Biographical encyclopedia
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126 [198] WALLIS
GRIMALDI [199] Civil War had broken out and Wallis, who had a keen sense of the prevailing wind, threw in his lot with the Parlia mentarians against King Charles I. Like Vieta [153] he made a name for himself by applying his mathematical training to deciphering code messages captured from Royalists. Because of this—and despite the fact that he voted against execution of the king—he received a professorial appoint ment at Oxford in 1649 under the Par liamentarian regime. The fact that he had been against execution, however, counted in his favor when in 1660 the son of Charles I came to the throne as Charles II. Wallis then became the king’s chaplain. Wallis wrote voluminously on mathe matics and was one of those who could serve as “calculating prodigies.” He is re ported to have worked out the square root of a fifty-three-digit number in his head, getting it correct to seventeen places. He was the first to extend the no tion of exponents to include negative numbers and fractions, so that x~2, for instance, was defined as \/x 2, while x1/2 was equivalent to and he was also the first (in 1656) to use » as the sym bol for infinity. In addition, also he was the first to interpret imaginary numbers geometrically (though he wasn’t entirely successful at this). Two centuries later Steinmetz [944] was to make this repre sentation fundamental to his theoretical treatment of alternating current circuits. Wallis was one of the first to write a se rious history of mathematics. Wallis took steps toward calculus, but it was his misfortune to be overshadowed by his younger contemporary Newton [231], soon to bring calculus into being. He was a vain and quarrelsome man, and an extremely nationalistic English man, eager to enter into disputes with foreigners such as Descartes [183]. He was among the first, therefore, to back Newton’s priority in calculus and to ac cuse Leibniz [233] of plagiarism, in what was the bitterest scientific quarrel in his tory. He also used his influence against the adoption of the Gregorian calendar by Great Britain on the ground that it implied subservience to Rome (and, hence, foreigners). The inevitable adop tion was delayed half a century as a re sult.
Wallis’s greatest contribution to sci ence, perhaps, was his role, along with his close friend Boyle [212], as one of those who, in 1663, founded the Royal Society. He accepted the challenge of the Society to investigate the behavior of colliding bodies and, in 1668, was the first to suggest the law of conservation of momentum. This was the first of the all important conservation laws. His findings were extended by Wren [220] and Huy gens [215]. [199] GRIMALDI, Francesco Maria (gree-mahl'dee) Italian physicist
1663
Grimaldi was the son of a silk mer chant of aristocratic lineage. He entered the Jesuit order at fifteen and became a professor at the University of Bologna after obtaining his doctoral degree there in 1647. He served as an assistant to Riccioli [185] for some time and drew the lunar map on which Riccioli placed his names. Grimaldi published his own most im portant discovery in a book that only ap peared some two years after his death. He had let a beam of light pass through two narrow apertures, one behind the other, and then fall on a blank surface. He found that the band of light on that surface was a trifle wider than it was when it entered the first aperture. There fore he believed that the beam had been bent slightly outward at the edges of the aperture, a phenomenon he called diffraction. This was clearly a case of light bend ing about an obstacle, as would be ex pected of waves but not of particles, and Grimaldi therefore accepted light as a wave phenomenon. More unusual still was the fact that he observed the band of light to show one to three colored streaks at its extremities. This he could not explain and it was not until the time
[200] HORROCKS
BROUNCKER [202] of Fraunhofer [450] a century and a half later that the phenomenon was taken out of cold storage and put to work. [200] HORROCKS, Jeremiah English astronomer Born: Toxteth Park, near Liver pool, 1618 Died: Toxteth Park, January 13, 1641
