Almost everything that distinguishes the modern world from earlier centuries is attributable to science, which achieved its most spectacular triumphs in the seventeenth century. The Italian Renaissance, though not medieval, is not modern; it is more akin to the best age of Greece. The sixteenth century, with its absorption in theology, is more medieval than the world of Machiavelli. The modern world, so far as mental outlook is concerned, begins in the seventeeth century. No Italian of the Renaissance would have been unintelligible to Plato or Aristotle; Luther would have horrified Thomas Aquinas, but would not have been difficult for him to understand. With the seventeenth century it is different: Plato and Aristotle, Aquinas and Occam, could not have made head or tail of Newton.
The new conceptions that science introduced profoundly influenced modern philosophy. Descartes, who was in a sense the founder of modern philosophy, was himself one of the creators of seventeenth-century science. Something must be said about the methods and results of astronomy and physics before the mental atmosphere of the time in which modern philosophy began can be understood.
Four great men—Copernicus, Kepler, Galileo, and Newton—are pre-eminent in the creation of science. Of these, Copernicus belongs to the sixteenth century, but in his own time he had little influence.
Copernicus (1473–1543) was a Polish ecclesiastic, of unimpeachable orthodoxy. In his youth he travelled in Italy, and absorbed something of the atmosphere of the Renaissance. In 1500 he had a lectureship or professorship of mathematics in Rome, but in 1503 he returned to his native land, where he was a canon of Frauenburg. Much of his time seems to have been spent in combating the Germans and reforming the currency, but his leisure was devoted to astronomy. He came early to believe that the sun is at the centre of the universe, and that the earth has a twofold motion: a diurnal rotation, and an annual revolution about the sun. Fear of ecclesiastical censure led him to delay publication of his views though he allowed them to become known. His chief work, De Revolutionibus Orbium Cœlestium, was published in the year of his death (1543), with a preface by his friend Osiander saying that the heliocentric theory was only put forward as a hypothesis. It is uncertain how far Copernicus sanctioned this statement, but the question is not very important, as he himself made similar statements in the body of the book.1 The book is dedicated to the Pope, and escaped official Catholic condemnation until the time of Galileo. The Church in the lifetime of Copernicus was more liberal than it became after the Council of Trent, the Jesuits, and the revived Inquisition had done their work.
The atmosphere of Copernicus's work is not modern; it might rather be described as Pythagorean. He takes it as axiomatic that all celestial motions must be circular and uniform, and like the Greeks he allows himself to be influenced by æsthetic motives. There are still epicycles in his system, though their centres are at the sun, or, rather, near the sun. The fact that the sun is not exactly in the centre marred the simplicity of his theory. Though he had heard of the Pythagorean doctrines, he does not seem to have known of Aristarchus's heliocentric theory, but there is nothing in his speculations that could not have occurred to a Greek astronomer. What was important in his work was the dethronement of the earth from its geometrical pre-eminence. In the long run, this made it difficult to give to man the cosmic importance assigned to him in the Christian theology, but such consequences of his theory would not have been accepted by Copernicus, whose orthodoxy was sincere, and who protested against the view that his theory contradicted the Bible.
There were genuine difficulties in the Copernican theory. The greatest of these was the absence of stellar parallax. If the earth at any one point of its orbit is 186,000,000 miles from the point at which it will be in six months, this ought to cause a shift in the apparent positions of the stars, just as a ship at sea which is due north from one point of the coast will not be due north from another. No parallax was observed, and Copernicus rightly inferred that the fixed stars must be very much more remote than the sun. It was not till the nineteenth century that the technique of measurement became sufficiently precise for stellar parallax to be observed, and then only in the case of a few of the nearest stars.
Another difficulty arose as regards falling bodies. If the earth is continually rotating from west to east, a body dropped from a height ought not to fall to a
point vertically below its starting-point, but to a point somewhat further west, since the earth will have slipped away a certain distance during the time of the fall. To this difficulty the answer was found by Galileo's law of inertia, but in the time of Copernicus no answer was forthcoming.
