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Ratio   Listen
noun
Ratio  n.  
1.
(Math.) The relation which one quantity or magnitude has to another of the same kind. It is expressed by the quotient of the division of the first by the second; thus, the ratio of 3 to 6 is expressed by 3/6 or ½; of a to b by a/b; or (less commonly) the second term is made the dividend; as, a:b = b/a. Note: Some writers consider ratio as the quotient itself, making ratio equivalent to a number. The term ratio is also sometimes applied to the difference of two quantities as well as to their quotient, in which case the former is called arithmetical ratio, the latter, geometrical ratio. The name ratio is sometimes given to the rule of three in arithmetic. See under Rule.
2.
Hence, fixed relation of number, quantity, or degree; rate; proportion; as, the ratio of representation in Congress.
Compound ratio, Duplicate ratio, Inverse ratio, etc. See under Compound, Duplicate, etc.
Ratio of a geometrical progression, the constant quantity by which each term is multiplied to produce the succeeding one.






Collaborative International Dictionary of English 0.48








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"Ratio" Quotes from Famous Books



... their own ill-regulated imaginations, to obtrude upon the world their crude and imperfect theories and systems, to the manifest retardation of knowledge:—an effect, too, liable to be induced in a direct ratio with the degree of talent and ingenuity by which their views may have been supported. Several of these may always be more successfully attacked by ridicule than by reason; inasmuch as they are, in this way, more likely to become the subjects ...
— A Voyage to the Moon • George Tucker

... never or hardly ever beheld. Which method also we reckon natural, then and there. Nor perhaps was the respective keeping of these two Oaths far out of due proportion to such respective display in taking them: inverse proportion, namely. For the theatricality of a People goes in a compound-ratio: ratio indeed of their trustfulness, sociability, fervency; but then also of their excitability, of their porosity, not continent; or say, of their explosiveness, hot-flashing, but ...
— The French Revolution • Thomas Carlyle

... obtain from the wind forces to restore the balance which the wind itself had disturbed. This could easily be done by using wings capable of being warped, and by supplementary adjustable surfaces in the shape of rudders. As the forces obtainable for control would necessarily increase in the same ratio as the disturbing forces, the method seemed capable of expansion to an almost unlimited extent. A happy device was discovered whereby the apparently rigid system of superposed surfaces, invented by Wenham, and improved by Stringfellow and Chanute, could be warped ...
— The Early History of the Airplane • Orville Wright

... set-off known to the moral law. Because A has defrauded B, that is no reason why B should defraud A. If it were so, society would go on forever in a compound ratio of crime. The first breach of the law would furnish excuse for the second, and their progeny would follow in sad progression to the end of time. This is not, however, the moral condition of the world. The lex talionis has been abolished ...
— The Vote That Made the President • David Dudley Field

... more uncertainty in apiarian science than other farming operations? It must be attributed to the fact, that among the thousands who are engaged in, and have studied agriculture, perhaps not more than one has given his energies to the nature and habits of bees. If knowledge is elicited in the same ratio, we ought to have a thousand times more light on one subject than the other, and still there are some things, even in agriculture, that ...
— Mysteries of Bee-keeping Explained • M. Quinby

... sit ad corrumpendos alios promptus ac sedulus ut non dubitarim dicere eum e vita tolli oportere et tanquam putridum membrum e corpore exsecari. Neque id tamen priusquam ejus sanandi causa omnis leviter medendi tentata sit ratio."—Pole to the Cardinal of Augsburg: ...
— The Reign of Mary Tudor • James Anthony Froude

... it was always better to find the route which would make long hauls easy and economical. He thus built his road with the idea of keeping down the operating costs and of showing a larger margin of profit than the others. From the very start the Great Northern was noted for its low ratio of operating expenses and its comparatively long trains and heavy trainloads. It was by this method that it really made ...
— The Railroad Builders - A Chronicle of the Welding of the States, Volume 38 in The - Chronicles of America Series • John Moody

... on the stage micrometer. Then it is clear that each division of the former represents 1/100 x 1/22 of an inch, or 1/2200th of an inch. For every fresh objective used, a fresh estimation of eye-piece and stage micrometer ratio is necessary. Having now got in the eye-piece micrometer a unit of measurement, it becomes a comparatively easy matter ...
— The Story of the Cotton Plant • Frederick Wilkinson

... asked suspicion; and the answer came, "The man in the chapeau blanc." There is something daring, something distinctive in a white hat; and it may be doubted whether the amount of comfort obtained by the revolutionary wearer is in a due ratio to the conspicuousness which his action entails on him. Members of Parliament are singularly emancipated from these fears of the brave; but members of Parliament cannot supply the whole contingent of white-hatted ...
— Lost Leaders • Andrew Lang

