comte, auguste - the positive philosophy vol I (другой вариант)

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the difficulty of getting at them, constitute, by their combination the eminently mathematical character of the science of astronomy. On the one hand, the perpetual necessity of deducing from a small number of direct measures, whether angular or horary, quantities which are not themselves immediately observable, renders the use of abstract mathematics indispensable; while, on the other hand, astronomical questions being always, in themselves, problems of geometry, or else of mechanics, must fall into the department of concrete mathematics. Again, the regularity of astronomical forms admits of geometrical treatment; and the simplicity of astronomical movements admits of mechanical treatment with a very high degree of precision There is perhaps no analytical process, no geometrical or mechanical doctrine, which is not employed in astronomical researches, and many of them have as yet had no other aim. Considering the simple nature of astronomical investigations, and the easy application to them of mathematical means, it is evident why astronomy is, by common consent placed at the head of the natural sciences. It deserves this place, first, by the perfection of its scientific character; anal, next, by the preponderant importance of the laws which it discloses.

Passing over, for the present, its utility in the measurement of time, the exact description of the globe, and the perfecting of navigation, which are not circumstances that could determine its rank, we may just observe that it affords an instance of the necessity of the loftiest scientific speculations to the satisfaction of the most ordinary wants. Hipparchus began to apply astronomical theory to the finding the longitude at sea. A prodigious amount of geometrical science has gone to improve our tables of longitude up to their present point; and if we cannot now get within half-a-dozen miles of a true estimate in the seas under the line, it is for want of more science still.

Those who say that science consists in an accumulation of observed facts may here see how imperfect is their account of the matter. The Chaldeans and Egyptians collected facts from observation of the heavens; but there was no astronomical science till the early Greek philosophers referred the diurnal movement to geometrical laws. The aim of astronomical researches was to establish what would be the state of the sky at some future time; and no accumulation of facts could effect this, till the facts were made the basis of reasonings. Till the rising of the sun, or of some star, could be accurately predicted, as to time and place, there was no astronomical science. Its whole progress since has been by

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introducing more and more certainty and precision into its predictions, and in using smaller and smaller data from direct observation for a more and more distant prevision. No part of natural philosophy manifests more strikingly the truth of the axiom that all science has prevision for its end: an axiom which separates science from erudition, which relates the events of the past, without any regard to the future.

However impossible may be the aim to reduce the phenomena of the respective sciences to a single law, supreme in each, this should be the aim of philosophers, as it is only the imperfection of our knowledge which prevents its accomplishment. The perfection of a science is in exact proportion to its approach to this consummation; and, according to this test, astronomy distances all other sciences. Supposing it to relate to our solar system alone, the point is attained; for the single general law of gravitation comprehends the whole of its phenomena. It is to this that we must recur when we wish to show what we mean by the explanation of a phenomenon, without any inquiry into its first or final cause; and it is here that we learn the true character and conditions of scientific hypothesis,—no other science having applied this powerful instrument so extensively or so usefully. After having exhibited these great general properties of astronomical philosophy, I shall apply them to perfect the philosophical character of the other principal sciences.

Regarding astronomical science, apart from its method and with a view to the natural laws which it discloses, its pre-eminence is no less incontestable. I have always admired, as a stroke of philosophic genius, Newton’s title of his treatise on Celestial Mechanics,—‘The Mathematical Principles of Natural Philosophy;’ for it would be impossible to indicate with a more energetic conciseness that the general laws of astronomical phenomena are the basis of all our real knowledge.