Horrocks (sometimes spelled Horrox) was the son of a watchmaker. He at tended Cambridge from 1632 to 1635 but did not get a degree. He served as a curate at Hoole in Lancashire from 1639 and practiced astronomy (in which he was self-taught) in his spare time. In his short life of twenty-three years he accomplished an amazing number of things. He corrected the Rudolphine Tables of Kepler [169] with regard to the transit of Venus across the face of the sun and predicted an occurrence on November 24, 1639. This was a Sunday and he just got away from church in time to view it—the first transit of Venus to be observed. He suggested that observations of such a transit from different observatories might set up a parallax effect that could be used to cal culate the distance of Venus and there fore the scale of the solar system. This eventually was done. He was the first astronomer to accept the elliptical orbits of Kepler whole heartedly. By observing the motions of the moon he was able to extend Kepler’s work by showing that the moon moved in an elliptical orbit about the earth and that the earth was at one focus of that ellipse. This completed the Keplerian system by applying it to the one known heavenly body that Kepler himself could not manage. Horrocks thought that some of the ir regularities of the moon’s motion might be due to the influence of the sun and that Jupiter and Saturn might exert an influence on each other. This was a foretaste of the theory of universal gravi tation, which Newton [231] was to de velop a generation after Horrocks’ early death. [201] GRAUNT, John (grant) English statistician Born: London, April 24, 1620 Died: London, April 18, 1674 Graunt was the son of a draper and, entering the family business, did well until his business was destroyed in the Great Fire of 1666. More or less by accident, he found himself studying the death records in London parishes and beginning to notice certain regularities. As a result, in 1662 he published a book on the matter; it served to found the science of statistics and of demography, which is the branch of statistics that deals with human popu lations. This is not bad for a busi nessman without training in mathe matics.
He noted things for the first time that anyone might have seen if he had looked, and it is to Graunt’s credit that he looked. He noted that the death rate in cities was higher than that in rural areas; that while the male birth rate was distinctly higher than the female birth rate, a smaller percentage of boys sur vived the early years, so that the propor tion evened out. He tried to detect the influence of occupation on the death rate and was perceptive enough to consider overpopulation as itself a cause of a rise in the death rate. He was the first to try to establish life expectancy and to publish a table in dicating the percentage of people who might be expected to live to a certain age, and how much longer they might, on the average, live, having reached a certain age. As a result of this book, Graunt was elected to the Royal Society at the sug gestion of Charles II himself. [202] BROUNCKER, William, 2d Vis count (brung'ker) English mathematician
April 5, 1684 Brouncker was bom into the nobility and inherited a viscount’s title in 1645. He received a doctor’s degree from Ox
[203] MARIOTTE
WILLIS [205] ford in 1647 and cut a minor figure in the history of mathematics of the time. In particular, he popularized the use of continued fractions (first introduced in 1613 by the Italian mathematician P. A. Cataldi) when he made use of such frac tions to evolve an expression for pi, which enabled him to calculate its value to ten decimal places. He is best known, however, for the fact that he was the first president of the Royal Society nominated to that post by Charles II and elected without opposi tion. He was then reelected year after year till he resigned in 1677. [203] MARIOTTE, Edmé (ma-ryut') French physicist Born: Dijon, 1620 Died: Paris, May 12, 1684 Mariotte’s life was strangely parallel to that of Boyle [212]. The two lives spanned the same decades and Mariotte was as devout as Boyle; Mariotte was, indeed, a Roman Catholic priest. As Boyle was an early member of the Royal Society in London, so Mariotte was an early member of the Academy of Sci ences in Paris. In 1676, fifteen years after Boyle, Mariotte discovered Boyle’s law indepen dently and with an important qualifica tion. He noticed that air expands with rising temperature and contracts with falling temperature. The inverse rela tionship of temperature and pressure therefore holds well only if the tempera ture is kept constant. This was a point Boyle had neglected to make. There is thus some justification for using the phrase Mariotte’s law. Mariotte also made important studies of rainfall and put forth modem views concerning the circulation of the earth’s water supply. He discovered the “blind spot” of the eye—the point where the optic nerve interrupts the retinal film. [204] PICARD, Jean (pee-kahr/) French astronomer Born: La Flèche, Sarthe, July 21, 1620