... rapidity. I drank, as I have said, for the effects, and in the first years of my drinking my first emotions were pleasurable. It sent the blood rushing to the brain, and induced a succession of vivid and pleasing thoughts. But invariably the depression that followed was in the same ratio down as the former was up, and after a time I lost that first pleasant, unnatural feeling, and drank only to satisfy an indescribable passion or craving. At first the wine glass may sparkle and foam, ...
— Fifteen Years in Hell • Luther Benson

... contain gearing in no more extensive context than as a means of transmitting action around a right angle. As for the windlass and hodometer, they do, it is true, contain whole series of gears used in steps as a reduction mechanism, usually for an extraordinarily high ratio, but here the technical details are so etherial that one must doubt whether such devices were actually realized in practice. Thus Vitruvius writes of a wheel 4 feet in diameter and having 400 teeth being turned by a 1-toothed pinion on a cart axle, but it is very doubtful ...
— On the Origin of Clockwork, Perpetual Motion Devices, and the Compass • Derek J. de Solla Price

... the great compromise of the Constitution, for without it the further work of the convention would have been impossible. In agreeing that three fifths of the slaves should be counted in apportioning representation, the convention made no innovation, but simply took over the federal ratio which Congress had recommended in 1783 as the basis for future apportionment of requisitions among the States. On this point there was no great difference of ...
— Union and Democracy • Allen Johnson

... office, or crime, on which ingenuity may not raise a doubt respecting either the letter or spirit of the constitution? And the same uncertainty and want of uniformity which would arise in the federal government, would arise in a much greater ratio in that of a state; so that no man could say certainly what were his duties or his rights. If such a state of things may now ensue, how would it be when the population of a single state should amount to several millions, and when ...
— The American Quarterly Review, No. 17, March 1831 • Various

... J. Will.—Quae ratio intercedat inter Dionis Cassii de Caesaris bellis gallicis narrationem et commentarios Caesaris de bello ...
— Dio's Rome, Volume 1 (of 6) • Cassius Dio

... ownership to a mere sixth of the Willie Meena. First he had given Billy half, then they had each given Rhodes a sixth; and now Judson Eells had stepped in with his contract and trimmed their holdings by a half. In another day or so, if the ratio kept up, Wunpost's sixth would be reduced to a twelfth, a twenty-fourth, a forty-eighth, a ninety-sixth—and he had discovered the mine himself! What philosophy or sophistry can reconcile a man to such buffets from the hand of Fate? Wunpost cursed and turned ...
— Wunpost • Dane Coolidge

... and Betty Martin," did issue from the neckcloth of Sir Bingo, but they were not much attended to; for it had not escaped the observation of the quicksighted gentry at the Well, that the Baronet's feelings towards the noble Earl were in the inverse ratio of those displayed by Lady Binks, and that, though ashamed to testify, or perhaps incapable of feeling, any anxious degree of jealousy, his temper had been for some time considerably upon the fret; a circumstance ...
— St. Ronan's Well • Sir Walter Scott

... a good way to prejudice a man in favour of a place which in itself may have little to recommend it. Mobile, however, has claims which are rapidly increasing its population and its trade; indeed the ratio of advance in both is equal to that of any other place in the States; in proof of which, I find by a report just issued of the returns of the foreign trade, exclusive of the coasting business, which is considerable, that the increase has been gradual and steady, and in five years ...
— Impressions of America - During The Years 1833, 1834, and 1835. In Two Volumes, Volume II. • Tyrone Power

... materials. Pompadour prints and white calicoes reign supreme, and look better than anything else. It is then that the poorer classes are able to dress best, the material being cheap. Winter stuffs are expensive, and to a great degree their effectiveness is in direct ratio to their cost; but during quite half of the Australian year the poor meet the rich, if not on an equality, at any rate on much fairer terms than at home with regard ...
— Town Life in Australia - 1883 • R. E. N. (Richard) Twopeny

... citizen, out of which comes the collective man, our national life. We have exalted the individual; the American citizen is a republic of one. Whether we have fifty millions, or ten millions, or a million, whatever may be the ratio of our population, the Government recognizes the individuality of the citizen as paramount. As God is the center of the universe, and Christ the center of the church, so the citizen is the center of this Government. All its laws, ...
— 'America for Americans!' - The Typical American, Thanksgiving Sermon • John Philip Newman

