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April 10, 2026
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"Geometry is that of mathematical science which is devoted to consideration of form and size, and may be said to be the best and surest guide to study of all sciences in which ideas of dimension or space are involved. Almost all the knowledge required by navigators, architects, surveyors, engineers, and opticians, in their respective occupations, is deduced from geometry and branches of mathematics. All works of art constructed according to the rules which geometry involves; and we find the same laws observed in the works of nature. The study of mathematics, generally, is also of great importance in cultivating habits of exact reasoning; and in this respect it forms a useful auxiliary to logic."
"A sensible parallax of about one second has been ascertained in the case of the double star [ Alpha Centauri ] of the constellation of the Centaur, and one of the third of that amount for the double star, 61 Cygni; which gave reason to presume that the distance of the former might be about twenty thousand millions of miles, and the latter of much greater amount. If we suppose that similar intervals exist between all the stars, we shall readily see that the space occupied by even the comparatively small number visible to the naked eye, must be vast beyond all powers of conception."
"It was first surmised by the ancient philosopher, Democritus, that the faintly white zone which spans the sky under the name of the Milky Way, might be only a dense collection of stars too remote to be distinguished. This conjecture has been verified by the instruments of modern astronomers."
"The evidence of the existence of other astral systems besides our own is much more decided than might be expected when we consider that the nearest of them must needs be placed at a mighty interval beyond our own."
"The elder Herschel, directing his wonderful tube towards the sides of our system, where stars are planted most rarely... was enabled with awe struck mind to see suspended in the vast empyrean astral systems, or, as he called them, firmaments, resembling our own. Like light cloudlets to a certain power of the telescope, they resolved themselves, under a greater power, into stars, though these generally seemed no larger than the finest particles of diamond dust. The general forms of these systems are various; but one at least has been detected as bearing a striking resemblance to the supposed form of our own. The distances are also various... The farthest observed by the astronomer were estimated by him as thirty-five thousand times more remote than Sirius, supposing its distance to be about twenty thousand millions of miles. It would thus appear, that not only does gravitation keep our earth in its place in the solar system, and the solar system in its place in our astral system, but it also may be presumed to have the mightier duty of preserving a local arrangement between that astral system and an immensity of others, through which the imagination is left to wander on and on without limit or stay, save that which is given by its inability to grasp the unbounded."
"We have seen that the law which causes rotation in the single solar masses, is exactly the same which produces the familiar phenomenon of a small whirlpool or dimple in the surface of a stream. Such dimples are not always single. Upon the face of a river where there are various contending currents, it may often be observed that two or more dimples are formed near each other with more or less regularity. These fantastic eddies, which the musing poet will sometimes watch abstractedly for an hour, little thinking of the law which produces and connects them, are an illustration of the wonders of binary and ternary solar systems."
"Seeing in our astral system many thousands of worlds in all stages of formation, from the most rudimental to that immediately preceding the present condition of those we deem perfect, it is unavoidable to conclude that all the perfect have gone through the various stages which we see in the rudimental. This leads us at once to the conclusion that the whole of our firmament was at one time a diffused mass of nebulous matter, extending through the space which it still occupies. So also, of course, must have been the other astral systems. Indeed, we must presume the whole to have been originally in one connected mass, the astral systems being only the first division into parts, and solar systems the second."
"The first idea which all this impresses upon us is, that the formation of bodies in space is still and at present in progress. We live at a time when many have been formed and many are still forming."
"All, we see, is done by certain laws of matter, so that it becomes a question of extreme interest, what are such laws? All that can yet be said, in answer, is, that we see certain natural events proceeding in an invariable order under certain conditions, and thence infer the existence of some fundamental arrangement which, for the bringing about of these events, has a force and certainty of action similar to, but more precise and unerring than those arrangements which human society makes for its own benefit, and calls laws. It is remarkable of physical laws, that we see them operating on every kind of scale as to magnitude, with the same regularity and perseverance."
"We advance from law to the cause of law, and ask, What is that? Whence have come all these beautiful regulations? Here science leaves us, but only to conclude, from other grounds, that there is a First Cause to which all others are secondary and ministrative, a primitive almighty will, of which these laws are merely the mandates. That great Being, who shall say where is his dwelling-place or what his history! Man pauses breathless at the contemplation of a subject so much above his finite faculties, and only can wonder and adore!"
