By W. W. ROUSE BALL, M.A., Fellow and late Tutor of Trinity College.

Scientific progress in the seventeenth and the earlier years of the eighteenth centuries.706

Mathematical and Applied Science in the sixteenth century. 707-8

Arithmetic. Introduction of logarithms and decimals.708-9

Development of Algebra and Trigonometry.709

Development of Geometry..710-1

Development of Mechanics..712

Development of Astronomy. Galileo. 713

His astronomical work..714

Development of Physics..715-6

Invention of the Infinitesimal Calculus.. 716-8

Leibniz and Newton.. 718

Newton's theory of gravitation.719

His Principia.. 720

Physical Optics.. 721

Development of Physics. Hydrodynamics. Heat. 722

Great development of mathematical science.722


By the late Sir MICHAEL FOSTER, K.C.B., F.R.S., Fellow of Trinity College, formerly Professor of Physiology.

Advance of the Natural Sciences in the seventeenth century. 723

Human Anatomy. Vesalius.723

Bacon and the new method.724

Physiology. Harvey's predecessors. 725

Harvey. 726

His successors.. 727

Boyle. Hooke. Mayow..728

Malpighi. 729

Chemistry: Boyle. Van Helmont. Sylvius.730

The iatro-chemical and iatro-physical schools.731

Stahl's phlogiston theory..732

Nervous Physiology.. 733

Higher Nervous Physiology. Botany.. 734

Structural Botany and Vegetable Physiology.735

Sexuality in plants. Zoology.736

Systematic Zoology and Comparative Anatomy.737

Mineralogy.. 738

Anticipation of Geology. Stensen. 739

Early Academies.. 740

Scientific Academies and Societies. 740-1




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.

In the early years of the seventeenth century the views of astronomers were recast ; the principles of Dynamics were laid down ; a science of Physics was initiated ; and, lastly, new branches of Mathematics were created and applied to these and other subjects. Before the close of the period treated in this volume the language of Mathematics had been settled ; the use of Analytical Geometry and the Infinitesimal Calculus had become familiar; the theory of Mechanics had been elaborated, and it had been shown that the planetary motions could be explained by the same laws as those affecting terrestrial bodies ; a large part of the theory of fluids had been established ; the geometrical and physical theories of Light had been worked out in considerable detail; something had been done towards creating a theory of Acoustics ; and the fundamental problems of vibratory motion were being attacked.

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.

As time went on, and more accurate observations were accessible,

additional epicycles had to be introduced to bring the theory into accordance with the facts, and it became increasingly complicated. In so far as Ptolemy and his followers supposed it necessary to resolve every celestial motion into a series of uniform circular motions, they erred greatly ; but, if their hypothesis be regarded as a convenient way of expressing known facts, it was not only legitimate but convenient. The geocentric theory was generally accepted, but never received universal assent. The merit of finally overthrowing it must be largely attributed to Copernicus (1473-154)3). He showed that the observed phenomena could be explained more simply on the hypothesis that the sun was at the centre of the universe, and that the earth and other planets moved round it ; but he offered no proof that these views were correct, and his explanations suffered from the fact that he supposed the heavenly bodies to move uniformly in circles. It was not until Kepler and Galileo took up the subject that the majority of scientific men abandoned the Ptolemaic theory.

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 power of Arithmetic in dealing with numerical calculations involving multiplication or division was greatly increased by the invention of logarithms. Their discovery was due to Napier of Merchistoun (1550-1617), who published his results in 1614, though he had privately

communicated a summary of them to Tycho Brahe so early as 1594. The principle depends on the construction of tables of the powers of some number (the base), such as will enable us to determine from the result the power to which the base was raised. Using such a table and the law of indices, we can by addition obtain the result of the multiplication of two or more numbers ; similarly, division and extraction of roots are reduced to easy steps. Tables of the powers of the base corresponding to the sines and tangents of all angles in the first quadrant for differences of a minute were given by Napier. In numerical calculations the best base is 10 : this was suggested by Henry Briggs (1561-1631) in 1616, and its advantage was recognised by Napier. Tables of the logarithms of natural numbers to the base 10 were issued by Briggs in 1617, and of sines and tangents of angles by Edmund Gunter of London in 1620, both then Gresham Lecturers in London. Fuller tables were issued later, and by 1630 a knowledge of logarithms was common. It is possible, with the aid of a table of logarithms, to construct a machine known as a " slide-rule," by which the results of logarithmic calculations can be read off at once without calculation. Slide-rules were invented by Gunter in 1624, and are now in general use in laboratories and workshops.

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.

