CHAPTER XXIII.

EUROPEAN SCIENCE IN THE SEVENTEENTH AND EARLIER YEARS OF THE EIGHTEENTH CENTURIES.

(1) MATHEMATICAL AND PHYSICAL SCIENCE.

THE seventeenth century is notable in the history of science for the development of those ideas which distinguish its modern treatment from that customary in the ancient and medieval world, and for the recognition of the principle that scientific theories must rest on the result of observations and experiments.

The influence of the Renaissance was felt in arts and letters a generation or more before it affected men of science ; but towards the end of the sixteenth century mathematicians began to open up new fields of study, and a few years later the ideas current in Mechanics and Physics were subjected to the test of experiment. These researches were undertaken independently in different parts of western Europe ; and the printing-press, the general use of one language (Latin), and increasing facilities fur travel, rendered the dissemination of new ideas comparatively easj For the first time in the history of science, British writers took a prominent part in its development.

We shall best be able to estimate the progress of mathematical and physical science during the seventeenth century, if we begin by noting the extent of the knowledge current about 1575 or 1580.

Turning first to the subject of Pure Mathematics, we may say that in Geometry the results attained by Euclid were then generally accessible, and the more elementary properties of Conic Sections were known ; but the standard of knowledge was considerably below that of the Greeks. In Arithmetic the fundamental processes and the use of the Arabic symbols were well established, though the methods employed were cumbrous. Algebra was syncopated - that is, abbreviations were used for those operations and quantities which constantly recur, but such abbreviations were subject to the rules of grammatical construction. Lastly, the more elementary propositions in Trigonometry were known. This knowledge would seem to be but a scanty equipment for the attack of new problems ; but in questions of Pure Mathematics it was used with more effect than could have been anticipated or than was supposed a few years ago. As to applied science, however, an astonishing ignorance still prevailed.

Of the several branches of applied science, the mechanics of rigid bodies is the oldest. The science of Statics, so far as it related to parallel forces, had been placed on a satisfactory basis by Archimedes, who rested it on the axiom that two equal weights suspended from a rigid weightless bar at equal distances from a fulcrum on which the bar rested would be in equilibrium. But the question of the resultant of forces, acting on a particle, had not been included in his discussions, and was still an unknown branch of the subject, with the exception of the result of the parallelogram theory for the particular case of two forces at right angles to each other acting on a particle. Dynamics as a science did not exist. It was indeed asserted on the authority of Aristotle, that the rate at which bodies fell varied directly as their weights - a statement which could have been easily disproved, had it been subjected to the test of experience ; but no theory of the subject had been propounded even on this false premiss.

In Astronomy, the authority of Ptolemy was, about 1580, almost as well established as that of Aristotle in science, though here, at any rate, observations of the stars were available, due partly to the general interest in Astrology. According to the Ptolemaic theory the Earth was at the centre of the universe, and around it revolved in successive order the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the fixed stars. These bodies were supposed to move uniformly along the circumferences of circles (epicycles) whose centres revolved uniformly along the circumferences of other circles - the centres of the last-mentioned circles (eccentrics) being at points near, but not coinciding with, the centre of the earth.

The only other subjects to which Mathematics had been applied and which need be here mentioned are Optics and Hydrostatics. In Optics the law of reflexion was known, and solutions of some of the more elementary geometrical problems connected with rays reflected at spherical surfaces were familiar through the writings of the Greeks and Arabs. In Hydrostatics the theory of floating bodies had been given by Archimedes, and probably his results were accessible to students. Of other branches of Physics, such as Sound and Electricity, we may say that the little that was known is not worth describing ; in these subjects the authority of Aristotle was unquestioned. Lastly, such knowledge of Chemistry as existed was mixed up with Alchemy, and was practically worthless.

This rapid summary will bring out more clearly than any general statement the fact that the origin of physical science and modern Mathematics cannot be assigned to a date earlier than the close of the sixteenth century. Into a world whose knowledge was so slight and limited a ferment of new ideas was then introduced, and within a few years the position of the subjects was revolutionised, and the number of thinkers interested in them was greatly increased.

It will be most convenient to review the subjects considered in the present section science by science-and, first, to trace their development very briefly to the middle of the seventeenth century, and, then, to take up again the history of each science to the end of the first quarter of the eighteenth century, which marks the close of the period treated in this volume. We begin as before with the subjects of Pure Mathematics.

The decimal notation for fractions was introduced about the same time as logarithms, and it was certainly used as an operative form by Briggs in 1617. A somewhat similar notation had been employed a few years earlier by Stevinus, Rudolff, Biirgi, and Napier, though probably only as a concise way of stating results. Up to that time fractions had been commonly written in the sexagesimal notation.

The introduction of these discoveries brought Arithmetic into its modern form, and subsequent improvements have been largely matters of detail.

Vieta's results were extended by Albert Girard (1595-1632), a Dutch mathematician. In 1629 Girard published a work which contains the earliest use of brackets, a geometrical interpretation of the negative sign, the statement that the number of roots of an algebraical equation is equal to its degree, and the distinct recognition of imaginary roots. Probably it also implies a knowledge that the first member of an algebraical equation can be resolved into linear factors. Girard's investigations were unknown to most of his contemporaries, and exercised but slight influence on the development of Mathematics.

A far more influential writer was Descartes (1596-1650). To his famous Discours on universal science, published at Leyden in 1637, were added three appendices on Optics, Meteors, and Geometry. The last of these, to which we shall refer again when dealing with Analytical Geometry, contains a section on Algebra. It has affected the language of the subject by fixing the custom of employing the letters at the beginning of the alphabet to denote known quantities, and those at the end of the alphabet to denote unknown quantities. Descartes here introduced the system of indices now in use, though he considered only positive integral indices : probably this was original on his part, but the suggestion had been made by previous writers, such as Bombelli, Stevinus, Vieta, Harriot, and Herigonus, though it had not been generally adopted. The meaning of negative and fractional indices was first given by John Wallis of Oxford (1616-1703), in his celebrated Âriihmetïca Inftnltorum, 1656. It is doubtful whether Descartes recognised that his letters might represent any quantities, positive or negative, and that it was sufficient to prove a proposition for one general case. He realised the meaning of negative quantities and used them freely. Further, he made use of the rule for finding a limit to the number of positive and of negative roots of an algebraical equation, which is still known by his name, and introduced the method of indeterminate coefficients for the solution of equations.

