Popular Science Monthly/Volume 76/February 1910/Scientific Faith and Works








THE ancient poets, at the beginning of their great epics, invoke the muse, and forthwith proclaim their subjects:

Arma virumque cano, I sing of arms and the man, says Virgil, Μᾒνιν ἀείδε θεά—Achilles' baleful wrath, Goddess, sing, are the words with which Homer begins the Iliad. A modern poet, full of sympathy with the changed times of to-day, Rudyard Kipling, makes one of his most attractive characters, the old Scotch engineer, exclaim,

I'm sick of all their quirks an' turns—the loves an' doves they dream—
Lord, send a man like Robbie Burns to sing the Song o' Steam!

In undertaking to do my part in the dedication of this splendid temple of science, I can but echo McAndrew's prayer, and wish that I had the words of a poet to sing the song of science. For what true devotee of science does not look upon her as a star-eyed goddess, and feel within himself at times feelings akin to those of the poet when breathing the divine afflatus? For the chief characteristic of both the poet and the scientist is the creative spirit, the poet creates beauty, or the appreciation of it, the scientist creates truth, or if he does not create truth, he at least creates the appreciation of it and of its results. I have chosen for my subject "Scientific Faith and Works." According to the Apostle Paul, "faith is the substance of things hoped for, the evidence of things not seen." In an eloquent panegyric, he recounts to us the deeds of the Hebrew patriarchs, "who by faith subdued kingdoms, wrought righteousness, obtained promises, stopped the mouths of lions, quenched the violence of fire, escaped the edge of the sword, out of weakness were made strong, waxed valiant in fight, turned to flight the armies of the aliens." I shall make it my task to show, by a not too literal application of the text, that similar effects may be produced through science. The more practical and prosaic Apostle James, on the other hand, in a chapter somewhat disparaging faith, exalts works, and issues the challenge, "Shew me thy faith without thy works, and I will shew thee my faith by my works." It is no doubt easier in the case of science to play the rôle of James than that of Paul. The works of science are abundant, and are appreciated of all. To catalogue them is an easy and somewhat commonplace task. But in order to better appreciate them let us take a brief glance at the world before it was under the influence of science as it is to-day.

If we consider the differences between ourselves and the ancients, we are at once struck by the fact that the chief dissimilarity is that they had little or nothing that can properly be called science. Deep thinkers they had, poets that have never been surpassed for lofty imagination and noble diction, teachers who devoted their lives to the attempt to solve the mysteries of existence, but the systematic study of the workings of nature is essentially modern. The great Hebrew nation, to whom we are indebted for so much that is fundamental in our religion and morals, brought the laws of conduct and the purity of life to an extent never equalled by the other nations of antiquity. Being essentially a race of simple shepherds and agriculturists, although in close contact with nature they produced no art, graphic or architectural, and left no engineering works to arouse our admiration for their resourcefulness. The sacred writings of the Hebrews are full of allusions to nature, in both its kind and terrible aspects. "Canst thou bind the sweet influences of the Pleiades? or loose the bands of Orion? Hast thou an arm like God? or canst thou thunder with a voice like him? Deep calleth unto deep at the noise of thy waterspouts: all thy waves and thy billows are gone over me. The heavens declare the glory of God, and the firmament sheweth his handiwork." These are specimens of the Hebrews' attitude toward nature, one of deep awe and reverence for its mighty Creator rather than of admiration for nature itself. The idea of studying into the workings of nature would, no doubt, have seemed preposterous and irreverent to such minds. The bow in the cloud was naturally accepted as a pledge made by God to men, while its circular form and unvarying arrangement of colors led to no curiosity to know why. The Egyptians, who so long were masters of the Hebrews, surpassed them in their interference with nature, and carried on engineering operations on an extensive scale, though of a simple character. They devised simple engines for raising the water of the Nile, and developed great irrigation systems, while the pyramids still remain a source of wonder to moderns. If we may believe all that students of the pyramids tell us, the Egyptians had no mean knowledge of astronomy as well. Certain it is that the Assyrians had a knowledge not only of astronomy, but of mathematics, having highly developed systems of numeration and methods of calculation, their sexagesimal system of numeration having come down to us in the division of the circle into three hundred and sixty degrees, against which anachronism the decimal system is but now beginning to struggle. The engineering operations of the Egyptians, however, were of a very simple sort, and their construction of the pyramids was probably permitted rather by the unlimited supply of forced labor than by the employment of devices for taking advantage of anything but brute force.