At the close of the sixteenth century the art of Algebra began to assume its modern or symbolic form. In this it has a language of its own and a system of notation which has no obvious connexion with the things represented, while the operations are performed according to rules distinct from those of grammar. The credit of introducing this was mainly due to Francis Vieta of Paris (1540-1603). In his principal work, published in 1591, he used letters for both known and unknown positive quantities. In it he also introduced for the powers of quantities a notation which was a marked advance on that previously prevalent by which new symbols had been introduced to represent the square, cube, etc., of quantities which had already occurred in the equations. In a posthumous work published in 1615 Vieta dealt with the elements of the theory of equations, and in particular explained how the coefficients in an algebraical equation involving one unknown quantity could be expressed as functions of the roots. Similar results are found in the Algebra by Thomas Harriot of London (1560-1621), which was first printed in 1631. It is more analytical than any Algebra that preceded

it, and marks an advance both in symbolism and notation. It is not certain whether he made use of Vieta's results or discovered the results independently ; but the former supposition seems the more probable.

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.

In Geometry new methods of considerable power were introduced at this time. One of these was due to Gérard Desargues (1593-1662) who in 1639 published a work containing the fundamental theorems on involution, homology, poles and polars, and perspective. Desargues gave lectures in Paris from 1626 for a few years, and it is believed exercised great influence on Descartes, Pascal, and other French mathematicians of the time. But his system of Projective Geometry fell into comparative

oblivion mainly owing to the fact that the system of Analytical Geometry introduced by Descartes was far more powerful as a method of research.

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.

More than one writer at this time concerned himself with the division of quantities, such as areas and volumes, into infinitesimals, and with the summation of such infinitesimals, thus escaping the long and tedious method of exhaustions used by the Greeks. In this connexion we should in particular mention the names of Kepler, Cavalieri, and somewhat later that of Fermât. The most important exposition of the subject was that given by Wallis in 1656, in which he applied it to determine the quadrature of a curve whot>e equation could be expressed in the form

y = [Sigma]ax[potence m]. These investigations foreshadowed the introduction of the infinitesimal calculus by Newton and Leibniz towards the end of the seventeenth century.

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.

As before, we begin with Mechanics. Simon Stevinus of Bruges (1548-1620), who died at the Hague, used, though he did not explicitly enunciate, the triangle of forces, which he treated as the fundamental theorem of Statics (1586). A similar position was taken up by Galileo (1564-1642). A year or two later the last-mentioned mathematician laid the foundations of the science of Dynamics. In 1589, when professor at Pisa, he made experiments from the leaning tower there on the rate at which bodies of different weights would fall. It was at once apparent that the generally accepted assertion of Aristotle was incorrect, and that, save for the resistance of the air, all bodies fell at the same rate, and through distances proportional to the square of the time which had elapsed from the instant when they were allowed to drop. Of this Galileo gave a public demonstration; but, though his Aristotelian colleagues could not explain the result, many of them preferred to assert that there must be some mistake rather than admit the possibility that Aristotle was wrong. The ridicule cast by Galileo on this argument caused friction, and in 1591 he was obliged to resign his chair. His writings at this time show that he had already formed correct ideas of momentum and centrifugal force. He had proved that the path of a projectile was a parabola, and was aware that the pendulum was isochronous. The last fact he discovered by noticing that the great bronze lamp hanging from the roof of the cathedral at Pisa performed its oscillations, whether large or small, in equal times. He nowhere stated the laws of motion in a definite form ; but probably he was acquainted generally with the principles of the first two laws as enunciated by Newton. His astronomical work was accomplished shortly after he left Pisa, and to this reference is made below. Towards the end of his life he again took up the subject of Mechanics, and a book by him, published in 1638, has been described as a masterpiece of popular exposition of its principles. In it he describes his pendulum experiments, and the theory of impact. A year or two later he invented a pendulum clock, though the fact was not generally known at the time. Mechanics were discussed by Descartes in 1644 ; but he did not substantially advance the theory. The correct

theory of impact was given by Wren and Wallis. The next marked development of the subject took place under the influence of Huygens and Newton and is referred to later.

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.

At first honours were showered upon him; but theological opposition arose so soon as it was realised that the observations tended to confirm

the Copernican theory. If that theory were true, some of the statements in the Bible could not be literally exact. Accordingly it was argued that, while the telescope might be a trustworthy instrument for terrestrial objects, it was not fitted to explore the heavens. In February, 1616, the Inquisition settled the matter, and declared that to suppose the sun the centre of the solar system was false, and contrary to Holy Scripture ; and they embodied this assertion in an edict of March 5, 1616, which has never been repealed. For the time, Galileo bowed to the storm. In 1632, however, he published some dialogues on the system of the world, in which he clearly expounded the Copernican theory, and showed that mechanical principles would account for the fact that a stone thrown straight up into the air would fall again to the place from which it was thrown-a fact which previously had been one of the chief difficulties in accepting the view that the earth was in motion. The book was approved by the papal censor before publication ; but none the less Galileo was summoned to Rome, forced to recant and do penance, and released only on promise of obedience to the edict of 1616.