There is an interesting book by E. A. Burtt, called The Metaphysical Foundations of Modern Physical Science (1925), which sets forth with much force the many unwarrantable assumptions made by the men who founded modern science. He points out quite truly that there were in the time of Copernicus no known facts which compelled the adoption of his system, and several which militated against it. 'Contemporary empiricists, had they lived in the sixteenth century, would have been the first to scoff out of court the new philosophy of the universe.' The general purpose of the book is to discredit modern science by suggesting that its discoveries were lucky accidents springing by chance from superstitions as gross as those of the Middle Ages. I think this shows a misconception of the scientific attitude: it is not what the man of science believes that distinguishes him, but how and why he believes it. His beliefs are tentative, not dogmatic; they are based on evidence, not on authority or intuition. Copernicus was right to call his theory a hypothesis; his opponents were wrong in thinking new hypotheses undesirable.
The men who founded modern science had two merits which are not necessarily found together: immense patience in observation, and great boldness in framing hypotheses. The second of these merits had belonged to the earliest Greek philosophers; the first existed, to a considerable degree, in the later astronomers of antiquity. But no one among the ancients, except perhaps Aristarchus, possessed both merits, and no one in the Middle Ages possessed either. Copernicus, like his great successors, possessed both. He knew all that could be known, with the instruments existing in his day, about the apparent motions of the heavenly bodies on the celestial sphere, and he perceived that the diurnal rotation of the earth was a more economical hypothesis than the revolution of all the celestial spheres. According to modern views, which regard all motion as relative, simplicity is the only gain resulting from his hypothesis, but this was not his view or that of his contemporaries. As regards the earth's annual revolution, there was again a simplification, but not so notable a one as in the case of the diurnal rotation. Copernicus still needed epicycles, though fewer than were needed in the Ptolemaic system. It was not until Kepler discovered his laws that the new theory acquired its full simplicity.
Apart from the revolutionary effect on cosmic imagination, the great merits of the new astronomy were two: first, the recognition that what had been believed since ancient times might be false; second, that the test of scientific truth is patient collection of facts, combined with bold guessing as to laws binding the facts together. Neither merit is so fully developed in Copernicus as in his successors, but both are already present in a high degree in his work.
Some of the men to whom Copernicus communicated his theory were German Lutherans, but when Luther came to know of it, he was profoundly shocked. 'People give ear,' he said, 'to an upstart astrologer who strove to show that the earth revolves, not the heavens or the firmament, the sun and the moon. Whoever wishes to appear clever must devise some new system, which of all systems is of course the very best. This fool wishes to reverse the entire science of astronomy; but sacred Scripture tells us that Joshua commanded the sun to stand still, and not the earth.' Calvin similarly, demolished Copernicus with the text: 'The world also is stablished, that it cannot be moved' (Psa. xciii. 1), and exclaimed: 'Who will venture to place the authority of Copernicus above that of the Holy Spirit?' Protestant clergy were at least as bigoted as Catholic ecclesiastics; nevertheless there soon came to be much more liberty of speculation in Protestant than in Catholic countries, because in Protestant countries the clergy had less power. The important aspect of Protestantism was schism, not heresy, for schism led to national Churches, and national Churches were not strong enough to control the lay government. This was wholly a gain, for the Churches, everywhere, opposed as long as they could practically every innovation that made for an increase of happiness or knowledge here on earth.
Copernicus was not in a position to give any conclusive evidence in favour of his hypothesis, and for a long time astronomers rejected it. The next astronomer of importance was Tycho Brahe (1546–1601), who adopted an intermediate position: he held that the sun and moon go round the earth, but the planets go round the sun. As regards theory he was not very original. He gave, however, two good reasons against Aristotle's view that everything above the moon is unchanging. One of these was the appearance of a new star in 1572, which was found to have no daily parallax, and must therefore be more distant than the moon. The other reason was derived from observation of comets, which were also found to be distant. The reader will remember Aristotle's doctrine that change and decay are confined to the sublunary sphere; this, like everything else that Aristotle said on scientific subjects, proved an obstacle to progress.
The importance of Tycho Brahe was not as a theorist, but as an observer, first under the patronage of the king of Denmark, then under the Emperor Rudolf II. He made a star catalogue, and noted the positions of the planets throughout many years. Towards the end of his life Kepler, then a young man, became his assistant. To Kepler his observations were invaluable.
