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.

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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.

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 fall of meteoric stones was occasionally reported by good witnesses during many ages. But science did not understand how stones should be formed in or beyond the atmosphere... The accounts of the fall of meteoric stones were held to be incompatible with the laws of nature, and specimens which had been seen to fall by hundreds of people were preserved in cabinets of natural history as ordinary minerals, 'which the credulous and superstitious regarded as having fallen from the clouds.' A committee of the French Academy of Sciences, including the celebrated Lavoisier, unanimously rejected an account of three nearly contemporary descents of meteorites which reached them on the strongest evidence. After two thousand years of incredulity, the truth in this matter was forced upon the scientific world about the beginning of the present century. There would have been at any time, of course, an instant cessation of skepticism if any one could have shewn, a priori, from ascertained principles in connection with the atmosphere, how stones were to be expected to fall from the sky. But what is this but to say that facts by themselves, however well attested, are wholly useless in such circumstances to the cultivators of physical science, while any kind of vague hypothesis can be brought forward in opposition to them? What is it but to put conjecture or prejudice above fact, and indeed utterly to repudiate the Baconian method?

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.

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In most instances, affectionate relatives and kind friends would wish to prolong the existence of the individual who has reached that age; but if we look at the happiness of mankind in general, we shall find reason to believe that, like all the other general principles of nature, this one carries the impress of an all-wise and beneficent Creator; and that if man had it in his power to alter the arrangement, it may be questioned if he could improve it. At this age the great desires of life are generally accomplished, and the tired laborer in the hardest fields of exertion, which are those of the intellect, has had some years of quiet meditation on the long battle of life to which his days of energy and hope were devoted. The world has, in general, little more use for him; and should he—however meritorious his services, however honored his gray hairs—too long remain an actual living man, seeming to fill a part of the arena in which younger and abler combatants are looking for places, the consciousness of being honored and beloved may give way before the suspicion that he has become an encumbrance to the circle he once adorned.

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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.

It has been among the visions of some dreaming philosophers that human life is capable of almost indefinite extension. The great Condorcet was one of these. He thought that by the removal of the two causes of evil—poverty and superfluity—by destroying prejudices and superstitions, and by various other operations, which he considered the purification of mankind, but which other people would call their pollution, the approach of death would by degrees be farther and farther indefinitely protracted. It is desirable that the practical views entertained by sanitary reformers should be kept widely distinct from any such theories, the character of which has been well drawn by Malthus when he says—"...Though I may not be able in the present instance to mark the limit at which further improvement will stop I can very easily mention a point at which it will not arrive."

Abstract perfection should always be the direction aimed at by human efforts, however imperfect they may be; and the success of sanitary legislation will be indicated by the nearness or the distance of its actual practice from this perfect idea.

Just suppose for a moment that every fact reported to us by others were viewed in the light of the skeptical system, as to the fallaciousness of the senses and the tendency to self-deception. Should we not from that moment be at a stand-still in all the principal movements of our lives?

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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.