Some good work was done in optics. John Baptist della Porta described, though he did not invent, the camera obscura. Burning gla.s.ses were explained. Leonard Digges even antic.i.p.ated the telescope by the use of double lenses.

Further progress in mechanics was made by Cardan who explained the lever and pulley, and by Simon Stevin who first demonstrated the resolution of forces. He also noticed the difference between stable and unstable equilibrium, and showed that the downward pressure of a liquid is independent of the shape of the vessel it is in and is dependent only on the height. He and other scholars a.s.serted the causation of the tides by the moon.

[Sidenote: Magnetism]

Magnetism was much studied. When compa.s.ses were first invented it was thought that they always pointed to the North Star under the influence of some stellar compulsion. But even in the fifteenth century it was noticed independently by Columbus and by German experimenters that the needle did not point true north. As the amount of its declination varies at {615} different places on the earth and at different times, this was one of the most puzzling facts to explain. One man believed that the change depended on climate, another that it was an individual property of each needle. About 1581 Robert Norman discovered the inclination, or dip of the compa.s.s. These and other observations were summed up by William Gilbert [Sidenote: Gilbert] in his work on _The Magnet, Magnetic Bodies and the Earth as a great Magnet_. [Sidenote: 1600] A great deal of his s.p.a.ce was taken in that valuable destructive criticism that refutes prevalent errors. His greatest discovery was that the earth itself is a large magnet. He thought of magnetism as "a soul, or like a soul, which is in many things superior to the human soul as long as this is bound by our bodily organs." It was therefore an appet.i.te that compelled the magnet to point north and south.

Similar explanations of physical and chemical properties are found in the earliest and in some of the most recent philosophers.

[Sidenote: Geography]

As might be expected, the science of geography, nourished by the discoveries of new lands, grew mightily. Even the size of the earth could only be guessed at until it had been encircled. Columbus believed that its circ.u.mference at the equator was 8000 miles. The stories of its size that circulated after Magellan were exaggerated by the people. Thus Sir David Lyndsay in his poem _The Dreme_ [Sidenote: 1528] quotes "the author of the sphere" as saying that the earth was 101,750 miles in circ.u.mference, each mile being 5000 feet. The author referred to was the thirteenth century Johannes de Sacro Bosco (John Holywood). Two editions of his work, _De Sphaera_, that I have seen, one of Venice, 1499, and one of Paris, 1527, give the circ.u.mference of the earth as 20,428 miles, but an edition published at Wittenberg in 1550 gives it as 5,400, probably an {616} attempt to reduce the author's English miles to German ones. [Sidenote: 1551] Robert Recorde calculated the earth's circ.u.mference at 21,300 miles.[2]

Rough maps of the new lands were drawn by the companions of the discoverers. Martin Waldseemuller [Sidenote: 1507] published a large map of the world in twelve sheets and a small globe about 4 1/2 inches in diameter, in which the new world is for the first time called America. The next great advance was made by the Flemish cartographer Gerard Mercator [Sidenote: Mercator, 1512-94] whose globes and maps--some of them on the projection since called by his name--are extraordinarily accurate for Europe and the coast of Africa, and fairly correct for Asia, though he represented that continent as too narrow.

He included, however, in their approximately correct positions, India, the Malay peninsula, Sumatra, Java and j.a.pan. America is very poorly drawn, for though the east coast of North America is fairly correct, the continent is too broad and the rest of the coasts vague. He made two startling antic.i.p.ations of later discoveries, the first that he separated Asia and America by only a narrow strait at the north, and the second that he a.s.sumed the existence of a continent around the south pole. This, however, he made far too large, thinking that the Tierra del Fuego was part of it and drawing it so as to come near the south coast of Africa and of Java. His maps of Europe were based on recent and excellent surveys.

[Sidenote: Astronomy]

Astronomy, the oldest of the sciences, had made much progress in the tabulation of material. The apparent orbits of the sun, moon, planets, and stars had been correctly observed, so that eclipses might be predicted, conjunction of planets calculated, and that {617} gradual movement of the sun through the signs of the zodiac known as the precession of the equinoxes, taken account of. To explain these movements the ancients started on the theory that each heavenly body moved in a perfect circle around the earth; the fixed stars were a.s.signed to one of a group of revolving spheres, the sun, moon and five planets each to one, making eight in all. But it was soon observed that the movements of the planets were too complicated to fall into this system; the number of moving spheres was raised to 27 before Aristotle and to 56 by him. To these concentric spheres later astronomers added eccentric spheres, moving within others, called epicycles, and to them epicycles of the second order; in fact astronomers were compelled:

To build, unbuild, contrive, To save appearances, to gird the sphere With centric and eccentric scribbled o'er Cycle and epicycle, orb in orb.