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 invention of the telescope and the almost simultaneous invention

of the microscope naturally attracted attention to the subject of Optics, and especially to the law of refraction. Kepler asserted in 1611 that for small angles of incidence the angle of incidence was proportional to the angle of refraction, and, applying this, he was able to give in general outline the theory of the telescope. The correct law of refraction was discovered by Willebrod Snell (1591-1626), professor of Mechanics at Leyden. It was stated again, and perhaps discovered independently, by Descartes in 1637. The latter gave a theoretical proof resting on inaccurate assumptions ; but Fermât deduced the laws both of reflexion and refraction from the assumption that light travels from a point in one medium to a point in another in the least time, and that the velocity of light decreases as the density of the medium increases.

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.

Galileo's work was carried on by his pupil Evangelista Torricelli of Florence (1608-47) who constructed a barometer. The description given of it was vague, but it suggested ideas to Pascal which led not only to his barometric experiments, but to proofs of the more elementary propositions relating to the pressure exerted by fluids. Later investigations were facilitated by the invention of the air-pump by Otto von Guericke of Magdeburg (1602-86). In England the subject was taken up by Robert Boyle (1627-91). His name is associated with the law which he discovered that the pressure exercised by a given quantity of a gas is proportional to its density. The law was re-discovered independently fourteen years later by Edme Mario tte (1620-81) in France, who did a great deal to popularise physical investigations in France, and was one of the founders of the French Académie des Sciences. The beginnings of experimental investigations on Heat were also indebted to the labours of Galileo, who invented a thermometer, though of an imperfect type; but it was nearly a century later before the subject was taken up systematically.

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.

A novel and potent instrument of research was developed in the infinitesimal calculus. This method of analysis, expressed in the notation of fluxions and fluents, was used by Newton (1642-1727) in or before 1666 ; but no account of it was published until 1692, though its

general outline was known by his friends and pupils long anterior to that year. The notation of the fluxional calculus is for most purposes less convenient than that of the differential calculus. The latter notation was invented by Leibniz (1646-1716), probably in 1675, and was published in 1684.

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.

The ideas of the infinitesimal calculus can be expressed either in the notation of fluxions or in that of differentials. There is no doubt that the differential notation is due to Leibniz ; but an acute controversy arose as to whether the general idea of the calculus was taken by him from a manuscript by Newton, to which it was supposed he had had access, or whether it was discovered independently. During the eighteenth century the prevalent opinion was against Leibniz; but to-day the majority of judges think it more likely that the inventions were independent. The controversy was complicated by bitter personalities. It was natural, en. xxiiî.

though unfortunate, that British mathematicians were thus led to confine themselves to the methods used by Newton. The consequence was that, shortly after Newton's death, the British school fell out of touch with the great continental mathematicians of the eighteenth century, and it was not until about 1820, when the value of analytical methods was recognised, that Newton's countrymen again took any considerable share in the development of Mathematics.

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.

We turn next to the subject of Mechanics, which was placed on a scientific basis through the researches of Newton. The investigations by Galileo on the fall of heavy bodies, and the theory of pendulums, were completed by Huygens (1629-95) in his Horologium Oscillatorium, published at Paris in 1673. In this work he determined the centrifugal force on a body moving in a circle with uniform velocity; he also considered the motion of bodies of finite size and not merely of particles. Newton's investigations on Mechanics are included in his Principia. It will suffice here to say that he based the subject on three laws of motion, and he applied the principles to the statics and dynamics of rigid bodies and fluids ; probably he carried the investigations as far as was possible

with the analysis at his command. He distinguished between mass and weight, and this was an important point. He also created the theory of attractions, which will be more naturally noted in connexion with his theory of gravitation.

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.

It would seem that Newton had long believed that every particle of

matter attracts every other particle, and suspected that the attraction varied as the product of their masses, and inversely as the square of the distance between them ; but it is certain that he did not then know what the attraction of a spherical mass on any external point would be, and did not think it likely that a particle would be attracted by the earth as if the latter were concentrated into a single particle at its centre. Hence he must have thought that his discoveries of 1679 were only approximately true when applied to the solar system. His mathematical analysis, however, now showed that the sun and planets, regarded as spheres, exerted their attractions as if their masses were collected at their centres; and thus his former results were absolutely true of the solar system, save only for a correction caused by the slight deviation of the sun, earth, and planets, from a perfectly spherical form.

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.

The publication of the Principia is one of the landmarks in the history of Mathematics. In it the phenomena of the solar system were shown to be deducible from laws which experience proved to be true on the earth, and thus it brought new worlds within the scope of man's investigations. The conclusions were generally accepted by the leading thinkers of the time ; but a generation or so had to pass before

their validity was universally admitted ; henceforth, few doubted that the reign of law extended throughout the universe of non-organic matter. Newton further considered the question whether it was possible to explain gravitation as the result of other laws. He could not frame a satisfactory hypothesis, and the problem is still unsolved.