We may see at a glance that astronomy is independent of all the natural sciences depending on Mathematics alone and though philosophically speaking, we put Mathematics at the head of the whole series, we practically regard it less as a natural science of itself (from the paucity of phenomena which it presents to observation) than as the repository of principles by which the natural sciences are interpreted and investigated. Philosophically speaking, astronomy depends on Mathematics alone, owing nothing to Physics, Chemistry or Physiology, which were either undiscovered, or lost in theological and metaphysical confusion, while astronomy was a true science in the hands of the ancient geometers. But the phenomena of the other sciences are dependent, naturally as well as

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systematically, on astronomical facts and can be perfectly studied only through astronomy. We cannot thoroughly understand any terrestrial phenomenon without considering what our globe is, and what part it bears in the solar system, as its situation and motions affect the conditions of everything upon it; and what would become of our physical, chemical, and physiological ideas, without consideration of the law of gravitation? In the remotest case of all, that of Social phenomena, it is certain that changes in the distance of the earth from the sun, and consequently in the duration of the year, in the obliquity of the ecliptic, etc., which in astronomy would merely modify some coefficients, would largely affect or completely destroy our social development. It is no exaggeration to say that Social physics would be an impossible science, if geometers had not shown us that the perturbations of our solar system can never be more than gradual and restricted oscillations round a mean condition which is invariable. If astronomical conditions were liable to indefinite variations, the human existence which depends upon them could never be reduced to laws.

Not less important is the influence of astronomical science on our own intelligence. It has done much more than relieve us from superstitious terrors and absurd notions about comets and eclipses,—notions which, as Laplace observed, would spring up again immediately if our astronomy were forgotten. This science has done much more for our understandings than that. It has done more than any other pursuit—- simply because it is the most scientific of all—to expose and destroy the doctrine of final causes, which is generally regarded by the moderns as the basis of every religious system, though it is in fact a consequence and not a cause. The knowledge of the motion of the earth has overthrown the very foundation of the doctrine, which supposed the universe to be subordinated to our globe, and therefore to Man. Since Newton’s time, the development of celestial Mechanics has deprived theological philosophy of its principal intellectual office, by proving that the order maintained throughout our system and the whole universe is by the simple gravitation of its parts. If we took an a priori view, we should say that, as we exist, our system must be such as to admit of our existence; and one necessary condition of this is such a degree of stability in our system as we actually find. This stability we scientifically perceive to be a simple consequence of mechanical laws working among the incidents of our system,—the extremely small planetary bodies in their relation to the larger sun; the small eccentricity of their orbits, and moderate incli-

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nation of their planes, which incidents, again, are necessary consequences of the mode of formation of the entire system. The stability by virtue of which we hold our existence is not found in the case of cornets, whose perturbations are not only great, but liable to indefinite increase; and their being inhabited is inconceivable. Thus, the doctrine of final causes would be reduced to the truism that there are no inhabited bodies in our system but those which are habitable. This brings us back to the principle of the conditions of existence which is the true positive transformation of the doctrine of final causes, and of far superior scope and profit in every way.

We have next to consider the divisions of the science. These arise immediately out of the fact, now familiar to us, that astronomical phenomena are either geometrical or mechanical. They are Celestial Geometry, which is still called Astronomy, from its having possessed a scientific character before the other; and Celestial Mechanics, of which Newton was the immortal founder. Though our business is with our own system the same division extends to Sidereal astronomy, supposing that kind of exploration to be within our power. As before, we see geometry to be more simple in its phenomena than mechanics, and that mechanics is dependent on geometry, without reciprocity. In fact, men were successfully inquiring into the forms and sizes of the heavenly bodies, and studying their geometrical laws, before anything was known of the forces which changed their positions. Whereas, the province of Celestial Mechanics is to analyse the motions of the stars, in order to refer them, by the rules of Rational Mechanics, to the elementary motions regulated by a universal and invariable mathematical law;—thence, again, departing to perfect the knowledge of real motions by scientifically determining them a priori, taking from observation the necessary data—the fewest possible—for the calculations of general mechanics. This is the link by which astronomy and physics are connected, and connected so closely that some great phenomena render the transition almost insensible; as in the theory of the Tides. But it is evident that the whole reality of celestial mechanics consists in its having issued from the exact knowledge of true movements, furnished by celestial geometry. It was for want of this point of departure that all attempts before the time of Newton, even Descartes’, however valuable in other ways, failed to establish systems of celestial mechanics. This division of the science into two parts has therefore nothing arbitrary in it, nor even scholastic: it is derived from the nature of the science, and is at once historical and dogmatic. As for

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the subdivisions, we need not trouble ourselves with them now.