The complexity of this system, which moved the mirth of Voltaire and, according to Milton, of the Almighty, was such as to make it doubted by some thinkers even in antiquity. Several men thought the earth revolved on its axis, but the hypothesis was rejected by Aristotle and Ptolemy. Heracleides, in the fourth century B. C., said that Mercury and Venus circled around the sun, and in the third century Aristarchus of Samos actually antic.i.p.ated, though it was a mere guess, the heliocentric theory.

Just before Copernicus various authors seemed to hint at the truth, but in so mystical or brief a way that little can be made of their statements. Thus, Nicholas of Cusa [Sidenote: Nicholas of Cusa, 1400-64] argued that "as the earth cannot be the center of the universe it cannot lack all motion." Leonardo believed that the earth revolved on its axis, and stated that it was a star and would look, to a man on {618} the moon, as the moon does to us. In one place he wrote, "the sun does not move,"--only that enigmatical sentence and nothing more.

[Sidenote: Copernicus, 1473-1543]

Nicholas Copernicus was a native of Thorn in Poland, himself of mixed Polish and Teutonic blood. At the age of eighteen he went to the university of Cracow, where he spent three years. In 1496 he was enabled by an ecclesiastical appointment to go to Italy, where he spent most of the next ten years in study. He worked at the universities of Bologna, Padua and Ferrara, and lectured--though not as a member of the university--at Rome. His studies were comprehensive, including civil law, canon law, medicine, mathematics, and the cla.s.sics. At Padua, on May 31, 1503, he was made doctor of canon law. He also studied astronomy in Italy, talked with the most famous professors of that science and made observations of the heavens.

Copernicus's uncle was bishop of Ermeland, a spiritual domain and fief of the Teutonic Order, under the supreme suzerainty, at least after 1525, of the king of Poland. Here Copernicus spent the rest of his life; the years 1506-1512 in the bishop's palace at Heilsberg, after 1512, except for two not long stays at Allenstein, as a canon at Frauenburg.

This little town, near but not quite on the Baltic coast, is ornamented by a beautiful cathedral. On the wall surrounding the close is a small tower which the astronomer made his observatory. Here, in the long frosty nights of winter and in the few short hours of summer darkness, he often lay on his back examining the stars. He had no telescope, and his other instruments were such crude things as he put together himself. The most important was what he calls the _Instrumentum parallactic.u.m_, a wooden isosceles triangle with legs eight feet long divided into 1000 {619} divisions by ink marks, and a hypotenuse divided into 1414 divisions. With this he determined the height of the sun, moon and stars, and their deviation from the vernal point. To this he added a square (quadrum) which told the height of the sun by the shadow thrown by a peg in the middle of the square. A third instrument, also to measure the height of a celestial body, was called the Jacob's staff. His difficulties were increased by the lack of any astronomical tables save those poor ones made by Greeks and Arabs. The faults of these were so great that the fundamental star, _i.e._, the one he took by which to measure the rest, Spica, was given a longitude nearly 40 degrees out of the true one.

[Sidenote: Copernican hypothesis]

Nevertheless with these poor helps Copernicus arrived, and that very early, at his momentous conclusion. His observations, depending as they did on the weather, were not numerous. His time was spent largely in reading the cla.s.sic astronomers and in working out the mathematical proofs of his hypothesis. He found hints in quotations from ancient astronomers in Cicero and Plutarch that the earth moved, but he, for the first time, placed the planets in their true position around the sun, and the moon as a satellite of the earth. He retained the old conception of the primum mobile or sphere of fixed stars though he placed it at an infinitely greater distance than did the ancients, to account for the absence of any observed alteration (parallax) in the position of the stars during the year. He also retained the old conception of circular orbits for the planets, though at one time he considered the possibility of their being elliptical, as they are.

Unfortunately for his immediate followers the section on this subject found in his own ma.n.u.script was cut out of his printed book.

The precise moment at which Copernicus {620} formulated his theory in his own mind cannot be told with certainty, but it was certainly before 1516. He kept back his books for a long time, but his light was not placed under a bushel nevertheless. [Sidenote: 1520] The first rays of it shown forth in a tract by Celio Calcagnini of which only the t.i.tle, "That the earth moves and the heaven is still," has survived.

Some years later Copernicus wrote a short summary of his book, for private circulation only, ent.i.tled "A Short commentary on his hypotheses concerning the celestial movements." A fuller account of them was given by his friend and disciple, [Sidenote: _Narratio prima_, 1540] George Joachim, called Rheticus, who left Wittenberg, where he was teaching, to sit at the master's feet, and who published what was called _The First Account_.

