A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history. … Only by taking an infinitesimally small unit for observation (the differential of history, that is, the individual tendencies of man) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.

After innumerable dynasties of giant creatures, after endless generations of fish and families of molluscs, man finally arrives, the degenerate product of a grandiose type, his mould perhaps broken by his Creator. Fired by his retrospection, these timid humans, born but yesterday, can now leap across chaos, sing an endless hymn, and configure the history of the universe in a sort of retrograde Apocalypse.

Among innumerable footsteps of divine providence to be found in the works of nature, there is a very remarkable one to be observed in the exact balance that is maintained, between the numbers of men and women; for by this means is provided, that the species never may fail, nor perish, since every male may have its female, and of proportionable age. This equality of males and females is not the effect of chance but divine providence, working for a good end, which I thus demonstrate.

Beneath multiple specific and individual distinctions, beneath innumerable and incessant transformations, at the bottom of the circular evolution without beginning or end, there hides a law, a unique nature participated in by all beings, in which this common participation produces a ground of common harmony.

By death the moon was gathered in Long ago, ah long ago;
Yet still the silver corpse must spin
And with another's light must glow.
Her frozen mountains must forget
Their primal hot volcanic breath,
Doomed to revolve for ages yet,
Void amphitheatres of death.
And all about the cosmic sky,
The black that lies beyond our blue,
Dead stars innumerable lie,
And stars of red and angry hue
Not dead but doomed to die.

Connected by innumerable ties with abstract science, Physiology is yet in the most intimate relation with humanity; and by teaching us that law and order, and a definite scheme of development, regulate even the strangest and wildest manifestations of individual life, she prepares the student to look for a goal even amidst the erratic wanderings of mankind, and to believe that history offers something more than an entertaining chaos—a journal of a toilsome, tragi-comic march nowither.

Consider now the Milky Way. Here also we see an innumerable dust, only the grains of this dust are no longer atoms but stars; these grains also move with great velocities, they act at a distance one upon another, but this action is so slight at great distances that their trajectories are rectilineal; nevertheless, from time to time, two of them may come near enough together to be deviated from their course, like a comet that passed too close to Jupiter. In a word, in the eyes of a giant, to whom our Suns were what our atoms are to us, the Milky Way would only look like a bubble of gas.

Consider the eighth category, which deals with stones. Wilkins divides them into the following classifications: ordinary (flint, gravel, slate); intermediate (marble, amber, coral); precious (pearl, opal); transparent (amethyst, sapphire); and insoluble (coal, clay, and arsenic). The ninth category is almost as alarming as the eighth. It reveals that metals can be imperfect (vermilion, quicksilver); artificial (bronze, brass); recremental (filings, rust); and natural (gold, tin, copper). The whale appears in the sixteenth category: it is a viviparous, oblong fish. These ambiguities, redundances, and deficiencies recall those attributed by Dr. Franz Kuhn to a certain Chinese encyclopedia entitled Celestial Emporium of Benevolent Knowledge. On those remote pages it is written that animals are divided into (a) those that belong to the Emperor, (b) embalmed ones, (c) those that are trained, (d) suckling pigs, (e) mermaids, (f) fabulous ones, (g) stray dogs, (h) those that are included in this classification, (i) those that tremble as if they were mad, (j) innumerable ones, (k) those drawn with a very fine camel's hair brush, (l) others, (m) those that have just broken a flower vase, (n) those that resemble flies from a distance.

Every leaf and twig was this morning covered with a sparkling ice armor; even the grasses in exposed fields were hung with innumerable diamond pendants, which jingled merrily when brushed by the foot of the traveler. It was literally the wreck of jewels and the crash of gems.

Firm support has been found for the assertion that electricity occurs at thousands of points where we at most conjectured that it was present. Innumerable electrical particles oscillate in every flame and light source. We can in fact assume that every heat source is filled with electrons which will continue to oscillate ceaselessly and indefinitely. All these electrons leave their impression on the emitted rays. We can hope that experimental study of the radiation phenomena, which are exposed to various influences, but in particular to the effect of magnetism, will provide us with useful data concerning a new field, that of atomistic astronomy, as Lodge called it, populated with atoms and electrons instead of planets and worlds.

