We see however that besides the sublime Achievements direct knowledge afforded to us, celestial of Celestial dynamics has powerfully contributed to per- Dynamics. feet the whole body of astronomical theories in regard to their definitive aim, — the exact prevision of the state of the heavens at any period whatever, jmst or future. Kepler's laws might suffice to determine the state of our system for a short time, proper data being chosen; but if we wish to extend the inquiry, back or forwards, to any considerable I^eriod, we find the most perfect theory of perturbations absolutely necessary. It is to celestial dynamics that we owe our power of ranging up and down the centuries, to fix the precise moments of various celestial phenomena, such as eclipses, with certainty, and with a minuteness only inferior to that which is possible in the case of present events.
Though we have, according to my view, completed our consideration of astronomical science, it would be felt to be a great omission if we passed over altogether what is now called Sidereal Astronomy. We will therefore see how much there is that we can conceive to be positive iu regard to cosmogony.
CHAPTER VI.
SIDERIAL ASTRONOMY AND COSMOGONY.
^ J- which appears to admit ot exact stuclv is that of the relative motions of the Multiple Stars, first discovered by Herschell. By multiple stars astronomers understand stars very near each other, whose angular distance never exceeds a half minute, and which, for this reason, appear to be one, not only to the naked eye, but to ordinary telescopes, only the most powerful lenses being able to separate them. The relative movements of these stars tend to deceive us as to their precise multiple character, as, for instance, by mutual occultations, which do not permit us to separate them. Among some thousands of multiple stars registered in the catalogues, before the southern heavens had been really explored, almost all were only double, and we have found none which are more than triple, — a circumstance which may be owing solely to the imperfection of our telescopes, as we knew of none but single stars before Herschell's time. However interesting the study of them is, they constitute only a particular case in the universe, as the intervals of the stars which compose them are probably much smaller than those which divide the suns of the universe, so that the study of their relative motions does not lead us up to any of the great general phenomena of the heavens, and the speciality would be more conspicuous if astronomers did as I think they ought.
— form their catalogues of those double stars only whose motions they have fully established. With regard to others, we cannot be sure whether their duality is a real relation or an accident. Knowing nothing whatever of their interval, or of the distance of either of them from us, we cannot Ite sure whether they form a system any more than any other two stars combined by chance in the MULTIPLE STARS. 225 heavens. Because a few incontestable examples are before us of a binary system, in wliicli the smaller circulates round the larger, it is anything- but philosophical to conclude the same to be the case with the whole multitude of double stars, some of which may appear so merely through an accident of position, apparent only to our own system.
Analogy is not applicable here; as what looks like analogy is merely the imperfection of our investigations. No astronomer would venture to assert that if our telescopes were what they may one day become, we might not find between stars now apparently independent a multitude of clustered intermediate stars which should render the case of duality almost general. The apparent nearness would not then be a sufficient gi'ound for presuming their mutual revolutions, because it is in virtue of their very small number that analogy now suggests that presumption. The only positive study in sidereal astronomy is that of the known relative motions of certain double stars, at present not more than seven or eight in number. We could never hope to assign with accuracy their orbits, or their periodic times, or any solid basis for dynamical conclusions.^ The importance of such inquiries is much diminished by the consideration that our system, which, in such a case, means our sun, belongs to no groups of the kind, — either investigated or merely pointed out. This circumstance seems to me not at all accidental; for, if our system made a part of a double star, which it is not difficult to imagine, it would pi'obably be impossible for us ever to be aware of the other part of such a duality, because in the direction of the sun it would be so near that its light would be lost to us in that of our sun. Such a case might, however, have a scientific interest for us, not only as elucidating the displacements of our system, but as allowing such great precision, as might arise from the position of the inquirer on one of the stars of the couple.