Finally, Copernicus was persuaded to give his own work to the public.

Foreseeing the opposition it was likely to call forth, he tried to forestall criticism by a dedication to the Pope Paul III. Friends at Nuremberg undertook to find a printer, and one of them, the Lutheran pastor Andrew Osiander, with the best intentions, did the great wrong of inserting an anonymous preface stating that the author did not advance his hypotheses as necessarily true, but merely as a means of facilitating astronomical calculations. At last the greatest work of the century, _On the Revolutions of the Heavenly Spheres_, [Sidenote: De revolutionibus...o...b..um caelestium, 1543] came from the press; a copy was brought to the author on his death bed.

The first of the six books examines the previous authorities, the second proposes the new theory, the third discusses the precession of the equinoxes, the fourth proves that the moon circles the earth, the fifth and most important proves that the planets, including the earth, move around the sun, and gives correctly the time of the orbits of all the planets then known, from Mercury with eighty-eight days to Saturn with thirty {621} years. The sixth book is on the determination of lat.i.tude and longitude from the fixed stars. Copernicus's proofs and reasons are absolutely convincing and valid as far as they go. It remained for Galileo and Newton to give further explanations and some modifications in detail of the new theory.

[Sidenote: Reception of the Copernican theory]

When one remembers the enormous hubbub raised by Darwin's _Origin of Species_, the reception of Copernicus's no less revolutionary work seems singularly mild. The idea was too far in advance of the age, too great, too paradoxical, to be appreciated at once. Save for a few astronomers like Rheticus and Reinhold, hardly anyone accepted it at first. It would have been miraculous had they done so.

Among the first to take alarm were the Wittenberg theologians, to whose attention the new theory was forcibly brought by their colleague Rheticus. Luther alludes to the subject twice or thrice in his table talk, most clearly on June 4, 1539, when

mention was made of a certain new astronomer, who tried to prove that the earth moved and not the sky, sun and moon, just as, when one was carried along in a boat or wagon, it seemed to himself that he was still and that the trees and landscape moved. "So it goes now," said Luther, "whoever wishes to be clever must not let anything please him that others do, but must do something of his own. Thus he does who wishes to subvert the whole of astronomy: but I believe the Holy Scriptures, which say that Joshua commanded the sun, and not the earth, to stand still."

In his _Elements of Physics_, written probably in 1545, but not published until 1549, Melanchthon said:

The eyes bear witness that the sky revolves every twenty-four hours. But some men now, either for love of novelty, or to display their ingenuity, a.s.sert that the earth moves. . . . But it is hurtful and dishonorable to {622} a.s.sert such absurdities. . . . The Psalmist says that the sun moves and the earth stands fast. . . . And the earth, as the center of the universe, must needs be the immovable point on which the circle turns.

Apparently, however, Melanchthon either came to adopt the new theory, or to regard it as possible, for he left this pa.s.sage entirely out of the second edition of the same work. [Sidenote: 1550] Moreover his relations with Rheticus continued warm, and Rheinhold continued to teach the Copernican system at Wittenberg.

The reception of the new work was also surprisingly mild, at first, in Catholic circles. As early as 1533 Albert Widmanstetter had told Clement VII of the Copernican hypothesis and the pope did not, at least, condemn it. Moreover it was a cardinal, Schonberg, who consulted Paul III on the matter [Sidenote: 1536] and then urged Copernicus to publish his book, though in his letter the language is so cautiously guarded against possible heresy that not a word is said about the earth moving around the sun but only about the moon and the bodies near it so doing. [Sidenote: 1579] A Spanish theologian, Didacus a Stunica (Zuniga) wrote a commentary on Job, which was licensed by the censors, accepting the Copernican astronomy.

But gradually, as the implications of the doctrine became apparent, the church in self-defence took a strong stand against it. [Sidenote: March 5, 1616] The Congregation of the Index issued a decree saying, "Lest opinions of this sort creep in to the destruction of Catholic truth, the book of Nicholas Copernicus and others [defending his hypothesis] are suspended until they be corrected." A little later Galileo was forced, under the threat of torture, to recant this heresy.

Only when the system had become universally accepted, did the church, in 1822, first expressly permit the faithful to hold it.

The philosophers were as shy of the new light as {623} the theologians.