I had made up my mind to find that for which I was searching even if it required the remainder of my life. After innumerable failures I finally uncovered the principle for which I was searching, and I was astounded at its simplicity. I was still more astounded to discover the principle I had revealed not only beneficial in the construction of a mechanical hearing aid but it served as well as means of sending the sound of the voice over a wire. Another discovery which came out of my investigation was the fact that when a man gives his order to produce a definite result and stands by that order it seems to have the effect of giving him what might be termed a second sight which enables him to see right through ordinary problems. What this power is I cannot say; all I know is that it exists and it becomes available only when a man is in that state of mind in which he knows exactly what he wants and is fully determined not to quit until he finds it.

I have accumulated a wealth of knowledge in innumerable spheres and enjoyed it as an always ready instrument for exercising the mind and penetrating further and further. Best of all, mine has been a life of loving and being loved. What a tragedy that all this will disappear with the used-up body!

I observed on most collected stones the imprints of innumerable plant fragments which were so different from those which are growing in the Lyonnais, in the nearby provinces, and even in the rest of France, that I felt like collecting plants in a new world… The number of these leaves, the way they separated easily, and the great variety of plants whose imprints I saw, appeared to me just as many volumes of botany representing in the same quarry the oldest library of the world.

If atoms do, by chance, happen to combine themselves into so many shapes, why have they never combined together to form a house or a slipper? By the same token, why do we not believe that if innumerable letters of the Greek alphabet were poured all over the market-place they would eventually happen to form the text of the Iliad?

In some remote corner of the universe, poured out and glittering in innumerable solar systems, there once was a star on which clever animals invented knowledge. That was the haughtiest and most mendacious minute of ‘world history’—yet only a minute. After nature had drawn a few breaths the star grew cold, and the clever animals had to die. ... There have been eternities when [human intellect] did not exist; and when it is done for again, nothing will have happened.

In the course of the history of the earth innumerable events have occurred one after another, causing changes of states, all with certain lasting consequences. This is the basis of our developmental law, which, in a nutshell, claims that the diversity of phenomena is a necessary consequence of the accumulation of the results of all individual occurrences happening one after another... The current state of the earth, thus, constitutes the as yet most diverse final result, which of course represents not a real but only a momentary end-point.

It is not for us to say whether Inspiration revealed to the Psalmist the wonders of the modern astronomy. But even though the mind be a perfect stranger to the science of these enlightened times, the heavens present a great and an elevating spectacle—an immense concave reposing on the circular boundary of the world, and the innumerable lights which are suspended from on high, moving with solemn regularity along its surface.

It is well to observe the force and virtue and consequence of discoveries, and these are to be seen nowhere more conspicuously than in those three which were unknown to the ancients, and of which the origins, although recent, are obscure and inglorious; namely, printing, gunpowder, and the magnet. For these three have changed the whole face and state of things throughout the world; the first in literature, the second in warfare, the third in navigation; whence have followed innumerable changes, insomuch that no empire, no sect, no star seems to have exerted greater power and influence in human affairs than these mechanical discoveries.

Jupiter is the largest of all the solar system’s planets, more than ten times bigger and three hundred times as massive as Earth. Jupiter is so immense it could swallow all the other planets easily. Its Great Red Spot, a storm that has raged for centuries, is itself wider than Earth. And the Spot is merely one feature visible among the innumerable vortexes and streams of Jupiter’s frenetically racing cloud tops. Yet Jupiter is composed mainly of the lightest elements, hydrogen and helium, more like a star than a planet. All that size and mass, yet Jupiter spins on its axis in less than ten hours, so fast that the planet is clearly not spherical: Its poles are noticeably flattened. Jupiter looks like a big, colorfully striped beach ball that’s squashed down as if some invisible child were sitting on it. Spinning that fast, Jupiter’s deep, deep atmosphere is swirled into bands and ribbons of multihued clouds: pale yellow, saffron orange, white, tawny yellow-brown, dark brown, bluish, pink and red. Titanic winds push the clouds across the face of Jupiter at hundreds of kilometers per hour.