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.

We have already explained how Newton deduced the motions of the solar system from the one assumption of universal gravitation. The similar problem in Optics was the possibility of making a single hypothesis from which all the known optical phenomena could be deduced. Two plausible theories of this kind had been already suggested. In one, known as the " corpuscular " or " emission " theory, it is assumed that a luminous object emits corpuscles which hit or affect the eye. In the other, known as the wave or undulatory theory, it is assumed that light is caused by a series of waves in an ether which fills space, the waves being set in motion by pulsations of the luminous body. It would seem that at one time Newton deemed the latter the more probable hypothesis ; but, though he could thus account for the phenomena of reflexion, refraction, and colours, it failed (as then propounded) to explain the rectilinear propagation of light ; and this he considered fatal to its claims. He accordingly turned to the corpuscular theory, and from it deduced the phenomena of reflexion, refraction, colours, and diffraction. To do this, however, he was obliged to add a somewhat artificial rider, that the corpuscles had alternating fits of easy

reflexion and easy refraction, communicated to them by an ether which filled space. His various researches on the subject were embodied in his Optics published in 1704.

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.

The death of Newton and the separation of the British school of mathematicians from their continental contemporaries may be taken as marking the close of an epoch. At the beginning of the seventeenth century Mathematics were only just breaking free from their medieval trammels, and Physics in the modern sense were non-existent. In but little more than a century Mathematics had been developed into an instrument of great power; the value of the calculus had been recognised, and the foundations of modern analysis laid ; the theories of Mechanics and gravitation had been established; and the problems of Physical Optics had been subjected to mathematical processes. In this extraordinary extension of knowledge all the leading nations of Europe had

taken part. Galileo, Descartes, Fermât, Huygens, Leibniz, and above all, Newton, form a group of workers which will be ever memorable in the history of science ; and the fabric of modern Mathematics and Physics is but the superstructure erected on the foundations which they laid.


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 Human Anatomy the scholastic spirit remained supreme up to the middle of the sixteenth century. The far-reaching, almost inspired labours of Galen had in quite early times produced a system of doctrines touching the structure and functions of the body of man so complete and consistent that it seemed to supply all that was needed to be known ; the study of these things came to mean the study of Galen, the written page was the authority, and enquiry was narrowed to interpretation. In 1543 Andreas Vesalius (1514-64), a young professor at Padua, published a book on the structure of the human body, based, not on what Galen taught, but on what Vesalius had himself seen, and what anybody might

see who looked with adequate care. This was a powerful exemplar of the new method of appealing to nature-to things as they are, instead of to authority. Others in modern times had dissected human bodies and appealed to these dissections as tests of truth-notably Mundinus, Carpi and Leonardo da Vinci-but none of them had produced a work so complete and so convincing as that of Vesalius. So convincing, indeed, was it that it may truly be said to have almost at one blow freed Human Anatomy from the old scholastic bonds and set it up as a striking model of the new system. The success of the work was largely due to the nature of the study. To prove his statements, to show that in this or that Galen was wrong, Vesalius had no need to use elaborate arguments or to appeal to carefully devised experiments ; he had only to lay bare the structure with his scalpel, and to ask his pupils to use their eyes. The path opened up by Vesalius was followed by his pupils Fallopius, Fabricius and others ; by the end of the century, the student of Human Anatomy in every medical school had ceased to ask what Galen had written, and only cared to know what his own eyes could teach him. The brilliant success thus gained by the new method applied to Human Anatomy could not fail to have an influence on other branches of learning, supported as that influence soon was by the striking results of the same new method in Mechanics and Physics. How completely this new method had laid hold of men's minds is shown by the brilliant exposition of it given by Francis Bacon (1560-1626). Though his published works belong to the seventeenth century, the Prqflcience and Advancement of Learning appearing in 1605 and the Novum Organum in 1620, Bacon's main ideas had come to him in the closing years of the preceding century. In the two works just mentioned, and in others, some published in his lifetime, and others at various times after his death, he elaborated in a formal exposition the principles of the method of investigating nature-the new method which, as we have just said, was being adopted by enquirers everywhere in all branches of natural knowledge. He went further : he drew up the outlines, and laboured to the time of his death to fill in the details, of a plan for the scientific work of the future, a programme of the steps to be taken in all branches of science in order to gather in with the least waste of time and labour, and in the most effective manner, the fruits of scientific enquiry. He made no notable contribution of his own to the advancement of natural knowledge ; there is no evidence that the men who in his own time and in the times immediately following were actively and effectively engaged in advancing natural knowledge were in any special way influenced by his writings ; indeed one of the greatest of these enquirers spoke slightingly of them. " He philosophises," said Harvey, " like a Lord Chancellor." And not only was no effort made by subsequent enquirers to carry out Bacon's programme, but the history of scientific discovery has shown thai his forecast of how scientific work ought to be
carried on was in many respects wrong-as, for instance, his idea that the collection of facts should be allotted to one set of men, and the drawing conclusions from the facts to another. In the great majority of cases, the discoverer of a new law of nature has to find his facts for himself. Nevertheless, Bacon's works gave a great impulse to the new method. Even those who had made discoveries without knowing anything of what Bacon had written were gratified and encouraged by learning from his works that they had, without distinct consciousness of it, been treading in the path of true philosophy ; while all scientific workers were helped by being able to quote in support of their methods of enquiry his incisive and illuminating words.

