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 electricity 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, rejDulsive 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 pur2:>oses of measurement, for which Coulomb's balance would not answer. These are the class of mulfipliers. Valuable and delicate as they are, they have uot 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.
ELECTRICAL STATICS.
The second part of electrology includes what is improperly called electrical statics; a term imj^utable to illusory hyjiotheses 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 distribirtion ^ody, 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 sui-face, 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 imjjortance, 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 points, disclosed by Franklin.^ „.. The laws of electric equilibrium between e(inilibriuin. several contiguous bodies afford a yet more difficult and extensive inquiry. Coulomb ^ Much has since been added to this class of investigations. — J. P. N.
ELECTRICAL STATICS AND DYNAMICS. 307 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 by each surface is more or less persistent, and manifests itself with moi'e or less rapidity, accoi'ding 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 mates no diffei'ence 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 i-esearch.^ ELECTRICAL DYNAMICS.
The third part of electrology is very pro- a >. >, perly called Electrical Dynamics, because it exiieriments 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 laboiu's of M. Ampere; always su])posing conjectures about the nature of electric phenomena to be discarded. M. Ampere ^ These specific facts are now comprehended witliin <j;eneral Laws.— J. P. N.
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 voltaic piles, habitually reduced to their greatest simplification; that is, almost always comj)osed of a single element.
M. Ampere so arranged his experiment as to guard the conducting threads from the perturbing influence of the earth's electricity; and this done, 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 jilace tiiemselves in directions ^^arallel 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 sake 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, thei-e 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, u,nd 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. Ampere. In the other case, — of the conductors not being in the same plane, — the action depends moreover on the mutual inclination of the j^lanes indicated by each of them, and by the common line of their middle j^oints; and the result of this second relation is wholly different. The perpendicularity of 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 maxiiinivt takiug place at the moment of coincidence; when the auffle is obtuse, the action becomes repellent, and increases as each plane approaches towards the prolongation of the other, a situation which ])roduces the maximiim 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; hut we have not yet attained such certainty as in the former case.
As for the influence of distance, M. Ampere 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 analogy 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 form and magnitude of the conductors. However, it may be mathematically demonstrated that, in the hypothesis adopted by M. Ampere, 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 transfen-iug 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 excey-)t 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. Ampere; 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, what- 310 - POSITIVE PHILOSOPHY.
ever 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 esjjecially when the turns are very close together. M. Ampere has shown the high importance of this form, in order to imitate, as exactly as possible, the phenomena characteristic of magnetized bodies.'
Physics x^hysics, noticing m turn the as])ects 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 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 philosoi:)hy, 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 ' M. Comte concludes the section on Electricity by a sHglit reference to tlie discoveries of Oersted, Araj;() and otliers, regarding its virtual identity with ail we term tiie magnetic forces. But as the whole of this most interesting and impoi-tant part of Physics has taken a new form siu(;e the date of his work, it lias not, for reasons assigned in tlie Preface, heen thought necessary to reproduce his remarks in this i)lace. — J. P. N.
CONCLUSION OF PHYSICS, 311 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 dej^artment 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, thi'ough the means afforded by its subordination to the anterior sciences.
Its nature. VV E 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 thei*e 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 jjrofound 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 consciousness, — Life: and we can easily understand that the primitive method of philosophizing must have exerted a more powerful and obstinate dominion over chemical l)henomena 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 difliculty IMPERFECTION^ AND CAPACITIES OF CHEMISTRY. 313 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 and perseverance to discover the principal phenomena of the science if they had not been constantly stimulated by the unbounded hopes arising from their chimerical notions of the constitution of matter. The complex and doubtful nature of the phenomena, in the /.. ^. • first place, and next the difl&culty of getting fection"^^^ at them, are quite enough to account for the tardy and incomplete j)ositivity of chemical conceptions, in comparison with all others in the inorganic region of nature. If, as we have seen. Physics is defective in several respects, much more must that science be so which, being at once more difficult and more recent, seeks the laws of composition and decomposition. Whichever way we look at it, whether speculatively, as to the value of its explanations, or actively, as to the previsions which they admit of, this science is evidently the least advanced of all the branches of inorganic philosophy. Indeed, it is hardly possible to call chemistry a science at all Avhile it scarcely ever leads to that precise prevision which is the criterion of perfection in speculative knowledge. We can rarely tell what will be the result of the smallest and fewest modifications introduced among the best explored chemical operations; and while that is the case, however important and numerous may be the facts collected, we are in possession of only erudition, and not science. To supjiose otherwise is to mistake a quarry for an edifice.
It is not to be hoped that chemistry can,-, ever attain a state of rationality so satisfactory as that of the sciences which relate to phenomena of a more simple character; and especially that of the eternal type of natural philosophy, — Astronomy. But so much of its inferiority seems to be due to a vicious philosophy, and to the defective education of philosophers, that I cannot but hope that a judicious philosophical analysis may contribute to a speedy perfecting of so important a science. This is the conviction that I desire to awaken by the rapid sketch which I propose to offer of chemical philosophy, regarded in all its essential aspects. Little as can be done within the bounds of tliis section, it is possible that some one eminent inquirer may be impressed by the necessity of suljmitting to a new and more rational elaboration the fundamental concej)tions which constitute the science.
