Augustus De Morgan

“ It immediately occurred to me that had I been any one of some scores of my paradoxers, I should, no doubt, have proceeded to raise the mob against the unscrupulous person who dared to hint to a young bride such maleficent—or at least immellificent—conduct towards her new lord. But, as it was, certain material contexts in the shop window suggested a less savage explanation. A paradoxer should not stop at reading the advertisements of Newton or Laplace; he should learn to look at the stock of goods. ”

“ Every one who understands life assurance sees that—bonus apart—the difference between an assurance office and a savings bank consists in the adoption, pro tanto, of the principle of community of goods. In the original constitution of the oldest assurance office, the Amicable Society, the plan with which they started was nothing but this: persons of all ages under forty-five paid one common premium, and the proceeds were divided among the representatives of those who died within the year. ”

“ And both are wont to say, sir, The philosophe who's not an ass Will drink his bottle a day, sir! "Astronomers! what can avail Those who calumniate us; Experiment can never fail With such an apparatus: Let him who'd have his merits known Remember what I say, sir; Fair science shines on him alone Who drinks his bottle a day, sir! ”

“ The ordinary clocks show time by the mean, not the real, sun: and it was always laid down that Easter depends on the opposition (or full moon) of the mean sun and moon, not of the real ones. Thus we see that, were the Calendar ever so correct as to the mean moon, it would be occasionally false as to the true one: if, for instance, the opposition of the mean sun and moon took place at one second before midnight, and that of the real bodies only two seconds afterwards, the calendar day of full moon would be one day before that of the common almanacs. ”

“ We have taken pains that in our cycle the new moons should follow the real new moons, so that the 14th of the moon should fall either the day before the mean full moon, or on that day, or not long after; and this was done on purpose, for if the new moon of the cycle fell on the same day as the mean new moon of the astronomers, it might chance that we should celebrate Easter on the same day as the Jews or the Quartadeciman heretics, which would be absurd, or else before them, which would be still more absurd. ”

“ A person pretending to chronology, without being able to distinguish the historical points—so clearly as they stand out—in which Sir H. N. speaks with authority, from the arithmetical points of pure reckoning on which he does not pretend to do more than directly repeat others, must be as fit to talk about the construction of Easter Tables as the Spanish are to talk French. ”

“ The calendar lunation being 291⁄2 days, the middle day is the fifteenth day, and this is and was reckoned as the day of the full moon. There is every right to presume that the original passover was a feast of the real full moon: but it is most probable that the moons were then reckoned, not from the astronomical conjunction with the sun, which nobody sees except at an eclipse, but from the day of first visibility of the new moon. ”

“ By the author of 'A new theory of Gravitation.' London, 1846, 8vo. Honor to the speculator who can be put in his proper place by one sentence, be that place where it may.
"But we have shown that the velocities are inversely as the square roots of the mean distances from the sun; wherefore, by equality of ratios, the forces of the sun's gravitation upon them are also inversely as the square roots of their distances from the sun." ”

“ That sound judgment which gives men well to know what is best for them, as well as that faculty of invention which leads to development of resources and to the increase of wealth and comfort, are both materially advanced, perhaps cannot rapidly be advanced without, a great taste for pure speculation among the general mass of the people, down to the lowest of those who can read and write. ”

“ The Easter question was merely the symbol of the struggle between what we may call the Jewish and Gentile sects of Christians: and it nearly divided the Christian world, the Easterns, for the most part, being Quartadecimans. It is very important to note that there is no recorded dispute about a method of predicting the new moon, that is, no general dispute leading to formation of sects: there may have been difficulties, and discussions about them. The Metonic cycle, presently mentioned, must have been used by many, perhaps most, churches. ”

“ Further, it appears that Clavius valued the celebration of the festival after the Jews, etc., more than astronomical correctness. He gives comparison tables which would startle a believer in the astronomical intention of his Calendar: they are to show that a calendar in which the moon is always made a day older than by him, represents the heavens better than he has done, or meant to do. But it must be observed that this diminution of the real moon's age has a tendency to make the English explanation often practically accordant with the Calendar. ”

“ The notion that the non-existence of God can be proved, has died out under the light of discussion: had the only lights shone from the pulpit and the prison, so great a step would never have been made. ”

“ Easter Day, on which the rest depend, is always the First Sunday after the fourteenth day of the calendar moon which happens upon or next after the Twenty-first day of March, according to the rules laid down for the construction of the Calendar; and if the fourteenth day happens upon a Sunday, Easter Day is the Sunday after. ”

“ What if, by constantly thinking of ourselves as descended from primeval monkeys, we should—if it be true—actually get our tails again? What if the first man who was detected with such an appendage should be obliged to confess himself the author of the Vestiges—a person yet unknown—who would naturally get the start of his species by having had the earliest habit of thinking on the matter? ”

“ The allusion made by Sir John Herschel, in his letter contained in the Athenæum of October 3, to the theoretical researches of Mr. Adams, respecting the newly-discovered planet, has induced me to request that you would make the following communication public. It is right that I should first say that I have Mr. Adams's permission to make the statements that follow, so far as they relate to his labors. I do not propose to enter into a detail of the steps by which Mr. Adams was led, by his spontaneous and independent researches, to a conclusion that a planet must exist more distant than Uranus. ”

“ Great advantage will result: at the worst we are but in the alchemy of some new chemistry, or the astrology of some new astronomy. Perhaps it would be as well not to be too sure on the matter, until we have an antidote to possible consequences as exhibited under another theory, on which it is as reasonable to speculate as on that of the Vestiges. ”

“ Although the Church, in finding the new moon, and from it the 14th day, uses neither the true nor the mean motion of the moon, but measures only according to the order of a cycle, it is nevertheless undeniable that the mean full moons found from astronomical tables are of the greatest use in determining the cycle which is to be preferred ... ”

