of the electric state by the simple contact of heterogeneous

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bodies. It was by this contact that Volta brought out the power of his wonderful instrument, while it is well known now that chemical action bears a chief part in it, and that contact contributes to it in only a secondary maimer, if even it be not altogether doubtful.

Besides these leading causes of electrization, there are many less important,—as changes in the mode of aggregation, the fusion of solids, and the evaporation of liquids. Even simple motion suffices, under special conditions, to induce an electric state, as M. Arago has shown in the experiment of the influence of the rotation of a metallic disc upon a magnetized needle, near but not contiguous. Our philosophers however must beware of passing into the other extreme from that with which they justly reproach their predecessors. It is, no doubt, prejudicial to electrology to neglect all sources of electrization but the most conspicuous: but it may be not less so to carry analysis too far, and see causes of electrization in all sorts of minute phenomena.[In this paragraph, M. Comte alludes to the now most fertile, but when he wrote, the comparatively unknown subject of the development of Electricity by Induction.— J. P. N.]

A special instrument, or class of instruments, naturally corresponds to each of the general modes of electrization, in order to realize the most favourable conditions for the production and support of the electric state. However important these may be, it is clear that we cannot here enter upon the consideration of them. But we must not pass over the instruments invented for the manifestation and measurement of the electric condition,—the electroscope and the electrometer. The most eminent philosophers have always attached the highest importance to the perfecting of these instruments, in the invention of which real genius has often been exhibited. Their perfection is of more consequence than that of electric producers; because very weak electric powers often answer best in delicate experiments, from their simplicity; while the utmost ingenuity is required in instituting means of manifesting and measuring the minutest electric effects.—Though the electric condition cannot be measured without being first manifested, and the manifestation leads to some sort of estimate, there is a real distinction between electroscopes and electrometers. Among simple electroscopes, the most remarkable for use in very delicate researches is that kind called condensers, which render feeble electrical effects sensible through their gradual accumulation: and all these instruments are so arranged as to show, by the method of experimentation itself, the positive or negative character of the elec-

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tricity under notice.—Coulomb’s electrical balance is certainly the most perfect of electrometers. It was by its means that he discovered, and that we every day demonstrate, the fundamental law of the variation of electric action, repulsive or attractive, inversely to the square of the distance; a law which could not be unquestionably obtained by any other means. As we have advanced in the science of electromagnetism, a new class of electrometers has been introduced, for purposes of measurement, for which Coulomb’s balance would not answer. These are the class of multiplers. Valuable and delicate as they are, they have not yet been applied, with so much certainty as the balance, to exact measurements, from the difficulty of proportioning the graduation to the intensity of the observed phenomenon.

Section II Electrical Statics

The second part of electrology includes what is improperly called electrical statics; a term imputable to illusory hypotheses about the nature of electricity: yet it is not a wholly absurd title, as it relates, in fact, to the distribution of electricity in a mass, or in a system of bodies, the electric state of which is regarded as invariable. We may therefore continue to use this abridged term, if we carefully keep clear of all mechanical notions of the equilibrium of any supposed electric fluid, and attach to it a sense analogous to that of Fourier, when he spoke of an equilibrium of heat, and of economists when they speak of an equilibrium of population.

Considering first the case of an isolated body, Coulomb has established a fundamental law which is (metaphorically expressed) the constant tendency of electricity to the surface, or, in rational language, that after an inappreciable instant of time electrization is always limited to the surface, however it may have been in the first place produced. As for the distribution of the electric state among the different parts of the surface, it depends on the form of bodies, being uniform for the sphere alone, unequal for all other forms, but always subject to regular laws. The analysis of these may be supposed to present insurmountable difficulties; nevertheless, Coulomb has established a general fact of great importance, by comparing the electric states proper to the extremities of an ellipsoid gradually elongated: he has perceived that their electrization increases rapidly as the figure is elongated, diminishing in the rest of the body; whence he deduced an explanation of that remarkable power of

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points, disclosed by Franklin. [Much has since been added to this class of investigations.— J. P. N.]