Kepler (1571–1630) is one of the most notable examples of what can be achieved by patience without much in the way of genius. He was the first important astronomer after Copernicus to adopt the heliocentric theory, but Tycho Brahe's data showed that it could not be quite right in the form given to it by Copernicus. He was influenced by Pythagoreanism, and more or less fancifully inclined to sun-worship, though a good Protestant. These motives no doubt gave him a bias in favour of the heliocentric hypothesis. His Pythagoreanism also inclined him to follow Plato's Timaeus in supposing that cosmic significance must attach to the five regular solids. He used them to suggest hypotheses to his mind; at last, by good luck, one of these worked.
Kepler's great achievement was the discovery of his three laws of planetary motion. Two of these he published in 1609, and the third in 1619. His first law states: The planets describe elliptic orbits, of which the sun occupies one focus. His second law states: The line joining a planet to the sun sweeps out equal areas in equal times. His third law states: The square of the period of revolution of a planet is proportional to the cube of its average distance from the sun.
Something must be said in explanation of the importance of these laws.
The first two laws, in Kepler's time, could only be proved in the case of Mars; as regards the other planets, the observations were compatible with them, but not such as to establish them definitely. It was not long, however, before decisive confirmation was found.
The discovery of the first law, that the planets move in ellipses, required a greater effort of emancipation from tradition than a modern man can easily realize. The one thing upon which all astronomers, without exception, had been agreed, was that all celestial motions are circular, or compounded of circular motions. Where circles were found inadequate to explain planetary motions, epicycles were used. An epicycle is the curve traced by a point on a circle which rolls on another circle. For example: take a big wheel and fasten it flat on the ground; take a smaller wheel (also flat on the ground) which has a nail through it, and roll the smaller wheel round the big wheel, with the point of the nail touching the ground. Then the mark of the nail in the ground will trace out an epicycle. The orbit of the moon, in relation to the sun, is roughly of this kind: approximately, the earth describes a circle round the sun, and the moon meanwhile describes a circle round the earth. But this is only an approximation. As observation grew more exact, it was found that no system of epicycles would exactly fit the facts. Kepler's hypothesis, he found, was far more closely in accord with the recorded positions of Mars than was that of Ptolemy, or even that of Copernicus.
The substitution of ellipses for circles involved the abandonment of the æsthetic bias which had governed astronomy ever since Pythagoras. The circle was a perfect figure, and the celestial orbs were perfect bodies—originally gods, and even in Plato and Aristotle closely related to gods. It seemed obvious that a perfect body must move in a perfect figure. Moreover, since the heavenly bodies move freely, without being pushed or pulled, their motion must be 'natural'. Now it was easy to suppose that there is something 'natural' about a circle, but not about an ellipse. Thus many deep-seated prejudices had to be discarded before Kepler's first law could be accepted. No ancient, not even Aristarchus of Samos, had anticipated such an hypothesis.
The second law deals with the varying velocity of the planet at different points of its orbit. If S is the sun, and P1, P2 P3, P4 P5 are successive positions of the planet at equal intervals of time—say at intervals of a month—then Kepler's law states that the areas P1SP2, P2SP3, P3SP4, P4SP5are all equal. The planet, therefore moves fastest when it is nearest to the sun, and slowest when it is farthest from it. This, again, was shocking; a planet ought to be too stately to hurry at one time and dawdle at another.
The third law was important because it compared the movements of different planets, whereas the first two laws dealt with the several planets singly. The third law says: If r is the average distance of a planet from the sun, and T is the length of its year, then r3divided by T2 is the same for all the different planets. This law afforded the proof (as far as the solar system is concerned) of Newton's law of the inverse square for gravitation. But of this we shall speak later.
Galileo (1564–1642) is the greatest of the founders of modern science, with the possible exception of Newton. He was born on about the day on which Michelangelo died, and he died in the year in which Newton was born. I commend these facts to those (if any) who still believe in metempsychosis. He is important as an astronomer, but perhaps even more as the founder of dynamics.