As the Hebrews were specialists in morals, so the Greeks were specialists in beauty, and pushed its culture to a degree never before or since attained. Had the Greeks left to us no masterpieces of literature, we should forever remember them by their magnificent temples, their incomparable sculpture, and their beautiful vases. Such a people must inevitably have had great thoughts to express in prose and verse, and it is not surprising that they were sensible of the beauties of the intellect, and pushed the study of geometry to a very considerable extent. The value which they attached to this study may be inferred from the inscription over the door of Plato's academy, "Let none enter who is not a geometrician," a motto which, by the way, I would gladly see placed over the gate of the modern college. Archytas of Tarentum, about 400 b.c., had devised apparatus for constructing various curves, had recognized the spherical form of the earth, and its daily rotation. Aristotle wrote a voluminous treatise on animals, showing careful observation of their habits, and even left a treatment of mechanical problems in which he almost recognizes the nature of the parallelogram of motions and of centrifugal force. In the domain of physics, however, he is not particularly happy, and is better at asking questions than in solving them. A hundred years later, however, Archimedes, the greatest of the Greek scientists, not only makes great advances in geometry, including a method that is in a measure the precursor of the integral calculus, but displays an acute knowledge of the principles of statics, including the principle of the lever, and of the fundamentals of hydrostatics, especially the principle named after him. With Archimedes, as with the other Greek philosophers, the practical applications accompanied, and probably generally preceded, the theoretical inquiries, and indeed this is still usually the case. The Romans, who succeeded the Greeks in importance in the ancient world, certainly did not do so on account of their cultivation of scientific studies, in which they played a poor part. Their very clumsy system of numeration would show their lack of mathematical talent, but on the other hand their extremely practical nature led them to the execution of great engineering works, their roads, aqueducts and baths still remaining for our admiration to-day. After the fall of the Romans succeeds the long night of the dark ages, learning being kept alive only by the Saracens, and the achievements of the Greeks being so far forgotten as to require to be discovered anew. Finally came the fall of Constantinople with the dispersal in Europe of many Greek scholars, the Renaissance, and the revival of learning. Conditions were then ripe for the prosecution of all sorts of intellectual pursuits, and we find the study of nature for itself taking on a development never before dreamed of. To these the church, in many cases, did not offer a welcome. Accustomed, during the middle ages, to the supreme domination over men's minds, she did not look with favor on a movement destined to set them free from all bonds except the truth. Copernicus died too soon to come into conflict with the power of the church, but upon his follower Galileo she wreaked her vengeance, and Giordano Bruno she burned at the stake. Nevertheless, the powerful genius of Galileo gave rise to so many and so important discoveries as to constitute him the father of modern science. Not satisfied with the introspective methods of the Greeks, who often contented themselves with considering how nature ought to work, he developed the modern method of the direct appeal to nature, by means of experiment finding out how she actually did work. When in the presence of the scoffing schoolmen he dropped the heavy and the light weight from the top of the tower of Pisa, and found them both to reach the ground together, he sounded the death-knell of the old and outworn Aristotelian philosophy.

It is not my intention here to consider the history of science, and its development from the small beginnings of the cinquecento through its glorious burst in the eighteenth century to full fruition in the nineteenth. Let us briefly recapitulate some of the changes which the works of science have made in the face of the earth, and of mankind inhabiting it. First and most important is the production of power, by which man's energies are inconceivably multiplied. The discovery of coal at just the right time to be utilized in the invention of the steam engine enabled man to command hitherto undreamed of forces, making the constructions and manufactures of the ancients seem like child's play. The raising of cotton, made practical by the invention of the cotton gin, largely transformed the clothing of the world, while the development of the iron and steel industry revolutionized methods of construction. With the command of power in centralized units came the development of the industrial system, and the tendency to crowd together into cities, leading to so many scientific problems yet unsolved. With the tremendous increase in the wants of humanity brought about by the increased power to supply them, the supply of natural energy in the form of coal, which at first seemed inexhaustible, seemed menaced, and other natural resources had to be developed, and more efficient methods of application found. Thus in our day the development of the internal combustion or gas engine, which threatens to crowd the steam engine to the wall, has finally permitted the application of petroleum, which by the aid of chemistry has furnished not only great stores of energy, but numerous useful products. Not the least important aspect of the power development is that part which is applied to transportation. The covering of the whole known world with lines of railway has made possible and easy movements from place to place not only of peoples, but of products, so that while a few centuries ago a large proportion of the population never moved more than a few miles from their birthplaces, being as good as fettered to the soil, now even the poorest may be easily displaced from country to country, the seas being no more of a barrier than the land. The increase of education by travel, and the tendency toward peace produced by the increased acquaintance of nations with each other, is not to be overestimated. Perhaps no more impressive example of man's power over nature is to be found than the sight of a great ocean steamship, lying at her dock and towering over the surrounding buildings, or ploughing her way at express speed over the stormy waves, whose power she hardly seems to feel. A notion of the huge demands made by ocean transportation on our resources of energy is obtained when we think that one of these marine monsters is using sixty or eighty thousand horsepower, while an express train uses from a thousand to fifteen hundred only. In view of this depletion of our coal supplies the question of water power has become urgent, »and science has succeeded in bridling our rivers and waterfalls for further supplies, while the transmission of this power by electricity has made manufacturing possible where it was not before, and is now being applied to transportation on a large scale. Not to be neglected in connection with the application of power is the question of illumination. When we think of the dark and dismal nights in the cities, not only of antiquity, but even of two centuries ago, making it impossible to go out in safety at night, and encouraging all sorts of crimes of violence, we must consider the successive application of gas, oil and electricity to have had no mean influence on the habits of mankind. The use of modern illuminants, especially electrical, has made possible the performance of more work, under more healthful conditions, and has completely changed the habits of man as regards the hours of darkness. Whether this has been entirely for his advantage we may leave until later.