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.

Long before Harvey, Michael Servetus (1511-53), in his Restitutw Christianismi, published in 1553, but written long before, used words showing that he rejected wholly the supposed passage of some blood through the septum, as to which Vesalius had simply hinted his doubts, and, further, that he had grasped the true features of the pulmonary circulation, the passage of all the blood from the right side of the heart through the lungs to the left side. The same truth was taught by Colombus (1516-59), Vesalius' pupil and successor at Padua; but there are some reasons for thinking that he had read Servetus' book. Andreas Caesalpinus (1519-1603), botanist, physician, and polemic philosopher, more than anatomist or physiologist, also enunciated views which, at all events, show that he grasped the truths both of the systemic and pulmonary circulations, the flow to the tissues along the arteries,

the return from the tissues to the heart by the veins, and the passage of blood through the lungs from the right to the left side of the heart.

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."

His first observations, as happens in many a progress, led him into a slough of despond ; he began to think that " the motion of the heart was only to be comprehended by God." But the patient study of that motion in the hearts of many living animals convinced him that Galen was wrong in regarding the heart as mainly an organ of suction, and that it was, on the contrary, essentially an organ of propulsion, inasmuch as its work consisted, not in sucking air from the lungs, but in driving blood by its contractile power through the body. This new view-dimly, but only dimly, seen by Caesalpinus-led Harvey at once to a true conception of the work of the auricles and ventricles with their respective valves, and thus to the wholly new idea that all, and not some only, of the contents of the right ventricle were discharged into the lungs and so found their way to the left side of the heart. This step led to another. Making observations to determine the quantity of blood discharged at each beat from the left ventricle, and noting the frequency of the beats, he saw that the blood driven along the arteries must find its way somehow into the veins and so return to the right side of the heart. Thus, by experiments and quantitative observations, working not after the manner of Fabricius but after that of Galileo, he reached a new view of the circulation of the blood, "of a motion as it were in a circle." And all his further observations confirmed this view, which, once fairly grasped, rendered intelligible various phenomena of the heart and blood vessels, as indeed of the body at large, hitherto obscure, and made plain the uses of those valves of the veins over which Fabricius had stumbled. It is worthy of notice that Harvey says nothing about the "spirits," so prominent in the

old Galenic doctrines. In an early passage he incidentally refers to them and dismisses them as irrelevant ; and, indeed, though the names were used long afterwards, his teaching was their death-blow. The new conception of the same blood flowing continuously through the whole body, undergoing changes all along the circle, did away with any need for them, and at the same time rendered possible true ideas of the nutrition of the body.

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.

Richard Lower (1631-91) and Giovanni Alfonso Borelli (1608-97) applied to the physical problems of the circulation-such as the work done by the heart, the velocity of the flow in the blood vessels, and the pressure exerted on the vascular walls-the new exact mechanical and physical learning in so complete a manner as to bring the knowledge of the subject very much to the condition in which it was when, nearly two centuries later, Poisseuille and Weber took up the same problems again. And Jean Pecquet's (1624-74) discovery, in 1651, of the thoracic duct discharging its contents into the veins of the neck, and his proof that the lacteals, discovered in 1622 by Gaspar Aselli, passed, not-as Aselli

thought and as suited Galenic doctrines-to the liver, but to the recepta-culum chyli, and so to the thoracic duct and the venous system, together with the descriptions by Olaus Rudbeck in 1653, and by others, of the •casa serosa or aquosa, that is of the general lymphatic system of the body, seemed to make the story of the flow of nutritive fluids in the body for the time complete.

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.

Neither Lower nor Borelli, who had treated very fully of breathing and had also come to the conclusion that air is taken up by the blood in the lungs, nor, again, Hooke, refers to the possibility of a part of the air only being taken up. John Mayow (164-3-79), who busied himself much with chemical matters, had in 1688 come to the conclusion that the air consists in part "of a certain vital, fiery, and in the highest degree fermentative spirit " which he called Spiritus nitro-aëreus or igneo-aëreus, It is clear that in his Spiritus nitro-aëreus Mayow had formed a conception of what more than a hundred years afterwards came to be called oxygen.