Galileo first discovered the importance of acceleration in dynamics. 'Acceleration' means change of velocity, whether in magnitude or direction; thus a body moving uniformly in a circle has at all times an acceleration towards the centre of the circle. In the language that had been customary before this time, we might say that he treated uniform motion in a straight line as alone 'natural', whether on earth or in the heavens. It had been thought 'natural' for heavenly bodies to move in circles, and for terrestrial bodies to move in straight lines; but moving terrestrial bodies, it was thought, would gradually cease to move if they were let alone. Galileo held, as against this view, that every body, if left alone, will continue to move in a straight line with uniform velocity; any change, either in the rapidity or the direction of motion, requires to be explained as due to the action of some 'force'. This principle was enunciated by Newton as the 'first law of motion'. It is also called the law of inertia. I shall return to its purport later, but first something must be said as to the detail of Galileo's discoveries.
Galileo was the first to establish the law of falling bodies. This law, given the concept of 'acceleration', is of the utmost simplicity. It says that, when a body is falling freely, its acceleration is constant, except in so far as the resistance of the air may interfere; further, the acceleration is the same for all bodies, heavy or light, great or small. The complete proof of this law was not possible until the air pump had been invented, which was about 1654. After this, it was possible to observe bodies falling in what was practically a vacuum, and it was found that feathers fell as fast as lead. What Galileo proved was that there is no measurable difference between large and small lumps of the same substance. Until his time it had been supposed that a large lump of lead would fall much quicker than a small one, but Galileo proved by experiment that this is not the case. Measurement, in his day, was not such an accurate business as it has since become; nevertheless he arrived at the true law of falling bodies. If a body is falling freely in a vacuum, its velocity increases at a constant rate. At the end of the first second, its velocity will be 32 feet per second; at the end of another second, 64 feet per second; at the end of the third, 96 feet per second; and so on. The acceleration, i.e. the rate at which the velocity increases, is always the same; in each second, the increase of velocity is (approximately) 32 feet per second.
Galileo also studied projectiles, a subject of importance to his employer, the duke of Tuscany. It had been thought that a projectile fired horizontally will move horizontally for a while, and then suddenly begin to fall vertically. Galileo showed that, apart from the resistance of the air, the horizontal velocity would remain constant, in accordance with the law of inertia, but a vertical velocity would be added, which would grow according to the law of falling bodies. To find out how the projectile will move during some short time, say a second, after it has been in flight for some time, we proceed as follows: First, if it were not falling, it would cover a certain horizontal distance, equal to that which it covered in the first second of its flight. Second, if it were not moving horizontally, but merely falling, it would fall vertically with a velocity proportional to the time since the flight began. In fact, its change of place is what it would be if it first moved horizontally for a second with the initial velocity, and then fell vertically for a second with a velocity proportional to the time during which it has been in flight. A simple calculation shows that its consequent course is a parabola, and this is confirmed by observation except in so far as the resistance of the air interferes.
The above gives a simple instance of a principle which proved immensely fruitful in dynamics, the principle that, when several forces act simultaneously, the effect is as if each acted in turn. This is part of a more general principle called the parallelogram law. Suppose, for example, that you are on the deck of a moving ship, and you walk across the deck. While you are walking the ship has moved on, so that, in relation to the water, you have moved both forward and across the direction of the ship's motion. If you want to know where you will have got to in relation to the water, you may suppose that first you stood still while the ship moved, and then, for an equal time, the ship stood still while you walked across it. The same principle applies to forces. This makes it possible to work out the total effect of a number of forces, and makes it feasible to analyse physical phenomena, discovering the separate laws of the several forces to which moving bodies are subject. It was Galileo who introduced this immensely fruitful method.
In what I have been saying, I have tried to speak, as nearly as possible, in the language of the seventeenth century. Modern language is different in important respects, but to explain what the seventeenth century achieved it is desirable to adopt its modes of expression for the time being.
The law of inertia explained a puzzle which, before Galileo, the Copernican system had been unable to explain. As observed above, if you drop a stone from the top of a tower, it will fall at the foot of the tower, not somewhat to the west of it; yet, if the earth is rotating, it ought to have slipped away a certain distance during the fall of the stone. The reason this does not happen is that the stone retains the velocity of rotation which, before being dropped, it shared with everything else on the earth's surface. In fact, if the tower were high enough, there would be the opposite effect to that expected by the opponents of Copernicus. The top of the tower, being further from the centre of the earth than the bottom, is moving faster, and therefore the stone should fall slightly to the east of the foot of the tower. This effect, however, would be too slight to be measurable.