Elementary Trigonometry was also worked out with tolerable completeness, partly by Vieta, and partly by Girard, while the name of Napier is associated with some of the fundamental properties of spherical triangles.

The Cartesian system of Analytical Geometry was expounded by Descartes in the tract on Geometry appended to his Discours. In effect, Descartes asserted that the position of a point in a plane could be completely determined if its distances, say x and y, from two fixed lines drawn at right angles in the plane were given, with the convention familiar to us as to the interpretation of positive and negative values ; and that, though an equation f(x, y) = 0 was indeterminate and could be satisfied by an infinite number of values of x and y, yet these values of x and y determined the coordinates of a number of points which form a curve, of which the equation f(x, y) - 0 expressed some geometrical property-that is, a property true of the curve at every point on it. Descartes asserted that a point in space could be similarly determined by three coordinates ; but he confined his attention to plane curves.

It was at once seen that, in order to investigate the properties of a curve, it was sufficient to select, as a definition, any characteristic geometrical property, and to express it by means of an equation between the (current) coordinates of any point on the curve-that is, to translate the definition into the language of Analytical Geometry. The equation so obtained contains implicitly every property of the curve, and any particular property can be deduced from it by ordinary Algebra without troubling about the Geometry of the figure. This may have been dimly recognised or foreshadowed by earlier writers ; but Descartes went further and pointed out the very important facts, that two or more curves can be referred to one and the same system of coordinates, and that the points in which two curves intersect can be determined by finding the roots common to their two equations.

We need not describe the details of Descartes1 work. His great reputation ensured appreciation of his investigations, and an edition of this tract with notes by Beaune and a commentary by van Schooten, issued in 1659, became a standard text-book ; henceforth the subject was familiar to mathematicians. It should perhaps be added that it is probable that the principles of Analytical Geometry had been worked out independently by Pierre de Fermât of Toulouse (1601-65) at least as early as by Descartes ; but, as they were not then published, we need not discuss this point further.

Before leaving the subject of Pure Mathematics, we must in passing mention the theory of numbers and that of probabilities. The former, under the stimulus of the writings of one of the greatest mathematicians, Fermât, attracted considerable attention. The latter was created by Pascal (1623-62) and Fermât.

Pure Mathematics are a useful if not necessary instrument of research; but the general reader takes more interest in the history of their application than in their own-in results rather than in methods. We turn now to consider the development of applied science during this period.

The most striking achievement of this period in the eyes of an ordinary citizen of the time was the establishment of the Copernican system of Astronomy. We have already alluded to the publication by Copernicus of his hypothesis. The next stage in its development was due to Kepler (1571-1630). He served under Tycho Brahe, one of the most skilful observers of his time, and making use of Brahe's observations succeeded, after many and laborious efforts, in reducing the planetary motions to three comparatively simple laws. The first two were published in 1609, and stated that the planets describe ellipses round the sun, the sun being in a focus ; and that the line joining the sun to any planet sweeps over equal areas in equal times. The third was published in 1619, and stated that the squares of the periodic times of the planets are proportional to the cubes of the major axes of their orbits. The laws were deduced from observations on the motions of Mars and the earth, and were extended by analogy to the other planets. These laws pointed to the fact that the sun and not the earth should be regarded as the centre of the solar system. We may add that Kepler attempted to explain why these motions took place by a hypothesis which is somewhat like Descartes' theory of vortices described below. He also suggested that the tides were due to the attraction of the moon.

The invention of the telescope at the beginning of the seventeenth century facilitated observations of the nearer planets. The earliest discoveries with its aid were made by Galileo. In the spring of 1609 he heard that an optician of Middelburg had made a tube containing lenses which served to magnify objects seen through it. This gave him the clue, and he constructed a telescope of the kind which still bears his name, and of which an ordinary opera-glass is an example. The instrument magnified three diameters - that is, made objects appear as though only at one-third of their real distance. Encouraged by this success, he constructed a larger instrument of thirty-two diameters' power which magnified an object more than a thousand times. Intense interest was excited by these discoveries. He placed one of his instruments on a church tower at Venice, and, to the amazement of the merchants, showed them their ships approaching the harbour hours before any details could be detected by the eye. Turning his instrument to the heavens, he saw the lunar mountains, Jupiter's satellites, the phases of Venus, Saturn's ring, and the solar spots ; from the motion of the latter he concluded that the sun rotates on its axis. In 1611, he exhibited in the garden of the Quirinal the wonders of the new worlds revealed by the telescope.

The dramatic persecution of Galileo has concentrated public attention on his work. But it should be noted that other mathematicians were also using the telescope to good advantage. In England Harriot had a large telescope through which he observed the satellites of Jupiter in 1610. Kepler also made various observations, and suggested that the eye-glass should be a convex lens. The transit of Venus was observed by Jeremiah Horrocks in Lancashire in 1639.

The acceptance of the Copernican system brought into prominence the problem of explaining the cause of the planetary motions. Descartes suggested in his Principia that space was filled with ether moving in whirlpools of varying sizes and under varying physical conditions. He supposed that the sun was the centre of a vortex in which the planets are swept round. Each planet was again the centre of another vortex in which its moons are swept round. He explained gravity by the action of these vortices, and suggested that smaller vortices round the molecules of bodies would account for cohesion. This suggestion was widely accepted, and is interesting as a genuine attempt to explain the phenomena of the universe by mechanical laws. But Descartes' assumptions were arbitrary, and unsupported by investigation. It is not difficult to prove that on his hypothesis the sun would be in the centre of these ellipses and not at a focus (as Kepler had shown was the case), and that the weight of a body at every place on the surface of the earth except the equator would act in a direction which was not vertical. It will be sufficient here to say that Newton considered the theory in detail, and showed that its consequences are not only inconsistent with each of Kepler's laws and with the fundamental laws of Mechanics, but also at variance with the laws of nature assumed by Descartes.

