The Essays of Adam Smith

by Adam Smith

By supposing, that in the solidity of the Sphere of each of the Five Planets there was formed another little Sphere, called an Epicycle, which revolved round its own centre, at the same time that it was carried round the centre of the Earth by the revolution of the great Sphere, betwixt whose concave and convex sides it was inclosed; in the same manner as we might suppose a little wheel inclosed within the outer circle of a great wheel, and which whirled about several times upon its own axis, while its centre was carried round the axis of the great wheel, they imagined they could account for the retrograde and stationary appearances of those most irregular objects in the heavens. The Planet, they supposed, was attached to the circumference, and whirled round the centre of this little Sphere, at the same time that it was carried round the earth by the movement of the great Sphere. The revolution of this little Sphere, or Epicycle, was such, that the Planet, when in the upper part of it; that is, when furthest off and least sensible to the eye; was carried round in the same direction with the centre of the Epicycle, or with the Sphere in which the Epicycle was inclosed: but when in the lower part, that is, when nearest and most sensible to the eye; it was carried round a direction contrary to that of the centre of the Epicycle: in the same manner as every point in the upper part of the outer circle of a coach-wheel revolves forward in the 348 same direction with the axis, while every point, in the lower part, revolves backwards in a contrary direction to the axis. The motions of the Planet, therefore, surveyed from the Earth, appeared direct, when in the upper part of the Epicycle, and retrograde, when in the lower. When again it either descended from the upper part to the lower, or ascended from the lower to the upper, it appeared stationary.

But, though, by the eccentricity of the great Sphere, they were thus able, in some measure, to connect together the unequal velocities of the heavenly bodies, and by the revolutions of the little Sphere, the direct, stationary, and retrograde appearances of the Planets, there was another difficulty that still remained. Neither the Moon, nor the three superior Planets, appear always in the same part of the heavens, when at their periods of most retarded motion, or when they are supposed to be at the greatest distance from the Earth. The apogeum therefore, or the point of greatest distance from the Earth, in the Spheres of each of those bodies, must have a movement of its own, which may carry it successively through all the different points of the Ecliptic. They supposed, therefore, that while the great eccentric Sphere revolved eastwards round its centre, that its centre too revolved westwards in a circle of its own, round the centre of the Earth, and thus carried its apogeum through all the different points of the Ecliptic.

But with all those combined and perplexed circles; though the patrons of this system were able to give some degree of uniformity to the real directions of the Planets, they found it impossible so to adjust the velocities of those supposed Spheres to the phenomena, as that the revolution of any one of them, when surveyed from its own centre, should appear perfectly equable and uniform. From that point, the only point in which the velocity of what moves in a circle can be truly judged of, they would still appear irregular and inconstant, and such as tended to embarrass and confound the imagination. They invented, therefore, for each of them, a new Circle, called the Equalizing Circle, from whose centre they should all appear perfectly equable: that is, they so adjusted the velocities of these Spheres, as that, though the revolution of each of them would appear irregular when surveyed from its own centre, there should, however, be a point comprehended within its circumference, from whence its motions should appear to cut off, in equal times, equal portions of the Circle, of which that point was supposed to be the centre.

Nothing can more evidently show how much the repose and tranquillity of the imagination is the ultimate end of philosophy, than the invention of this Equalizing Circle. The motions of the heavenly bodies had appeared inconstant and irregular, both in their velocities and in their directions. They were such, therefore, as tended to embarrass and confound the imagination, whenever it attempted to trace them. The invention of Eccentric Spheres, of Epicycles, and of the 349 revolution of the centres of the Eccentric Spheres, tended to allay this confusion, to connect together those disjointed appearances, and to introduce harmony and order into the mind’s conception of the movements of those bodies. It did this, however, but imperfectly; it introduced uniformity and coherence into their real directions. But their velocities, when surveyed from the only point in which the velocity of what moves in a Circle can be truly judged of, the centre of that Circle, still remained, in some measure, inconstant as before; and still, therefore, embarrassed the imagination. The mind found itself somewhat relieved from this embarrassment, when it conceived, that how irregular soever the motions of each of those Circles might appear, when surveyed from its own centre, there was, however, in each of them, a point, from whence its revolution would appear perfectly equable and uniform, and such as the imagination could easily follow. Those philosophers transported themselves, in fancy, to the centres of these imaginary Circles, and took pleasure in surveying from thence, all those fantastical motions, arranged, according to that harmony and order, which it had been the end of all their researches to bestow upon them. Here, at last, they enjoyed that tranquillity and repose which they had pursued through all the mazes of this intricate hypothesis; and here they beheld this, the most beautiful and magnificent part of the great theatre of nature, so disposed and constructed, that they could attend, with delight, to all the revolutions and changes that occurred in it.