The first of the few orbits of double stars known to us ^ M. Comte quite underrates the importance of the phenomena of the multiple stars. The orbits of a very considerable number are now distinctly ascertained, and tlie laws of motion in tlieir orbits. The existence of a motion of revolution is tixed, witli regard to the far greater number. — J. P. N. I. Q was investigated by Savary. They all present a very considerable eccentricity, tlie smallest of which is double, and the greatest four times greater than that of the most eccentric in our system. Of their periodic times, the shortest slightly exceeds forty years, and the longest six hundred. We cannot perceive that the eccentricity and the duration bear any fixed relation to each other, and neither seems to depend at all on the angular distance of the respective pairs of stars. This is the sum of what we know about the double stars; and unless we could learn something of their linear distance from our system and from each other, our conceptions can neither be accurate, nor of great importance. M. Savary has proposed a method, founded on the known velocity of light, by which these distances will, if ever, be estimated: ^ but the uncertainty of some of the elements which must enter into the question is so great that the most that can be hoped for is the fixing of certain limits within which the real distance may be supposed to lie: and this is all that M. Savary himself proj^osed. At present, we know only the nearer limit, beyond which, not only the double stars, but the whole starry host, are known to lie.
„ ^ Proceeding now to ascertain what we may „^ rationally conceive of our own cosmogony, 1 need hardly say that we must put aside altogether any notion of creation, as unintelligible, — all that we are able to conceive of being successive transformations in the sky; and of these, only such as have produced its present state. Here, again, we find our own system to be the only subject of knowledge. We are in possession of some facts in regard to it which may bear testimony to its immediate origin; but we can form no reasonable conjectures about the formation of the suns themselves. The phenomena necessary for such a purpose are not only not explored but not explorable. Whatever may be the interest of Herschell's curious observations on the progressive condensation of the nebulae, they do not warrant his conclusion of their transformation into stars; " ^ They are calculated; but hy strictly j^'eoinetrical methods. ^ Tliia portion of Herscliell'.s speculation must be abandoned.
COSMOGONY OF LAPLACE. 227 for from sucli a conclusiou must flow consequences about form and motion which must be in harmony with established phenomena; and of these we have absolutely none.
The beginning of positive cosmogoiay was Origin of when geometers, pursuing the mathematical Positive theory of the figures of the planets, showed Cosmogony, that they were originally in a state of fluidity. We cannot go further back than this: and we must set out with an existing sun, turning on its axis with an indeterminate velocity, admitting, for the formation of the planetary system, no agencies which we do not now see at work, in the phenomena which we habitually witness, though they may have wrought formerly on a larger scale. These restrictions are indispensable to the scientific character of the inquiry; and, after all, our cosmogonic theories, however guarded, must remain essentially conjectural, if ever so plausible. No mathematical principles can enter here as into celestial mechanics, leading us up to a definite theory and excluding every other. No abstract theory of formations is possible; and the utmost we can do is to collect such information as can be had, construct hypotheses from it, and compare them carefully and continuously with the whole of the phenomena that we explore. Such hypotheses, whatever degree of consistency they may attain, can never, like the law of gravitation, take rank among general facts: for we can never be sure that some other hypothesis may not turn up which would equally well answer the jwesent purpose, and some others besides.
The cosmogony of Laplace seems to me to „ ^.
present the most plausible theory of any yet Lanlace proi^osed. It has the eminent merit of requiring, for the formation of our system, only the simple agents, weight and heat, which meet us everywhere, and which are the only two principles of action which are absolutely general. The point in which I differ from Laplace is with regard to comets, which he regards as strangers in our system whereas Lagrange's view of What he fancied to be instances of nebulous matter turn out to be galaxies, or vast groups of stars. — J. P. N.
228 POSITIVE riiiLosoriiY.
tliem, before cited, appears to be preferable, as being consistent witli tbe independence of our solar group.
The hypothesis of Laplace tends to explain the general cii'cumstances of our system, viz., the common direction of all the planets from west to east; that of their rotations; and that of all the satellites: also, the small eccentricity of all the orbits; and finally, the small inclination of their planes, especially in comparison with that of the solar equator.
It is supposed by this theory that the solar atmosphere was originally extended to the limits of our system, in virtue of its extreme heat; that it was successively contracted by cooling; and that the planets were formed by this condensation. The theory rests on two mathematical considerations. The first involves the necessary relation between the successive expansions or contractions of any body whatever aiid the duration of its rotation; by which the rotation should be quickened as the dimensions lessen and becomes slower as they increase, so that the angular and linear variations sustained by the sum of the areas become exactly compensated. The other consideration relates to the connection between the angular velocity of the sun's rotation and the possible extension of its atmosphere, the mathematical limit of which is at the distance at which the centrifugal force, due to this rotation, becomes equal to the corresponding gravity: so that if any portion of the atmosphere should be outside of this limit, it woiild cease to belong to the sun, though it must continue to revolve with the velocity it had at the moment of separation. From that moment, it ceases to be involved in any further consequences from the cooling of the solar atmosphere. It is evident, from this, how the solar atmosphere must have diminished, as to its mathematical limit, without intermission, in regard to the parts situated at the solar equator, as the cooling was for ever accelerating the rotation.