The view that the velocity of light was finite, so boldly assumed by Fermât, had originated in the seventeenth century. Galileo made experiments on the subject, but was unable to arrive at a definite result, though he and the leading physicists seem to have supposed that the view was correct. It was not until 1676 that it was proved. This was done by Olaus Römer (1644-1710), a young Dane then living in Paris, by observations of the eclipses of Jupiter's moons. The theories of physical optics current at this time will be considered later.

Hydrostatics also received considerable attention during the earlier years of the seventeenth century. Here too the earliest experiments seem to have been made by Galileo, who showed that the air has weight, estimated its pressure by the height of the water column it could sustain, and definitely refuted the Aristotelian view that a vacuum could not exist. He also described his experiments on various physical subjects, notably on fluids. These investigations fairly entitle him to be termed the founder of modern Physics.

Another branch of Physics originated at this time was that connected with Electricity and Magnetism. Although there had been a few previous observations on the subject by Cardan, Mercator, and Porta, it may be said to have commenced with the work of William Gilbert (1540-1603), physician in ordinary to Queen Elizabeth. His experiments were published in 1600.

The necessity of an experimental foundation for science was in the course of this period advocated with considerable effect by Francis Bacon (1561-1626) in his Novum Organum, published in 1620. Here he laid down the principles which should guide those making experiments in any branch of Physics, and gave rules by which the results of induction could be tested. Bacon's book appealed to men of education, and helped to secure recognition for the proposition that experiment and observation are necessary preludes to the formation of scientific theories. For practical purposes, however, it was of but little use. Bacon thought that investigations could be made by rule, and did not realise that the creation of scientific hypotheses was impossible without imagination. The book had more influence among philosophers and men of letters than among scientific students.

Towards the middle of the seventeenth century the progress of scientific learning received a great stimulus, especially in England and France, from the foundation of academies or societies, created for the purpose of encouraging scientific investigations and providing a' common meeting-place where those engaged in it could interchange ideas. Some account of these associations and of the part which they played in the history of science will be found in another section of this chapter.

Great as was the advance in knowledge made during the first half of the seventeenth century, that from 1660 to 1730 was even more marked.

In the branches of Pure Mathematics previously mentioned it will suffice to say that Algebra and Trigonometry became more analytical, and that Newton's discovery of the binomial theorem and his work on the theory of equations were especially notable. Towards the end of the period the extension of Trigonometry to imaginary quantities was made by Abraham Demoivre of London (1667-1754) whose name is associated with the fundamental theorem on the subject. No new developments of Pure Geometry took place during this period ; but the classical methods were applied to various problems with extraordinary ingenuity by Newton in the first book of the Principia. The methods of Analytical Geometry were also developed and it became a familiar tool in the hands of mathematicians.

The idea of a fluxion or differential coefficient, as treated in this period, is simple. When two quantities-for instance, the radius of a sphere and its volume-are so related that a change in one causes a change in the other, the one is said to be a function of the other. The ratio of the rates at which they change is termed the differential coefficient or fluxion of the one with regard to the other, and the process by which this ratio is determined is known as differentiation. Knowing the differential coefficient and one set of corresponding values of the two quantities, we are able by summation to determine the relation between them ; but often the process is difficult. If however we can reverse the process of differentiation, we can obtain this result directly. This process of reversal is termed integration, and was first employed by Newton and Leibniz. It was at once seen that problems connected with the quadrature of curves, and the determination of volumes (which were soluble by summation, as had been shown by the employment of indivisibles) were reducible to integration. In Mechanics also, by integration, velocities could be deduced from known accelerations, and distances traversed from known velocities. In short, wherever things change according to known laws, here was a possible method of finding the relation between them. It is true that, when we try to express observed phenomena in the language of the calculus, we usually obtain an equation involving the variables, and their differential coefficients-and possibly the solution may be beyond our powers. Even so, the method is often fruitful and its use marked a real advance in thought and power.

With the various applications-important though they were-of the calculus to Geometry and Mechanics we need not concern ourselves, but one application is sufficiently important to demand a word in passing. This was the discovery in 1712 by Brook Taylor (1685-1731) of the well-known theorem by which a function of a single variable can be expanded in powers of it. It was published in 1715, though no satisfactory proof was given at the time.

Leibniz was a man of extraordinary versatility; and, in addition to his diplomatic activity, played a prominent part in the literary and philosophical history of his time. Mathematics were not his main interest, and he produced very little mathematical work of importance besides his papers on the calculus ; his reputation in this subject rests largely on the attention which he drew to it. In 1686 and 1694 he wrote papers on the principles of the new calculus. In these, his statements of the objects and methods of the infinitesimal calculus are somewhat obscure, and his attempt to place the subject on a metaphysical basis did not tend to clearness ; but the fact that all the results of modern Mathematics are expressed in the language invented by him has proved the best monument of his work.

Newton elaborated the calculus more completely than Leibniz, but his methods were buried in note-books inaccessible to all save a few friends ; and the general adoption of Leibniz' notation was largely due to the fact that, through a text-book published in 1696 by the Marquis de L'Hospital of Paris, it was at once made known to all interested in the subject. It was also regularly used by Peter Varignon (1654-1722), the most eminent French mathematician of the time, and by the brothers James Bernoulli (1654-1705) and John Bernoulli (1667-1748)- men of remarkable ability who applied the new calculus to solve numerous problems. The Bernoullis were the most prominent continental teachers of this period and their influence was exceptionally potent. The accounts at first given of Newton's method of fluxions were less complete; and more than a generation passed after the production of L'Hospital's work, before Colson in 1736, and Maclaurin in 1742, published systematic expositions of the fluxional method.