These, the System of Concentric, and that of Eccentric Spheres, seem to have been the two Systems of Astronomy, that had most credit and reputation with that part of the ancient world, who applied themselves particularly to the study of the heavens. Cleanthes, however, and the other philosophers of the Stoical sect who came after him, appear to have had a system of their own, quite different from either. But though justly renowned for their skill in dialectic, and for the security and sublimity of their moral doctrines, those sages seem never to have had any high reputation for their knowledge of the heavens; neither is the name of any one of them ever counted in the catalogue of the great astronomers, and studious observers of the Stars among the ancients. They rejected the doctrine of the Solid Spheres; and maintained, that the celestial regions were filled with a fluid ether, of too yielding a nature to carry along with it, by any motion of its own, bodies so immensely great as the Sun, Moon, and Five Planets. These, therefore, as well as the Fixed Stars, did not derive their motion from the circumambient body, but had each of them, in itself, and peculiar to itself, a vital principle of motion, which directed it to move with its own peculiar velocity, and its own peculiar direction. It was by this internal principle that the Fixed Stars revolved directly from east to west in circles parallel to the Equator, greater or less, according to their distance or nearness to the Poles, and with velocities so proportioned, 350 that each of them finished its diurnal period in the same time, in something less than twenty-three hours and fifty-six minutes. It was, by a principle of the same kind, that the Sun moved westward, for they allowed of no eastward motion in the heavens, but with less velocity than the Fixed Stars, so as to finish his diurnal period in twenty-four hours, and, consequently, to fall every day behind them, by a space of the heavens nearly equal to that which he passes over in four minutes; that is, nearly equal to a degree. This revolution of the Sun, too, was neither directly westwards, nor exactly circular; but after the Summer Solstice, his motion began gradually to decline a little southwards, appearing in his meridian to-day, further south than yesterday; and to-morrow still further south than to-day; and thus continuing every day to describe a spiral line round the Earth, which carried him gradually further and further southwards, till he arrived at the Winter Solstice. Here this spiral line began to change its direction, and to bring him gradually, every day, further and further northwards, till it again restored him to the Summer Solstice. In the same manner they accounted for the motion of the Moon, and that of the Five Planets, by supposing that each of them revolved westwards, but with directions and velocities, that were both different from one another, and continually varying; generally, however, in spherical lines, and somewhat inclined to the Equator.

This system seems never to have had the vogue. The system of Concentric as well as that of Eccentric Spheres gives some sort of reason, both for the constancy and equability of the motion of the Fixed Stars, and for the variety and uncertainty of that of the Planets. Each of them bestows some sort of coherence upon those apparently disjointed phenomena. But this other system seems to leave them pretty much as it found them. Ask a Stoic, why all the Fixed Stars perform their daily revolutions in circles parallel to each other, though of very different diameters, and with velocities so proportioned that they all finish their period at the same time, and through the whole course of it preserve the same distance and situation with regard to one another? He can give no other answer, but that the peculiar nature, or if one may say so, the caprice of each Star directs it to move in that peculiar manner. His system affords him no principle of connection, by which he can join together, in his imagination, so great a number of harmonious revolutions. But either of the other two systems, by the supposition of the solid firmament, affords this easily. He is equally at a loss to connect together the peculiarities that are observed in the motions of the other heavenly bodies; the spiral motion of them all; their alternate progression from north to south, and from south to north; the sometimes accelerated, and again retarded motions of the Sun and Moon; the direct retrograde and stationary appearances of the Planets. All these have, in his system, 351 no bond of union, but remain as loose and incoherent in the fancy, as they at first appeared to the senses, before philosophy had attempted, by giving them a new arrangement, by placing them at different distances, by assigning to each some peculiar but regular principle of motion, to methodize and dispose them into an order that should enable the imagination to pass as smoothly, and with as little embarrassment, along them, as along the most regular, most familiar, and most coherent appearances of nature.