In regard to the point of view from which the science should be regarded, Lacaille thought it would simplify matters extremely to place his observer on the surface of the sun. And so it would, if the thing could be done in accordance with positive knowledge; but undoubtedly the solar station should be the ultimate and not the original one, under a rational system of astronomical study. And when, as in the case of this work, the object is the analysis of the scientific method, and the observation of the logical filiation of the leading scientific ideas, it matters less to obtain a clearer exposition of general results than to adhere to the positive method.

I suppose my readers to be well acquainted with the two fundamental facts of the diurnal and annual rotation of our globe, as data without which nothing could be clearly understood of the essential methods and general results of astronomical science. I am not giving a treatise on astronomy, nor even a summary, but a series of philosophical considerations upon the different parts of the science, in which any extended special exposition would be misplaced.

We must first see what methods of observation astronomers need, and are possessed of.

Chapter II

Methods of Study of Astronomy

Section I Instruments

All astronomical observation is, as we have seen, comprehended in the measurement of times and of angles. The two considerations concerned in attaining the great perfection we have reached are the perfecting the instruments, and the application by theory of certain corrections, without which their precision would be misleading.

The observation of shadows was the first resource of astronomers, when the rectilinear propagation of light was established. Solar shadows, and also lunar, were very valuable in the beginning, and much was obtained from the simple device of a style so fixed as to cast a shadow corresponding with the diurnal rotation to be observed: but the alterations rendered necessary by the annual motion, and impossible to make on that apparatus, rendered the instrument unfit for precise observations. Again, by comparing the length of the shadow cast by a vertical

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style with the height of the style, the corresponding angular distance of the sun from the zenith was computed: and a valuable method this was: but the penumbra rendered the accurate measurement of the shadow impossible. The difficulty, aggravated by its unequal amount at different distances from the zenith, was partly removed by the use of very large gnomons; but not completely. These imperfections determined astronomers to get rid as soon as possible of the process of gnomonic measurement. Shadows will always be at hand to measure by when better means are wanting: and one application of this instrument remains in our observatories,—as the basis of the meridian line, regarded as dividing into two equal parts the angle formed by the horizontal shadows of the same length which correspond to the two equivalent parts of the same day. In this case, the penumbra is harmless, as it affects the two parts equally; and as for the obliquity of the sun’s motion, that may be mainly got rid of by choosing the period of either solstice,—espe- cially the summer one. It is easy, too, to rectify the observation by the stars.

Proceeding to more exact methods, and, first, with regard to measurement of time, it is clear that the most perfect of all chronometers is the sky. It seems as if it would be enough, after knowing precisely the latitude of one’s observatory, to measure the distance of any star from the zenith, and learn its horary angle, and, as an immediate consequence, the time that has elapsed, by resolving the spherical triangle formed by the pole, the zenith, and the star. If a sufficiently wide observation of this kind had been made, and numerical tables formed for certain selected stars, great results might have been obtained from this natural method, but it is insufficient, and it has the defect of making the measure of time depend on that of angles, which is the least perfect of the two, in our day. This method is therefore used only in the absence of a better, as in nautical astronomy; and its commonest service is in regulating other chronometers, by a comparison with that of the heavens themselves. Artificial methods of measuring time are therefore indispensable in astronomy.