Portions of the atmosphere, thus parted with, must form gaseous zones, situated just beyond the resjDective limits and this constituted the first condition of our planets. By the same process the satellites were formed out of the atmospheres of their respective planets. Once detached from the sun, our planets must become first liquid and then solid, in the course of their own cooling.
CONCLUSION. 229 without being further affected by solar changes: but the irregularity of the cooling, and the unequal density of parts of the same body must change, in almost every case, the primitive annular form, which remains in the rings of Saturn alone. In most cases, the whole gaseous zone has gathered, in the way of absorption, round the preponderating portion of the zone as a nucleus: thence the body assumed its spheroidal form, with a revolving motion in the same direction as its movement of translation, on account of the excess of the velocity of the upper molecules in comparison with that of the lower.
This theory answers to all the appearances of our system, and explains the difficulty of the primitive impulsion of the planets. It shows, also, that the formation of the system has been successive, the remotest jjlanets being the most ancient, and the satellites the most modern.^ If from points of view like these the stability of our system can scarcely be regarded as absolute, what it may lead us to suspect is that, by the continuous resistance of the general medium, oiu* system must at length be reunited to the solar mass from which it came forth, tiU a new dilatation of this mass shall occur in the immensity of a future time, and organize in the same way a new system, to follow an analogous career. All these prodigious alternations of destruction and I'enewal must take place without affecting the most general phenomena, occasioned by the mutual action of the suns; so that these revolutions of our system, too vast to be more than barely conceived of by our minds, can be only secondary, even local events, in relation to really universal transformations. It is not less remarlvable that the natural history of our system should be, in its turn, as certainly independent of the most prodigious changes that the rest of the universe can imdergo: so that whole systems ai-e, perhaps frequently, developed or condensed in other regions of space, ^ The author subjoins a proposed mathematical verification of Laplace's cosmogony, which is not given in the text, as it does not seem to rest on aile([uate foundations. If an arithmetical verification be ever obtained, it will prol)ahly be in connection with the periods of the rotations of the ditt'erent planets; — periods already in so far connected with the nebular hypothesis by the investigations of an American inquirer — Mr. Kirkwood. — I. P. N.
without our attention being in any way drawn towards these immense events.
T,., 1,• The end I had in view in this exposition ot astronomical 2:)hilosophy will be attained if I have clearly exhibited, in regard both to method and to doctrine, the true general character of this admirable science, which is the immediate foundation of the whole of Natural Philosophy. We have seen the human mind, by means of geometrical and mechanical researches, and with the help of constantly improving mathematical aids, attaining to a precision of logical excellence superior to any that other branches of knowledge admit of. We see the various phenomena of our system numerically estimated, as the different aspects of the same general fact, rigorously defined, and continually reproduced before our eyes in the commonest terrestrial phenomena; so that the great end of all our positive studies, the exact prevision of events, has been attained as completely as could be desired, in regard alike to the certainty and extent of the prevision. We have seen how this science must operate in liberating thd human intellect for ever from all theological and metaphysical thraldom by showing that the most general phenomena are subjected to invariable relations, and that the order of the heavens is necessary and spontaneous.
This last consideration belongs more particularly to a subsequent part of this work; but it has been our business to point out as we went along how the development of astronomical science has shown us that the universe is not destined for the passive satisfaction of Man; but that Man, superior in intelligence to whatever else he sees, can modify for his good, within certain determinate limits, the system of phenomena of which he forms a part, — being enabled to do this by a wise exercise of his activity, disengaged from all oppressive terror, and directed by an accurate knowledge of natural laws. Lastly, we have seen that the field of positive i)hilosoi)hy lies wholly within the limits of our solar system, the study of the universe being inaccessible in any positive sense. ^ ^ As befoi'e remarked, M. Conite speaks much too absolutely here, in oversight of what niodein a.strouoniical researches have really accomplished. — J. P. N.