Died: Paris, July 12, 1682 Picard, who eventually became a Roman Catholic priest, studied astron omy under Gassendi [182] and, in 1655, succeeded him as a professor of astron omy at the Collège de France and was one of the charter members of the French Academy of Sciences. He also helped to found the Paris Observatory and scoured Europe for men to serve in it worthily; among them, Cassini [209] from Italy and Roemer [232] from Den mark. Picard was the first to put the tele scope to use not merely for simple obser vations but for the accurate measure ment of small angles. This innovation made use of an improvement of the mi crometer invented by Gascoigne [195] and then reinvented by Huygens [215], He also popularized the use of Huygens’ pendulum clock to record times and time intervals in connection with astronomic observations. The feat for which Picard is most re nowned is the measurement of the cir cumference of the earth, the first mea surement more accurate than that of Eratosthenes [48] nineteen centuries ear lier. Picard made use of Eratosthenes’ principle, substituting a star for the sun. The use of a point instead of a large body made greater accuracy of measure ment possible. In 1671 he published the figure for the length of a degree of longitude at the equator as 69.1 miles, giving the earth a circumference of 24,876 miles and a ra dius of 3,950 miles (close to the values accepted today). According to one story it was the use of Picard’s values in place of somewhat smaller ones that in 1684 gave Newton [231] the correct answer to the moon’s motion, replacing the incor rect answer of 1666. [205] WILLIS, Thomas English physician
January 27, 1621 Died: London, November 11, 1675
Willis, the son of a steward of a manor, obtained his master’s degree 129 [206] VTVIANI
PASCAL [207] from Oxford in 1642. He was a member of the losing Royalist cause during the Civil War and decided not to enter the embattled church. He turned to medicine instead, getting his license to practice in 1646. After the Restoration, of course, his activity in the Royalist cause worked in his favor and in 1666 he set up a practice in London, which was profitable indeed and he quickly became the most fashionable physician in the land. He was, however, a capable practi tioner. He studied epidemic disease and was the first great epidemiologist. He gave the first reliable clinical description of typhoid fever, was the first to describe myasthenia gravis, and childbed fever. It was he who named the latter “puerperal fever,” from the Latin phrase for “child bearing.” In 1664, he wrote a treatise on the brain and nerves that was the most complete and accurate up to that time. Most interesting of all, perhaps, was his discovery (or rediscovery in case it was known to some of the Greek physi cians) of the sugar content in urine among some people with diabetes. In this way he distinguished diabetes mellitus, the most serious form, from other varie ties. He died of pneumonia and was buried in Westminster Abbey. [206] VIVIANI, Vincenzo (vih-vee-ah'- nee) Italian mathematician Bom: Florence, Tuscany, April 5, 1622
Died: Florence, September 22, 1703
Viviani was introduced to Galileo [166] by Ferdinand II of Tuscany [193]. He worked with Galileo and later with Torricelli [192]. He was a mathematician primarily and was perhaps the leading geometer of his time. He was also a practical engineer and succeeded Galileo as superintendent of the rivers of Tus cany. It might be argued that his most im portant accomplishment, however, was his founding of the Accademia del Ci- mento, one of the first great scientific societies and a forerunner of the Royal Society soon to be established in En gland.
[207] PASCAL, Blaise (pas-kalO French mathematician and physicist
Auvergne, June 19, 1623 Died: Paris, August 19, 1662 Fortunately, in view of his short life and the fact that the last decade of it was devoted to theology and introspec tion, Pascal managed to accomplish a good deal. He was a sickly child whose mother died when he was three; and in infancy his life was, on one occasion, believed to have ended. Nevertheless, he was, mentally, a prodigy. His father, himself a mathematician and a govern ment functionary, supervised his child’s education and was determined that he study ancient languages first. He denied him, therefore, any books on mathe matics.
When the young Pascal inquired as to the nature of geometry and was told it was the study of shapes and forms, he went on, at the age of nine, to discover for himself the first thirty-two theorems in Euclid in the correct order. (This story, told by his sister, appears too good to be true.) The awe-struck father then gave in and let the boy study mathe matics.
