science itself doubtful to impartial minds.
Newton's discoveries on elementary colours. 297 Newton's discoveries of the unequal re- Newton's dis- frangibility of the different elementary coveries on colours form an indispensable complement elementary of the law of refraction. From the fact of colours, the decomposition of light in a prism, it clearly follows that the relation of the sine of incidence, though constant for each colour, varies in the different portions of the solar spectrum. The total increase which it undergoes from the red rays to the violet measures the disjjersion proper to each substance, and must complete the determination of its re- fracting power in the common tables, where only the mean refraction can be inserted. This estimate constitutes, from its minuteness, one of the most delicate ojierations of optics, and does not admit of so much exactness as that of the re- fracting action properly so called, especially in bodies which bend the light but little, as the gases; but it is ascertained for a considerable number of substances, solid or liquid. In comparing the changes of the dispersive power as we pass from one body to another, we discover that the varia- tions are not, as Newton supposed, in proportion to the re- fracting power: and indeed we find, in more than one case, that the light is least dispersed by substances which refract it most. The discovery of this discrepancy between two qualities which appear to be analogous was made by Dollond, about the middle of the last century. It is an idea of high importance in Optics, as it indicates the possi- bility of achromatism by the compensation of the opposite action pertaining to two different substances which, with- out that, could not cease to disperse the light but by ceas- ing to bend it.
The laws of refraction show us that there can be none but purely geometrical difficulties in the analysis of the effects of homogeneous media wpon the light which traverses them. The great complication which might arise from the form of the refracting body is diminished in ordinary cases by our satisfying ourselves with plane, spherical, or cylin- drical surfaces: but we should yet find the inquiry embar- rassing, and especially in regard to the dispersion, if we did not confine it to an approximate estimate of the few commonest circumstances.
298 POSITIVE PHILOSOPHY.
SECTION IV.
DIFFRACTION.
The modification called diffraction lias now become one of the essential parts of Optics. It was entered upon by Grimaldi and Newton, advanced by the researches of Dr. Young, and completed by those of Fresnel. It consists of the deviation, always accomj^anied by a more or less marked dispersion, that light undergoes, in passing close by the edges of any body or opening. Its simplest way of mani- festing itself is by the unequal and variously-coloured fringes, some exterior and some interior, which surround the shadows produced in a darkened room. The famous general principle of interferences, discovered by Dr. Young, is the most important idea connected with this theory. It was not appreciated, remarkable as it is, till Fresnel made use of it to explain several interesting phenomena, diflB.- cult to analyse; and, among others, the celebrated pheno- menon of the coloured rings, which were by no means fully accounted for by Newton's admirable efforts. The law of interferences is this: that when two luminous cones emanate from the same point, and follow, for any reason, two distinct courses, but little inclined towards each other, the intensities proper to the two lights neu- tralize and augment each other alternately, increasing by equal and minute degrees, the value of which is deter- mined, the difference in length between the entire paths traversed by the two cones. It is a j^ity that this im- portant principle should have suffered, like the rest, from being implicated with chimerical conceptions on the nature of light.
We have done all that the nature of this Work admits, in regard to Optics; and we must pass over the subjects of the double refraction projier to various crystals, the general law of which was discovered by Huygheus. We must also omit the phenomena of polarization, disclosed by Malus. In what I have brought forward, I hope that, while I have pointed out the gaps in this science, of which we are too DIFFRACTION. 299 little conscious at present, I have also placed in a clear light the great and numerous results obtained during the last two centuries, notwithstanding the disastrous prepon- derance of vain hypotheses about the nature of light over the spirit of rational experimentation.
300 CHAPTER VI.
ELECTROLOGY.
y.. ' I "HIS last branch of Physics, relating as it J- does to the most complex and least manifest phenomena, could not be developed till after the I'est. The electrical machine indeed is as old as the air- jjump; but it was not till a century later that the study assumed a scientific character, through the distinction of the two electricities, Muschenbroek's experiments with the Leyden "jar, and then through Franklin's great meteoro- logical discovery, which was the first manifestation of the influence of electricity in the general system of nature. Up to that time, the isolated observations of philosophers had only suggested the character of generality inherent in this part of Physics, as in all others, by continually adding to the number of substances susceptible of electrical pheno- mena: and it was not till the end of the last century that this department of Physics presented anything like the rational character which belongs to the others. It is owing to the labours of Coulomb that it takes its place, and still an inferior place, with the rest. C d'tion ■^*^ other science offers so great a variety of curious and important phenomena; but facts do not constitute science, though they are its founda- tion 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 ab- ^,. sence of ascertained laws, arbitrary hypohvpotheses thesis has run riot. The simple confidence with which students have explained all phenomena by endowing imaginary fluids with new pro- perties for every fresh occurrence, reminds us of the old metaphysical explanations, — the ancient entities being HYPOTHESES ABOUT ELECTRICITY. 301 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 dis- coveries of the last half-century, though the discoveries, once made, have been afterwards attached to the hypo- theses. 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 esjiecially adapted to that use. And, though less mischievous than in Optics, hypotheses of this order do harm in electrology, as everywhere else, by con- cealing from most minds the real needs of the science. It should be remembered, moreover, that anti-scientific action like this extends its inflvience over the succeeding and more complex sciences, which, on account of their greater difli- culty, require the severest method, the type of which will naturally be looked for in the antecedent sciences. It is a serious injury 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 mag- netism, in which even eminent physicists have shared. Such consequences show how a study which is naturalh' favourable to the positive development of human intelli- gence may, by vicious methods of philosophizing, become fatal to our understandings.
