method of computing logarithms, and an edition of Apollonius from both Greek and Arabic sources. In his paper on An Estimate of the Degrees of the Mortality of Mankind, drawn from curious Tables of the Births and Funerals at the City of Breslau ; with an Attempt to ascertain the Price of Annuities upon Lives, he laid the foundations of a new and important branch of applied mathematics. Having in boyhood occupied himself with magnetic experiments, in middle life he travelled in the tropics and made the first magnetic map, published in 1701 under the title “A general chart, showing at one view the variation of the compass." Drawing curves on this chart through points of declination, he invented a graphical method of wide future usefulness. From naval captain he became professor of geometry at Oxford, then astronomer royal till his death in 1742. One of his most notable achievements in astronomy was the discovery of actual changes in the apparent relative positions of the fixed stars, Aldebaran, Arcturus, and Sirius — answering a question centuries old. REFERENCES FOR READING Ball. Short History of Mathematics. Chapters XV, XVI. Lodge. Pioneers of Science. VII, VIII, IX. Mach. Science of Mechanics. Newton. Principia. CHAPTER XIV NATURAL AND PHYSICAL SCIENCE IN THE EIGHTEENTH CENTURY The seventeenth and eighteenth centuries mark the period in which, owing to the use of the several vernacular languages of Europe in the place of the medieval Latin, thought became nationalized. Thus it was that . . . people could make journeys of exploration in the region of thought from one country to another, bringing home with them new and fresh ideas. Such journeys were those of Voltaire to England in 1726 . . . of Adam Smith in 1765 to France. Merz. IN the preface to one of his volumes of essays, Lord Morley speaks of the eighteenth century as the scientific Renaissance. Such it undoubtedly was, for it was in this century and especially in its latter half, that chemistry, geology, botany, zoölogy, and physics, began to make deep impression on the learned world, while astronomy and mathematics ventured upon bolder and more far-reaching generalizations than they had ever before made. Science as a special discipline, or as a branch of learning worthy of the highest consideration, had as yet scarcely begun to make itself felt, but the names of Newton and Descartes were frequently heard in the salons of Paris and keen observers like Voltaire perceived the rising of a new tide in the affairs of men. A growth of popular interest might naturally have been expected after the great discoveries of the sixteenth and seventeenth centuries. What was not looked for was the concurrence of those political and social upheavals ever since rightly known as revolutions; viz. the French Revolution, the American Revolution and, probably most important of all, the Industrial Revolution. CHEMISTRY: DECLINE OF THE PHLOGISTON THEORY. - We have already touched upon the work of Boerhaave and Hales in the field of organic chemistry, so-called, and may now pass on to the studies of Black, Bergmann and others on the gas sylvestre (carbonic acid) of Van Helmont. Dr. Joseph Black of Edinburgh, a physician of note and, as we shall see, one of the first to put the science of heat on a sure foundation, seeking to explain the phenomena accompanying the making and the slaking of “quick” lime, phenomena now familar to every beginner in chemistry but in 1750 puzzling to all, — remembered that Hales had found that "air" could be driven off from certain substances by heating, and suspected that in the burning of limestone to make quicklime, something might be driven off, the loss of which would make it lighter. This something he tried to obtain by causing acid to act upon limestone (in the ordinary laboratory fashion of to-day) and collecting the gas evolved by the aid of Hales' pneumatic trough. He next weighed the gas and the remaining limestone and found that the weight of the former agreed with the loss of weight of the latter. He then reversed the experiment, causing "fixed air" (as he called it) to bubble through a solution of lime, whereupon, as he had anticipated, a white, chalk-like powder appeared and fell to the bottom. This simple experiment proved extremely fruitful, and we can now see that in its use of analysis and synthesis, in its partly quantitative character, and in the chemical reasoning employed, it was also highly instructive. Best of all, it did not require any hypothetical, immaterial or mystical "phlogiston" for satisfactory explanation of all the hitherto puzzling phenomena involved. Black invented for the gas thus driven off by heat or acid the term "fixed air," because it was evidently "fixed" in the limestone or chalky precipitate, and because any gas or vapor not obviously something else, was still supposed to be "air,". the true nature and chemical composition