Almost equally important with transportation is communication, which has in like manner changed the possibilities and habits of mankind. At the time of our revolution it took weeks to get any news to or from Europe, while even as late as the civil war our news was two weeks old when it reached England. What a contrast to the present, when the news of the fall of a cabinet or the overthrow of a sultan last night in any part of the world is put before us at breakfast this morning, and that not only in the centers of population, but in remote country districts. Nations can not now ignore each other's feelings and desires, while those misapprehensions which lead to war are made many times less frequent. The use of the ocean cable and of the telephone has largely transformed methods of doing business. Time is money, and although the increased facility of locomotion has led hosts of business men to circulate from one end of the country to the other, this can now in large measure be saved by the use of the telephone.

More important for the existence of man even than transportation and communication is food. The applications of science have made not one, but thousands of blades of grass grow where one grew before. Chemistry has shown how to fertilize the exhausted soil, engineering has furnished water where none was, and caused the desert to blossom as the rose. Its latest feat, in the anxiety due to the exhaustion of the nitrate beds, has been the fixation of the nitrogen of the air, which in Norway combines the harnessing of the waters with the compulsion, in the electric arc, of the nitrogen to unite with the oxygen, thus yielding unlimited nitrates for the restoration of our exhausted food supplies. Here also transportation comes in, so that the famines which formerly vexed large portions of the earth have now lost their terrors. When we think of the misery of the English agricultural classes before the abolition of the corn laws we may well praise the development of transportation which has enabled her to eat out of our full hand. At the same time the application of thermodynamics to freezing machinery has enabled us to send our meat across the ocean to become the roast beef of old England. The effects of all this upon the farmer can not be passed by. Commanding the markets of the world, ploughing his fields by steam or electricity, grinding his grain by gasoline, feeding his stock from silos, milking his cows by vacuum, cooling his cream by cold-producing machinery, separating it in a centrifugal creamer, making his cheese by the aid of chemistry so that he duplicates the product of any locality in the world, in easy reach of the city by automobile or trolley-car, and in communication with all his neighbors by telephone, he is no longer an object of derision, a hayseed, but an example of the works of science, demanding an equal part of influence in the government of the country, and gladly contributing of his rich store to the endowment of institutions like this for the education of his youth and the further advancement of science.

Again let us consider what science has done for the amelioration of health. When we consider the crowding, the filth, the misery of the greater part of the populace in the cities of antiquity, of the middle ages, and of our own times in many cities of the orient, we can but feel that the application of science to sanitation, to sewerage, water supply, and housing, has been of immense benefit, although it has by no means kept up with the needs of civilization. The discoveries of preventive medicine have removed the terrors from small-pox and yellow fever, and made impossible the wholesale devastation of great cities by plagues which were common only a few centuries ago. In our own days we have seen the work of the microscopist reveal the cause of the most various diseases, from malaria and cholera to the hookworm disease, while the marvelous work of the surgeon's knife fills us with amazement. If it be desirable to live long, science has largely contributed to benefit mankind in this way. With the improvement in the conditions of work has come the possibility for increased amusement. Music is stored up in the phonograph, to be carried to the remotest corners of Asia and Africa, while the kinematograph has rendered all corners of the earth accessible to the multitude, and has vivified the scenes of history.

Not the least important of the works of science is its effect in the promotion of general peace. As the nations are more closely linked together by the means of transportation and communication, their interests become more nearly alike, and they do not so easily plunge into wars. The applications of science to war have at the same time made it more terrible and deadly, so that nations do not dare to expose themselves to the chance of physical or commercial extermination thereby involved. If the development of the aeroplane shall make it possible for a fast cruiser like the Lusitania to be sent out equipped with rapid flying-machines which, on catching the strongest battleship shall make it possible to sail over her at too great a height to be shot at, but near enough to drop high explosives that shall destroy her, war will be at an end. The late Edward Atkinson once stated that all that was necessary to end war was the invention of a gun that should pick off generals at headquarters as the Boer sharpshooters picked off the British captains and colonels.

But I have said enough in praise of the works of science. It is no doubt possible to exaggerate their praise. A most judicious and learned observer, his Excellency James Bryce, in a Phi Beta Kappa address at Harvard two years ago, has examined the question, "What is progress," and whether all our modern improvements have constituted real progress from the times of the ancients. His conclusion is somewhat disappointing, and at the end the beam inclines very slightly in the positive direction. He does consider it probable, however, that the advances of science have rendered more tolerable human life, and have lengthened its span. We must not forget, indeed, that with nearly every new advance some disadvantage is connected, that with the development of industrialism there is connected great injustice, that the results of crowding in cities have led to great misery and sickness, problems not yet solved, and that the recent survey of Pittsburg has revealed conditions which could doubtless be paralleled elsewhere, but which cause us to blush for our boasted civilization. At the same time, these defects are not to be charged to science, but to the failure to utilize it. On the other hand the increase of insanity due to the greater strenuousness of life brought on by modern conditions is not so easily explained away.