Galileo ardently adopted the heliocentric system; he corresponded with Kepler, and accepted his discoveries. Having heard that a Dutchman had lately invented a telescope, Galileo made one himself, and very quickly discovered a number of important things. He found that the Milky Way consists of a multitude of separate stars. He observed the phases of Venus, which Copernicus knew to be implied by his theory, but which the naked eye was unable to perceive. He discovered the satellites of Jupiter, which, in honour of his employer, he called 'sidera medicea'. It was found that these satellites obey Kepler's laws. There was, however, a difficulty. There had always been seven heavenly bodies, the five planets and the sun and moon; now seven is a sacred number. Is not the Sabbath the seventh day? Were there not the seven-branched candlesticks and the seven churches of Asia? What, then, could be more appropriate than that there should be seven heavenly bodies? But if we have to add Jupiter's four moons, that makes eleven—a number which has no mystic properties. On this ground the traditionalists denounced the telescope, refused to look through it, and maintained that it revealed only delusions. Galileo wrote to Kepler wishing they could have a good laugh together at the stupidity of 'the mob'; the rest of his letter makes it plain that 'the mob' consisted of the professors of philosophy, who tried to conjure away Jupiter's moons, using 'logic-chopping arguments as though they were magical incantations'.
Galileo, as everyone knows, was condemned by the Inquisition, first privately in 1616, and then publicly in 1633, on which latter occasion he recanted, and promised never again to maintain that the earth rotates or revolves. The Inquisition was successful in putting an end to science in Italy, which did not revive there for centuries. But it failed to prevent men of science from adopting the heliocentric theory, and did considerable damage to the Church by its stupidity. Fortunately there were Protestant countries, where the clergy, however anxious to do harm to science, were unable to gain control of the State.
Newton (1642–1727) achieved the final and complete triumph for which Copernicus, Kepler, and Galileo had prepared the way. Starting from his three laws of motion—of which the first two are due to Galileo—he proved that Kepler's three laws are equivalent to the proposition that every planet, at every moment, has an acceleration towards the sun which varies inversely as the square of the distance from the sun. He showed that acceleration towards the earth and sun, following the same formula, explains the moon's motion, and that the acceleration of falling bodies on the earth's surface is again related to that of the moon according to the inverse square law. He defined 'force' as the cause of change of motion, i.e. of acceleration. He was thus able to enunciate his law of universal gravitation: 'Every body attracts every other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.' From this formula he was able to deduce everything in planetary theory: the motions of the planets and their satellites, the orbits of comets, the tides. It appeared later that even the minute departures from elliptical orbits on the part of the planets were deducible from Newton's law. The triumph was so complete that Newton was in danger of becoming another Aristotle, and imposing an insuperable barrier to progress. In England, it was not till a century after his death that men freed themselves from his authority sufficiently to do important original work in the subjects of which he had treated.
The seventeenth century was remarkable, not only in astronomy and dynamics, but in many other ways connected with science.
Take first the question of scientific instruments.2 The compound microscope was invented just before the seventeenth century, about 1590. The telescope was invented in 1608, by a Dutchman named Lippershey, though it was Galileo who first made serious use of it for scientific purposes. Galileo also invented the thermometer—at least, this seems most probable. His pupil Torricelli invented the barometer. Guericke (1602–86) invented the air pump. Clocks, though not new, were greatly improved in the seventeenth
century, largely by the work of Galileo. Owing to these inventions, scientific observation became immensely more exact and more extensive than it had been at any former time.
Next, there was important work in other sciences than astronomy and dynamics. Gilbert (1540–1603) published his great book on the magnet in 1600. Harvey (1578–1657) discovered the circulation of the blood, and published his discovery in 1628. Leeuwenhoek (1632–1723) discovered spermatozoa, though another man, Stephen Hamm, had discovered them, apparently, a few months earlier; Leeuwenhoek also discovered protozoa or unicellular organisms, and even bacteria. Robert Boyle (1627–91) was, as children were taught when I was young, 'the father of chemistry and son of the Earl of Cork'; he is now chiefly remembered on account of 'Boyle's Law', that in a given quantity of gas at a given temperature, pressure is inversely proportional to volume.