Just as in the animal and vegetable kingdoms, an individual comes into being, so to speak, grows, remains in being, declines and passes on, will it not be the same for entire species? If our faith did not teach us that animals left the Creator's hands just as they now appear and, if it were permitted to entertain the slightest doubt as to their beginning and their end, may not a philosopher, left to his own conjectures, suspect that, from time immemorial, animal life had its own constituent elements, scattered and intermingled with the general body of matter, and that it happened when these constituent elements came together because it was possible for them to do so; that the embryo formed from these elements went through innumerable arrangements and developments, successively acquiring movement, feeling, ideas, thought, reflection, consciousness, feelings, emotions, signs, gestures, sounds, articulate sounds, language, laws, arts and sciences; that millions of years passed between each of these developments, and there may be other developments or kinds of growth still to come of which we know nothing; that a stationary point either has been or will be reached; that the embryo either is, or will be, moving away from this point through a process of everlasting decay, during which its faculties will leave it in the same way as they arrived; that it will disappear for ever from nature-or rather, that it will continue to exist there, but in a form and with faculties very different from those it displays at this present point in time? Religion saves us from many deviations, and a good deal of work. Had religion not enlightened us on the origin of the world and the universal system of being, what a multitude of different hypotheses we would have been tempted to take as nature's secret! Since these hypotheses are all equally wrong, they would all have seemed almost equally plausible. The question of why anything exists is the most awkward that philosophy can raise- and Revelation alone provides the answer.

Might one not say that in the chance combination of nature's production, since only those endowed with certain relations of suitability could survive, it is no cause for wonder that this suitability is found in all species that exist today? Chance, one might say, produced an innumerable multitude of individuals; a small number turned out to be constructed in such fashion that the parts of the animal could satisfy its needs; in another, infinitely greater number, there was neither suitability nor order: all of the later have perished; animals without a mouth could not live, others lacking organs for reproduction could not perpetuate themselves: the only ones to have remained are those in which were found order and suitability; and these species, which we see today, are only the smallest part of what blind fate produced.

Most people … do not know that when the white man came Honolulu was a treeless, sandy plain, with a fringe of cocoanut trees along the shore. Honolulu, as it is to-day, is the creation of the foreigner. It is his handiwork. Walk into one of the numerous yards where plants and trees and vines are growing, as though on their native soil, and you will find that every one of them has been imported within a comparatively recent period. … Here is the rubber tree, the banyan, the baobab, the litchee, the avocado, the mango, and palms innumerable.

Nature is an endless combination and repetition of very few laws. She hums the old well-known air through innumerable variations.

No place affords a more striking conviction of the vanity of human hopes than a publick library; for who can see the wall crouded on every side by mighty volumes, the works of laborious meditation, and accurate inquiry, now scarcely known but by the catalogue, and preserved only to encrease the pomp of learning, without considering how many hours have been wasted in vain endeavours, how often imagination has anticipated the praises of futurity, how many statues have risen to the eye of vanity, how many ideal converts have elevated zeal, how often wit has exulted in the eternal infamy of his antagonists, and dogmatism has delighted in the gradual advances of his authority, the immutability of his decrees, and the perpetuity of his power.
Non unquam dedit
Documenta fors majora, quam fragili loco
Starent superbi.
Seneca, Troades, II, 4-6
Insulting chance ne'er call'd with louder voice,
On swelling mortals to be proud no more.
Of the innumerable authors whose performances are thus treasured up in magnificent obscurity, most are forgotten, because they never deserved to be remembered, and owed the honours which they have once obtained, not to judgment or to genius, to labour or to art, but to the prejudice of faction, the stratagem of intrigue, or the servility of adulation.
Nothing is more common than to find men whose works are now totally neglected, mentioned with praises by their contemporaries, as the oracles of their age, and the legislators of science. Curiosity is naturally excited, their volumes after long enquiry are found, but seldom reward the labour of the search. Every period of time has produced these bubbles of artificial fame, which are kept up a while by the breath of fashion and then break at once and are annihilated. The learned often bewail the loss of ancient writers whose characters have survived their works; but perhaps if we could now retrieve them we should find them only the Granvilles, Montagus, Stepneys, and Sheffields of their time, and wonder by what infatuation or caprice they could be raised to notice.
It cannot, however, be denied, that many have sunk into oblivion, whom it were unjust to number with this despicable class. Various kinds of literary fame seem destined to various measures of duration. Some spread into exuberance with a very speedy growth, but soon wither and decay; some rise more slowly, but last long. Parnassus has its flowers of transient fragrance as well as its oaks of towering height, and its laurels of eternal verdure.