It is not, however, for all these works of science that I wish to arouse your enthusiasm. As I have before stated, I consider James the more prosaic apostle, while it is Paul that stirs our feelings. What is the object of science, and is it worth our devotion? What are its purposes and methods, and what may we hope from it? Does it consist in building railroads and bridges, laying cables, digging tunnels and canals, and converting coal into ice? I believe it does not. Let us suppose that the advance of science, the adoption of socialism, or what not, has furnished every working man not only with three acres and a cow, but with hot and cold water, sanitary plumbing, steam heating, with cold brine for refrigeration, milk and beer laid on in pipes, with electric lighting, heating and power for the sewing machine, vacuum cleaner and the few remaining domestic necessities, with a telephone for communication and for the enjoyment of contemporary music, a phonograph and automatic piano for that of the past, an automobile and flying machine for transportation and sport, and that the hours of labor have been reduced to four, will universal happiness then reign? I fear not, if this is all. For life does not consist exclusively of eating and drinking, nor yet of pleasure. Unless what we call the soul is improved as well as the body, life is likely to be a poor thing. It is here that we come to the improvement of morals and of taste, and the need for art, literature and science. I mention these together, for their purposes are the same. They elevate the mind, kindle the imagination and give a more lofty outlook on the universe in general. It is the satisfaction of man's legitimate curiosity, his desire to know the how and the why of nature, that is, in my opinion, the true end of science. There are in the world, we are told by the late William Kingdon Clifford, three classes of persons: in the first place, scientific thinkers, secondly, persons who are engaged in work upon what are called scientific subjects, but who in general do not, and are not expected to, think about these subjects in a scientific manner, and lastly those whose work and thoughts are unscientific. Scientific thought is not determined by the subject thought of. The subject of science is the universe, its limitations those of the human mind. When the captain of a ship finds its position by means of observations with the sextant, or when an engineer constructs a dynamo with the aid of a drawing and data known to be correct, he does not engage in scientific thought, although he makes use of experience previously collected. When the computer in the office of the Nautical Almanac computes an eclipse of the moon, foretelling it to a second of time several years before the event, he is not engaged in scientific thought, but is making use of technical skill. When, on the other hand, Adams and Leverrier, computing the positions of the planet Uranus, found them not verified in fact, but by the assumption of a new hypothesis, were able to discover the planet Neptune, they were engaged in scientific thought of a high order. The collection of facts, as one collects postage stamps or coins, does not constitute science. In order to have science the facts must be fitted into a definite system, in accordance with a classification on the basis of what we call laws. It is a prerequisite for the existence of any science whatever that we admit that nature is subject to uniformity, that is, that similar circumstances of similar things will be followed by similar results. The belief that the order of nature is reasonable, that is, that there is a correspondence between her ways and our thoughts, and that this correspondence can be found out, is what I have called scientific faith. The method of the inductive sciences, those that concern the facts of nature, is first to observe a class of seemingly related facts in order to find out what they have in common, then if possible to form some hypothesis as to their relation, then to compare the different cases with the hypothesis in order to see whether it is justified. When this process has been successfully carried out, we arc able to predict what will occur in given circumstances, although these circumstances have not occurred. This is what we mean by discovering a law of nature, namely, finding a common property of a class of phenomena, such that under all circumstances the phenomena which will ensue can be described. This is what constitutes the difference between scientific and technical thought. Technical knowledge enables us to deal with cases that have occurred before, while scientific knowledge enables us to deal with what has not occurred before.

This is a matter that is not always understood in this country. It is a matter of common knowledge that this country stands very high in technical knowledge, but it is not so often pointed out that her contribution to science has as yet been distressingly small. Numerous examples might be given. We have just been celebrating the anniversary of Fulton's steamboat, with well-deserved enthusiasm. Nevertheless we must remember that Fulton did not invent the steamboat, nor did he construct the first one. He combined knowledge then existing with practical sense and business acumen, and was able to build a boat so large and successful as to convince the world of a new mode of transportation. In recent times the question of developing the power of Niagara involved the construction of turbines larger than had ever been built. These were built in Philadelphia, by means of the technical skill there existing, but the designs were made in Geneva by the well known engineers Faesch and Piccard. As a matter of fact the Swiss had long since developed the theory of the turbine, and were prepared to design one of any size on the principles already found sound. More recently the steam turbine has come into the field formerly the exclusive possession of the reciprocating steam engine. Curiously, the first successful turbines came from England, then a large number were developed in Germany and France, while at the present time we have one very successful American turbine. Now the physical principles involved in the turbine are quite different from those of the reciprocating engine, and involve considerable theoretical knowledge of the properties of fluids in rapid motion, some of which were familiar in the case of water, but which were of a different sort for an expansive vapor like steam. It is very noticeable that the best treatises on the steam turbine to-day are German, and begin with a large amount of theory on the properties of rotating discs, then of the thermodynamics of vapors, and finally of the flow of steam through jets, before the technical matters are touched. We are now hoping for the development of the gas-turbine, which shall combine the two advantages of the gas-engine and the turbine, and which will demand for its success all the knowledge of thermodynamics which we possess. As a final example take the case of wireless telegraphy. This country was a pioneer in ordinary telegraphy, having not only Morse to contribute the technical knowledge, but before him Henry with his scientific development of the electromagnet, but the wireless telegraph was imported in an advanced state of development, from England, where the scientific acumen of Maxwell had predicted the action of the electric waves. I am sorry to say that I feel that there is a tendency among our engineers or at least among our engineering students to try to do their work with a very small amount of scientific thinking, and it seems to me that this tendency must be overcome if we wish to maintain a successful competition in either science or technology with such a thorough-going scientific nation as Germany.