„-.. First, — what is the general object of Cheniistrv Chemistry? Vast and complex as is its subject, the definition of Chemistry is easier than that of Physics. We are already prepared for it, indeed, by having contrasted that of Physics with it. It is easy to characterize the phenomena of chemistry, in a direct and marked manner; for all indicate an alteration, greater or smaller, in the constitution of bodies: that is, a composition or decom2:)Osition, and generally both, taking into the account the whole of the substances which participate in the action. Thus, at all epochs of scientific development, since chemistry first became an object of speculative study, chemical researches have steadily manifested a remarkable originality, which has prevented their being confounded with other parts of natural philosophy; even while Physics itself was was mixed xvp, as its title shows, with physiology; which was the case up to a very recent time. — It is by this general character of its phenomena that Chemistr}^ is distinguished from Physics which precedes it, and Physiology which follows it. The three sciences may be considered as having for their object the molecular activity of matter, in all the different modes of which it is susceptible. Each corresponds to one of three successive degrees of activity, which are essentially and naturally distinguished from each other. The chemical action obviously presents something more than the physical action, and something less than the vital. The physical activity modifies the arrangement of particles in bodies; and these modifications are usually slight and transient, and never alter the substance. The chemical activity, on the contrary, besides these alterations in the structure and the state of aggregation, occasions a profound and durable change in the very composition of the particles: the bodies which occurred in the phenomenon are no longer recognizable, — so much has the aggregate of their properties been disturbed. — Again, physiological phenomena show us the molecular activity in a CHARACTER AND 'CONDITIOX OF CHEMICAL ACTIOX. 315 much higher degree of energy; for, as soon as the chemical combination is effected, the bodies become, once more, completely inert; whilst the vital state is characterized, over and above all physical and chemical effects, by a double continuous motion of composition and decomposition, adapted to maintain, within certain limits of variation and of time, the organization of the body by incessantly renewing its substance. This is the gradation, which no sound philosophy can ever confound, of the three modes of molecular activity.
Two more characteristics of this science must be pointed out: one relating to its nature, and the other to its general conditions.
Chemistry would not be classed among the Specific chainorganic sciences unless its phenomena were racter of its genei'al; that is, unless every substance were action, susceptible of chemical action, more or less. And it is because chemistry is thus radically different from physiology that it ranks as the last of the inorganic sciences, — physiological phenomena being, by their nature, i^eculiar to certain substances, organized in certain modes. Nevertheless, it is incontestable that chemical phenomena present, in every case, something specific, or, to use Bergm aim's energetic expression, elective. Not only does each material element produce chemical effects which are altogether peculiar to it, but it is the same with their innumerable combinations of different orders, among the most analogous of which certain fundamental diiferences are observable, even so as to be adopted as their characteristics. While therefore physical differences among different bodies are those of degree only, chemical properties are specific. Physical properties afford the common foundation of material existence; and it is by chemical properties that individuality is manifested.
The other characteristic relates to the p,.. mode of chemical action. The immediate ac^t'ion ^*'" ° contact of antagonistic particles is absolutely necessary to chemical action; and therefore one at least of the substances concerned must be fluid or gaseous. When this condition does not already exist, it must be artificially procured by liquefying the substance. It is the earliest axiom in the science, that comhination cannot take place, except under this condition; and there is not an instance upon record of chemical action between two solids, unless at a temjjerature which obscures the true state of as^gregation of substances; and the action is never so j^owerful as when both substances are liquid. These facts establish the eminently molecular character of chemical effects, and especially in comparison with physical effects. The distinction from physiological effects is, though less marked, as real, the latter requiring, as we shall see hereafter, the junction of solids with fluids. „ ^.. The definition of Chemistry, then, is that it relates to the laws of the phenomena of composition and decomposition, which result from the molecular and specific mutual action of difl'erent substances, natural or artificial.
It will be long, we must fear, before a more precise definition than this can be given. Meantime, however incomplete, the most rational that can as yet be offered is of imjjortance as far as it goes. In this view, and connecting, as usual, the consideration of science with that of prevision, the aim proposed should be this: — the characteristic properties of substances, simple or compound, being given, and those properties being placed in a chemical relation in well-defined circumstances, to determine in what their action will consist, and what will be the chief properties of the new products. This problem is, at all events, determinate; and nothing contained in it could be omitted without its ceasing to be so; and the formula therefore contains nothing superfluous. On the other hand, if we could obtain such solutions as are indicated, the application of chemistry to the three great objects, vital phenomena, the natural history of the globe, and industrial operations, would be rationally organized, instead of being, as now, the almost accidental result of the spontaneous development of science. Each question would at once be referred to our formula, the data of whi<-h would be supplied by the circumstances peculiar to the apj^lication. Far distant as we are from being able thus to conduct our inquiries, this is the end to be kept in view: and chemists all agree that the most advanced portions of their science are those few ELEMENTS AND THEIR COMBINATIONS. 317 and simple questions in which this aim has been more or less completely attained.