“ But choose which pendulum you will, You'll never make your way, sir, Unless you drink—and drink your fill,— At least a bottle a day, sir!" Old times are changed, old manners gone!
There is a new Mathematical Society, [791] and I am, at this present writing (1866) , its first President. We are very high in the newest developments, and bid fair to take a place among the scientific establishments. Benjamin Gompertz, who was President of the old Society when it expired, was the link between the old and new body: he was a member of ours at his death. ”

“ Here is the very phrase which is often wanted to signify that celebrity which puts its mark, good or bad, on the national history, in a manner which cannot be asserted of many notorious or famous historical characters. ”

“ No one had guessed the true reason, which is that the thing called the moon in the Gregorian Calendar is not the moon of the heavens, but a fictitious imitation put wrong on purpose, as will presently appear, partly to keep Easter out of the way of the Jews' Passover, partly for convenience of calculation. ”

“ The only question which could arise was whether the members of the society of working men—for this repute still continued—were of that class of educated men who could associate with the Fellows of the Astronomical Society on terms agreeable to all parties. We found that the artisan element had been extinct for many years; there was not a man but might, as to education, manners, and position, have become a Fellow in the usual way. The fact was that life in Spitalfields had become harder: and the weaver could only live from hand to mouth, and not up to the brain. ”

“ In the very earliest age of Christianity, a controversy arose as to the mode of keeping Easter, some desiring to perpetuate the Passover, others to keep the festival of the Resurrection. The first afterwards obtained the name of Quartadecimans, from their Easter being always kept on the fourteenth day of the moon (Exod. xii. 18, Levit. xxiii. 5.) . But though it is unquestionable that a Judaizing party existed, it is also likely that many dissented on chronological grounds. ”

“ De Morgan, never assumed that that gentleman had 'that particular subject to begin'—on the contrary, he supposed that one whom we all knew to be eminent as a thinker had come to a conclusion upon it, and would perhaps vouchsafe a guiding word to one who was, as yet, seeking the solution of the Great Problem of Theology. ”

“ So far as I could make it out, these parties did not think it unlawful to lay by out of income, except when this was done in a manner which involved calculation of death-chances. It is singular they did not see that the entrance of chance of death was the entrance of the very principle of the benefit society described in the Acts of the Apostles. The family of the one who died young received more in proportion to premiums paid than the family of one who died old. ”

“ Frost, he and Muggleton are the two "witnesses." I shall content myself with one specimen of Mr. Frost's science:
"I was once invited to hear read over 'Guthrie [812] on Astronomy,' and when the reading was concluded I was asked my opinion thereon; when I said, 'Doctor, it appears to me that Sir I. Newton has only given two proofs in support of his theory of the earth revolving round the sun: all the rest is assertion without any proofs.'—'What are they?' inquired the Doctor.—'Well,' I said, 'they are, first, the power of attraction to keep the earth to the sun ”

“ Clavius, to meet his view of the amount of that error, put forward the moon's age a day 8 times in 2,500 years. As we cannot enter at full length into the explanation, we must content ourselves with giving a set of rules, independent of tables, by which the reader may find Easter for himself in any year, either by the old Calendar or the new. ”

“ Many persons will be surprised at this assertion. They imagine that our country is the great instance of the refusal of all unpractical knowledge in favor of what is useful. I affirm, on the contrary, that there is no country in Europe in which there has been so wide a diffusion of speculation, theory, or what other unpractical word the reader pleases. ”

“ With us, since the beginning of the last century, scores upon scores—perhaps hundreds, for I am far from knowing all—of annuals have run, some their ten years, some their half-century, some their century and a half, containing questions to be answered, from which many of our examiners in the universities have culled materials for the academical contests. ”

“ A public instructor, who undertakes to settle for the world whether a reader of Clavius, the constructor of the Gregorian Calendar, is fool or knave, upon information derived from a compiler—in this matter—of his own day ”

“ SPECULATIVE THOUGHT IN ENGLAND. In the year 1845 the old Mathematical Society was merged in the Astronomical Society. The circle-squarers, etc., thrive more in England than in any other country: there are most weeds where there is the largest crop. ”

“ If the amusement given by paradoxers should prevent a useless discussion some years hence, I and the paradoxers shall have done a little good between us—at any rate, I have done my best to keep the heavy weight afloat by tying bladders to it. ”

“ I soon came to the information that some additions to Delambre's [739] statement of the rule for finding Easter, belonging to distant years, had been made by Sir Harris Nicolas! [740] Now as I myself furnished my friend Sir H. N. with Delambre's digest of Clavius's [741] rule, which I translated out of algebra into common language for the purpose, I was pretty sure this was the ignorant reading of a person to whom Sir H. N. was the highest arithmetical authority on the subject. ”

“ The general solution of equations of all degrees is a vexed question, which cannot have the mysterious interest of the circle problem, and is of a comparatively modern date. [762] Mr. Vogel announces a forthcoming treatise in which are resolved the "last impossibilities of pure mathematics."
Elective Polarity the Universal Agent. By Frances Barbara Burton, authoress of 'Astronomy familiarized,' 'Physical Astronomy,' &c. London, 1845, 8vo. [763] The title gives a notion of the theory. ”

“ Adams communicated to me values which he had obtained for the heliocentric longitude, excentricity of orbit, longitude of perihelion, and mass, of an assumed exterior planet,—deduced entirely from unaccounted-for perturbations of Uranus. The same results, somewhat corrected, he communicated, in October, to the Astronomer Royal. M. Le Verrier, in an investigation which was published in June of 1846, assigned very nearly the same heliocentric longitude for the probable position of the planet as Mr. Adams had arrived at, but gave no results respecting its mass and the form of its orbit. ”