October 9, 1863
Always, however great the height of the balloon, when I have seen the horizon it has roughly appeared to be on the level of the car though of course the dip of the horizon is a very appreciable quantity or the same height as the eye. From this one might infer that, could the earth be seen without a cloud or anything to obscure it, and the boundary line of the plane approximately the same height as the eye, the general appearance would be that of a slight concavity; but I have never seen any part of the surface of the earth other than as a plane.
Towns and cities, when viewed from the balloon are like models in motion. I shall always remember the ascent of 9th October, 1863, when we passed over London about sunset. At the time when we were 7,000 feet high, and directly over London Bridge, the scene around was one that cannot probably be equalled in the world. We were still so low as not to have lost sight of the details of the spectacle which presented itself to our eyes; and with one glance the homes of 3,000,000 people could be seen, and so distinct was the view, that every large building was easily distinguishable. In fact, the whole of London was visible, and some parts most clearly. All round, the suburbs were also very distinct, with their lines of detached villas, imbedded as it were in a mass of shrubs; beyond, the country was like a garden, its fields, well marked, becoming smaller and smaller as the eye wandered farther and farther away.
Again looking down, there was the Thames, throughout its whole length, without the slightest mist, dotted over its winding course with innumerable ships and steamboats, like moving toys. Gravesend was visible, also the mouth of the Thames, and the coast around as far as Norfolk. The southern shore of the mouth of the Thames was not so clear, but the sea beyond was seen for many miles; when at a higher elevation, I looked for the coast of France, but was unable to see it. On looking round, the eye was arrested by the garden-like appearance of the county of Kent, till again London claimed yet more careful attention.
Smoke, thin and blue, was curling from it, and slowly moving away in beautiful curves, from all except one part, south of the Thames, where it was less blue and seemed more dense, till the cause became evident; it was mixed with mist rising from the ground, the southern limit of which was bounded by an even line, doubtless indicating the meeting of the subsoils of gravel and clay. The whole scene was surmounted by a canopy of blue, everywhere free from cloud, except near the horizon, where a band of cumulus and stratus extended all round, forming a fitting boundary to such a glorious view.
As seen from the earth, the sunset this evening was described as fine, the air being clear and the shadows well defined; but, as we rose to view it and its effects, the golden hues increased in intensity; their richness decreased as the distance from the sun increased, both right and left; but still as far as 90º from the sun, rose-coloured clouds extended. The remainder of the circle was completed, for the most part, by pure white cumulus of well-rounded and symmetrical forms.
I have seen London by night. I have crossed it during the day at the height of four miles. I have often admired the splendour of sky scenery, but never have I seen anything which surpassed this spectacle. The roar of the town heard at this elevation was a deep, rich, continuous sound the voice of labour. At four miles above London, all was hushed; no sound reached our ears.

Oersted would never have made his great discovery of the action of galvanic currents on magnets had he stopped in his researches to consider in what manner they could possibly be turned to practical account; and so we would not now be able to boast of the wonders done by the electric telegraphs. Indeed, no great law in Natural Philosophy has ever been discovered for its practical implications, but the instances are innumerable of investigations apparently quite useless in this narrow sense of the word which have led to the most valuable results.

Our atom of carbon enters the leaf, colliding with other innumerable (but here useless) molecules of nitrogen and oxygen. It adheres to a large and complicated molecule that activates it, and simultaneously receives the decisive message from the sky, in the flashing form of a packet of solar light; in an instant, like an insect caught by a spider, it is separated from its oxygen, combined with hydrogen and (one thinks) phosphorus, and finally inserted in a chain, whether long or short does not matter, but it is the chain of life. All this happens swiftly, in silence, at the temperature and pressure of the atmosphere, and gratis: dear colleagues, when we learn to do likewise we will be sicut Deus [like God], and we will have also solved the problem of hunger in the world.

Our knowledge is the amassed thought and experience of innumerable minds.

Our oceans are facing innumerable threats-from overfishing and pollution to ocean acidification and invasive species-yet we haven’t had a blueprint for its use and development, incredible as that seems.

Since the discovery of oxygen the civilised world has undergone a revolution in manners and customs. The knowledge of the composition of the atmosphere, of the solid crust of the earth, of water, and of their influence upon the life of plants and animals, was linked to that discovery. The successful pursuit of innumerable trades and manufactures, the profitable separation of metals from their ores, also stand in the closest connection therewith.

So numerous are the objects which meet our view in the heavens, that we cannot imagine a point of space where some light would not strike the eye;—innumerable stars, thousands of double and multiple systems, clusters in one blaze with their tens of thousands of stars, and the nebulae amazing us by the strangeness of their forms and the incomprehensibility of their nature, till at last, from the limit of our senses, even these thin and airy phantoms vanish in the distance.

The astronomer who studies the motion of the stars is surely like a blind man who, with only a staff [mathematics] to guide him, must make a great, endless, hazardous journey that winds through innumerable desolate places. What will be the result? Proceeding anxiously for a while and groping his way with his staff, he will at some time, leaning upon it, cry out in despair to Heaven, Earth and all the Gods to aid him in his misery.