of the atmosphere being still (in 1750) quite unknown. At this point Bergmann, a Swedish chemist of distinction, by the use of litmus (which Boyle had recommended as a test for acids) and other means, discovered that the "fixed air" of Black is an acid, and accordingly named it "aërial acid." Bergmann also weighed the new gas, finding it heavier than air, and discovered that it is very soluble in water. To sum up: It was now known that there exists an invisible, odorless gas, resembling air but heavier than air and more soluble in water; that it is acid, and capable of attaching itself to lime, making a kind of chalk; that it will not support life, yet is present in the human breath, as well as in some mineral waters; and that it is given off during fermentations. It only remained for Lavoisier to discover (in 1779) that this gas is compounded of two very common elements — carbon and oxygen — tightly bound together, and may therefore be called, as it often is today, "carbonic acid." But before this could happen other investigations had to prepare the way, and especially the discovery of the new "element," oxygen. A NEW CHEMISTRY. PRIESTLEY AND LAVOISIER. We have now reached a period of remarkable activity and rapid progress in chemical research. While Black was hard at work upon chemical problems in Scotland, and Bergmann in Sweden, Cavendish was similarly engaged in England, and in 1766 reported to the Royal Society his discovery of a new kind of gas to which, for the reason that it took fire whenever flame was applied to it, and also because he believed it to be the cause of the occasional explosions in mines, he gave the name "inflammable air." Cavendish obtained this gas by treating iron, tin, zinc, or other metals with sulphuric acid, very much as Black had obtained fixed air by treating limestone with acids. Inflammable air was, however, obviously quite unlike fixed air, since it was lighter than air not heavier and was readily burned. It resembled it, nevertheless, in that a lighted candle plunged into it went out, and animals died in it just as they did in fixed air. It had another peculiar property; viz. that of forming with air an explosive mixture. This new gas as we now know was hydrogen. Not long after, in 1772, other new gases were separated and studied; viz. nitrogen by Rutherford, and nitric oxide by Priestley. It was on August 1, 1774, however, that Priestley made his most important discovery, and one that proved to be the very corner-stone of the splendid edifice in which modern chem istry now dwells, namely, the discovery of oxygen. Joseph Priestley, fearless reformer, Unitarian clergyman, and tireless experimenter in natural philosophy, had already made important and interesting discoveries when, in 1774, as stated above, he decomposed by heat the reddish powder obtained by calcining mercury, and collected and examined the gas given off. Candles and glowing coals burned in this gas with extraordinary energy, and mice lived in it under a bell glass even longer than in ordinary air. And, since it was derived from a burnt, i. e. dephlogisticated, metal and yet was colorless and odorless like ordinary air, Priestley named it "dephlogisticated air." The following is his own account of his work: There are, I believe, very few maxims in philosophy that have laid firmer hold upon the mind than that air, meaning atmospheric air, is a simple elementary substance, indestructible and unalterable at least as much so as water is supposed to be. In the course of my inquiries I was, however, soon satisfied that atmospheric air is not an unalterable thing; for that, according to my first hypothesis, the phlogiston with which it becomes loaded from bodies burning in it, and the animals breathing it, and various other chemical processes, so far alters and depraves it as to render it altogether unfit for inflammation, respiration, and other purposes to which it is subservient; and I had discovered that agitation in the water, the process of vegetation, and probably other natural processes, restore it to its original purity. . . ... Having procured a lens of twelve inches diameter and twenty inches focal distance, I proceeded with the greatest alacrity, by the help of it, to discover what kind of air a great variety of substances would yield, putting them into the vessel, which I filled with quicksilver, and kept inverted in a basin of the same. . . . With this apparatus, after a variety of experiments. . . on the 1st of August, 1774, I endeavored to extract air from mercurius calcinatus per se; and I presently found that, by means of this lens, air was expelled from it very readily. Having got about three or four times as much as the bulk of my materials, I admitted water to it, and found that it was not imbibed by it. But what surprised me more than I can express was that a candle burned in this air with a remarkably vigorous |