From the complex nature of the pheno- p,,• mena, there can be but little application of Mathematics 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 302 POSITIVE PHILOSOPHY.
illusory, the other real, — iu which the application of mathe- matics has been attempted.
Those who have occupied themselves with aDolication 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 stibstratum, necessary for the manifestation of the phenomenon, but unconcerned in its production; with which office the fluid is charged. It is clear that mathe- matical labours so baseless can serve no other purpose than that of analytical exercise, without adding a cation ^^ 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. Ampere 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 j^rincipal parts of electrology, we must exclude all that belongs to the chemical or physiological in- fluence 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 measui'ement of electrical phenomena: the second, to the comparison of the electric state proper to the different parts of the same mass, or to difiierent con- tiguous 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.
CAUSES OF ELECTRIZATION. 303 SECTION I.
ELECTRIC PRODUCTION.
The sum of our observations leads us to regard the elec- tric condition of bodies as being, more or less evidently, an invariable consequence of almost all the modifications they can undei'go: but the chief causes of elec- trization offer themselves, in the order of [iSon their power and scientific importance, thus: chemical compositions and decompositions: variations of temperature: friction: pressure: and, finally, simple con- tact. This distribution differs widely from that first indi- cated by inquiry, — fi'iction 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; \mt we may be assured that the order sj^ecified above will never be radically changed.
There is no doubt that chemical actions are the most general sources of electricity, as tion™^^^ ^^ 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 Jction"^^"^^"^^^ only in the single case of heated tourmalin. We now know that marked differences of temperature be- tween consecutive bars of different kinds, whether homo- geneous or otherwise in the particular case, suffice to induce a marked electrical condition, the more intense as the elements are more numerous, — the thermometrical condi- tions remaining the same. — These two causes are so jiower- ful, and so difiicult to exclude, that the estimate of the others bec(mies 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.
304 POSITIVE PHILOSOPHY.
T^...Thus, even about friction, which used to be Jriction. \, „ 1...regarded as so poweriul 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.
y. 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 p,,, heterogeneous 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 manner, if even it be not altogether doubtful.
-^,, Besides these leading causes of electrizatioa, there are many less important, — as changes in the mode of aggregation, the fusion of solids, and the evaporation of liquids. Even simple motion sufiices, under special conditions, to induce an electric state, as M. Arago has shovm in the experiment of the in- fluence of the rotation of a metallic disc upon a magnetized needle, near but not contiguous. Our philosophers how- ever must beware of passing into the other extreme from that with which they justly rej^roach 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.^ I,., 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 sujjport of the electric state. However important these may be, it is clear that we cannot here enter upon the consideration of them.
' In this paragraph, M. Comte alludes to the now most fertile, but when he wrote, the coiiii)aratively unknown subject of the development of Electricity by Induction. — J. 1*. N.
ELECTRICAL INSTRUMENTS. 305 But we must uot pass ovei" the instruments invented for the manifestation and measurement of the electric con- dition,— the electroscojie and the electrometer. The most eminent philosophers have always attached the highest im- l>ortance 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 simplicit}'; 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 electro- scopes, the most remarkable for use in very delicate re- searches, 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 dis- covered, and that we every day demonstrate, the funda- mental 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 electro- magnetism, a new class of electrometers has been intro- duced, for pur2:>oses of measurement, for which Coulomb's balance would not answer. These are the class of mulfi- pliers. 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 propor- tioning the graduation to the intensity of the observed phenomenon.
306 POSITIVE PHILOSOPHY.
SECTION II.
ELECTRICAL STATICS.
The second part of electrology includes what is impro- perly 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 distribu- tion 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 analo- gous 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 funda- mental law which is (metaphorically ex- pressed) 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, how- ever 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 difficul- ties; 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 inex- haustible i-esearch.^ SECTION III.
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.
308 POSITIVE PHILOSOPHY.
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 sim- plification; 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 inclina- tion 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