The different sorts of madness are innumerable.

The digestive canal is in its task a complete chemical factory. The raw material passes through a long series of institutions in which it is subjected to certain mechanical and, mainly, chemical processing, and then, through innumerable side-streets, it is brought into the depot of the body. Aside from this basic series of institutions, along which the raw material moves, there is a series of lateral chemical manufactories, which prepare certain reagents for the appropriate processing of the raw material.

The discovery of the conic sections, attributed to Plato, first threw open the higher species of form to the contemplation of geometers. But for this discovery, which was probably regarded in Plato’s tune and long after him, as the unprofitable amusement of a speculative brain, the whole course of practical philosophy of the present day, of the science of astronomy, of the theory of projectiles, of the art of navigation, might have run in a different channel; and the greatest discovery that has ever been made in the history of the world, the law of universal gravitation, with its innumerable direct and indirect consequences and applications to every department of human research and industry, might never to this hour have been elicited.

The dog [in Pavlov’s experiments] does not continue to salivate whenever it hears a bell unless sometimes at least an edible offering accompanies the bell. But there are innumerable instances in human life where a single association, never reinforced, results in the establishment of a life-long dynamic system. An experience associated only once with a bereavement, an accident, or a battle, may become the center of a permanent phobia or complex, not in the least dependent on a recurrence of the original shock.

The earliest signs of living things, announcing as they do a high complexity of organization, entirely exclude the hypothesis of a transmutation from lower to higher grades of being. The first fiat of Creation which went forth, doubtlessly ensured the perfect adaptation of animals to the surrounding media; and thus, whilst the geologist recognizes a beginning, he can see in the innumerable facts of the eye of the earliest crustacean, the same evidences of Omniscience as in the completion of the vertebrate form.

The experiences are so innumerable and varied, that the journey appears to be interminable and the Destination is ever out of sight. But the wonder of it is, when at last you reach your Destination you find that you had never travelled at all! It was a journey from here to Here.

The farther researches we make into this admirable scene of things, the more beauty and harmony we see in them: And the stronger and clearer convictions they give us, of the being, power and wisdom of the divine Architect, who has made all things to concur with a wonderful conformity, in carrying on, by various and innumerable combinations of matter, such a circulation of causes, and effects, as was necessary to the great ends of nature. And since we are assured that the all-wise Creator has observed the most exact proportions, of number, weight and measure, in the make of all things; the most likely way therefore, to get any insight into the nature of those parts of the creation, which come within our observation, must in all reason be to number, weigh and measure. And we have much encouragement to pursue this method, of searching into the nature of things, from the great success that has attended any attempts of this kind.

The glimpses of chemical industry's services to man afforded by this book could be presented only by utilizing innumerable chemical products. The first outline of its plan began to take shape on chemically produced notepaper with the aid of a chemically-treated graphite held in a synthetic resin pencil. Early corrections were made with erasers of chemically compounded rubber. In its ultimate haven on the shelves of your bookcase, it will rest on a coating of chemical varnish behind a pane of chemically produced glass. Nowhere has it been separated from that industry's products.

The meaning of geography is as much a sealed book to the person of ordinary intelligence and education as the meaning of a great cathedral would be to a backwoodsman, and yet no cathedral can be more suggestive of past history in its many architectural forms than is the land about us, with its innumerable and marvellously significant geographic forms. It makes one grieve to think of opportunity for mental enjoyment that is last because of the failure of education in this respect.

The nervous system is the most complex and delicate instrument on our planet, by means of which relations, connections are established between the numerous parts of the organism, as well as between the organism, as a highly complex system, and the innumerable, external influences. If the closing and opening of electric current is now regarded as an ordinary technical device, why should there be any objection to the idea that the same principle acts in this wonderful instrument? On this basis the constant connection between the external agent and the response of the organism, which it evokes, can be rightly called an unconditioned reflex, and the temporary connection—a conditioned reflex.

The next object which I have observed is the essence or substance of the Milky Way. By the aid of a telescope anyone may behold this in a manner which so distinctly appeals to the senses that all the disputes which have tormented philosophers through so many ages are exploded at once by the irrefragable evidence of our eyes, and we are freed from wordy disputes upon this subject, for the Galaxy is nothing else but a mass of innumerable stars planted together in clusters.