I have hitherto said nothing of the advances in pure mathematics, but these were very great indeed, and were indispensable to much of the work in the physical sciences. Napier published his invention of logarithms in 1614. Co-ordinate geometry resulted from the work of several seventeenth-century mathematicians, among whom the greatest contribution was made by Descartes. The differential and integral calculus was invented independently by Newton and Leibniz; it is the instrument for almost all higher mathematics. These are only the most outstanding achievements in pure mathematics; there were innumerable others of great importance.
The result of the scientific work we have been considering was that the outlook of educated men was completely transformed. At the beginning of the century, Sir Thomas Browne took part in trials for witchcraft; at the end, such a thing would have been impossible. In Shakespeare's time, comets were still portents; after the publication of Newton's Principia in 1687, it was known that he and Halley had calculated the orbits of certain comets, and that they were as obedient as the planets to the law of gravitation. The reign of law had established its hold on men's imaginations, making such things as magic and sorcery incredible. In 1700 the mental outlook of educated men was completely modern; in 1600, except among a very few, it was still largely medieval.
In the remainder of this chapter I shall try to state briefly the philosophical beliefs which appeared to follow from seventeenth-century science, and some of the respects in which modern science differs from that of Newton.
The first thing to note is the removal of almost all traces of animism from the laws of physics. The Greeks, though they did not say so explicitly, evidently considered the power of movement a sign of life. To common-sense observation it seems that animals move themselves, while dead matter only moves when impelled by an external force. The soul of an animal, in Aristotle, has various functions, and one of them is to move the animal's body. The sun and planets, in Greek thinking, are apt to be gods, or at least regulated and moved by gods. Anaxagoras thought otherwise, but was impious. Democritus thought otherwise, but was neglected, except by the Epicureans, in favour of Plato and Aristotle. Aristotle's forty-seven or fifty-five unmoved movers are divine spirits, and are the ultimate source of all the motion in the heavens. Left to itself, any inanimate body would soon become motionless; thus the operation of soul on matter has to be continuous if motion is not to cease.
All this was changed by the first law of motion. Lifeless matter, once set moving, will continue to move for ever unless stopped by some external cause. Moreover the external causes of change of motion turned out to be themselves material, whenever they could be definitely ascertained. The solar system, at any rate, was kept going by its own momentum and its own laws; no outside interference was needed. There might still seem to be need of God to set the mechanism working; the planets, according to Newton, were originally hurled by the hand of God. But when He had done this, and decreed the law of gravitation, everything went on by itself without further need of divine intervention. When Laplace suggested that the same forces which are now operative might have caused the planets to grow out of the sun, God's share in the course of nature was pushed still further back. He might remain as Creator, but even that was doubtful, since it was not clear that the world had a beginning in time. Although most of the men of science were models of piety, the outlook suggested by their work was disturbing to orthodoxy, and the theologians were quite justified in feeling uneasy.
Another thing that resulted from science was a profound change in the conception of man's place in the universe. In the medieval world, the earth was the centre of the heavens, and everything had a purpose concerned with man. In the Newtonian world, the earth was a minor planet of a not specially distinguished star; astronomical distances were so vast that the earth, in comparison, was a mere pin-point. It seemed unlikely that this immense apparatus was all designed for the good of certain small creatures on this pin-point. Moreover purpose, which had since Aristotle formed an intimate part of the conception of science, was now thrust out of scientific procedure. Anyone might still believe that the heavens exist to declare the glory of God, but no one could let this belief intervene in an astronomical calculation. The world might have a purpose, but purposes could no longer enter into scientific explanations.
The Copernican theory should have been humbling to human pride, but in fact the contrary effect was produced, for the triumphs of science revived human pride. The dying ancient world had been obsessed with a sense of sin, and had bequeathed this as an oppression to the Middle Ages. To be humble before God was both right and prudent, for God would punish pride. Pestilences, floods, earthquakes, Turks, Tartars, and comets perplexed the gloomy centuries, and it was felt that only greater and greater humility would avert these real or threatened calamities. But it became impossible to remain humble when men were achieving such triumphs:
Nature and Nature's laws lay hid in night.