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.

The progress of Physiology in another direction is so closely inter-

woven with the progress of Chemistry that it will be better to consider the two together. During the latter part of the sixteenth and earlier part of the seventeenth century, though the day of alchemy was past, there was great activity in the preparation of new chemical substances ; this was due partly to natural curiosity, partly to the demand for new remedies and for new industrial materials. And these preparations were conducted to a very large extent by the method of exact measurement which in Physics was proving so fruitful. But there was no corresponding progress in chemical theory; "chemists," said Boyle, "have been much more happy in finding experiments than the causes of them, or in assigning the principles by which they may best be explained." Chemists continued to accept the three "elements" or "principles" of Paracelsus, or rather of Valentine, namely, sulphur, mercury, and salt-that is to say, the classification of substances into those which were combustible and were lost by combustion, those which were volatile and recovered after combustion, and those which remained after combustion. Nicolas Lefèvre (d. 1674) and others, it is true, speaking of "oil" instead of sulphur, of "spirit" instead of mercury, added to the three active two passive principles -"water" or "phlegm" and "earth"; but this implied no great change.

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.

A very different man was Francis Sylvius (de La Boé) (1614-72), a zealous exponent of Harvey's teaching, and of all the new views in

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.

Both schools did much, and the English school previously mentioned perhaps even more, to advance knowledge ; but the close of the century witnessed a remarkable development of chemical conceptions, which turned biological doctrines aside from the line which they had seemed to be taking. The exact part played by heat or fire in chemical actions had from quite early times been the subject of great discussion, Boyle (as we have seen) having had much to say about it; and now a wholly new notion was started. Johann Joachim Becher (1635-82) in attempting to revive Valentine's old "elements" in the form that all things consisted of three earths, "terra lapidea, improperly called salt, terra ßuida,

improperly called mercury, and terra pinguis, improperly called sulphur," maintained that, when a substance was burnt, the terra pinguls previously contained in it escaped ; indeed that this escape of terra pinguis was the essential feature of combustion. Taking up this idea, George Ernest Stahl (1660-1734) developed it more fully into what became known as the phlogiston theory. By phlogiston Stahl meant, not fire itself, but "the material and principle of fire"; and this he regarded as a material substance working in the following way. Everything which can burn does so by virtue of its holding phlogiston., and the act of burning is the giving out or loss of it. That which holds no phlogiston cannot of itself burn; but it may support combustion by taking in the phlogiston given out by the burning body. Thus, air which is to a large extent free from phlogiston is a great supporter of combustion ; and many other things also free from it can bring about combustion.

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.

Nicolaus Stensen was the first to show, in 1664, that the fleshy part of

the muscle-the fleshy fibres, and not the tendinous part-was the active contracting part, the contraction of the whole muscle being the result of the contraction of the individual fibres; and he came very near to quite recent views of the essential nature of muscular contraction, Borelli, profiting by Stensen's discoveries and applying to the subject his exact Mechanics and Physics, brought, at one stride as it were, the knowledge of muscular mechanics almost up to the knowledge of to-day. On one point he failed to free himself from the old Galenic views ; he maintained that contraction was essentially an inflation, an increase in bulk. The nerves in his view were occupied not by animal spirits, but by a fluid, the succus nerveus, a "highly subtle and spirituous," yet still a strictly physical, fluid, incapable of acting at a distance. Sensation and movement were, according to him, brought about not by this succus flowing to and fro, but by means of "concussions'" passing along it. He admitted that the mere advent of a concussion to the substance of a muscle could not of itself cause an inflation and contraction ; he supposed that it excited in the muscle some change possibly of a "fermentative," that is to say, of a chemical, nature.

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.

While this remarkable progress was taking place in the so to speak lower regions of Nervous Physiology, there was no corresponding advance in the higher regions. Solid additions to our knowledge of the anatomy of the brain were, it is true, furnished by Thomas Willis (1621-75), the chief merit of whose work rumours of the time however attributed to Richard Lower, who assisted him in it; but, when we turn to the functions of the brain, we find nothing much beyond fanciful speculations. Descartes, ignoring Harvey's work and making use of the old Galenic doctrines, expounded the body of man, including the nervous system, as a machine capable of being explained by the new mechanical-physical learning with the help of various assumptions, as, for instance, that the nerves were tubes along which the flow of animal spirits was regulated by valves ; this body however, though capable of doing much by itself, especially by what we now call reflex actions, was governed by the " rational soul " hovering around the pineal gland. Van Helmont taught the existence of an anima sensitloa motivaque, which, though residing in the pylorus of Lhe stomach, carried out by means of Lhe brain and nervous system the psychical work as well as Lhe sensations and movements of

the body ; this soul however was mortal, though it contained within itself, after the fashion of a kernel, the "immortal mind." Stahl, as we have seen, carried on van Helmont's idea of anima sensitiva, though stripped of its fanciful wrappings. And Willis, though his experience as a physician led him to associate the corpora striata with movement and sensation, and the optic thalami with vision, both however acting as instruments of the higher cortex, revelled in conceptions at least as fanciful as those just mentioned. He likened the vital spirits in the blood to flame, and the animal spirits in the nervous system to light ; and, while he explained all the actions of the nervous system as the functions of a corporeal and mortal soul present in brutes no less than in man, he claimed for man the possession also of a rational immortal soul, which performed all the higher psychical functions.