The fundamental principles of Newton's theory of gravitation seem to have occurred to him shortly after he had taken his degree at Cambridge. His reasoning at this time, 1666, appears to have been as follows. He knew that gravity extended to the tops of the highest hills ; and he conjectured that it might extend as far as the moon, and be the force which retained it in its orbit about the earth. This hypothesis he verified by the following argument. If a stone is allowed to fall near the surface of the earth, the attraction of the earth causes it to move through sixteen feet in one second. Now Newton, as also other mathematicians, had suspected from Kepler's law that the attraction of the earth on a body would be found to decrease as the body was removed further away from the earth, inversely as the square of the distance from the centre of the earth. He knew the radius of the earth and the distance of the moon, and therefore on this hypothesis could find the magnitude of the earth's attraction at the distance of the moon. Further, assuming that the moon moved in a circle, he could calculate the force that was necessary to retain it in its orbit. In 1666, his estimate of the radius of the earth was inaccurate, and, when he made the calculation, he found that this force was rather greater than the earth's attraction on the moon. This discrepancy did not shake his faith in the belief that gravity extended to the moon and varied inversely as the square of the distance ; but he conjectured that some other force - such, for example, as Descartes1 vortices - acted on the moon as well as gravity.

In 1679 Newton repeated his calculations on the lunar orbit; and, using a correct value of the radius of the earth, he found the verification of his former hypothesis was complete. He then proceeded to the general theory of the motion of a particle under a centripetal force - that is, one directed to a fixed point - and showed that the vector to the particle would sweep over equal areas in equal times. He also proved that, if a particle describes an ellipse under a centripetal force to a focus, the law must be that of the inverse square of the distance from the focus; and, conversely, that the orbit of a particle projected under the influence of such a force would be a conic. In 1684 Halley asked Newton what the orbit of a planet would be, if the law of attraction were that of the inverse square, as was commonly suspected to be approximately the case. Newton asserted that it was an ellipse, and sent the demonstration which he had discovered in 1679. Halley, at once recognising the importance of the communication, induced Newton to undertake the investigation of the whole problem of gravitation, and to publish his results.

The first book of the Principia is given up to the consideration of the motion of particles or bodies in free space either in known orbits, or under the action of known forces, or under their mutual attraction. It is prefaced by an introduction on the science of Dynamics ; it also contains geometrical investigations of various properties of conic sections. The second book treats of motion in a resisting medium. The theory of Hydrodynamics was here created, and it was applied to the phenomena of waves, tides, and acoustics. In the third book, the theorems of the first are applied to the chief phenomena of the solar system; and the masses and distances of the planets and (when sufficient data exist) of their satellites are determined. In particular, the motion of the moon, with its various inequalities, and the theory of the tides, are worked out in detail, and as fully as was then possible. Newton also investigated the theory of comets, showed that they belonged to the solar system, and illustrated his results by considering certain special comets. The complete work was published in 1687. A second edition was brought out in 1713 by Roger Cotes of Cambridge (1682-1716) under Newton's direction. The demonstrations throughout are geometrical, but are rendered unnecessarily difficult by their conciseness, and by the absence of any clue to the method by which they were obtained. The reason why the arguments were presented in a geometrical form appears to have been that the infinitesimal calculus was then unknown ; and, had Newton used it to demonstrate results which were in themselves opposed to the prevalent philosophy of the time, the controversy as to the truth of his results would have been hampered by a dispute concerning the validity of the methods used in proving them.

It should be noted that Newton's conclusions could not have been reached, had not observational Astronomy also developed. This was largely due to the excellent work done at Greenwich under Flamsteed (1646-1719), Halley (1656-1742), and Bradley (1692-1762), who successively occupied the position of Astronomer Royal. The last-named explained the aberration of light (1727), and thus obtained an independent determination of the velocity of light.

The achievements of the seventeenth century in Astronomy and Mechanics were so great that they have thrown some of the other work of the time into comparative obscurity. The investigations in Physical Optics were, however, of singular interest. Here again Newton played the leading part. When, in 1669, he was appointed to a professorship at Cambridge, he at first chose Optics for the subject of his lectures and researches ; and before the end of that year he had worked out the details of his discovery of the decomposition of a ray of white light into rays of different colours by means of a prism, from which the explanation of the phenomenon of the rainbow followed. In consequence of a chapter of accidents he failed to correct the chromatic aberration of two colours by means of a couple of prisms ; hence he abandoned the hope of making a refracting telescope which should be achromatic, and, instead, designed a reflecting telescope, which is of a somewhat different design from those suggested by James Gregory and N. Cassegrain.

The wave theory had been roughly outlined in 1665 by Robert Hooke. It was elaborated in a paper by Huygens in 1678, and expounded at greater length in his Traité de la Lumière, published in 1690. From it Huygens deduced the laws of reflexion, refraction, and double refraction. He was acquainted with the phenomena of polarisation ; but he was unable to explain them since he assumed the vibrations in the ether to be longitudinal. It was not until the nineteenth century, when Fresnel worked out the theory on the hypothesis that the vibrations were transverse, that it was put on a satisfactory basis. Huygens was among the most illustrious mathematicians of his age, and the wave theory may be fairly deemed to be due to him. The immense reputation of Newton induced a general acceptance at the time of the corpuscular theory as enunciated by him-an unfortunate result of his extraordinary achievements, and the more curious because his writings show that on some grounds he deemed the wave theory the more probable. In science, as in other subjects, too much reliance should not be placed on individual authority.

The theory of Hydrodynamics, including therein Sound and vibrations of fluids, may be said to have been created by Newton in the second book of his Principia. He determined experimentally the velocity of sound in air and other media. The difficulties of mathematical analysis involved are great, and he was not able to carry the theory very far. In connexion with the theory of Sound, may also be mentioned the names of Brook Taylor, who gave the theory of the transverse vibrations of strings, Joseph Sauveur (1653-1715), and Francis Hauksbee (1650-1713).

