made in a form which appeals to his im- been possible a hundred years earlier! agination, and in the particular sciences Geometry for them meant the application preliminary to the engineering profession of mathematical knowledge to all the this has been largely done by the aid branches of physical science. It was not of geometrical and graphical methods. for them the pure theory of lines and cirTwenty years ago these methods were cles and curves, but a process of calcu scarcely discovered, or the few known lating and investigating the facts of were neglected or scouted. To-day the nature. Thus the revival of geometry in most scientific government in Europe per- the sixteenth and seventeenth centuries mits the calculations and plans of the was on Egyptian rather than Greek lines. largest engineering structures which are Newton, with astounding ingenuity, used submitted for its approval to be made by geometry as his main instrument for inpurely graphical processes. Here, then, vestigating the motions of the moon and we have an instance of theory placing at planets. The early occupants of the the disposal of practice one of the most Gresham chairs of both geometry and asefficient instruments of modern calculation tronomy were amongst the most distinand investigation, and this, indeed, is pe- guished scientific men of their time, culiarly the light in which, owing to early especially interested in the application of tradition and present needs, geometry mathematics to the problems of nature ought, I think, to be dealt with at Gresham and to the practical sides of life. Those College. I do not mean by this that the were the days when England was building sympathies of the City should be entirely up a greater empire for itself on the other with what we may term the Egyptian as side of the world, and if you were to ask contrasted with the Greek view of science, me what beyond their indomitable pluck but solely that the City has already entered carried our sailors and colonists over the upon the labor of reconciling theory and Atlantic and Pacific in their frail and dipractice, and that for a long time to minutive craft, I should reply, The labors come more efficient work might probably of the Gresham professors of geometry be done in this college by spreading and and astronomy. It was they who published utilizing existing knowledge than by ex- the first tables and manuals for English tending the boundaries of pure theory. seamen, explained and improved the comThe Gresham lecturer will, I fully believe, pass, the sextant, and the construction of best supply existing needs, if he deals ships. Briggs, the first occupant of the rather with the applications of geometry chair of geometry, wrote a work entitled, to practical life, than if he discourses on "The North-west Passage to the South the more complex aspects of his subject. Sea through the Continent of Virginia," I have said that this seems to me con- and another entitled, "Tables for the Imsonant with the early traditions of the provement of Navigation." It was Briggs college. When Sir Thomas Gresham who was mainly instrumental in introducfounded this college, the old mediaval ing the use of logarithms, that most wonconceptions of education were dying, and derful feature of modern calculation, the modern science and modern thought were use of which is imperative on every seaman in their birth-throes. The Renascence and astronomer of to-day. His colleague with its revival of learning had resuscitated in the chair of astronomy, Gunter (1619the knowledge of the Greek geometry. 26) drew up a table of logarithmic sines But the minds of men were not content and tangents for the first time- -a table with pure theory; they were anxious to familiar now to every navigator and landunderstand the laws of the physical uni- surveyor. He was also the first discoverer verse astrology was being replaced by of the slide-rule, now found in every archiastronomy, chemistry was deposing al- tect and engineer's office, while for long chemy. The old forms remained, but his sun-dials at Whitehall remained standthey were filled with a new life. Sir ard time-keepers. Gellibrand, his sucThomas Gresham, indeed, when he cessor (1626-36) wrote a treatise on the founded his college established his seven variation of the magnetic needle, and an professorships on the lines of an old med-" Epitome of Navigation" for seamen. iæval university, in which all knowledge was forced into one of the seven divisions - divinity, astronomy, geometry, music, law, physic, and rhetoric. But what a different view the early science professors those of astronomy and geometry took of their subjects to what would have No less active in this direction was Samuel Foster, who held the astronomy chair from 1641 to 1652. He explained the use of the quadrant for finding position at sea, and wrote more than one work bringing home the results of theory to the seventeenth-century seamen. Lawrence Rooke, 66 who successively held the chairs of as tronomy and geometry, published Directions for Seamen going to the East or West Indies to keep a Journal." To Sir Christopher Wren, who was Gresham professor from 1657-60, there is no need to make any reference in the City. His practical applications of theory are well known; that he published books on navigation and the structure of ships, that he first gave a theory of the pendulum, and improved the telescope, is perhaps less generally remembered. In his days there was a scientific enthusiasm at Gresham College which we can hardly realize any where now. Wren, we hear, had special charge of the planet Saturn, and his colleague Rooke of