The peculiar taste both in pure and in mixed nature of those relations about which it is conversant, from its simple and definite phraseology, and from the severe logic so admirably displayed in the concatenation of its innumerable theorems, are indeed immense, and well entitled to separate and ample illustration.

The phrase 'nature and nurture' is a convenient jingle of words, for it separates under two distinct heads the innumerable elements of which personality is composed. Nature is all that a man brings with himself into the world; nurture is every influence without that affects him after his birth.

The progress of synthesis, or the building up of natural materials from their constituent elements, proceeds apace. Even some of the simpler albuminoids, a class of substances of great importance in the life process, have recently been artificially prepared. ... Innumerable entirely new compounds have been produced in the last century. The artificial dye-stuffs, prepared from materials occurring in coal-tar, make the natural colours blush. Saccharin, which is hundreds of times sweeter than sugar, is a purely artificial substance. New explosives, drugs, alloys, photographic substances, essences, scents, solvents, and detergents are being poured out in a continuous stream.

The responsibility for maintaining the composition of the blood in respect to other constituents devolves largely upon the kidneys. It is no exaggeration to say that the composition of the blood is determined not by what the mouth ingests but by what the kidneys keep; they are the master chemists of our internal environment, which, so to speak, they synthesize in reverse. When, among other duties, they excrete the ashes of our body fires, or remove from the blood the infinite variety of foreign substances which are constantly being absorbed from our indiscriminate gastrointestinal tracts, these excretory operations are incidental to the major task of keeping our internal environment in an ideal, balanced state. Our glands, our muscles, our bones, our tendons, even our brains, are called upon to do only one kind of physiological work, while our kidneys are called upon to perform an innumerable variety of operations. Bones can break, muscles can atrophy, glands can loaf, even the brain can go to sleep, without immediately endangering our survival, but when the kidneys fail to manufacture the proper kind of blood neither bone, muscle, gland nor brain can carry on.

There is probably no other science which presents such different appearances to one who cultivates it and to one who does not, as mathematics. To this person it is ancient, venerable, and complete; a body of dry, irrefutable, unambiguous reasoning. To the mathematician, on the other hand, his science is yet in the purple bloom of vigorous youth, everywhere stretching out after the “attainable but unattained” and full of the excitement of nascent thoughts; its logic is beset with ambiguities, and its analytic processes, like Bunyan’s road, have a quagmire on one side and a deep ditch on the other and branch off into innumerable by-paths that end in a wilderness.

There they stand, the innumerable stars, shining in order like a living hymn, written in light.

Those that can readily master the difficulties of Mathematics find a considerable charm in the study, sometimes amounting to fascination. This is far from universal; but the subject contains elements of strong interest of a kind that constitutes the pleasures of knowledge. The marvellous devices for solving problems elate the mind with the feeling of intellectual power; and the innumerable constructions of the science leave us lost in wonder.

To be placed on the title-page of my collected works: Here it will be perceived from innumerable examples what is the use of mathematics for judgement in the natural sciences and how impossible it is to philosophise correctly without the guidance of Geometry, as the wise maxim of Plato has it.

We are like the explorers of a great continent, who have penetrated its margins in most points of the compass and have mapped the major mountain chains and rivers. There are still innumerable details to fill in, but the endless horizons no longer exist.

Were the succession of stars endless, then the background of the sky would present us an uniform luminosity, like that displayed by the Galaxy—since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all.

When I behold a fashionable table set out in all its magnificence, I fancy that I see gouts and dropsies, fevers and lethargies, with other innumerable distempers lying in ambuscade among the dishes. Nature delights in the most plain and simple diet. Every animal but man keeps to one dish. Herbs are the food of this species, fish of that, and flesh of a third. Man falls upon everything that comes in his way; not the smallest fruit or excrescence of the earth, scarce a berry or a mushroom can escape him.

Who could have believed that … the introduction into the human body of a small particle of matter from a cow’s udder might be the means of saving thousands of human lives? We learn from these and innumerable similar instances that the highest truths lie hid in the simplest facts; that, unlike human proclamations, nature’s teachings are not by sound of trumpet, but often in the stillest voice, by indirect hints and obscure suggestions.

Whoever looks at the insect world, at flies, aphides, gnats and innumerable parasites, and even at the infant mammals, must have remarked the extreme content they take in suction, which constitutes the main business of their life. If we go into a library or newsroom, we see the same function on a higher plane, performed with like ardor, with equal impatience of interruption, indicating the sweetness of the act. In the highest civilization the book is still the highest delight.