There is a tendency to-day in some quarters to disparage the use of hypotheses. With this tendency I do not sympathize. It is difficult to see how scientific advances can be made without the use of hypotheses, nor has that been the ordinary custom. The phrase of Newton has been quoted, "Hypotheses non hingo," but certainly that must be interpreted as meaning that he did not form unnecessary explanations of phenomena rather than that he did not proceed by means of working hypotheses, for he did. By making the hypothesis that the earth attracted bodies according to the inverse square of the distance, and calculating whether the fall of the moon toward the earth was of the amount required by this supposition, he was able to predicate the law of gravitation, and by the calculation that the orbit of a body attracted according to this law would be an ellipse he was able to explain the law of planetary motion discovered by Kepler. It is difficult to see how Kepler could have arrived at his law of elliptic motion if he had not first guessed that the orbits of the planets were circles or conic sections, and then verified it by comparison with the observations on their apparent positions.

The chief test of the success of a scientific hypothesis and of a train of reasoning therefrom is found in the ability to make predictions. Of this probably the most striking example in all science is the law of gravitation just alluded to. All the observations of the last two hundred } r ears have only resulted in confirming Newton's conclusion, while the accuracy of astronomical prediction exceeds that of any part of science. Such is an example of scientific faith. Another famous example is Hamilton's famous discovery of conical refraction. On looking through a piece of Iceland spar at an object one sees it doubled. The laws of this double refraction had been thoroughly described by Fresnel, who related them to a certain geometrical surface invented by him. By the study of the geometry of this surface, which was found to possess two singular points, Hamilton showed that on looking through the crystal in a certain direction at a point, one would see not two points but a whole continuous circle. This experiment was made by Hamilton's friend Lloyd, who saw the circle, confirming in the most brilliant manner the wonderful imagination of Hamilton, who saw in his mind's eye what never yet man had seen.

Another example of successful hypothesis is afforded by the kinetic theory of gases, which explains the properties of gases by the hypothesis that they consist of extremely small particles in very rapid motion, which by striking each other and the walls of the containing vessel by the impacts give rise to the pressure which the gas exerts. On this theory the friction which a current of gas exerts on a portion moving less rapidly, thereby setting it in motion, is of the same nature as the action that a crowd of men jumping from a moving train to a car upon a parallel track would have, their momentum tending to set the second car on which they alighted in motion. One of the remarkable predictions of this theory is the result of Maxwell that the viscosity of the gas is independent of its density, a result which has been well verified by experiment.

As a final example of scientific thought, let me briefly refer to the hypothesis of the luminiferous ether. About one hundred years ago, this hypothesis, that light consisted of a motion of the nature of waves, obtained the victory over the old notion that light consisted of small particles shot out from the luminous object with great rapidity. The laws of the propagation of these waves were thoroughly described by Fresnel, but what the properties of the substance in which they were propagated, and called the ether, might be, was long a matter of difficulty. Green had shown that an elastic solid of a certain sort would possess many of the properties of the ether, but this mechanical theory was insufficient in certain ways. It was the conjecture of Faraday that the actions of electrified and magnetic bodies upon each other, so thoroughly investigated by him, were transmitted to each other by means of the ether, and it was the genius of Maxwell and his wonderful scientific imagination, that enabled him to erect this conjecture into a remarkably perfect theory. By means of the hypothesis that electrical and magnetic actions are subject to the laws of mechanics, Maxwell was able to apply to electric currents the equations of Lagrange for dealing with the motion of the most general mechanical systems of bodies. In this way Maxwell explained the laws of the induction of currents, the difficulty of starting or stopping a current corresponding to the inertia of a heavy body. Presently by the aid of an auxiliary assumption the properties of the ether were described, and the remarkable result found that electrical and magnetic effects would be propagated with the velocity of light. From this it was a short step to declare light waves to be electromagnetic waves. Such waves were not known at the time of Maxwell's paper in 1865, and his theory waited long for acceptance. In 1888, however, Heinrich Hertz, guided by his great master Helmholtz into acceptance of Maxwell's theory, succeeded, in a most brilliant series of experiments, in producing the very waves predicted by Maxwell, and in showing that they traveled with the velocity of light. These are the waves made use of by Marconi for transmitting intelligence, and conquering the sea in peace and in war. But this is not all, for Maxwell, in his description of the manner in which the ether transmitted the electromagnetic waves, assumed that it was subject to certain stresses, so that a surface receiving a beam of light would experience a certain pressure, the amount of which he calculated. This result awaited verification until 1900, when the Russian physicist Lebedew, and in 1903 still more exactly the Americans Nichols and Hull, now president and professor, respectively, at Dartmouth College, gave it a magnificent verification. Thus by faith Maxwell subdued kingdoms, obtained promises, out of weakness was made strong, turned to flight the armies of the aliens of ignorance.