As to other physical subjects, we may say that in all of them, at this time, there was intelligent observation and experiment. In particular the subject of Heat was attacked on the right lines by Boyle, Hooke, Newton and others, though the experimental data available were but slight. So, too, as to the work of the time in Electricity, which attracted the attention of Boyle, Halley, Newton, Picard, and Hauksbee.

(2) OTHER BRANCHES OF SCIENCE.

The seventeenth century may, in a broad way, be spoken of as the period during which the Natural Sciences-according to our modern classification of them-Botany, Zoology, Anatomy, Physiology, Geology, and, we may add Chemistry, took definite shape, and began to be built up, each in its own way, as an independent branch of knowledge. The labours of the eighteenth and nineteenth centuries were, in their turn, largely directed towards carrying forward what had then been begun. But the impulse which led to this great development is to be found in the preceding century, or even earlier: in the revolt against the scholastic spirit which formed so large a part of the Renaissance.

The sciences in question, though having their birth partly in mere natural curiosity, sprang largely from the Art of Medicine. The treatment of disease led to enquiry into the structure and action of the body of man, and this in turn to the study of animals. The use of herbs as remedies moved men to observe the features and qualities of plants ; and the science of Chemistry, though it began as Alchemy in the search for the transmutation of metals, and continued to be supported by the needs of industrial life, was in the main developed by the desire to find substances which should cure diseases. In the sixteenth century, and long afterwards, the men who were building up the several natural sciences were to be found among the teachers of the medical schools.

Hence it is not wonderful that the first great triumph of the revolt against the scholastic spirit, though it was won in a limited and strictly medical branch of knowledge, namely Human Anatomy, served as a bright example to nearly all the branches of natural knowledge, and exerted a powerful influence upon them.

In spite of its success in the case of Anatomy, the new method was slow in laying hold of Physiology. More than half a century passed before it did so ; but, when in 1628 William Harvey (1578-1657), by the publication of his Exercltatio de Motu Cordts, shattered the Galenic Physiology as completely as Vesalius had put an end to the Galenic Anatomy, the effects were profound and far-reaching.

According to Galen, the crude venous blood, enriched in the liver by the food brought from the alimentary canal and endowed with the nutritive qualities spoken of as the "natural spirits," flows from the heart to all parts of the body along the veins, and returns back to the heart along the same channels. Some of this blood, passing from the right side of the heart to the left by minute pores in the septum of the ventricles, invisible to the eye of man, mixes there with air sucked in through the lungs by the action of the heart. This mixture is by the innate heat of the heart " concocted " into arterial blood, endowed with " vital spirits " which flows from the heart along the arteries to all parts of the body, returning by the same channels. When it reaches the ventricles of the brain, the arterial blood, by the help of air drawn in through the pores of the ethmoid, or sieve-like, bone, gives rise to " animal spirits," and, flowing as a pure spirit along the nerves, carries out sensation and movement.

Thus the doctrines of Galen had been attacked before Harvey's time ; but how little effect had been produced by these attacks is shown by the teachings of Fabricius of Aquapendente (1537-1619), who, at the close of the sixteenth century, in the chair at Padua once held by Vesalius, was, by the fame of his learning, drawing students from all parts of the world, among them William Harvey. Although Fabricius did more than anyone after Vesalius to advance Anatomy, to the end of his days he taught almost pure Galenic doctrines of the circulation, ignoring what Servetus and Caesalpinus had written, and refusing to see the real meaning of his own great discovery of the valves in the veins. It was a mixed teaching, then, of new Anatomy and old Physiology which Harvey got from Fabricius at Padua, while he studied there from 1597 to 1602. But he probably learnt much outside the anatomical theatre ; for during those years Galileo Galilei was working at and teaching the new Mechanics and Physics in Padua. It was perhaps partly at least through Galileo's influence that Harvey was led to apply the experimental method to Physiology, and to "give his mind to vivisections."

Freed, as it were, by the work of Harvey from the bonds of the Galenic doctrines, Physiology expanded rapidly in the succeeding years, developing in several more or less independent directions. Its progress was greatly helped by three things : by the rapid advance of mechanical and physical learning, by the invention of the compound microscope, and, somewhat later, by the growth of a serious, no longer fantastical, Chemistry. Harvey himself, though as we have seen he seems to have been guided by the methods of the Italian physicists, made little direct use of their results. He had no microscope to help him, and his unassisted eye failed to learn how the blood passed from the small visible arteries to the small visible veins in the lungs and in the rest of the body ; he could only say, it passed " somehow." There is in his books hardly a word of Chemistry, and, in his much later treatise on generation, such Chemistry as he makes use of is of the ancient kind. " He did not care for chemists," says Aubrey, " and was wont to speak against them with an undervalue."

His successors, however, fruitfully availed themselves of these aids. The compound microscope and the new Mechanics were soon made use of. In 1661, in a letter to Borelli on the structure of the lungs studied with the help of the compound microscope, Marcello Malpighi (1628-94) announced his discovery of minute channels, the capillaries, joining the ends of the pulmonary arteries to the beginnings of the pulmonary veins. These were more clearly seen by John Swammerdam (1637-80), and, even still more clearly, in the tail of the tadpole by Antony Leeuwenhoek (1632-1723); and, in a short time, this closed mode of junction of arteries and veins was found to obtain all over the body. Swammerdam, moreover, in 1658, and Leeuwenhoek in 1668, had discovered the red blood corpuscles, observed also, but at first not understood, by Malpighi.

