the molecules, are more difficult to conceive thau the fact itself, and are, in truth, as absurd as the explanations that Molicre puts into the mouth of his metaphysical doctors. It is lamentable that we should have such comments to make in these days. Nobody now tries to exj^lain the specific gravity proper to any substance or structure: and why should we attempt it with regard to specific colour, which is quite as primitive an attribute? — In physiology, the consideration of colours is of high importance, in connection with the theory of vision; and in natural history, it may prove a useful means of classification: but, in optics, the object of the true theory of colours is mei'ely to perfect the analysis of light, so as to estimate the influence of structure or other circumstance upon transmitted or reflected colour, without entering into the causes of specific colouring. The field of inquiry is vast enough, without any such illusory research as this.
STUDY OF DIRECT LIGHT.
„,.. The first department is that of Optics, proj^erly so called, or the study of direct light. This and catoptrics are the only part of the science cultivated by the ancients; but this braiich is as old as the knowledge of the law of the rectilinear propagation of light in every homogeneous medium. This primary law malces purely geometrical questions of problems relating to the theory of shadows; questions difficult to manage in many cases, but not in the most imjjortant, — those of very distant luminous bodies, or bodies of extremely small dimensions. The theory depends, both for the shadow and the penumbra, on the determination of an extensible surface, circumscribed at once by the luminous and tlie illuminated body. — Whatever its real antiquity may be, this first part of Optics is still very imperfect, regarded from the second point of. r. • view; that is, with regard to the laws of the intensity of light, or what is called photometry. Important as it is to have a clear knowledge, our notions are as yet either vague or j^recarious as to how the PHOTOMETRY. 293 intensity of light is modified by such circumstances as its direction, whether emergent or incident; its distance; its absorption by the medium; and, finally, its colour. We are met by a grand difiiculty at the pi, <. outset. We have no photometrical instruments that can be depended on for enabling us to verify oiir conjeet^^res on the different modes of gradation of light.
All our photometers rest on a sort of vicious circle, being devised in accordance with the laws which they are destined to verify, and generally according to the most doubtful of all, in virtue of its metaphysical origin, — that which relates to distance. We have called light an emanation; have calculated its intensity by the square of its distance; and then, Avithout confirming this conjecture by any experiment whatever, we have proceeded to found the whole of photometry upon it. And when this conjecture was replaced by that of undulations, we accepted the same j^hotometry, neglecting the consideration that it must require revision from its very basis. It is clear what our jireseut photometry must be, after such treatment as this. The law relating to direction, in the ratio of the sine of the angle of emergence or of incidence, is no better demonsti'ated than that of distance, though it comes from a less suspicious source. It has nothing about it at present like Fourier's labours on radiating heat; and yet it seems as if it would admit of an analogous mathematical elaboration. The only part of photometry which has, as yet, any scientific consistency is the mathematical theory of gradual absorption of light by any medium. Bouguer and Lambert have given us some interesting knowledge about this: but even here we are on unstable ground, for want of precise and unquestionable experiments. Again, the photometrical influence of colour has been the subject of some exact observations; but we are not yet in possession of general and precise conclusions, unless it be the fixing of the maximum of brightness in the middle of the solar spectrum. Thus, to sum up, in this first, oldest, and simjilest department of optics, philosophers have scarcely outstripped popular observation, — leaving out what belongs to geometry, and the measurement of the velocity of the propagation of light, which is furnished by astronomy.
CATOPTEICS.
It is otherwise with regard to catoptrics, and yet more, dioptrics, if we discard questions about the first causes of reflection and refraction. Scientific studies have largely extended and perfected universal ideas about those two orders of general phenomena; and the varied effects belonging to them are now referred with great precision to a very small number of uniform laws, of remarkable simplicity.
The fundamental law of catoptrics, well reff&etioiT ° known by the ancients, and abundantly confirmed by experiment, is that whatever may be the form and nature of the reflecting body, and the colour and intensity of the light, the angle of reflection is always equal to the angle of incidence, and in the same normal plane. Under this law, the analysis of the effects produced by all kinds of mirrors is reduced to simple geometrical problems, which might, it is true, involve some long and difficult calculations, according to the forms of some bodies, if it were not usually sufficient to examine the simple forms of the plane, the sphere, and, at most, the circular cylinder. If we pretended to absolute precision in the analysis of images, we might encounter considerable geometrical difficulties: but this is not necessary. This analysis depends, in general, mathematically speaking, on the theory of caustic curves, created by Tschirnhavisen. But even in the application of this theory, some conjectures are hazarded; and the want of direct and exact experiments, and the uncertainty which attends almost all the parts of the theory of vision, prevent our depending too securely on the reality of the remote results of any general principle that we can yet employ.