Jupiter, and their observations and lectures turned on the great discoveries then being made with regard to these peerless chiefs of the solar sys tem. the land. But I can only now refer to one fact from which in itself a true idea of the original activity of Gresham College might be formed. Gresham College was the cradle of the Royal Society. It was within its walls, and notably within the rooms of the professor of geometry, Lawrence Rooke, that the makers of England's earliest scientific reputation, men like John Wallis, Robert Boyle, and Lord Brouncker, together with the Gresham professors, Christopher Wren, Robert Hooke, and Sir William Petty, used to meet to discuss experiments, and it was at Gresham College that they received their charter of incorporation as the Royal Society in 1662. A French traveller, who visited England in the year 1663, and whose diary has recently been established, gives us an account of several visits to the Royal Society's meetings at Gresham College: "On May 23," he writes, "I was at the Academy of Gresham, where every Wednesday an assembly is held to make a variety of experiments upon matters not yet fully understood, but which are described according to each one's knowledge, while an account of them is written is always a person of quality, is seated at the top of a great square table, and the secretary at one side. The Academicians are seated on benches running round the ball. The president is Lord Brouncker, and the secretary is Mr. Oldenburg. The president has a little wooden hammer in his hand, with which he strikes the table to call to silence those who want to speak when another is speaking; thus there is no confusion or clamor. But perhaps the most brilliant of the Gresham professors was Robert Hooke, who held the chair of geometry from 1665 to 1703. He also published "Directions for Seamen;" he delivered and afterwards published "Lectures for improving Navigation and Astronomy." But more than all he invented the watch, with the de-out by the secretary. The president, who clared object of measuring time at sea, where no pendulum clock could be of service. The first account of the construction of the watch was given by the Gresham professor of geometry in his lectures at the college on "Several new Kinds of Watches for the Pocket wherein the Motion is regulated by Springs." Hooke improved also the reflecting telescope; he invented a marine barometer, and several new kinds of lamps. He wrote a treatise on the sails of windmills. He laid the foundation of the modern science of elasticity, and made the earliest researches of scientific value on the strength of materials. After the great fire of London, Hooke, like his former colleague Sir Christopher Wren, presented a model for the rebuilding of the City. Indeed, it is no exaggeration to say that in the seventeenth century it was to the Gresham professors that practical men seeking help from theoretical science naturally turned. "It was reported that salt of tartar put upon toads, vipers, or other venomous beasts caused them to die; some one said that quicksilver had the same effect; that these animals could not live in Ireland, as they could not bear the soil, and that experiments had been made by putting them on soil brought from England along with the animals; when they thought to escape, and approached the soil of the country, they always had to turn back, and did this until they died. Further, that a branch of holly placed in a certain lake in Ireland, I might, had I the time at my disposal, | in such wise that a part was in the earth, bring still further evidence to show that a part in the water, and a part in the air, the earliest of Sir Thomas Gresham's lec-after some time. -a year or thereabouts turers were essentially occupied with the applications of science to practical life, and that this tradition lasted so long as the post of Gresham lecturer meant in itself one of the highest distinctions in VOL. LXXIII. 3771 LIVING AGE. - changed its nature; the part in air remained indeed wood, but that in the water became petrified, and that in the earth metallic in character. In order to procure in ponds fish of all sorts which are Even geometry in its more abstruse speculations, when it transcends the space in which we live and theorizes of another, of which ours is as poorly representative as a landscape painted on flat canvas is poorly representative of the wealth of form and distance in the scene it depicts difficult of transport, it is only necessary | the physical world which surrounds it, and to carry the eggs of the fish one requires, in doing this may modify indefinitely our and these will afterwards hatch out; this practical conduct or our command of the a lord from Ireland said he had put into forces of nature. practice. Further, it was noted that the germination of insects does not arise from decay; for the intestines of an animal and other parts which easily corrupt having been placed in a glass closed with cottonwool, so that no fly or other animal could enter, but only the air could penetrate, they had been preserved for six weeks without maggot or other thing being observed.... Bodies weighed in the air had been afterwards weighed in a very deep pit, and had been found to weigh one-sixteenth less. That bodies which sunk in water came up again when one put more water into the vessel, which proved the compression of water by water. Sir Robert Moray told me that the president wished to give to the public a new science of the movement of bodies in water, and so to improve the art of navigation; with this end in view he was experimenting on the ease with which bodies