In the Galenic doctrines, the use of the air in breathing was to temper the great innate heat of the heart and to provide for the escape of the " fuliginous vapours " generated during the formation of the vital spirits. Fabricius, who making use of the new mechanical learning was able to give a fairly good and correct account of the mechanics of breathing, still held to the old Galenic idea as to the use of the inspired air. The acceptance of the Harveian teaching entailed some change in this old idea, but Harvey himself was silent about it. The first step towards the truth was taken by Robert Boyle (1627-91), who, unlike Harvey, had attached himself with zeal to the rising chemical learning. In his New Experiments Physico-Mechanical touching the Air (1660), he showed that in air rarefied by the air-pump flame was extinguished and at the same time life (the life of a mouse) came to an end; thus proving that the action of the air in breathing, so far from being a tempering of heat, was on the contrary to be compared to a favouring of combustion as the source of heat. Then Robert Hooke (1635-1702) in 1667, in an experiment made before the Royal Society, showed that an animal, a dog, could be kept alive, in the absence of all movements of the chest or indeed of the lungs, by artificial respiration. He thus proved the essential feature of breathing to be the exposure of the venous blood brought by the pulmonary artery to fresh air, and that the movements of the chest were merely the means of providing repeated supplies of fresh air. This important conclusion was followed up by Lower, who in 1669 showed that the difference between venous and arterial blood, as indicated by the difference in colour, was not profound, as the Galenic doctrine supposed, but transitory, and due to the mere exposure of the venous blood to the fresh air, and to the taking-up by the blood of some of the air during the exposure ; thus he was able, by giving air, to turn the purple venous blood into bright red arterial blood, and, by keeping air away, to effect the converse change.

And in a tract on respiration, besides giving an admirable account of the mechanics of respiration, he showed that the air which is taken up by the venous blood in the lungs during its change into arterial blood is not the whole air, but the nitro-aerial part of it, that is the oxygen. Thus building on the foundation laid by their countryman Harvey, a small knot of Englishmen constructed almost the whole edifice of the theory of breathing.

One effect of Harvey's new teaching was a demand for more exact knowledge of the finer structure and nature of the parts through which the blood was continually flowing ; for the views of the older anatomists on this matter were very vague : what was not visible fibre and blood vessels they were content to call parenchyma, and any small soft part they spoke of as a gland. This demand Malpighi was, with the help of the microscope, one of the first and one of the most successful to supply. By a series of remarkable researches on the viscera, he laid the foundation of that knowledge of the tissues which forms so large a part of modern physiology. Making use of the discoveries of the ducts of pancreatic and salivary glands by Wirsung, Wharton and Stensen, and the works of Sylvius on the features of glands, he studied the kidney, the liver and the spleen. He expounded the structure of the kidney, going far beyond the initial discovery by Bellini of the uriniferous tubules. He showed that the substance of the liver was not, as Glisson had taught, a uniform parenchyma disposed irregularly between the blood vessels, but was arranged in minute masses, which he called acini, after the fashion of the salivary and other glands ; that the liver was, in fact, a huge secreting gland, secreting bile through the gall duct. And he proved that the spleen was not a gland at all but a contractile vascular organ. Thus incidentally, at one stroke, he demolished the old idea of the liver concocting two kinds of bile, the lighter yellow, and the heavier black bile, the scum and faex as it were of fermentation, the former being discharged into the intestine and the latter going to the spleen. He turned his microscope also to other parts of the body, to the skin, the tongue, the uterus, the brain, horns, hairs, bones, and the scattered lymphatic glands; he showed that each part had a definite texture or structure, special to itself; and, though the idea of "the tissues " did not come into use until long afterwards, he was on its track. He complained that the acini of the liver were so minute that their finer " structure " could not be laid bare by the very best microscope. One cannot help fancying that, with a more powerful instrument at his command, he might have been led to a knowledge of the hepatic cell and so to the cellular constitution of the organs which he studied. Other observers also, notably Leeuwenhoek, applied the microscope to the study of the structure of parts of the body; but none went so far as Malpighi.

Later in the seventeenth century, Boyle laid the foundations of modern Chemistry by severely criticising in his Sceptical Chemist (1661) those "principles" or "elements," and propounding the pregnant idea, that all matter was made up of minute "corpuscles" capable of arranging themselves in groups, small and simple, or large and complex; that each such group constituted a chemical substance ; and that chemical change was a rearrangement of groups, a chemical compound being a union of the constituents and capable of differing in qualities from either of them ; and he attained to far-seeing views as to the part played by heat in determining the arrangement of the corpuscles. But his conceptions were slow in making way.

Two other men had a much more immediate effect on the chemical learning of the century. Jean-Baptiste van Helmont (1577-1644), in whom the exact quantitative observer and experimentalist was strangely joined to the visionary, besides discovering many new chemical substances, laid hold of some important truths. He introduced the idea of "gas" as something distinct from either air or vapour, and recognised as gas sylvestre what we now know as carbonic acid gas. He developed in detail a doctrine of fermentations, and applied it to Physiology. His description of the chemical processes of the living body as a series of six "fermentative concoctions," by which the dead food is converted into blood, first venous, then arterial, and subsequently into the living active tissues-though marred by his spiritualistic ideas and his ignoring all that Harvey had done-contains much that is interesting.

Physiology and in Physics, who, while vigorously endeavouring to extend purely chemical knowledge (he was the first to have a Laboratorium), strove also to apply it to the problems of living beings and so became at the same time the great teacher of the day in both Chemistry and Medicine. Taking up the work of Johann Rudolf Glauber (1603-68), who in discovering his sal mirabile, sodium sulphate, since and even still known as "Glauber's salt," had considered it to be a compound of an acid with an alkali ; and, assisted by the labours of his pupil Otto Tachenius (d. 1670 c.), who even more clearly recognised that all salts were similarly compounds of acids and bases, and who thus gained a general conception of chemical affinity, Sylvius drew the distinction between acidum and lixivium or alkalinum-the basis of a classification of chemical substances ; he strove, indeed, to explain many if not all chemical phenomena, both in the living body and elsewhere, as the results of the actions of acids and alkalis. The bubbles rising up in the fermenting vat were according to him brought about in the same way as the bubbles which came when oil of vitriol was thrown upon chalk ; fermentation was to him the same thing as effervescence. He used the two terms indifferently and strove to explain, not only digestion in which the discoveries of Stensen, Wharton, and his own pupil Régnier de Graaf (1641-73), led him to attach great importance to saliva and pancreatic juice, the one in his view being alkaline, the other acid, but most of the changes in the body as a series of "effervescences," aided by "precipitations." Nowhere did he find need to appeal to any spiritualistic forces ; chemical action was adequate to explain all the phenomena of the living body ; and the chemical actions met with there he regarded as identical with the chemical actions seen in the beakers and retorts of the laboratory. Thus he became the chief exponent of what was called the "iatro-chemicar' school.