The laws of electric equilibrium between several contiguous bodies afford a yet more difficult and extensive inquiry. Coulomb studied them only in the limited and insufficient single case of spherical masses. However, we learn from his labours that the nature of substances exercises no influence over the electric distribution established among them, the mode depending merely on their form and their magnitude; only, the electric state assumed be each surface is more or less persistent, and manifests itself with more or less rapidity, according to the degree of conductibility in the body. Coulomb analysed completely the mutual action of two equal spheres; discovering that the electric condition is always null at the point of contact, scarcely sensible at 20 degrees from that point, fast increasing from 60 to 90 degrees, and then more slowly increasing up to 180 degrees, Which is its maximum. If the globes are unequal, the smallest is the most strongly affected: and it makes no difference whether they are electrized together, or the one before the other. The question becomes more complex when more than two bodies are concerned. Coulomb examined only a series of globes ranged in a straight line; but if they had been so placed as that each should touch three or four others, the mode of electric distribution would inevitably have undergone great changes. The subject must be regarded as merely initiated by this great philosopher; and no one has added anything to it since his time. It offers to electricians a subject of almost inexhaustible research. [These specific facts are now comprehended within General laws.—J. P. N.]

Section III Electrical Dynamics

The third part of electrology is very properly called Electrical Dynamics, because it relates to the motions which result from electrization. Recent as is its origin, it is superior to the others in its scientific condition, through the labours of M. Ampère; always supposing conjectures about the nature of electric phenomena to be discarded. M. Ampère has referred the analysis of the effects observed in this branch of electrology to one great and general phenomenon, the laws of which he has fully ascertained; the direct and mutual action of two threads, charged with electricity by piles, habitually reduced to their greatest simplification; that is, almost always composed of a single element.

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M. Ampère so arranged his experiment as to guard the conducting threads from the perturbing influence of the earth’s electricity; and this clone, he could easily seize the elementary laws of the phenomenon under his notice. He found that when the two conductors are sufficiently mobile, they tend to place themselves in directions parallel to each other; and that they then attract or repel each other, according to the conformity or contrariety of the two electric currents. In looking for the laws of the case, it is necessary, for the salve of generality and simplicity, to keep in view only infinitely small portions of the different conductors. These laws, mathematically considered, relate either to the influence of the direction, or to that of the distance.

As to the direction, there are the two cases to be considered of the conducting elements being in the same plane, or in different planes. In the first case, the intensity of the action depends only on the angle formed by each of the two elements with the line which joins their middle points: it is null at the same time with this angle, and increases with it, attaining its maximum when it becomes right. All phenomena, direct or indirect, appear to be exactly represented if this intensity is made to vary in proportion to the sine of the inclination, according to the formula adopted by all the successors of M. Ampère. In the other case,—of the conductors not being in the same plane,—the action depends moreover on the mutual inclination of the planes indicated by each of them, and by the common line of their middle points; and the result of this second relation is wholly different. The perpendicularityof the two planes determines the absence of all action: there is attraction while the angle is acute, and it increases as the angle diminishes, its maximum taking place at the moment of coincidence; when the angle is obtuse, the action becomes repellent, and increases as each plane approaches towards the prolongation of the other, a situation which produces the maim of repulsion. The supposition which arises in this case is that the action is in proportion to the cosine of the angle of the two planes; but we have not yet attained such certainty as in the former case.

As for the influence of distance, M. Ampère supposed that, in analogy with Coulomb’s law of common electric attraction and repulsion, the action of two conducting elements is always reciprocal to the square of the distances of their middle points. But analog is not sufficient to conclude upon; and direct observation is out of the question when the parts taken are infinitely small, and the result sought must be affected by the forin and magnitude of the conductors. However, it maybe math-

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ematically demonstrated that, in the hypothesis adopted by M. Ampère, the action of a rectilinear conductor, of an indefinite length, upon a magnetized needle, must vary exactly in the inverse ratio of their shortest distance. This consequence has been precisely verified by experiment; and it places beyond a doubt the reality of the proposed law.