"Analogy would lead us to conclude that the combinations of the primordial matter, forming our so-called elements, are as universal or as liable to take place everywhere as are the laws of gravitation and centrifugal force. We must therefore presume that the gases, the metals, the earths, and other simple substances, (besides whatever more of which we have no acquaintance,) exist or are liable to come into existence under proper conditions, as well in the astral system, which is thirty five thousand times more distant than Sirius, as within the bounds of our own solar system or our own globe."
"We cannot doubt after what we know of the power of heat that the nebulous form of matter was attended by the condition of a very high temperature."
"There is nothing at all singular or special in the astronomical situation of the earth. It takes its place third in a series of planets, which series is only one of numberless other systems forming one group. It is strikingly-if I may use such an expression-a member of a democracy. Hence, we cannot suppose that there is any peculiarity about it which does not probably attach to multitudes of other bodies—in fact, to all that are analogous to it in respect of cosmical arrangements."
"It is remarkable of the simple substances that they are generally in some compound form. Thus oxygen and nitrogen, though in union they form the aerial envelope of the globe, are never found separate in nature. Carbon is pure only in the diamond. And the metallic bases of the earths, though the chemist can disengage them, may well be supposed unlikely to remain long uncombined, seeing that contact with moisture makes them burn. Combination and re-combination are principles largely pervading nature. There are few rocks, for example, that are not composed of at least two varieties of matter, each of which is again a compound of elementary substances. What is still more wonderful with respect to this principle of combination, all the elementary substances observe certain mathematical proportions in their unions. It is hence supposed that matter is composed of infinitely minute particles or atoms, each of which belonging to any one substance, can only (through the operation of some as yet hidden law) associate with a certain number of the atoms of any other."
"The earliest stratified rocks contain no matters which are not to be found in the primitive granite. They are the same in material, but only changed into new forms and combinations; hence they have been called by Mr. Lyell, metamorphic rocks. But how comes it that some of them are composed almost exclusively of one of the materials of granite; the mica schists, for example, of mica—the quartz rocks, of quartz, &c.? For this there are both chemical and mechanical causes. Suppose that a river has a certain quantity of material to carry down, it is evident that it will soonest drop the larger particles, and carry the lightest farthest on. To such a cause is it owing that some of the materials of the worn-down granite have settled in one place and some in another. Again, some of these materials must be presumed to have been in a state of chemical solution in the primeval seas. It would be, of course, in conformity with chemical laws, that certain of these materials would be precipitated singly, or in modified combinations, to the bottom, so as to form rocks by themselves."
"When we hear of carbon beginning to appear in the ascending series of rocks, we are unavoidably led to consider it as marking a time of some importance in the earth's history, a new era of natural conditions, one in which organic life has probably played a part."
"The appearance... of limestone beds in the early part of the stratified series, may be presumed to be connected with the fact of the commencement of organic life upon our planet, and, indeed, a consequent and a symptom of it. ...My hypothesis may indeed be unsound; but, whether or not, it is clear, taking organic remains as upon the whole a faithful chronicle, that the deposition of these limestone beds was coeval with the existence of the earliest, or all but the earliest, living creatures upon earth."
"Zoophyta, polyparia, crinoidea, conchifera, and crustacea are the orders of the animal kingdom thus found in the earliest of earth's sepulchres."
"When we come to consider specific characters, we see that a difference exists—that, in short, the species and even genera are no longer represented upon earth. More than this, it will be found that the earliest species comparatively soon gave place to others, and that they are not represented even in the next higher group of rocks."
"One important remark has been made, that a comparatively small variety of species is found in the older rocks, although of some particular ones the remains are very abundant..."
"Ascending to the next group of rocks, we find the traces of life become more abundant, the number of species extended, and important additions made in certain vestiges of fuci, or sea plants, and of fishes. This group of rocks has been called by English geologists, the Silurian System, because largely developed at the surface of a district of western England, formerly occupied by a people whom the Roman historians call Silures."