Meanwhile, Borelli was in like manner explaining everything from a mechanical-physical standpoint, teaching, for instance, that digestion in the stomach was a mere mechanical crushing of the food by muscular action into minutest fragments, and that secretion was a sifting through the sieve of the secreting organ of particles whose size and shape allowed them to pass through adaptive minute pores. Thus he in turn became the founder of the "iatro-physical" school.

The phlogiston theory was so powerfully advocated and proved so attractive that-though it argued burning to be a loss, and though it was thus in direct contradiction to the teaching of Boyle and Mayow- who showed that certain things, metals for instance, increased in weight by burning-the theory not only gained immediate and general acceptance, but also remained dominant during the whole of the century.

Stahl by his phlogiston theory not only profoundly influenced Chemistry and thus indirectly Physiology, but also exercised a most powerful effect on all biological enquiry by his earnest advocacy of spiritualistic conceptions. He put forward and brilliantly maintained the conception that all the chemical events of the living body, even though they might superficially resemble them, were at the bottom wholly different from the chemical changes taking place in the laboratory, since in the living body all chemical changes were directly governed by the sensitive soul (anima sensitiva) which pervaded all parts and presided over all events. The pendulum swung back from the somewhat crude materialism of Sylvius ; in the views of the eighteenth century Stahl's "sensitive soul" was dominant, and under the weaker title of " vital force " is powerful even at the present day.

In the seventeenth century some at least of the modern doctrines of the nervous system began also to take shape. In the Galenic teaching the " animal spirits " were concocted in the ventricles of the brain by a mingling of the vital spirits, brought by the arterial blood, with air drawn in directly from without through the pores of the ethmoid bone. Within the several ventricles these animal spirits carried out the various functions of the soul, which they supplied with sensations by flowing upwards along the nerves. Flowing downward along the nerves, they entered the fibres, the tendinous part of a muscle, and, by swelling these up, brought about enlargement or contraction of the muscle, the fleshy part of which played a wholly passive part, and so gave rise to movement.

An important advance was made by Francis Glisson (1597-1677), who on the one hand introduced the idea and the word " irritability," as applied to muscular and other tissues, to denote the faculty of being irritated-a conception destined to play so important a part in physiology and pathology, and on the other hand made and described the experiment which still remains as a classic lecture experiment, that a muscle in contracting does not displace water, showing that contraction is a change of form only, not of bulk. In this experiment the old Galenic teaching received its last and fatal blow.

About all these higher functions of the nervous system and the nature of the soul the exact observers Malpighi, Borelli, Lower, Sylvius and the rest were silent. Only one of these spoke on the subject, and then with a few words, mostly negative. In a lecture delivered at Paris on the anatomy of the brain (1669), Stensen, after criticising severely the views of Descartes and of Willis, on the ground that it is impossible to explain the movements of a machine, so long as we remain ignorant of the structure of its parts, and after explaining the great difficulties met with in studying the structure of the brain, anticipated modern discoveries by the suggestion that its fibres were arranged "according to some definite pattern, on which doubtless depends the diversity of sensations and movements."

These various descriptive works contained of course many references to, and discussions on, the structure and uses of the parts of plants ; but they were for the most part fragmentary, and in some cases erroneous. In the latter part of the seventeenth century a remarkable advance was marked by the almost simultaneous production, in 1671, of preliminary accounts of the structure of plants by Malpighi and Nehemiah Grew, followed by the fuller work of Malpighi in 1674, and of Grew in 1682. These works cover very much the same ground and in many cases announce the same discoveries arrived at independently, though Grew in his later work had the advantage of knowing what Malpighi had written. The two, at one bound, brought up the knowledge of the anatomy, and especially the finer anatomy, of plants, from a mere collection of scattered and more or less dubious observations to a solid and compact body of exact doctrine. They showed-Malpighi writing with the greater lucidity and pointedness, and Grew with more copious details-that the elements of the structure of a plant were woody fibres, spiral vessels, and the cells of the parenchymatous parts with the addition of the less general lactiferous vessels. They further showed how these elements were built up in the stem, with its bark, wood and pith and medullary rays, in the roots, leaves, flowers, fruits and seeds ; and how the elements, forming the roots, were first gathered up into the stem and then separated again into the branches, thus establishing the continuity of all parts. They thus laid the foundation of the Histology of Plants, to which Robert Hooke and Leeuwenhoek made some slight additions, but which otherwise remained untouched for more than a hundred years.

One other important advance was made in the seventeenth century. Although from quite early times botanists had recognised that some plants might be spoken of as fruit-bearing and female and others as not fruit-bearing and male, and Theophrastus had called attention to the fact that the female date-palm only produces fruit when the dust of the male is shaken over it, the view that the influence of a male element was necessary for the full development of a female organ into fruit was rarely expressed, and then in most cases obscurely. Some botanists, for instance Caesalpinus, held that no such influence was necessary ; and Malpighi in his very careful account of the development of seed and of the earlier stages of the growth of the embryo refers nowhere to any influence of the pollen, which he otherwise carefully described; he seems to have regarded the seed as merely a kind of bud. Grew ascribed some subtle influence to the anthers, but his account is most obscure ; and even Hay, who seems after some hesitation to have finally accepted the doctrine of sexuality, never attempted to obtain proof of the matter by experiment. In 1691, however, and more fully in 1694, Rudolf Jacob Camerarius (1665-1721) gave the direct experimental proof-namely, by removing them-that the anthers were essential to fertilisation, and showed by his careful account that he had fully grasped the importance of his discovery.