An interesting conclusion that may be drawn from the history of scientific endeavor is that there is an accepted time for each discovery, that is, that a certain stage of human progress the discovery is certain to be made, independently of the existence of any particular investigator. Such a truth is apt to put the scientist in that humble mood characteristic of the true man of science, and to show him how unimportant in the scheme of nature is any particular individual, but it need not leave him in the state described in the hymn, "Great God, how infinite art Thou, what worthless worms are we!" Examples of this conclusion are numerous. The discovery of Neptune simultaneously by Adams and Leverrier has already been mentioned. Singularly enough the planet was seen first by Galle, at Berlin, on September 23, 1846, and then independently by Professor Challis, at Cambridge, on September 29, he being ignorant of Galle's discovery. The statement of the Second Law of Thermodynamics in 1850 by Clausius and Lord Kelvin, and the discovery that the specific heat of saturated vapor is negative by Clausius and Rankine and others. The published work of Sir Oliver Lodge on electric waves shows that it admits of no doubt that had not Hertz published his researches when he did Lodge would have obtained many of his results. The work of Helmholtz and Lord Kelvin is full of interesting parallelisms, while the important application by Helmholtz of thermodynamics to chemical phenomena was anticipated by our own Willard Gibbs. Coming down to the present time, it is no disparagement to Wilbur and Orville Wright to say that had they not succeeded in the conquest of the air the same result would shortly have been achieved by Blériot, Voisin and others. I have no doubt that, had not Columbus discovered America in 1492, some other intrepid navigator would have done so in ten years. Had not Peary discovered the pole—but I pause, as fiction is sometimes stranger than truth.

I will now, with your permission, undertake to make a rough classification of the sciences, and make some remarks on the differences in their methods. Sitting serene at the head as queen of all is mathematics. Ready she is to serve all, and what a servant she can be is witnessed by those other sciences that have most need of her. Mathematics is probably the most misunderstood of all the sciences. Huxley called it "that science which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation." To this a sufficient answer might be that she does not need to, but a better one is that it is not true. Intuition and induction have a great part in all mathematical discoveries, as all of the great mathematicians agree. Mathematics has no subject matter, but may be applied to anything that has exact relations. To sing the beauties of mathematics to those ignorant of that subject is as futile as to praise music to the tone-deaf, or painting to the color-blind. I have a friend who describes a symphony as a horrid noise. The president of a great eastern university has said that the manipulation of mathematical symbols is a mark of no particular intellectual eminence. Presumably he had never tried it. To the often-repeated charge that mathematics will turn out only what is put in we may reply that while from incorrect assumptions it can not get correct results it has the power of so transforming the data as to reveal to us totally unexpected truths. Witness the magnificent generalizations of Adams and Leverrier, of Hamilton, and of Maxwell already quoted. There is no doubt that the invention of the infinitesimal calculus has furnished man with the most powerful and elegant instrument of thought ever devised. Allow me to try in a few words to tell why this is so. Natural phenomena are not, as a rule, discrete, like integral numbers, but continuous, like points on a line, so that there is no least difference between one and another. We say that they are continuous, and that they vary continuously. The examination of continuous change is the function of the differential calculus. When we undertake to define so simple a matter as the speed of a point, we can not say that the velocity is the distance traversed in a given time, unless during the whole of that time the speed is the same. If it is continually changing we must divide the time into less and less intervals, and find the ratio of the distance to the time required when both become smaller than any quantity conceivable, in other words we must find the limit approached by this ratio. Thus all questions relating to rates of change, to slopes of curves, to curvature, and the like, require the method of limits, as applied in the differential calculus. On the other hand, consider the case of two bodies attracting each other according to any law of the distance. Since the body is more than a point, from what point of the body shall the distance be measured. Obviously each small portion of the body contributes its part in the attraction, with a different amount according to where it is, all these amounts requiring to be added together to make the whole. But how many parts shall there be, and how large. Obviously there is no bound to the number, nor to the size, one increasing as the other decreases. We must accordingly take the limit which this sum of all the actions approaches as we increase the number of parts while diminishing their size below any limit whatever. This is the method of the integral calculus, Now as observation enables us to deal with bodies of finite size only, the inference to the laws of the ultimate parts can be made only deductively by the calculus. In practise, however, the inverse process is more frequently employed, that is, the actions of points infinitely near each other in space, time or other circumstances are assumed to follow some simple law, thus giving us what are called differential equations, the integration of which gives us conclusions as to what happens on the large scale, which conclusions can be compared with experiment. It is on account of the logical importance of the method, the universality of its applicability, and the intellectual power developed, that I could wish that as a counterpart to Plato's motto should he placed over every college gateway, "Let none depart hence who knows not the calculus," at least as to what it deals with, and its fundamental principles.

I am glad to say that in some of our colleges are now given courses in what is termed "culture calculus." It seems to me that this subject is more deserving of the name of culture than the familiarity with the immoralities of the Greek gods.