Every phenomenon which exhibits continuous change might serve, in a rough way, to mark time: various chemical processes, or even the beating of our own pulses, might afford a measure, more or less inaccurate: astronomical phenomena are excluded, because they are what we want to measure: and we therefore have recourse to physical means, and find weight the best. The ancients tried it in the form of the flow of

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liquids; and to water clocks succeeded the hourglass, but the uncertainty of these led to solids being preferred; and in the form of weight having a vertical descent. By no care, however, could the disturbances caused by natural forces be remedied, till Galileo, by his creation of rational dynamics, suggested the pendulum. Whether it is or is not correct to assign to Galileo the idea of using the pendulum as a measurer of time, it is certain that his discoveries suggested it, and that Huyghens enabled us to use it. He had recourse to the highest principles of science to render this service, and discovered the principle of vires vivae, which besides being scientifically indispensable, afforded to art new means of modifying oscillations without changing the dimensions of the apparatus. Considered as a collection of discoveries for a single aim, Huyghens’ treatise De Horologio oscillatorio, is perhaps the most remarkable example of special researches that the history of the human mind has yet exhibited. From that time, the perfecting of astronomical clocks became merely a matter of art. In regard to fixed clocks, two things hate to be attended to,— the diminution of friction, by improved methods of suspension, and the correction by a compensating apparatus of irregularities caused by variations of temperature. As for portable chronometers, worked by a spiral spring, they are a marvellous invention; but they belong to the province of art, and not science.

In regard to the measurement of angles it is clear that an instrument which would admit of an allowance for minutes and seconds, must be of a size incompatible with minute precision. It must always be that large apparatus must be so affected in its weight and temperature as to be impaired in its accuracy. The large telescopes of modern times are intended to show us stars otherwise invisible: and no one thinks of using them for purposes of precise measurement. It is generally agreed now that instruments for measuring angles should not be more than ten feet in diameter when we are dealing with an entire circle; and they are usually not more than six or seven. The wonder then is flow we are to estimate angles to a second, as we do every day with circles whose size would scarcely indicate minutes. It is done by the concurrent use of three methods,—the eye piece, the use of the vernier (so called after its inventor), and the repetition of angles.

It was long before it occurred to astronomers to use their lenses for any purpose than the discovery of new objects: but at last it occurred to them to replace the ancient transoms and modern sights by an eye-piece which should secure the advantages without the inaccuracies of a large

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instrument. Morin first made this use of a lens. Auzout followed with his invention of the reticle; and, a century after, Dollond gave us a power of absolute precision by his invention of the achromatic object-glass. Vernier proposed in 1631 to divide intervals into parts much more minute than could be marked. He enabled us to ascertain angles, within half a minute, or circles divided only into sixth-parts of a degree. The precision obtainable by his simple apparatus is indefinite, being limited only by our difficulty in detecting the coincidence of the line of the vernier with that of the limb. The union of the third method with these two gives us the perfection we have attained. It is strange that we should have been so long in perceiving that, the imperfection of angular instruments having nothing to do with the dimensions of the angle to be measured, we should gain much by increasing, in fixed proportions, the magnitude of the angles, which is equivalent to diminishing the imperfection of the instrument. The repetition of angles served every purpose immediately, with regard to terrestrial objects, on account of the steadiness of the point of view; but there was the difficulty, with regard to the heavenly bodies, of their perpetual change of place. Borda applied himself to measure the distance from the zenith of the stars when they crossed the meridian; and the star then remains sensibly at the same distance from the zenith long enough to allow the operation of the multiplication of the angle. By these means, angular instruments are matched with horary in regard to precision. They require from the observer a diligent patience in applying all the minute precautions and rectifications which experience has proved to be indispensable to the fullest use of these instruments.

Then, we have Roemer’s meridional eye-glass, which fixes the instant of the passage of a star over the meridian. The plane of the meridian is made in this case purely geometrical, by being described by the optic axis of a simple eyeglass, properly disposed; which is enough when all we want to know is the precise moment of the star’s passage. Then there are the micrometrical instruments, by which we measure the diameters of stars, and, generally all small angular intervals. These are the material instruments of observation,—horary and angular. We must nor advert to the intellectual means,—that is, to the corrections which astronomers must apply to the results exhibited be their instruments. There would be little use in perfecting our instruments, if refraction and parallax introduced as much error into our observations as we had got rid of by the improvement of our apparatus.