The study of animals made marked progress in the seventeenth century in two directions, affording in this respect a parallel to the study of plants. In the preceding century and even earlier the spirit of the new method of research had led men to be no longer content with the study of Aristotle's writings and the fabulous stories of travellers, but to observe for themselves, to describe the features and habits of such animals as came within their notice, and even to attempt a classification. As the zeal for travel, which was one of the marks of the age, brought back to Europe not only accounts but actual specimens of creatures hitherto unknown, and collections began to be made in the form of museums, both private and public, as well as of zoological gardens (the date of the earliest of these it seems difficult to fix), a body of exact zoological knowledge gradually grew up, expounded in such works as those of Conrad Gesner (1516-65) and of Aldrovandus (1527-1605).

In the sixteenth century, and even earlier, the new spirit of observation and enquiry did not fail to turn men's minds to the phenomena of the earth, especially as disclosed by mining operations. It led George Bauer (Georgius Agricola, 1494-1555), who lived near the mines of the Erzgebirge, to a very extensive study of metals and other minerals, and he may be said to have laid the foundations of Mineralogy. Among the objects of which he spoke as Jbssilia he included the remains of extinct animals ; but he did not recognise these as such ; he made no distinction between them and minerals possessing definite forms, and thought that they all arose in the same way-that all were the products of natural forces.

While minerals were thus being studied from the mining point of view, it was natural that the men who had been led to study animals and plants, and especially those who gathered collections of these and formed museums, should also turn their attention to minerals, precious stones and fossils. Thus Caesalpinus, Conrad Gesner, Aldrovandus and others treated of these as well as of plants and animals. But they, or at least the majority of them, failed to distinguish between ordinary minerals and the mineralised remains of extinct animals ; they spoke of the latter as "sculptured minerals," lapidesßgurati, and regarded them as lusus naturae, as the products of a mysterious vis plastica or lapidifica. This view, however, was not accepted by all. Even in the fifteenth and, later, in the sixteenth century both those remarkable men, Leonardo da Vinci and Bernard Palissy, "the Potter," (1499-1589), had argued forcibly that these fossils must be the remains of animals and plants which were once living. Yet it held its ground in a remarkable manner far on into the seventeenth century, and did not wholly disappear until the end of that century or even the beginning of the next. Hence, though many collections of fossil plants and animals were made, and many specimens carefully described, little use was made of them to interpret the history of the earth.

One man only followed in the path begun by Da Vinci, who had not only contended that fossils were the remains of once living plants and animals, but had also suggested how their presence in various places and at various depths could be explained by the action of water. That singular man, Nicolaus Stensen, in a little tract, De solido intra solidum, published in 1669, a brief preliminary statement (intended to be followed by a larger and fuller work which, however, never saw the light), after showing that fossils were really the remains of plants and animals, went on to infer from the features of the soil in which they were embedded, and from the other circumstances of their occurrence, the changes which had taken place leading to their deposition. The little work was in fact a remarkable anticipation of modern geological doctrines; but it produced no lasting effect and was soon forgotten. The seventeenth century passed away without any advance on the beginning thus made.

The story of the progress of science in the seventeenth century would not be complete without a reference to the scientific societies which were tokens of the scientific activity of the time, and powerfully promoted the advance of scientific knowledge.

During the fifteenth century the friends of the new studies began to form, in various cities of Italy, clubs or societies, the members of which, meeting together under the protection and very frequently at the house of some great or wealthy personage, used to discuss and take measures to promote the new ideas which were stirring them. A society of this kind, founded at Florence by Cosimo de1 Medici, which devoted itself to the study of the writings of Plato, thought to emphasise its platonic character by calling itself an Accademia ; and the name after a while came to be adopted by similar societies. During the sixteenth and seventeenth centuries these societies, or Academies, multiplied rapidly ; they became the fashion, so that nearly every large city in Italy had at least one, and the chief cities several. Most of the Academies busied themselves with letters or with art ; they assumed fantastic names ; they were in many cases short-lived, some of them being put down by the Church, or remaining insignificant.

Societies created for the purpose of encouraging scientific investigation, and providing a common meeting-place for the interchange of ideas.

The first society for the prosecution of physical science was established at Naples in 1560, under the name of Academia Secretorum Naturae, and under the presidency of Baptista Porta. In the course of the seventeenth century two of the Italian Academies which devoted themselves to science became famous. At Florence, a society, begun informally in 1651, under the patronage of Ferdinand II, was formally established in 1657, under the name of the Accademia del Cimenta, by Prince Leopold, at whose palace it met, and who gave it unstinted help. It devoted itself mainly to mathematical and physical science ; many, if not most, of the greater scientific men of the time were among its members ; it discussed, devised and carried out experimental researches, and in 1667 published an account of its labours under the title of Saggi di naturali esperienze fatte nelT Accademia del Cimenta. In 1667, however, Leopold's energies being withdrawn from it on his being created a Cardinal, and several of its active members, such as Borelli, having left Florence, the Academy came to an end.

At Rome, at even an earlier date, in 1603, a similar society was founded by Prince Federigo Cesi under the name of the Accademia del Lincei, which devoted itself mainly to the natural sciences. Like its sister at Florence, it authorised publications, and like its sister it had a short life only, coming to an end in 1630, upon the early death of its founder. Long afterwards-in 1784-the name was revived in the present Reale Accademia del Lincei. An Accademia flsico-matematica was founded at Rome by Giovanni Giustino Ciampini in 1677. The scientific Academy at Naples had been suppressed by Philip II, and was succeeded by another Academy of Sciences in 1695.

The Academies belonging to other European countries were founded at later dates.