BOOK III.
PHYSICS.
GENERAL VIEW.
GENERAL VIEW.
ASTRONOMY was a positive science, in Imperfect its geometrical aspect, from the earliest condition of days of the School of Alexandria; but the science. Physics, which we are now to consider, had no positive character at all till G-alileo made his great discoveries on the fall of heavy bodies. We shall find the state of Physics far less satisfactory than that of Astronomy, not only on account of the greater complexity of its phenomena, but under its speculative aspect, from its theories being less pure and systematized, and, under its j^ractical aspect, from its previsions being less extended and exact. The precepts of Bacon and the conceptions of Descartes have advanced it considerably in the last two centuries, in its character of a positive science; but the empire of the primitive metaphysical habits is not to be at once overthrown; and Physics could not be immediately imbued with the positive spirit, which Astronomy itself, our only completely positive science, did not assume in its mechauical aspect till the middle of that period. The further we go among the sciences, the more we shall find of the old unscientific spirit, and not only in their details, but impairing their fundamental conceptions. If we now compare the philosophy of Physics with the perfect model offered to us by astronomical philosophy, I hope we shall perceive the possibility of giving to it, and afterwards to the other sciences in their turn, the same positivity as the first.
tliough their phenomena are far from admitting of an equal perfection of simpHcity and geiierality.
First, we must see what is the domain of Physics, properly so called. ,,. Taken together with Chemistry (for the pi'esent), the object of the two is the knowledge of the general laws of the Inorganic world. This study has marked characters, to be analysed hereafter, distinguishing it from the science of Life, which follows it in our encyclopedic scale, as well as from that of astronomy,.^, which precedes it. The distinction between Cheiiiistry.rhysics and Chemistry is much less easy to establish; and it is one more difficult to pronounce ujjon from day to day, as new discoveries bring to light closer relations between them. Though the division between these sciences is less obvious than between any other two in the scale, it is not the less real and indispensable, as we shall see by three considerations which, perhaps, might be insufficient apart, but which, when united, leave no uncertainty.
Its <'enen.rt ^ First, the generality which characterises ■"^ "^ ' physical researches contrasts with the speciality inherent in the chemical. Every physical consideration is applicable to all bodies whatever, while chemistry studies the action appropriate to a j)articular substance. If we look at their classes of phenomena, we find that gravity manifests itself in the same way in all bodies; and the same with phenomeua of heat, of sound, of light, and even electrical effects. The diffei'ence is only in degree. But, in the compositions and decompositions of Chemistry, we have to deal with specific properties, which vary not only in elementary substances, but in their most analogous combinations. The only exception which can be alleged, in the whole domain of Physics, is that of magnetic phenomena; but modern researches tend to prove that they are a mere modification of electrical phenomena, which are unquestionably general. The general properties of Physics were, in the metaphysical days of the science, regarded as consisting of two classes; those which were necessarily, and those which were contingently universal. But the false distinction arose from the notion of that age, DISTINCTION BETWEEN PHYSICS AND CHEMISTRY. 233 that the business of science was to inquire into the nature o£ bodies, — the study of their properties being a mere secondary affair. Now that we know our business to be with the properties alone, we see the error, and need only ask whether we can conceive of any body absolutely devoid of weight, or of temperature.
In the second place, Physics relates to Dealing with masses, and Chemistry to molecules; inso- masses or much that chemistry was formerly called niolecules. Molecular Physics. But, real as this distinction is, we must not carry it too far, but remember that purely physical action is often as molecular as chemical action; as in the case of gravity. Physical phenomena observed in masses are usually only the sensible results of those wliich are going on among their particles: and, at most, we can except from this only phenomena of sound, and perhaps of electricity. As for the necessity of a certain mass, to manifest physical action, that is equally indispensable in chemistry. The best way of expressing the general fact which lies at the bottom of this distinction is, perhaj)s, that in chemistry, one at least of the bodies concerned must be in a state of extreme division; while this is so far from being a necessary condition of physical action that it is rather an impediment to it. This is a 2:)roof of a real distinction between the two sciences, though it may not be a very marked one.