By a continued application of this method, all the data must finally be reducible to the knowledge of the essential proj^erties of simple substances, which would lead to that of the different immediate principles: and consequently, to the most comj^lex and remote combination. As for the study of the elements, that must, of course, -p, be a matter of direct, experimental elaboration, divided into as many parts as there ai*e undecomposed substances. Whether or not it may be possible to discover, by rational methods, relations between the chemical properties of each element and its aggregate physical properties, we must lay down as indispensable a direct exploration of the chemical characters of each element. This general basis once obtained from experiment, all other chemical problems must be susceptible of a rational solution, under a small number of invariable laws.
The classes of combinations naturally divide ^, i •. f themselves into two, according, first, to the simplicity, or the greater or less degree in which the immediate pi'iuciples are compounded: and, secondly, the number of elements combined. Chemical action is observed to become more difticult the more substances are compounded: the greater part of compound atoms belong to the first two orders; and beyond the third their comjiosition seems almost impossible: and, in the same way, in regard to the number of elements, combinations lose their stability in proportion as the elements are multiplied: there are usually only two; and scarcely any body involves more than four. Thus, the number of chemical classes must always be very small in regard to the distinction under notice: and each of them must have a corresponding law of combination, according to which the result might be certainly auticii^ated through a knowledge of the data. This would be the scientific perfection of chemistry. Our prodigious remoteness from such a state is ascribable to the feebleness of our faculties, and, in an accessory way, to their vicious direction. We must remember that the great aim has begun to be fulfilled in one secondary department of chemical research, — the study of proportions, as we shall see hereafter.
318 POSITIVE PHILOSOPHY".
What has been done in that one category makes us ask why an analogous perfection should not be attained in other departments. We may sum up this account of the requi-Rational sites, with the fully rational definition of definition. Chemistry, that it has for its object, — the properties of all simple bodies being given, to find those of all the compound bodies which may be formed from them. Every science falls short of its definition: but a real definition is the first evidence that a science has attained some consistency: it then measures its own advancement from one epoch to another; and it always keeps inquirers in a right direction, and supports them in a philosophic progress.
-_.. Looking now at our means of investigation, vestio-ation ^^^ shall find that in chemistry the law holds good that the complication of phenomena coincides with the extension of our means of inquiry. ^,.,. Here Observation begins to find its full development. Up to this time it has been more or less j^artial. In astronomy, it is confined to the sense of sight: in physics we use hearing and touch also; and chemistry employs, besides these, taste and smell. How much is thus gained we may know by imagining what would become of chemistry, if we were without taste and smell, which are often the only means by which we can recognize effects produced. The important thing to observe under this head is that thei'e is nothing accidental, nor even empirical, in such a correspondence; for, as we shall hereafter see, the sound physiological theory of sensations shows that the apparatus of taste and smell, unlike that of the other senses, operates in a chemical manner, and thus shows these two senses to be specially adapted for the percej^tion of phenomena of composition and decomposition. -n,., As for E'ajBenmewi, it is enough tosay that the greater number ot cliemicai ]inenomena, and especially the most instructive, are of artificial jiroduction. Still, we must remember that the essential character of experimentation consists in the institution, or the choice of the circumstances of the phenomenon, in order to a more evident and decisive investigation. This j)ro- MEANS OF INVESTIGATION. 319 cess is more difficult in cliemistry than in physics, because it is more difficult to institute two parallel cases, undisturbed by the intrusion of irrelevant influences; and yet this is the fundamental condition of experimentation. On this account, I dissent from the ordinary supposition that the experimental method is more appropriate to chemical than to physical researches. Though this is my view, and though the greater advancement of physics gives it the advantage over chemistry, in the use of experiment, I can liave no doubt of the powerful influence of experimentation in chemistry, independently of its having supplied new subjects of observation. From the early days of the science, the immortal series of Priestley's experiments, and yet more, those of Lavoisier, have offered admirable models, almost comparable to the most perfect researches in physics, and qviite enough to prove that there is nothing in the nature of chemical phenomena to prevent the extended and luminous employment of the experimental method.
The third means. Comparison, which we p have before seen to be inapplicable in Astronomy, and of especial use in Physology, begins to have a real use in Chemistry. The essential condition of this valuable method is that there shall be an extended series of cases, analogous but distinct, in which a pheuomenon shall be modified more and more, whether by successive simplifications or gradations. It is evident that this can take place fully only with regard to vital phenomena; accordingly, it is only by physiological analysis that a clear idea of its value can be obtained. But chemical phenomena approach those of physiology nearly enough, not onlv to demand this method, but to indicate that without it the science can never find the road to perfection. The existence of natural families in chemistry is now admitted by the best inquirers: but the classification remains to be made. The need of the classification must lead to the use of the comparative method, both being based on the common consideration of the uniformity of certain preponderant l^henomena in a long series of different bodies. There is even such a connection between the two orders of ideas that the construction of a natural chemical classification is impossible without a large aj)plication of the comparative