of diverse shapes moved through water. . . . That a method of learning the difference of weight of various liquids was to weigh in them a body attached by a fine thread of silver or other metal, and the difference of the weights of this body enabled one to estimate the weights of the liquids. ... "The meeting concluded with the exhibition of a number of experiments made with an air-pump invented by Robert Boyle." even this abstruse geometry may some day react on practical life, by the modifications it is capable of producing in the current ideas of space and force. I recognize to the full this educational value in geometry, and in all forms of pure science; but I believe that there are other institutions - notably the great universi. ties which sufficiently emphasize this side of learning. On the other hand, I think that there is a gap which Gresham College is well suited to fill, and I believe that to fill it would not be out of accordance with its early traditions. By this gap I understand the want of an institution which, while recognizing the edu cational value of science, would mainly devote itself to pointing out, in a popular manner, the bearing of the conclusions of modern science on practice and the applications which can be made of them to ordinary life. In particular, it seems to me that the lectures on geometry can be made especially serviceable in this direction, if geometry be interpreted in the wide sense current in the seventeenth century, and Some of these experiments may sound which it retains to this day in France. strange to modern ears trained to a more The modern development of graphical and scientific view of natural phenomena; but geometrical methods has placed a powertheir general drift is in the right direction, ful instrument of calculation and investiand their bearing on the needs of every- gation in the hands of those who have day life sufficiently obvious to warrant us neither the time nor opportunity of learnin asserting that it was in Gresham Col-ing to handle the abstruse tools of analege and around its professors that in the seventeenth century those interested in the practical and experimental sides of science collected. I believe that the dignity and importance of the college in its early days were largely due to its being closely in touch with the wants of practical life. I have no wish to minimize the educational value of purely theoretical sciI recognize how great a factor it has been and is in the intellectual and spiritual growth of the nation. Investigations like those of Darwin and Maxwell, which appear at first sight to have no practical applications, may profoundly alter our whole view of human life, or of ence. lytical mathematics. Wherever quantity of any sort has to be measured and reasoned upon, there these geometrical methods find their applications. Their applications are indeed so manifold that it is difficult to enumerate them; to questions of force and motion, to problems in the strength of materials, in the structure of bridges and roof-trusses, of machinery in motion, of cutting and embanking - they have been long applied, and form the basis of much of modern engineering practice. But there are other fields which would constitute more suitable topics for a Gresham lecturer. The graphical representation of statistics at once suggests E From Chambers' Journal. A CRISIS IN THE CITY. itself. Mortality, trade, goods and personal traffic, furnish statistics which if dealt with in a graphical manner very At the opening of the session of Parliaoften suggest conclusions which are of ment in November last year, in the course the greatest interest to those dealing with of the preliminary fencing that usually problems of insurance and commerce- distinguishes such an occasion, the House conclusions more readily deducible from of Lords heard both Lord Granville and the geometrical than from the numerical the prime minister, with grave and caurepresentation of statistics. What may be achieved in this direction is admirably illustrated by the graphical album of trade returns published annually by the French government. The like geometrical methods have in recent years been applied to the principles of political economy, till the theory of prices has become almost a branch of applied geometry. But it is not alone in these very specialized subjects that we may reason geometrically. The whole field of physical science is occupied with the investigation, representation, and reasoning upon quantity, and therefore is essentially a field for the application of geometrical methods, but the bearings of physical science on practical life are too wide and too well known to be enlarged upon now. I had intended originally to take to-night some single point in this field, and explain how geometry might be used to elucidate it; but on second thoughts it seemed to me probable that the geometrical preliminaries would have absorbed all the time at my disposal, and that accordingly I might with more advantage lay general stress on the importance of the practical applications of geometry. In doing this, I have possibly had the future of Gresham College more in view than my own candidature for the lectureship in geometry. But I believe that, quite apart from the present election, the college has a future worthy of its earliest days, and that, not improbably, this future, if in another field, will still lie within the same broad lines that the City has already laid down for itself in the matter of technical education, the motto of which I take to be: Practice enlightened by theory, theory guided by practical needs. Work on such lines as these, accompanied