Of the natural sciences there are two fundamental ones, physics and biology. Physics has to do with all the universe, in so far as it possesses energy, and exerts forces one part upon another, and in so far as it does not possess life. Biology deals with all matter possessing this difficultly defined attribute, but so far as we know, even the phenomena of living matter are subject to the laws of physics. I presume that every biologist will admit that life does not create energy, but merely directs it. Nevertheless, the question of vitality is to-day far beyond the explanation of the physicist. The subdivisions of physics have been, for convenience only, set off as individual sciences, chiefly because the whole subject would be too large for the treatment of any individual scientist. The most important part of physics is dynamics, which treats of the laws of motion, and the forces which are associated therewith. Of this a great division is celestial mechanics, which, as we have seen in the cases of Galileo and Newton, contributed in great part to the inductive establishment of the laws of motion in general. The remainder of astronomy is now catalogued as astrophysics and is dealt with by purely physical methods and instruments. As a subdivision of astronomy may be reckoned geodesy, which deals with the form of the earth, deduced from astronomical measurements and from its gravitational attraction.

Chemistry is that part of physics which deals with the properties of substances that have individual characteristics by which they may be always distinguished, and which combine with each other in definite proportions. Its methods are those of physics, its main instrument is the physical balance, and it is in recent years concentrating more attention upon those physical relations connected with temperature, pressure, and electrical relations, all of which are now found to yield to mathematical treatment in a manner until recently unsuspected.

The methods of physics and chemistry usually involve the controlling of certain of the circumstances under which phenomena occur, so that the changes in others may be more easily observed. This is usually done in a laboratory furnished with many means of controlling circumstances, for instance, temperature, pressure, electrical or magnetic state, so that the same circumstances may be reproduced again and again. Meteorology, or as it is now somewhat grandiloquently called, cosmical physics, has to do with those phenomena of the atmosphere, the ocean, or the magnetic state of the earth, which are not controllable by man, and which can not, therefore, be repeated at pleasure in the laboratory, but must be observed when and where they occur. The same applies to geology, which is the application of physics, chemistry and even biology, or any science whatever, to the earth, in relation to its physical constitution and its history. Geography deals with the face of the earth, and uses the results of geology to study the earth as fit to be the dwelling place for man. There remain the technical applications of physics in all kinds of engineering, civil, mechanical, electrical, chemical or mining, involving the strength of materials, elasticity and the direction of the natural sources of energy to the purposes of man. All these applications of physics need, and are highly susceptible to, mathematical treatment, and for that reason they are the most perfectly developed of all the sciences.

Let us now turn to the biological sciences. The two fundamental divisions, zoology and botany, dealing with animals and plants, seem to run continuously one into the other, like chemistry and physics. Under both we have the subdivisions of morphology for the study of form and physiology for function. Under zoology we put anatomy, and the various more specialized sciences which find their technical application in medicine. There still remain anthropology, the study of man and his practises, psychology, which deals with the workings of what we call his mind, or that of animals, sociology, properly a part of anthropology, dealing with man when living with his fellows, and economics striving to teach him how to get along with them still better.

This classification is admittedly rough, but it does not separate closely connected things as some that I have seen do. For those who desire finer splitting I refer to the classification of the Scientific Congresses of St. Louis in 1904. Of these biological sciences the methods are somewhat different, they are mostly still in the descriptive stage, and have rarely attained sufficient quantitative information to be capable of mathematical treatment. And yet that must be their ultimate object, for without mathematics there is no exact description. That this is not impossible even in biology may be seen from the following example. If a bacterial culture be inoculated into a jelly with the point of a needle, it will be seen under the microscope to grow in all directions from the original center, and if pains are taken to ensure the physical homogeneity of the jelly the shape of the colony will be an almost perfect circle. If the diameter of this circle be measured at regular intervals, I have no doubt that a quantitative law of growth can be deduced, and even a differential equation found, which will turn out to resemble that of certain physical phenomena, say the conduction of heat. We may observe that the instruments and methods of the physiologist and the experimental psychologist are already largely physical, and their researches are carried on in laboratories. In proportion as the various circumstances are rendered more amenable to external control, so the methods of biology will more nearly approach those of physics. Whereas biology was until recently chiefly a science of observation, it has now become in a high degree experimental. The physiologist removes or alters organs, removes eggs from the natural parent and places them in a foster-mother, cuts off the heads and tails of worms and observes the conditions of survival and regeneration. If the force of gravity were removed, in what direction would a plant grow? If an egg be subjected to centrifugal force in which direction will the head of the animal appear? These are the sort of questions that the biologist is now attacking. Nor is he without mathematical statements. The great generalization of Darwin of fifty years ago has ever since concentrated attention on problems of development and heredity. Darwin's conclusions were the results of the observations of a long life. Now the experimental method enables one to hasten and accelerate conclusions. The gentle monk and acute man of science, Gregor Mendel, forty years ago in his cloister at Brünn by his careful experiments on the crossing of thousands of peas, and by comparisons of their seeds, flowers and stems, succeeded in unveiling a law which has profoundly influenced ideas on heredity, not only in plants but in animals. He finds that in the process of hybridization there are certain characteristics which are transmitted entire to the offspring, and are termed dominant, others which seem to disappear or become latent in the process, which he terms recessive. When however the hybrids are bred together both qualities reappear in the offspring, and in a definite proportion of three of the dominant to one of the recessive. In the next generation another definite proportion occurs, and so on. We here have a very definite arithmetical relation, which is susceptible of very exact study and confirmation.

