1719-44] Anglo-French rivalry in India

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French Company eked out a precarious existence by subletting its privileges to some merchants of St Malo. In 1719-20 they were entangled in the grandiose schemes of the financier Law; the Company was reconstituted; and it was not till some years after that date that an improvement in their fortunes took place. From 1657, on the other hand, there had been no breach in the continuity of the English trade. Every year a great fleet of fifteen or twenty East Indiamen made their way to Indian ports. Far from being dependent on state subsidies, the Company had taken the Exchequer heavily into its debt. There is, in fact, at this period no comparison between the two Companies; the one gives an impression of solidarity, prosperity and power, the other of debility, bankruptcy, and decay.

The importance of the longer English tradition in the East has often been unduly underrated. Historians are perhaps too prone to concentrate attention on the acquisition of territory in Hindustan, too apt to look upon the Indian Empire as the work of highly gifted men, hampered and shackled by a carping body of unimaginative traders. That conception embodies a phase of the truth; but it can easily be overstated. The real base of operations was in England. Especially is this true of the time prior to our acquisition of the Gangetic province of Bengal. The strength or weakness of the Company is not solely to be measured by the roll of the garrisons in the Indian settlements or the thickness of the curtains and bastions that encircled their forts. It depends rather on the latent resources and political influence of the great corporation of Leadenhall Street, the volume of its steadily increasing trade, and the unbroken means of communication between East and West formed by the fleets that annually sailed from British ports. The causes that determined the issue of the conflict between England and France will be dealt with in a later volume. But an adequate appreciation of the difference between the resources of the two Companies during the seventeenth century, while it sets in high relief the brilliance of the French attack upon the British position after 1744, will also go some way to explain why that effort was not more prolonged and more successful. Burke declared that the constitution of the Company began in commerce and ended in Empire; and the aphorism rightly understood involves a propter as well as a post hoc. The more closely the history of the English East India Company is investigated, the more certain becomes the conviction that only because it was built up upon a broad basis of mercantile integrity, did it attain even higher powers, grow till it compelled the State to take it into partnership, and, in spite of many shortcomings and some deep stains, fulfil a unique and splendid function in British history.

C. M. H. V.

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CHAPTER XXIII

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

(1) MATHEMATICAL AND PHYSICAL SCIENCE

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

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

Science in the sixteenth century

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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 th 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 (epicycels) 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,

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Science in the sixteenth century

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 Cophicus (1473-1543). 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 ele mentary 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 inven tion of logarithms. Their discovery was due to Napier of Merchistoun (1550-1617), who published his results in 1614, though he had privately

Introduction of logarithms and decimals

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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.

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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, Bürgi, 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.

IF 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