In the third place, the constitution of changes of bodies, — the arrangement of their molecules, arrangement or — may l)e changed, in exhibiting physical composition phenomena; but the composition of their ^ molecules, molecules remains unchangeable: whereas, in Chemistry,. not only is there always a change of state in one of the bodies concerned, but the mutual action of the bodies alters their nature; and it is this alteration which constitutes the phenomenon. Many physical agents can, no doubt, work changes of composition and decomposition, if their operation be very energetic and prolonged; and it is this which forms such counection as there is between the two sciences: but, at that point of activity, physical agencies pass the boundary, and become chemical.
Positive philosophy requires that we should draw off altogether from the study of agents, to which it may be imagined that phenomena are to be referred. Any number of persons may discover a supposed agent, — as, for instance, the universal ether of modern philosophers, by which a variety of phenomena may be supposed to be explained; and we may not be able to dis2:)rove such an agency. But we have no more to do with modes of operation than with the nature of the bodies acted upon. We are concerned with phenomena alone; and what we have to ascertain is their laws. In departing from this rule, we leave behind us all the certainty and consistency of real science.
Keeping within our true limits, then, we see that if chemical phenomena should be reduced by analysis into the form of purely physical actions, — an achievement very possible to the present generation of scientific men,— our fundamental distinction between the two sciences will not be shaken. It will still be true that in a chemical fact something more is involved than in a simply physical one: namely, the cha.racteristic alteration undergone by the molecular composition of the bodies, and therefore by the whole of their properties. Such a distinction is secure amidst any scientific revolution that can ever hajjpen.
. Fi'om these three considerations, taken o/pi[vsics" together, we derive our description of Physics. This science consists in studying the laws which regulate the general properties of bodies, commonly regarded in the mass, and always placed in circumstances which admit of their molecules remaining unaltered, and generally in their state of aggregation. With a view to the great end of all science, we must add that the aim of physical theories is to foresee, as exactly as possible, all the phenomena that will be exhibited by a body placed in any set of given circumstances, excluding, of course, such as could alter its nature. This is not the less true because we can rarely attain the prescribed aim. The imperfection is in our knowledge alone. In estimating the true character of any science, the only way is, first, to suppose the science perfect, and then to study the fundamental difficulties presented by this ideal perfection.
Our description shows us how much more complexity we shall find in physical than in astronomical inquiries. In METHODS OF PHYSICAL INQUIRY. 235 astronomy we study bodies, known to us only t,, by sight, under two aspects only, tueir torms and motions. All considerations but these are excluded. But in Physics, on the contrary, the bodies we haye to study are recognized by all our senses, and are regarded under an aggregate of general conditions, and therefore amidst a complication of relations. It is clear, not only that this science is inferior to astronomy, but that it would be impractica,ble if the group of fundamental obstacles was not compensated for, up to a certain jjoint, by the extension of our means of exploration. We meet here the law, before laid down, that in proportion as phenomena become complicated they thereby become explorable under a proportionate yariety of relations.
Of the three procedures which constitute,,. i ^. r our art of obserying, the last. Comparison, inquiry is scarcely more applicable here than with regard to astronomical phenomena. Its proper application is, in fact, to the jihenomena of organized bodies, as we shall see hereafter. But the other two methods are entirely suitable to Physics. Obseryation was, ^i, _,. in astronomy, restricted to the use of a single sense; but in Physics, all our senses find occupation. Yet would Obseryation effect little without the aid of Experiment, the regulated use of which is the great resource of physicists in all questions that involye any complexity. This procedure consists in ob- r.
serymg beyond the range of natural circumstances; — in placing bodies in artificial conditions, expressly instituted to enable us to examine the action of the phenomena we wish to study under a particular point of yiew. We can see at once how eminently this art is adapted to physical researches; and how it must there find its triumphs: since there are hardly any bounds to our power of modifying bodies, for the purpose of studying their phenomena. In chemistry, experiment is commonly supposed to be more complete than in any other department: but I think it is of a higher order in yjhysics, for the reason that in chemistry the circumstances are always artificially arranged, while in physics we haye the choice of natural 236 POSITIVE PITILOSOPHY.
or artificial circumstances; and the jiliilosopliical character of experimentation consists in choosing the freest possible case that will show us what we want. We have a wider range, and a choice of simpler cases, in physics than in chemistry; and in physics, therefore, is experiment supreme.
Application of The next great virtue of physics is its mathematical allowing the aj^plication of mathematical analysis. analysis, which enters into this science, and