., Every luminous reflection upon any body tion not found ""''I'^tever is accompanied by an absorption or more or less, but always of a great part of the incident light; and this gives rise to a second interesting question in cato^jtrics. But our knowledge about it DIOPTRICS. 295 amounts to very little, from our backwardness in photometry; so that we have not yet laid hold of any law. We do not know whether the loss is the same in all cases of incidence: nor whether it is connected with the degree of brightness: nor what is the influence of colour upon it: nor whether its variations in different reflecting bodies are in harmony with other sj^ecific, and especially optical characters. These questions are not only untouched: they have never been proposed. All that we know is simj>ly that the absorption of light appears to be always greater (but to what degree we are ignorant) by reflection than by transmission. From this has resulted, in recent times, the use of lenticular beacons, introduced by Fresnel.
A more advanced kind of inquiry belongs to the study of transj^areut substances; but here, again, the laws are ill understood. In these bodies, reflection accompanies refraction, and we have the opportunity of inquiring by what laws, general or special, the division between transmitted and reflected light takes place. We only know that the last is more abundant in proportion as the incidence is more oblique; and that reflection begins to become total from a certain inclination proper to each substance, and measured exactly with regard to several bodies. The inclination appears to be less in proportion as the substance is more refracting: but the supposed law of the case is connected with chance conjectures upon the nature of light, and requires to be substantiated by direct experiment.
DIOPTRICS.
Of all the departments of Optics, dioptrics is at present the richest in certain and exact knowledge, reduced to a few simple laws, embracing a large variety of phenomena. The fundamental law of refraction was wholly,,,, unknown to the ancients, and was discovered i-gfraction at the same time, under two distinct and equivalent forms, by Snellius and Descartes. It consistsi of the constant proportion of the sines of the angles that the refracted ray and the incident ray, always contained in the same normal plane, form with the perpendicular to the refracting surface, in whatever direction the refraction may be. The fixed relation of these two sines, when the light passes from a vacuum into any medium whatever, constitutes the most important optical coefficient of every natural body, and holds a real rank in the aggregate of its physical characteristics. The philosophers have laboured at its determination with much care and success, by ingenious and exact processes: they have prepared very extensive tables, which may rival, as to precision, our tables of specific gi-avity— the uncertainty not exceeding a hundredth part of the numerical value of the refracting power. If the light passes from one medium to another, the relation of the refraction depends on the nature of both: but in every case, the inverse passage gives it always a precisely reciprocal value; as experiment has constantly shown.
Again, while a body undergoes no chemical change, and becomes only more or less dense, the relation of refraction which belongs to it varies in proportion to the specific gravity; as may be easily shown, especially with regard to liquids, and yet more to gases, in which we can so extensively modify density by temperature and pressure. This is why philosophers have adopted, in preference to the proper relation of refraction, its quotient by the density, which they have named refracting power; in order to obtain more fixed and specific characters in the dioptric comparison of different substances. There is substantial ground for this distinction, though its origin was suspicious. But it must be observed that the refracting power varies when the substance does not undergo any chemical change, but passes, as we have seen in the case of water, through different states of aggregation. These variations in the refracting power have given occasion to conflicts between the advocates of the two hypothetical systems,— each of which requires an invariability in the refracting power which we do not know to exist: and the difficulty of sej^arating what is really established from what they require is one of the mischievous consequences of anti-scientific hypotheses, and one which may well render the acitual character of the science itself doubtful to impartial minds.
Newton's discoveries on elementary colours. 297 Newton's discoveries of the unequal re- Newton's disfrangibility 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 refracting 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 refracting 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 variations are not, as Newton supposed, in proportion to the refracting 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 possibility of achromatism by the compensation of the opposite action pertaining to two different substances which, without that, could not cease to disperse the light but by ceasing 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 cylindrical surfaces: but we should yet find the inquiry embarrassing, and especially in regard to the dispersion, if we did not confine it to an approximate estimate of the few commonest circumstances.
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 manifesting 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 phenomenon 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 neutralize and augment each other alternately, increasing by equal and minute degrees, the value of which is determined, the difference in length between the entire paths traversed by the two cones. It is a j^ity that this important 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 preponderance of vain hypotheses about the nature of light over the spirit of rational experimentation.
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 airjjump; 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 meteorological 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 phenomena: 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 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 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 properties 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 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 esjiecially 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 inflvience over the succeeding and more complex sciences, which, on account of their greater difliculty, 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 magnetism, in which even eminent physicists have shared. Such consequences show how a study which is naturalh' favourable to the positive development of human intelligence 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 illusory, the other real, — iu which the application of mathematics 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 mathematical 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 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 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 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.
CAUSES OF ELECTRIZATION. 303 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 undei'go: but the chief causes of electrization 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 contact. This distribution differs widely from that first indicated 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 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 jiowerful, 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.
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 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 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 condition,— the electroscojie and the electrometer. The most eminent philosophers have always attached the highest iml>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}';