Under this law, electric action would seem to be, mathematically, in analogy with that of gravitation. But this case affords a lesson against incaution in transferring to the study of these singular movements the ordinary procedure of abstract dynamics. Gravitation is independent of mutual direction, which is the determining influence in electrical dynamics: and thus the parallel fails. We see, further, how many more difficulties are in the way of the analysis of electric forces than in that of molecular gravitation. If this last is, from its complexity, unmanageable except in the simplest cases, it is no wonder that electrical dynamics has not been mathematically studied further than in one dimension, and never at all in surface. Even this much would be hardly effected but for a last fundamental idea, established by M. Ampère; that in an infinitely small extent, and as long as the distance is not sensibly changed, the electric action is identical for two conducting elements issuing at the same extremities, whatever may be otherwise their difference of form. Such a property must introduce valuable analytical simplifications, tending to establish a remarkable analogy between electric, and ordinary dynamic decompositions.

These are the grounds on which the study of the various action of electrized threads proceeds. Among the many dispositions of these conductors, the most interesting case is that of the spiral form; and especially when the turns are very close together. M. Ampère has shown the high importance of this form, in order to imitate, as exactly as possible, the phenomena characteristic of magnetized bodies.[M. Comte concludes the section on Electricity by a slight reference to the discoveries of Oersted, Arago and others, regarding its virtual identity with all we term the magnetic forces. But as the whole of this most interesting and important part of Physics has taken a new form since the date of his work, it has not, for reasons assigned in the Preface, been thought necessary to reproduce his remarks in this place.—J. P. N.]

We have now reviewed the philosophy of Physics, noticing in turn the aspects presented by the study of the properties common to all substances and all structures. These are not so much branches of a single study as distinct sciences. Part of our business has been to carry on a

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philosophical operation, hardly necessary in astronomy, but becoming more and more so as we descend to the more complex sciences;—that of disengaging real science from the influence of the old metaphysical philosophy, under which it still suffers deplorably, and which manifests itself in Physics through illusory and arbitrary conceptions about the primitive agents of phenomena. I have been able only to indicate the mischief, and where it resides, and I must leave the work of purification to rational philosophers, whose attention will, we must hope, be more and more drawn to this vital question. It is with the same view that I have endeavoured to assign the true application of mathematical theories to the principal branches of physics, pointing out by the way the danger of the excessive systematization which is too often sought by carrying the use of this powerful instrument further than the complex nature of the corresponding phenomena would fairly allow. While giving my chief attention throughout to the method, I have pointed out, in brief, the principal natural laws relating to each department of science, discovered by human effort during the two centuries which have elapsed since the birth of Physics, properly so called: and I have shown what gaps are disclosed in the course of such a survey.

Our next study will be of the last science which belongs to the class of general knowledge, or that of inorganic nature. Chemistry relates to the molecular and specific reactions which different substances exert upon each other. It is a more complex, and consequently more imperfect science than those which we have reviewed: but its general character may be perfected, through the means afforded by its subordination to the anterior sciences.

Book IV: Chemistry

Chapter I

We have now to review the last of the sciences which relate to the inorganic world. Chemistry has for its object the modifications that all substances may undergo in their composition in virtue of their molecular reactions. Without this new order of phenomena, the most important operations of terrestrial nature would be incomprehensible to us; and there is no other class of phenomena so intimate and so complex. Inert bodies can never appear so nearly like vital ones as when they produce in each other those rapid and profound perturbations which characterize chemical effects. We shall see hereafter that the spirit of all theological and metaphysical philosophy consists in conceiving of all phenomena as analogous to the only one which is known by immediate con- sciousness,—Life: and we can easily understand that the primitive method of philosophizing must have exerted a more powerful and obstinate dominion over chemical phenomena than any other, in the inorganic world.—We must consider, too, that direct and spontaneous observation must have been applied in the first place only to very complicated phenomena, such as vegetable combustions, fermentations, etc., the analysis of which now requires all the resources of our science: and that the most important chemical phenomena are produced only in artificial circumstances, which were long in being devised, and very difficult at first to institute. Easy as it is now for even the most ordinary inquirers to use known substances for the disclosure of new relations, we can hardly imagine the difficulty there must have been, in the infancy of chemistry. in creating suitable subjects for observation: and we cannot suppose that the ancient investigators of nature could have had energy