altitude of the triangle. Arriving thus at the parallelogram of forces in equilibrium, he expresses his astonishment by exclaiming "Here is a wonder and yet no wonder." In studying pulleys and their combinations he arrives at the far-reaching result that in a system of pulleys in equilibrium "the products of the weights into the displacements they sustain are respectively equal" — a remark containing the principle of virtual displacement. He reaches correct results in regard to basal and lateral pressure by reasoning analogous to that about the chain, and by assuming on occasion that a definite portion of the liquid is temporarily solidified. By ingenious experiments he proves the dependence of fluid pressure on area and depth, and takes proper account of upward and lateral pressure. He studies the conditions of equilibrium for floating bodies, showing that the centre of gravity of the body in question must lie in a perpendicular with that of the water displaced by it, and that the deeper the centre of gravity of the floating body the more stable is the equilibrium. In analyzing the lateral pressure of a fluid Stevinus anticipates the calculus point of view by dividing the surface into elements on each of which the pressure lies between ascertainable values. Increasing the number of divisions, he says it is manifest that one could carry this process so far that the difference between the containing values should be made less than any given quantity however small — all quite in harmony with our present definitions of a limit. Stevinus' work and that of Galileo seem to have been quite independent of each other, the former confining his theory to statics, the latter laying a solid foundation for the new science of dynamics. Torricelli, a disciple of Galileo best known for his invention of the mercurial barometer, extended dynamics to liquids, studying the character of a jet issuing from the side of a vessel. Throughout this period the universities lagged. In Italy Galileo lectured to medical students who were supposed to need astronomy for medical purposes — i.e. astrology. At Wittenberg ... there was a professor for arithmetic and the sphere, and one for Euclid, Peurbach's planetary theory and the Almagest, but their students were few. So, says a German writer, we face the extraordinary fact that the most educated of the nation were as helpless in the problems of daily life as a marketwoman of to-day. The university lectures in mathematics were mainly confined to the most elementary computation, — matters taught more thoroughly in the commercial schools, particularly after the invention of printing. GIORDANO BRUNO (1548-1600).—In the Appendix will be found the judgment and sentence of the Inquisition upon Galileo, together with his recantation, —one of the darkest pages in the history of Science. Another victim of the Inquisition was Bruno, an Italian philosopher, who, having joined the Dominican order at the age of fifteen, was later accused of impiety and subjected to persecution. Bruno fled from Rome to France, and later to England, where at Oxford he disputed on the rival merits of the Copernican and the so-called Aristotelian systems of the universe. In 1584 he published an exposition of the Copernican theory. Bruno, moreover, attacked the established religion, jeered at the monks, scoffed at the Jewish records, miracles, etc., and after revisiting Paris, and residing for a time in Wittenberg, rashly returned to Italy, where he was apprehended by the Inquisition and thrown into prison. After seven years of confinement he was excommunicated and, on Feb. 17, 1600, burnt at the stake. In 1889 a statue in his honor was unveiled in Rome at the place of his execution, the Square of the Flower Market. Thus was the end of the sixteenth century illuminated by the flames of martyrdom. REFERENCES FOR READING BALL. Short History of Mathematics, Chapters XII, XIII. FAHIE. Life of Galileo. GALILEO GALILEI. Two New Sciences. (Translated by Crew and De Salvio.) MACH. Science of Mechanics (for Galileo and Stevinus). CHAPTER XII NATURAL AND PHYSICAL SCIENCE IN THE SEVEN TEENTH CENTURY THE CIRCULATION OF THE BLOOD: HARVEY (1578-1657).—The blood has always been regarded as one of the principal parts of the body. Hippocrates considered it one of his four great "humors," and in the Hebrew Scriptures it is stated that “the blood... is the life." Yet up to the seventeenth century nothing definite was known of its movements throughout the body. That it was under pressure must have been known, for it flowed or "escaped" freely from wounds, and flow results only from pressure of some sort, while escape is relief from detention. The arteries had been misinterpreted for centuries and were early considered to be air tubes, because they were studied only after death when as we now know they are empty. Even the dissections of the anatomists of the sixteenth century had failed to reveal the complete and true office of the arteries, and it remained for Harvey, an English pupil of the Italian anatomist Fabricius, to make largely through the vivisection of animals and observation of the heart and arteries in actual operation - discoveries of basic importance in anatomy, physiology, embryology, and medicine (see Appendix). While working in Italy, Harvey learned of and doubtless saw the valves in the veins which were discovered by Fabricius. These valves are thin flaps of tissue so placed as to check the flow of blood in one direction while offering no resistance to that flowing the other way. On his return to England, Harvey apparently pondered on the function of these valves and saw that they could be of use only by permitting the flow of the blood in one direction while preventing its movement in the opposite direction. At this time it was supposed that the blood simply oscillated, or moved back and forth like a pendulum, a view which, if the valves had any meaning, was now plainly untenable. Harvey therefore set to work to study the beating of the heart and the flowing of the blood, and soon came to the conclusion that there must be a steady flow or streaming in one direction, and not an oscillation back and forth as was generally supposed. But to prove was here, as always, harder than to believe, and much time and labor were required to settle the question. At length, however, by dissections and vivisections of the lower animals, and after publishing (in 1628) a brochure presenting his facts and meeting objections, Harvey succeeded, with the result that his name justly stands to-day beside those of the Greek and Alexandrian Fathers of Medicine, Hippocrates and Galen. It is one of the ironies of fate that while Harvey rightly reasoned from circumstantial evidence that the blood must steadily flow from the arteries to the veins, he himself never actually saw that flowing, — a sight which any schoolboy may now see, but impossible before the introduction of the microscope, and first enjoyed by Malpighi in 1661, only four years after Harvey's death. In embryology, also, Harvey proved himself an original and penetrating observer. In his day and earlier it was supposed that the embryo, in the hen's egg, for example, exists even at the very outset as a perfect though extremely minute chick, with all its parts complete. This "preformation" theory was opposed by Harvey, whose doctrine of "epigenesis" was substantially that of modern embryology: viz. that the embryo chick is gradually formed by processes of growth and differentiation from comparatively simple and undifferentiated matter, somehow set apart and prepared in the body of the parents. The ATMOSPHERIC PRESSURE: TORRICELLI'S BAROMETER. problem of the existence and nature of voids and vacua had always been an interesting puzzle for philosophers. The Greeks assumed the existence of empty spaces or "voids," and as late as the age of Elizabeth it was the orthodox belief that "nature abhors a vacuum." Galileo, even, held to it in 1638. (Cf. p. 246.) Evangelista Torricelli (1608-1647), inspired by the Dialogues of Galileo (1638), published on Motion and other subjects in 1644. He resided with Galileo and acted as his amanuensis from 1641 until Galileo's death. In experimenting with mercury he found that this did not rise to 33 feet, but instead to hardly as many inches. He next proved, by comparing the specific gravity of water and mercury, that the same "pressure" was at work in both cases, and boldly affirmed that this pressure was that of the atmosphere. The tube of mercury used in his experiments was what we now call a barometer (baros, weight), but it was for a long time called "the Torricellian Tube," as the empty space above the mercury is still called the "Torricellian vacuum." This invention or discovery of Torricelli's was one of the most fertile ever made, for at one blow it demolished the ancient superstition that "nature abhors a vacuum," explained very simply two ancient puzzles (why water rises in a pump, and why it rises only 33 feet), determined accurately the weight of the atmosphere, proved it possible to make a vacuum, and gave to mankind an entirely new and invaluable instrument, the barometer. Torricelli's results and explanations were received at first with incredulity, but were soon confirmed, notably by Pascal (1623-1662) in a treatise, New Experiments on the Vacuum. In one of these Pascal used wine instead of water or mercury in the Torricellian tube, with satisfactory results, and in another, reasoning that if Torricelli were right, liquids in the tube should stand lower on a mountain than in a valley, persuaded his brother-in-law, Perier, to ascend the Puy de Dôme (near Clermont, France) in September, 1648, on which mountain the column was found to be much shorter. This and other brilliant work by Pascal have given him a high rank among natural philosophers. Since it was now easy to obtain a vacuum by the Torricellian experiment, fresh attempts were made to produce vacua otherwise. Von Guericke, burgomaster of Magdeburg in Hannover, after many failures, finally succeeded in pumping the air out of a hollow metallic globe. It was in this experiment that the air-pump was introduced. Guericke found that his globe had to be very strong to resist crushing by the atmospheric pressure, and in the popular demonstration now known as that of the Magdeburg hemi |