When he was only sixteen Pascal pub lished a book on the geometry of the conic sections that for the first time carried the subject well beyond the point at which Apollonius [49] had left it nearly nineteen centuries before. Des cartes [183] refused to believe that a six teen-year-old could have written it, and Pascal, in turn, would not admit the value of Descartes’s analytic geometry. In 1642, when he was only nineteen, Pascal had invented a calculating ma chine that, by means of cogged wheels, could add and subtract. He patented the final version in 1649 and sent one model to that royal patron of learning. Queen Christina of Sweden. He hoped to profit from it but didn’t. It was too expensive 130 [207] PASCAL
PASCAL [207] to build to be completely practical. Nev ertheless, it was the ancestor of the me chanical devices that reached their cul mination in the pre-electronic cash regis ter.
Pascal corresponded with the lawyer- mathematician Fermat [188] and to gether they worked on problems sent them by a certain gentleman gambler and amateur philosopher who was puz zled as to why he lost money by betting on the appearance of certain combina tions in the fall of three dice. In the course of settling the matter, the two men founded the modem theory of prob ability. This had incalculable importance for the development of science because it lifted from mathematics (and the world in general) the necessity of absolute cer tainty. Men began to see that useful and reliable information could be obtained even out of matters that were completely uncertain. The fall of a particular coin can be either heads or tails, but which one, in any particular instance, is unpre dictable. However, given a vast number of falls, separately unpredictable, conclu sions as to the general nature of the falls (such as that the number of heads would be approximately equal to the number of tails) can be drawn with considerable confidence. Two centuries later, mathematical physicists such as Maxwell [692] were applying such considerations to the be havior of matter and producing great re sults out of the blind, random, and com pletely unpredictable movements of indi vidual atoms. Pascal also applied himself to physics. In studying fluids he pointed out that pressure exerted on a fluid in a closed vessel is transmitted undiminished throughout the fluid and that it acts at right angles to all surfaces it touches. This is called Pascal’s principle and it is the basis of the hydraulic press, which Pascal described in theory. If a small piston is pushed down into a container of liquid, a large piston can be pushed upward at another place in the container. The force pushing up the larger piston will be to the force pushing down the small one, as the cross-sec tional area of the large is to the cross sectional area of the small. This multi plication of force is made up for by the fact that the small piston must move through a correspondingly greater dis tance than the large. As in the case of Archimedes’ [47] lever, force times dis tance is equal on both sides. In fact the hydraulic press is a kind of lever. Pascal also interested himself in the new view of the atmosphere initiated by Torricelli [192], If the atmosphere had weight, then that weight should decrease with altitude, since the higher you went, the less air would remain above you. This decrease in the weight of the atmo sphere should be detectable on a barom eter.
Pascal was chronically sick, suffering continuously from indigestion, headaches (a postmortem investigation showed he had a deformed skull), and insomnia, so he contemplated no mountain climbing for himself. However, on September 19, 1648, he sent his strong, young brother- in-law carrying two barometers up the sides of the Puy-de-Dôme (the mountain near which Pascal was bom). The brother-in-law climbed about a mile and found the mercury columns had dropped three inches. The brother-in-law must have enjoyed mountain climbing for he repeated the experiment five times. This established the Torricellian view quite definitely, even against the persistent doubting of Descartes. It showed, more over, that a vacuum existed above the at mosphere against Descartes’s denial of the existence of a vacuum and his con tention that all space is filled with mat ter. (Pascal also repeated Torricelli’s original experiment, using red wine in stead of mercury. Because red wine is even lighter than water, Pascal had to use a tube forty-six feet long to contain enough fluid to balance the weight of the atmosphere. ) In the year of the mountain climb Pascal came under the influence of Jan senism (a Roman Catholic sect marked by strong anti-Jesuit feeling). In 1654 he had a narrow escape from death when the horses of his carriage ran away. He interpreted this as evidence of divine dis pleasure and his conversion became
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