"Not one species of any creature which flourished before the tertiary (Ehrenberg's infusoria excepted) now exists; and of the mammalia which arose during that series, many forms are altogether gone, while of others we have now only kindred species. Thus to find not only frequent additions to the previously existing forms, but frequent withdrawals of forms which had apparently become inappropriate—a constant shifting as well as advance—is a fact calculated very forcibly to arrest attention. A candid consideration of all these circumstances can scarcely fail to introduce into our minds a somewhat different idea of organic creation from what has hitherto been generally entertained."
"Some other idea must then be come to with regard to the mode in which the Divine Author proceeded in the organic creation. Let us seek in the history of the earth's formation for a new suggestion on this point."
"The fact of the cosmical arrangements being an effect of natural law, is a powerful argument for the organic arrangements being so likewise, for how can we suppose that the august Being who brought all these countless worlds into form by the simple establishment of a natural principle flowing from his mind, was to interfere personally and specially on every occasion when a new shell-fish or reptile was to be ushered into existence on one of these worlds. Surely this idea is too ridiculous to be for a moment entertained."
"The first chapter of the Mosaic record is not only not in harmony with the ordinary ideas of mankind respecting cosmical and organic creation, but is opposed to them, and only in accordance with the views here taken. When we carefully peruse it with awakened minds, we find that all the procedure is represented primarily and pre-eminently as flowing from commands and expressions of will, not from direct acts. ...Thus the scriptural objection quickly vanishes, and the prevalent ideas about the organic creation appear only as a mistaken inference from the text, formed at a time when man's ignorance prevented him from drawing therefrom a just conclusion."
"To a reasonable mind the Divine attributes must appear, not diminished or reduced in any way, by supposing a creation by law, but infinitely exalted. It is the narrowest of all views of the Deity, and characteristic of a humble class of intellects, to suppose him acting constantly in particular ways for particular occasions. It, for one thing, greatly detracts from his foresight, the most undeniable of all the attributes of Omnipotence. It lowers him towards the level of our own humble intellects. Much more worthy of him it surely is, to suppose that all things have been commissioned by him from the first, though neither is he absent from a particle of the current of natural affairs in one sense seeing that the whole system is continually supported by his providence."
"This statistical regularity in moral affairs fully establishes their being under the presidency of law. Man is now seen to be an enigma only as an individual; in the mass he is a mathematical problem. It is hardly necessary to say, much less to argue, that mental action, being proved to be under law, passes at once into the category of natural things. Its old metaphysical character vanishes in a moment, and the distinction usually taken between physical and moral is annulled, as only an error in terms. This view agrees with what all observation teaches, that mental phenomena flow directly from the brain."
"While the external forms of all these various animals are so different, it is very remarkable that the whole are, after all, variations of a fundamental plan, which can be traced as a basis throughout the whole, the variations being merely modifications of that plan to suit the particular conditions in which each particular animal has been designed to live. Starting from the primeval germ, which, as we have seen, is the representative of a particular order of full-grown animals, we find all others to be merely advances from that type, with the extension of endowments and modification of forms which are required in each particular case; each form, also, retaining a strong affinity to that which precedes it, and tending to impress its own features on that which succeeds."
"The limbs of all the vertebrate animals are, in like manner, on one plan, however various they may appear."
"The same law of development presides over the vegetable kingdom. ...where a special function is required for particular circumstances, nature has provided for it, not by a new organ, but by a modification of a common one, which she has effected in development."
"These facts clearly shew how all the various organic forms of our world are bound up in one—how a fundamental unity pervades and embraces them all, collecting them, from the humblest lichen up to the highest mammifer, in one system, the whole creation of which must have depended upon one law or decree of the Almighty, though it did not all come forth at one time. After what we have seen, the idea of a separate exertion for each must appear totally inadmissible."
"What mystery is there here—and how shall I proceed to enunciate the conception which I have ventured to form of what may prove to be its proper solution! It is an idea by no means calculated to impress by its greatness, or to puzzle by its profoundness. It is an idea more marked by simplicity than perhaps any other of those which have explained the great secrets of nature. But in this lies, perhaps, one of its strongest claims to the faith of mankind."