The method of Mendel, which we may call that of experimental evolution, is now of wide application, and there are laboratories which do nothing else but breed and cross under very exact control. Among one of the large-scale experimenters in this line may be mentioned Mr. Luther Burbank, who, though a master of method and subsidized by the Carnegie Institution, seems to be devoted rather to practical than to scientific results.

In connection with the laboratory or experimental method in evolution, must be mentioned a most promising application of mathematics to biology in the new science of biometrics, or the application of the methods of probability or statistics to great numbers of similar objects. If the doctrines of evolution or of variation are ever to be accurately proved it must be in this manner. To illustrate, suppose we have a phenomenon in which chance is involved, and that two events are equally likely, such as throwing head or tail with a coin. Suppose we have a vertical board in which are stuck horizontal pegs in a regular arrangement of rows and columns. Suppose a shot be dropped over the middle of this array of pegs, and assume that if it strikes a peg it is equally likely to drop to the right or the left. The next time it strikes a peg the chances are the same. It is obviously very unlikely that a shot will continually fall on the same side, while the likeliest thing that can happen is that it shall fall in the middle. Hence if a large number of shot are let fall they will be found, if caught where they fall, to be arranged in a form limited by a curve highest in the middle, and gradually falling symmetrically toward both sides, known as the curve of errors. This curve represents graphically the result of an infinite number of causes acting, each as likely to produce a certain effect as its opposite. Let us now take some biological subject of investigation, say the length of a certain kind of shell. Many thousands being measured, it is found that they vary from the average, but in such a way that very few differ very far from the mean. If the number having any given length is plotted vertically corresponding to the deviation from the mean laid off horizontally, we shall obtain a curve which will generally closely resemble the curve of errors. If this is the case we shall conclude that the causes of the variations in length are perfectly at random, but if we find that the curve is unsymmetrical, or for instance has two summits, we shall know that at least two sorts of causes are acting. Thus questions of heredity and variation may be mathematically studied. This method has been greatly developed by the mathematician, Karl Pearson, who has now devoted himself to the study of evolution by mathematical means.

Finally, that apparently most remote of the sciences from the exactness of physical laws, economics, has been brought under the treatment of mathematics, not only by statistical methods like those just described, but by methods of the calculus. The distinguished mathematician and economist Cournot applied to the theory of wealth methods like those used in mechanics to treat of equilibria, so that very complicated economic principles were amenable to treatment by symbols.

I have, I think, said enough to show the power of science to transform the world, and to develop the mind of man. Is not this development of high spiritual value, and is not the pursuit of truth irrespective of prejudice and authority a noble object, worthy of the devotion of a lifetime? Of the moral values of science it would be easy to give arguments. One has but to consider the self sacrifice of many of its devotees, who consider neither toil nor time if only the good of the race be advanced. Galileo was tortured, Giordano Bruno was burned, and to-day the daily papers bring us news of lives lost in the study of the cholera, of the plague, of the sleeping sickness. The spirit of science is well illustrated by the gift to the Pasteur Institute by M. Osiris last summer of thirty millions of francs. He was led to do this by the fact that the director, Doctor Roux, having won a prize of one hundred thousand francs for the discovery of a diphtheria serum, though not a rich man, immediately turned it over to the institute. Feeling that a cause capable of producing such unselfishness must deserve support, M. Osiris made it this large bequest. Lord Rayleigh, in like manner, donated his Nobel prize of forty thousand dollars to the physical laboratory at Cambridge.

In closing, permit me to recommend the scientific career to young men as one of great satisfaction, whether one succeeds in it or not. To be even a soldier in this noble army, to feel oneself the follower of Faraday, of Helmholtz and of Maxwell, to push on the standard of truth, is worth more than to dress in purple and fine linen and to own many automobiles. There are in this country of eighty millions only about five thousand scientists. The country needs you, young men; it is a patriotic duty to put her where she should stand intellectually among the nations. Would that I might reach the rich, and sing to them the praises of this sort of service. In other lands the rich serve the state, why not here? Surpass your less fortunate brothers not in your pleasures, but in your achievements. And then the American college will be exempt from some of the criticism that it meets to-day. Finally let us bear in mind that while we admire the palaces of science like this, they are not necessary for the performance of good work, and that those of us who are obliged to work in less sumptuous abodes may be consoled with the reflection that most of the great discoveries in science were made with simple apparatus, in humble quarters, but by great men. It is the spirit that quickeneth. For the true scientific spirit may we ever pray, for the works of the Lord are great, sought out of all them that have pleasure therein.

  1. An address delivered at the dedication of the Laboratory of Physics, University of Illinois, November 26, 1909.