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."

Partly owing to the use of herbs as remedies, partly to natural curiosity and the love of beautiful flowers, the sixteenth century was very active in the recognition and description of plants. From the middle of the century onwards Botanic Gardens were established at Padua, Pisa, Bologna, Leyden, and elsewhere; and during the latter half of the sixbeenth and beginning of the seventeenth century a number of elaborate, sometimes highly illustrated descriptions of plants, often known as " herbals," were published by men, many of whose names are in common use as names of plants, such as Fuchs, Gesner, Dodoens, de L'Écluse (Clusius), de L'Obéi (Lobelius), and Bauhin. These descriptions naturally implied a study of the organs of plants, and various methods of naming them, as well as attempts at classification. The most important, perhaps, and one of the earliest of such classifications was that by Caesalpinus (1583), drawn up however more from an à priori philosophical than from a direct natural history point of view. A classification introduced later by Joachim Jung (1587-1657) published after his death in 1678, as well as one by Robert Morison (1620-83), appear to have been used. John Ray (1628-1705), who in his Hlstorla Plantantm, published between 1686 and 1704, proposed an arrangement

which, though continuing the fundamentally false distinction between trees and herbs laid down by Caesalpinus, separated monocotyledons from dicotyledons, and may be regarded as the most notable approach to the natural system.

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.

In describing structure, both Malpighi and Grew in their works introduced considerations of function, the former more happily than the latter. Looking upon the woody fibres as organs for conducting fluid or sap, the spiral vessels or tracheae, as he called them, as air passages, and the lactiferous vessels as channels for special juices, Malpighi was led by the study of the young cotyledons of germinating seeds (which he recognised as leaves) to the important view, that the crude sap carried upwards from the roots was in the leaves, under the influence of the sun's rays, elaborated into more perfect sap ; and that this, descending again, was carried to growing parts or stored up in various places. And Ray, who treats of Vegetable Physiology incidentally only, had independently arrived at the same conclusion. As in his researches on the animal body, so in his study of plants, Malpighi does not attack the chemical side of the problem of nutrition; and Grew, who did attempt it, was not very successful. Except for this want of chemical truth, Malpighi and Grew may be said to have laid some of the

foundations of Vegetable Physiology as well as those of Vegetable Histology.

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).

This study of the Natural History of Animals, pursued mainly out of natural curiosity, and not for its use in Medicine or otherwise, continuing to make great progress in the seventeenth century, found a brilliant expositor in the man of science who was doing a like service for Botany-namely, John Ray. Francis Willughby (1635-72), first the pupil, and then the intimate friend of Ray, had studied animals while Ray was chiefly studying plants, the two carrying out their studies in close concert ; but he died early without having published any important

part of the abundant material, especially on fishes and birds, which he had gathered together. This work of Willughby, Ray, who had himself a large share in it, brought out after the former's death. He himself produced a large work on quadrupeds and reptiles ; and a like work of his on insects, was published after his death. Thus Bay, making use of Willughby's labours, gave a full account of the greater part of the animal kingdom ; and the classification which he adopted was not only accepted at the time, but has remained, with changes and extensions, the basis of the classification in use to the present day. Ray in fact may be regarded as the founder of Systematic Zoology.