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The corrections required are of two kinds. The first relate to the errors caused by the position of the observer,—the ordinary refraction and parallax. No deep astronomical knowledge is required for the correction of these. The second class arising from the same cause, since they proceed from the observer being on a moving planet, are founded on primary astronomical theories: they are the annual parallax, the precession of the equinoxes, aberration, and notation. Our business now is with the first and most important class.

Section II

Refraction

The light which comes to us from any star must be more or less turned aside by the action of the terrestrial atmosphere. We must estimate the amount of this deviation before our observations can answer any theoretical purpose. The star is, by this refraction, made to appear too near the zenith, while left in the same vertical plane. Only at the zenith is the error absent, while it increases as the star descends to the horizon. This error, primarily affecting distances from the zenith must affect, indirectly, all other astronomical measurements, except azimuths: but it would be easy to calculate them, if we once knew the law of diminution and increase of refraction at different distances from the zenith. Philosophers have tried the logical way and the empirical, and have ended by combining the two.

If our atmosphere were homogeneous, the refraction of light would be uniform and calculable. But our atmosphere is composed of strata; and the consequent refractions are excessively unequal, and increasing as the light penetrates a denser stratum, so that its passage constitutes a curve of the last degree of complication. Even this would be calculable, with more or less pains, if we knew the law of variation of these atmospheric densities: but we do not and cannot know that law. We have no exact knowledge of the laws of temperature, and cannot estimate atmospheric changes, either as to number or degree: and all mathematical processes founded on laws of pressure, etc., may be good as exercises, but are of no value in estimating refraction. As to the empirical method, if the refraction remained always constant at the same height, we might construct tables; and, by extending our observations, and instituting various comparisons, we might hope to obtain such a mass of materials as would afford us some certain results. This is what astronomers have, in fact, patiently and laboriously done, by the help of the improved in-

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struments we have spoken of. They have used whatever geometrical help they could make applicable: but the results are discouraging enough. There is nothing like uniformity in the results: for the changes in the atmosphere are beyond our calculation and measurement. We study the barometer, the thermometer, and the hygrometer, at the right moment; we can learn from them only the changes taking place on the spot in which we are; and our tables of refraction vary as our observatories, and even in one observatory at different times. Delambre found differences of four or five minutes between one day and another, after taking all imaginable pains. All that we can do is to confine our observations to the nearest possible approach to the zenith; and to place no reliance on what we attempt near the horizon. By doing this, we shall find our astronomical observations less affected by the unmanageable difficulties of refraction than might be anticipated.

Section III

Parallax

The difficulty of the parallaxes can be dealt with much more easily and satisfactorily than that of the refractions. Observations of the heavenly bodies made in different places could not be exactly compared without a reference, in idea, to those which would be made from an imaginary observatory, situated in the middle of the earth, which is besides the true centre of apparent diurnal motions. This correction, which is called the parallax, is analogous to that which is constantly made in measurements of the earth’s surface, under the more logical name of reduction to the centre of the station. The eject of the parallax, like that of refraction, is upon the distance of stars from the zenith alone, leaving the star in the same vertical plane, and placing it too far from the zenith, instead of too near, as in the case of refraction. In this instance too, as in the other, though not according to the same law, the deviation increases as the star descends to the horizon. In like manner, too, there must be secondary modifications for all the other astronomical quantities, except with regard to the azimuths. The rectification is easy in comparison with the other case from the absence of the hopeless difficulties caused by our ill-understood atmosphere. The similar course of the two difficulties, producing counteracting ejects, has, we may observe, relaxed the attention of astronomers to the facts of refraction and parallax, by partly concealing their influence on actual observations.

The parallax does not, like refraction, affect all the stars alike, but,