"The whole train of animated beings, from the simplest and oldest up to the highest and most recent, are, then, to be regarded as a series of advances of the principle of development, which have depended upon external physical circumstances, to which the resulting animals are appropriate."
"I contemplate the whole phenomena as having been in the first place arranged in the counsels of Divine Wisdom, to take place, not only upon this sphere, but upon all the others in space, under necessary modifications, and as being carried on, from first to last, here and elsewhere, under immediate favor of the creative will or energy."
"We are drawn on to the supposition, that the first step in the creation of life upon this planet was a chemico-electric operation, by which simple germinal vesicles were produced."
"I suggest, then... that the first step was an advance under favor of peculiar conditions, from the simplest forms of being, to the next more complicated, and this through the medium of the ordinary process of generation."
"It must be borne in mind that the gestation of a single organism is the work of but a few days, weeks, or months, but the gestation (so to speak) of a whole creation is a matter probably involving enormous spaces of time."
"The historical era is, we know, only a small portion of the entire age of our globe. We do not know what may have happened during the ages which preceded its commencement, as we do not know what may happen in ages yet in the distant future. All, therefore, that we can properly infer from the apparently invariable production of like by like is, that such is the ordinary procedure of nature in the time immediately passing before our eyes."
"Mr. Babbage's illustration powerfully suggests that this ordinary procedure may be subordinate to a higher law which only permits it for a time, and in proper season interrupts and changes it."
"The law of organic development is still daily seen at work to certain effects, only somewhat short of a transition from species to species."
"Now it is possible that wants and the exercise of faculties have entered in some manner into the production of the phenomena which we have been considering; but certainly not in the way suggested by Lamarck, whose whole notion is obviously so inadequate to account for the rise of the organic kingdoms, that we only can place it with pity among the follies of the wise."
"It may be asked, if He, as appears, has chosen to employ inferior organisms as a generative medium for the production of higher ones, even including ourselves, what right have we, his humble creatures, to find fault? There is, also, in this prejudice, an element of unkindliness towards the lower animals, which is utterly out of place. These creatures are all of them part products of the Almighty Conception, as well as ourselves. ...Let us regard them in a proper spirit, as parts of the grand plan, instead of contemplating them in the light of frivolous prejudices, and we shall be altogether at a loss to see how there should be any degradation in the idea of our race having been genealogically connected with them."
"The nobler orders of being, including man himself, were contemplated from the first, and came into existence by virtue of a law, the operation of which had commenced ages before their forms were realized."
"Under the flowing robes of nature, where all looks arbitrary and accidental, there is an artificiality of the most rigid kind. The natural, we now perceive, sinks into and merges in a Higher Artificial. ...we conclude, when we attain a knowledge of the artificiality which is at the basis of nature, that nature is wholly the production of a Being resembling, but infinitely greater than ourselves."
"Is our race but the initial of the grand crowning type? Are there yet to be species superior to us in organization, purer in feeling, more powerful in device and act, and who shall take a rule over us! There is in this nothing improbable on other grounds. The present race, rude and impulsive as it is, is perhaps the best adapted to the present state of things in the world; but the external world goes through slow and gradual changes, which may leave it in time a much serener field of existence. There may then be occasion for a nobler type of humanity, which shall complete the zoological circle on this planet, and realize some of the dreams of the purest spirits of the present race."
"Of late years... it has been successfully shewn that the human race might have had one origin, for anything that can be inferred from external peculiarities."
"It appears from this inquiry that color and other physiological characters are of a more superficial and accidental nature than was at one time supposed."
"There are nations, such as the inhabitants of Hindostan, known to be one in descent which nevertheless, contain groups of people of almost all shades of color, and likewise discrepant in other of those important features on which much stress has been laid."
"The style of living is ascertained to have a powerful effect in modifying the human figure in the course of generations, and this even in its osseous structure."
"While there is such a persistency to ordinary observation, it would also appear that nature has a power of producing new varieties, though this is only done rarely. Such novelties of type abound in the vegetable world, are seen more rarely in the animal circle, and perhaps are least frequent of occurrence in our own race."