The systematic zoologists paid more attention to external features than to internal structure ; but it was only natural that the enquirers who found the actual dissection of the human body so fruitful of new truths and new ideas should turn to the dissection of the bodies of animals ; and, indeed, many of the anatomists, notably Fabricius, following the example of Galen, did, in a more or less desultory fashion, examine and describe the structure of various animals. In the middle of the seventeenth century, however, two men took up this work in a more thorough fashion, being therein greatly assisted by the introduction of the microscope. Malpighi's account of the anatomy of the silk-worm (1669) was the pioneer of exact Comparative Anatomy and Histology in respect to animals, doing for them what his Anatome Plantarum did for plants. About the same time, Swammerdam was applying the same methods, in a still more thorough and extensive way, not only to various kinds of insects in their several stages of metamorphosis, but to other animals as well, such as the snail and the frog. A few only of Swammerdarn's results were published in his lifetime ; the greater part did not see the light until long after his death, when in 1737 Boerhaave published under the title of B'iblla Naturae the writings which he had left behind. These two men, Malpighi and Swammerdam, may be said to have created the science of Comparative Anatomy. The same century saw, however, other important works. Leeuwenhoek, applying the microscope in all directions, discovered spermatozoa, made known infusoria and rotifera, and studied hydra and aphthis. Malpighi, carrying the study of the formation of the chick in the egg far beyond the rough attempts of Fabricius, laid the foundations of Embryology Francesco Redi (1670), in proving that maggots were not bred out of mere corruption, since they did not appear in rotting flesh if the access of flies was prevented, not only dealt a heavy blow at the widely accepted theory of spontaneous generation, but introduced a new and fruitful method of Experimental Biology. Of less, perhaps, but still great value, were Redi's works (1684) on the structure and economy of parasitic animals, and (1664) on vipers, in which he gave an admirable account of the poison mechanism, and incidentally showed that the poison was not absorbed by the alimentary canal. He also wrote on the

torpedo. Stensen carefully described the anatomy of the ray ; and Frederik Ruysch (1638-1731), by the singular skill with which he developed the art of injecting blood vessels and other channels with coloured materials, assisted largely the progress not only of human but also of comparative anatomy.

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.

In the seventeenth century the labours of John Woodward (1665-1728), who made large collections of fossils and minerals and most carefully studied and described them, were perhaps the most effective in establishing the truth that fossils were really the remains of plants and animals which were once alive ; and in this he was vigorously supported later by Jean-Jacques Scheuchzer (1672-1733) and others. But Woodward and the rest were content with the explanation that the distribution of these fossils at different places and at different depths from the surface was

simply a result of the Mosaic deluge. And indeed, though Athanasius Kircher (1602-80) studied and carefully described volcanoes, and though a posthumous work by Robert Hooke on earthquakes shows that he had grasped the idea that fossils might be used as helps to tell the tale of the earth, most of the attempts of the century to explain how the earth had gained its present features were either fantastic developments of the biblical history or speculative cosmogonies like those of Descartes and Leibniz.

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.

Towards the middle of the seventeenth century the progress of scientific learning in its various branches received a great stimulus, in several European countries, from the foundation of Academies or

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.

In England a society, similar to the Italian Academies, was established in 1645 at London, meeting at Gresham College or elsewhere, under the private name of the "Invisible College." In 1648 the society was divided, some members continuing to meet, fitfully owing to the troubles of the time, in London, but most of them at Oxford. In 1660 the meetings in London were revived with success, and on July 15, 1662, the society was formally incorporated by charter as the " Royal Society of London," a second charter being granted in 1663. It is known how keen and useful an interest was taken by John Evelyn in the early progress of the Royal Society ; his project of a Mathematical College, like his friend Abraham Cowley's Philosophical College, remained, however, unaccomplished. William Molyneux is regarded as the founder of the Dublin Philosophical Society (1684). In France, at Paris, a similar society, about the middle of the seventeenth century, met at the house of Melchisedec Thevenot, a man distinguished by his travels and his interest in science; it was before this society that Stensen gave his remarkable lecture on the brain, attacking the teaching

of Descartes and others. And there seem to have been other like societies or Academies at Paris. In 1666 (the Académie Française having been founded earlier, in 1635), the place of these informal Academies was taken by the Académie des Sciences, established by Louis XIV, on the advice of Colbert. In 1699 it was reorganised and began to issue publications. In Germany, a society similar to the Italian Academies was established by Johann Lorenz Bausch, a physician of Schweinfurt, in 1662; it was familiarly known as "the Argonauts" but more formally as the Academia naturae curiosorum. Under this latter name it was, in 1687, definitely established under statutes, at Vienna, with privileges granted by the Emperor Leopold. Leibniz, who was a member of the Royal Society (from 1673) and of Ciampini's Roman Physical and Mathematical Academy, induced the Elector Frederick III (soon to become King Frederick I of Prussia) through the influence of his consort the Hanoverian Sophia Charlotte to establish a Society of Sciences, of which Leibniz himself was made the first president, and which in 1711 became the " Academy of Sciences." His efforts, however, to bring about the establishment of a general Academy of Sciences at Vienna were unsuccessful. At one time they had nearly approached realisation ; and he put forth in both Latin and German schemes for the proposed Societas Imperialis Germanica, and drafted statutes for it. But the project was in the end defeated (about 1714) by Jesuit opposition and by lack of funds. In Russia, as has been seen in a previous chapter, an Academy of Sciences was founded at Moscow by the Tsar Theodore III so early as 1681. But this institution, into the foundation of which religious purposes largely entered, was superseded by the Academy of Sciences founded by Peter the Great at St Petersburg in 1724, designed as a general centre of education and learning.

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