God said 'Let Newton be', and all was light.
And as for damnation, surely the Creator of so vast a universe had something better to think about than sending men to hell for minute theological errors. Judas Iscariot might be damned, but not Newton, though he were an Arian.
There were of course many other reasons for self-satisfaction. The Tartars had been confined to Asia, and the Turks were ceasing to be a menace. Comets had been humbled by Halley, and as for earthquakes, though they were still formidable, they were so interesting that men of science could hardly regret them. Western Europeans were growing rapidly richer, and were becoming lords of all the world: they had conquered North and South America, they were powerful in Africa and India, respected in China and feared in Japan. When to all this were added the triumphs of science, it is no wonder that the men of the seventeenth century felt themselves to be fine fellows, not the miserable sinners that they still proclaimed themselves on Sundays.
There are some respects in which the concepts of modern theoretical physics differ from those of the Newtonian system. To begin with, the conception of 'force', which is prominent in the seventeenth century, has been found to be superfluous. 'Force', in Newton, is the cause of change of motion, whether in magnitude or direction. The notion of cause is regarded as important, and force is conceived imaginatively as the sort of thing that we experience when we push or pull. For this reason it was considered an objection to gravitation that it acted at a distance, and Newton himself conceded that there must be some medium by which it was transmitted. Gradually it was found that all the equations could be written down without bringing in forces. What was observable was a certain relation between acceleration and configuration; to say that this relation was brought about by the intermediacy of 'force' was to add nothing to our knowledge. Observation shows that planets have at all times an acceleration towards the sun, which varies inversely as the square of their distance from it. To say that this is due to the 'force' of gravitation is merely verbal, like saying that opium makes people sleep because it has a dormitive virtue. The modern physicist, therefore, merely states formulae which determine accelerations, and avoids the word 'force' altogether. 'Force' was the faint ghost of the vitalist view as to the causes of motions, and gradually the ghost has been exorcized.
Until the coming of quantum mechanics, nothing happened to modify in any degree what is the essential purport of the first two laws of motion, namely this: that the laws of dynamics are to be stated in terms of accelerations. In this respect, Copernicus and Kepler are still to be classed with the ancients; they sought laws stating the shapes of the orbits of the heavenly bodies. Newton made it clear that laws stated in this form could never be more than approximate. The planets do not move in exact ellipses, because of the perturbations caused by the attractions of other planets. Nor is the orbit of a planet ever exactly repeated, for the same reason. But the law of gravitation, which dealt with accelerations, was very simple, and was thought to be quite exact until two hundred years after Newton's time. When it was amended by Einstein, it still remained a law dealing with accelerations.
It is true that the conservation of energy is a law dealing with velocities, not accelerations. But in calculations which use this law it is still accelerations that have to be employed.
As for the changes introduced by quantum mechanics, they are very profound, but still, to some degree, a matter of controversy and uncertainty.
There is one change from the Newtonian philosophy which must be mentioned now, and that is the abandonment of absolute space and time. The reader will remember a mention of this question in connection with Democritus. Newton believed in a space composed of points, and a time composed of instants, which had an existence independent of the bodies and events that occupied them. As regards space, he had an empirical argument to support his view, namely that physical phenomena enable us to distinguish absolute rotation. If the water in a bucket is rotated, it climbs up the sides and is depressed in the centre; but if the bucket is rotated while the water is not, there is no such effect. Since his day, the experiment of Foucault's pendulum has been devised, giving what has been considered a demonstration of the earth's rotation. Even on the most modern views, the question of absolute rotation presents difficulties. If all motion is relative, the difference between the hypothesis that the earth rotates and the hypothesis that the heavens revolve is purely verbal; it is no more than the difference between 'John is the father of James' and 'James is the son of John'. But if the heavens revolve, the stars move faster than light, which is considered impossible. It cannot be said that the modern answers to this difficulty are completely satisfying, but they are sufficiently satisfying to cause almost all physicists to accept the view that motion and space are purely relative. This, combined with the amalgamation of space and time into space-time, has considerably altered our view of the universe from that which resulted from the work of Galileo and Newton. But of this, as of quantum theory, I will say no more at this time.