Such were the systems of Astronomy that, in the ancient world, appear to have been adopted by any considerable party. Of all of them, the system of Eccentric Spheres was that which corresponded most exactly with the appearances of the heavens. It was not invented till after those appearances had been observed, with some accuracy, for more than a century together; and it was not completely digested by Ptolemy till the reign of Antoninus, after a much longer course of observations. We cannot wonder, therefore, that it was adapted to a much greater number of the phenomena, than either of the other two systems, which had been formed before those phenomena were observed with any degree of attention, which, therefore, could connect them together only while they were thus regarded in the gross, but which, it could not be expected, should apply to them when they came to be considered in the detail. From the time of Hipparchus, therefore, this system seems to have been pretty generally received by all those who attended particularly to the study of the heavens. That astronomer first made a catalogue of the Fixed Stars; calculated, for six hundred years, the revolutions of the Sun, Moon, and Five Planets; marked the places in the heavens, in which, during all that period, each of those bodies should appear; ascertained the times of the eclipses of the Sun and Moon, and the particular places of the Earth in which they should be visible. His calculations were founded upon this system, and as the events corresponded to his predictions, with a degree of accuracy which, though inferior to what Astronomy has since arrived at, was greatly superior to any thing which the world had then known, they ascertained, to all astronomers and mathematicians, the preference of his system, above all those which had been current before.

It was, however, to astronomers and mathematicians, only, that they ascertained this; for, notwithstanding the evident superiority of this system, to all those with which the world was then acquainted, it was never adopted by one sect of philosophers.

Philosophers, long before the days of Hipparchus, seem to have abandoned the study of nature, to employ themselves chiefly in ethical, rhetorical, and dialectical questions. Each party of them too, had by this time completed their peculiar system or theory of the universe, and no human consideration could then have induced them to give up any part of it. That supercilious and ignorant contempt too, with 352 which at this time they regarded all mathematicians, among whom they counted astronomers, seems even to have hindered them from enquiring so far into their doctrines as to know what opinions they held. Neither Cicero nor Seneca, who have so often occasion to mention the ancient systems of Astronomy, takes any notice of that of Hipparchus. His name is not to be found in the writings of Seneca. It is mentioned but once in those of Cicero, in a letter to Atticus, but without any note of approbation, as a geographer, and not as an astronomer. Plutarch, when he counts up, in his second book, concerning the opinions of philosophers, all the ancient systems of Astronomy, never mentions this, the only tolerable one which was known in his time. Those three authors, it seems, conversed only with the writings of philosophers. The elder Pliny, indeed, a man whose curiosity extended itself equally to every part of learning, describes the system of Hipparchus, and never mentions its author, which he has occasion to do often, without some note of that high admiration which he had so justly conceived for his merit. Such profound ignorance in those professed instructors of mankind, with regard to so important a part of the learning of their own times, is so very remarkable, that I thought it deserved to be taken notice of, even in this short account of the revolutions of the philosophy of the ancients.

Systems in many respects resemble machines. A machine is a little system, created to perform, as well as to connect together, in reality, those different movements and effects which the artist has occasion for. A system is an imaginary machine invented to connect together in the fancy those different movements and effects which are already in reality performed. The machines that are first invented to perform any particular movement are always the most complex, and succeeding artists generally discover that, with fewer wheels, with fewer principles of motion, than had originally been employed, the same effects may be more easily produced. The first systems, in the same manner, are always the most complex, and a particular connecting chain, or principle, is generally thought necessary to unite every two seemingly disjointed appearances: but it often happens, that one great connecting principle is afterwards found to be sufficient to bind together all the discordant phenomena that occur in a whole species of things. How many wheels are necessary to carry on the movements of this imaginary machine, the system of Eccentric Spheres! The westward diurnal revolution of the Firmament, whose rapidity carries all the other heavenly bodies along with it, requires one. The periodical eastward revolutions of the Sun, Moon, and Five Planets, require, for each of those bodies, another. Their differently accelerated and retarded motions require, that those wheels, or circles, should neither be concentric with the Firmament, nor with one another; which, more than any thing, seems to disturb the harmony of the universe. The 353 retrograde and stationary appearance of the Five Planets, as well as the extreme inconstancy of the Moon’s motion, require, for each of them, an Epicycle, another little wheel attached to the circumference of the great wheel, which still more interrupts the uniformity of the system. The motion of the apogeum of each of those bodies requires, in each of them, still another wheel, to carry the centres of their Eccentric Spheres round the centre of the Earth. And thus, this imaginary machine, though, perhaps, more simple, and certainly better adapted to the phenomena than the Fifty-six Planetary Spheres of Aristotle, was still too intricate and complex for the imagination to rest in it with complete tranquillity and satisfaction.