Bodin in France and Bacon in England both rejected it; the former was conservative at heart and the latter was never able to see good in other men's work, whether that of Aristotle or of Gilbert or of the great Pole. Possibly he was also misled by Osiander's preface and by Tycho Brahe. Giordano Bruno, however, welcomed the new idea with enthusiasm, saying that Copernicus taught more in two chapters than did Aristotle and the Peripatetics in all their works.

Astronomers alone were capable of weighing the evidence scientifically and they, at first, were also divided. Erasmus Reinhold, of Wittenberg, accepted it and made his calculations on the a.s.sumption of its truth, as did an Englishman, John Field. [Sidenote: 1556] Tycho Brahe, [Sidenote: Tycho Brahe, 1546-1601] on the other hand, tried to find a compromise between the Copernican and Ptolemaic systems. He argued that the earth could not revolve on its axis as the centrifugal force would hurl it to pieces, and that it could not revolve around the sun as in that case a change in the position of the fixed stars would be observed. Both objections were well taken, of course, considered in themselves alone, but both could be answered by a deeper knowledge.

Brahe therefore considered the earth as the center of the orbits of the moon, sun, and stars, and the sun as the center of the orbits of the planets.

The attention to astronomy had two practical corollaries, the improvement of navigation and the reform of the calendar. Several better forms of astrolabe, of "sun-compa.s.s" (or dial turnable by a magnet) and an "astronomical ring" for getting the lat.i.tude and longitude by observation of sun and star, were introduced.

[Sidenote: Reform of calendar]

The reform of the Julian calendar was needed on account of the imperfect reckoning of the length of the {624} year as exactly 365 1/4 days; thus every four centuries there would be three days too much. It was proposed to remedy this for the present by leaving out ten days, and for the future by omitting leap-year every century not divisible by 400. The bull of Gregory XIII, [Sidenote: February 24, 1582] who resumed the duties of the ancient Pontifex Maximus in regulating time, enjoined Catholic lands to rectify their calendar by allowing the fifteenth of October, 1582, to follow immediately after the fourth.

This was done by most of Italy, by Spain, Portugal, Poland, most of Germany, and the Netherlands. Other lands adopted the new calendar later, England not until 1752 and Russia not until 1917.

[1] _I.e._ the principle thus formulated in the _Encyclopaedia Britannica_, s.v. "Mathematics": "If s is any cla.s.s and zero a member of it, also if when x is a cardinal number and a member of s, also x + 1 is a member of s, then the whole cla.s.s of cardinal numbers is contained in s."

[2] Eratosthenes (276-196 B.C.) had correctly calculated the earth's circ.u.mference at 25,000, which Poseidonius (c. 135-50 B.C.) reduced to 18,000, in which he was followed by Ptolemy (2d century A.D.).

SECTION 5. PHILOSOPHY

[Sidenote: Science, religion and philosophy]

The interrelations of science, religion, and philosophy, though complex in their operation, are easily understood in their broad outlines.

Science is the examination of the data of experience and their explanation in logical, physical, or mathematical terms. Religion, on the other hand, is an att.i.tude towards unseen powers, involving the belief in the existence of spirits. Philosophy, or the search for the ultimate reality, is necessarily an afterthought. It comes only after man is sophisticated enough to see some difference between the phenomenon and the idea. It draws its premises from both science and religion: some systems, like that of Plato, being primarily religious fancy, some, like that of Aristotle, scientific realism.

The philosophical position taken by the Catholic church was that of Aquinas, Aristotelian realism. [Sidenote: The Reformers] The official commentary on the _Summa_ was written at this time by Cardinal Cajetan.

Compared to the steady orientation of the Catholic, the Protestant philosophers wavered, catching often at the latest style in thought, be it monism or pragmatism. Luther was the {625} spiritual child of Occam, and the ancestor of Kant. His individualism stood half-way between the former's nominalism and the latter's transcendentalism and subjectivism. But the Reformers were far less interested in purely metaphysical than they were in dogmatic questions. The main use they made of their philosophy was to bring in a more individual and less mechanical scheme of salvation. Their great change in point of view from Catholicism was the rejection of the sacramental, hierarchical system in favor of justification by faith. This was, in truth, a stupendous change, putting the responsibility for salvation directly on G.o.d, and dispensing with the mediation of priest and rite.

[Sidenote: Att.i.tude towards reason]

But it was the only important change, of a speculative nature, made by the Reformers. The violent polemics of that and later times have concealed the fact that in most of his ideas the Protestant is but a variety of the Catholic. Both religions accepted as axiomatic the existence of a personal, ethical G.o.d, the immortality of the soul, future rewards and punishments, the mystery of the Trinity, the revelation, incarnation and miracles of Christ, the authority of the Bible and the real presence in the sacrament. Both equally detested reason.