by the expansion due to modern scientific requirements, would, I fully believe, restore the college to something like its old position among the teaching bodies of London, and reverse the judgment of that Cambridge historian of mathematics who has recently remarked that," with the beginning of the eighteenth century, an appointment at Gresham College ceased to be a mark of scientific distinction." tious words, refer to "the events which have recently taken place in the city of London." As a matter of course, little was elicited in the way of information as to the nature of the events in question; but the statement of Lord Salisbury that the governor of the Bank of England had found it his duty to communicate with the government on the subject, and that the city owed that gentleman an incalculable debt of gratitude, was sufficient to indicate the gravity of the situation. It is not often that what is agitating Lombard Street and Capel Court rises to national importance in the view of statesmen; but the crisis of November last was entirely exceptional. Looking back to the time of financial trouble within living memory - to 1878, when the City of Glasgow Bank fell, and further back still to that Black Friday in 1866 when the news of Overend, Gurney, & Co.'s failure spread panic far and wide-everybody acquainted with commercial affairs felt that the possibilities of disaster this autumn were more terrible still. No wonder a shock of dismay passed over men's minds when the word went round that one of the greatest houses in the City was in difficulties! For generations its name had been a synonym for financial stability and vast wealth. At home and abroad it had passed into a proverb. Their repute was the growth of a century of mercantile skill and uprightness displayed in the very front ranks of commerce. The crash of their fall, if it had been accomplished, would literally have made the farthest corners of the earth tremble. But the peculiarity of the crisis of 1890 was that the worst was forestalled. The very magnitude of the threatened disaster inspired a determination that it must not happen, and, by happy chance, there were men at the head of affairs equal to the emergency. The governor of the Bank of England, acting in concert with the chancellor of the exchequer, took strong meas. ures, and prepared, if need should be, to follow them up effectually; whilst the chief bankers in London and the provinces rallied round him, under the sense of a common danger. This wise boldness had its due reward, for the "panic" stage of the crisis was never reached. The plague was stayed, and the widespread ruin and misery that must otherwise have ensued was averted. This chapter of our most recent commercial history is a tale with a most obvious moral. In fact, apart from the magnitude of the interests involved, the disaster was of the most ordinary type, such as every day overtakes some speculator hasting to be rich. The conditions, indeed, of a commercial crisis are always with us. So far from being surprised when it arrives, we may well wonder why, under the present constitution of our money market, it occurs so seldom. We have an immense system of credit resting upon an utterly inadequate cash reserve. This is manifest, whether we consider the figures of our home and foreign trade, the liabilities of our banks, the annual income of the nation, or the financial operations of which our Clearing House accounts give evidence. greatest dealer in money—namely, the Bank of England, and, at a time of pressure, they depend on the supply that can be drawn from it. The provincial bankers in England, as well as the Scotch and Irish banks, have their spare cash with their agents in London, and the reserve of these in turn is represented by their balances with the central institution. No doubt the banks in the metropolis and throughout the country have a certain amount of gold in hand for ordinary daily requirements; but to maintain this at a high level would interfere with profits. The function is, therefore, practically thrust upon one institution of keeping the gold reserve for all; and it is plainly impossible that this can be done adequately by any such arrangement. It is often forgotten that the Bank of England owes a duty not to the public alone, but also to its shareholders, who have a right to expect a fair return for their money. When the bank pays a ten per cent. dividend, the return to a shareholder who has bought bank stock at recent prices is very little over three per cent. How, then, can it be demanded that the Bank of England shall assume the entire burden of maintaining a reserve for the benefit of all the banks in the country, some of which equal or even excel it in the amount of their deposits? We shall see, at all events, by a glance at the bank account published weekly, that the reserve is not equal to such a preposterous requirement. Let us take a very favorable specimen of these weekly accounts, that, namely, for the week ending Wednesday, the 3rd December, 1890, which stood as follows:ISSUE DEPARTMENT. It is generally agreed that the deposits in the banks of the United Kingdom cannot be less than £600,000,000, most of this sum repayable in gold on demand. The London Clearing House totals reach the incredible amount of £7,000,000,000 annually. Now, if we confine our attention simply to the deposit liabilities of our banking institutions, the question arises, What provision is made for the liquidation of them? The answer is, that there exists in the United Kingdom only one considerable cash reserve. The smaller dealers in money all group themselves round the |