... regiment adjacent to them, in some woods farther west, had suffered no less heavily, and the woods were here literally dotted with the bodies of the dead. Our conclusion was that all the Frenchmen had been put out of action. It should be remembered that the ratio of wounded to killed is at least four to one. Colonel Allen said that he could not imagine worse destruction than these two regiments suffered. Evidently it was part of the price the French army so willingly paid ...
— The Note-Book of an Attache - Seven Months in the War Zone • Eric Fisher Wood

... Valliere, and Lamoignon—it is very well for such gentlemen to declaim against modern prices! But what is to be done? Books grow scarcer every day, and the love of literature, and of possessing rare and interesting works, increases in an equal ratio. Hungry bibliographers meet, at sales, with well furnished purses, and are resolved upon sumptuous fare. Thus the hammer vibrates, after a bidding of Forty pounds, where formerly it used regularly ...
— Bibliomania; or Book-Madness - A Bibliographical Romance • Thomas Frognall Dibdin

... Cost of Production, but upon Reciprocal Demand and Supply. 3. —As illustrated by trade in cloth and linen between England and Germany. 4. The conclusion states in the Equation of International Demand. 5. The cost to a country of its imports depends not only on the ratio of exchange, but on the efficiency of its labor. Chapter XV. Of Money Considered As An Imported Commodity. 1. Money imported on two modes; as a Commodity, and as a medium of Exchange. 2. As a commodity, it obeys the same laws of Value as other imported Commodities. Chapter XVI. ...
— Principles Of Political Economy • John Stuart Mill

... gold has gone up another hundred points, Mr. Sefton," said the President. "Our credit in Europe has fallen in an equal ratio and our Secretary of State has found no way to convince foreign governments that they are ...
— Before the Dawn - A Story of the Fall of Richmond • Joseph Alexander Altsheler

... turns his back upon the comforts of an elder civilization, to face the savage youth, the primordial simplicity of the North, may estimate success at an inverse ratio to the quantity and quality of his hopelessly fixed habits. He will soon discover, if he be a fit candidate, that the material habits are the less important. The exchange of such things as a dainty menu for rough fare, of the stiff leather shoe for the soft, shapeless moccasin, of ...
— The Son of the Wolf • Jack London

... of things," she said slowly. "You don't realize the comparative ratio of one thing to another. Any man can give happiness to a woman who loves him—but that's no bargain! He merely gives her happiness by taking his own. Do you call that a fair exchange? To you, drunk with romance, perhaps it is. But in reality it's robbery. He has to pay higher for his pleasures ...
— Sally Bishop - A Romance • E. Temple Thurston

... certain types of stubbornness that increase in direct ratio to the pressure applied. To this type Barraclough belonged. He had yet to find the man who could induce him to talk against his will. Woman? Ah, that's a different matter. The argument took ...
— Men of Affairs • Roland Pertwee

... more than a hundred per cent. since spring, and rents and boarding are advancing in the same ratio. ...
— A Rebel War Clerk's Diary at the Confederate States Capital • John Beauchamp Jones

... computations place Mercury third in the order of density among the members of the solar system, the earth ranking as first and Venus as second. Mercury's density is now believed to be less than the earth's in the ratio of 85 to 100. Accepting this estimate, we find that the force of gravity upon the surface of Mercury is only one third as great as upon the surface of the earth—i.e., a body weighing 300 pounds on the earth would weigh only ...
— Other Worlds - Their Nature, Possibilities and Habitability in the Light of the Latest Discoveries • Garrett P. Serviss

... the assumption that the turkey and the sucking pig and their kindred spirits are yet to be found among us or among some of us, anyhow, it is only logical to assume that the food is not served in courses at the ratio of a little of everything and not enough of anything, but that it is brought on and spread before the company all together and at once—the turkey or the pig or the ham or the chickens; the mashed potatoes overflowing ...
— Cobb's Bill-of-Fare • Irvin Shrewsbury Cobb

... cheerful fashion the conversation proceeded, the girl, who was by no means insensible to his bright eager face and well-knit figure, dividing her time in the ratio of three parts to her book and one to him. Time passed all too soon for the mate, when they were interrupted by a series of hoarse unintelligible roars proceeding from ...
— Many Cargoes • W.W. Jacobs

... They show that the diurnal tide at Cape Bryant, Cape Sheridan, Point Aldrich, and Cape Morris Jesup follows that at Fort Conger by respective intervals of 3-1/2, 5, 6, and 8 hours. They also show that in going northward from Fort Conger to Point Aldrich the ratio of the two principal diurnal constituents approximates more and more nearly to the theoretical ratio; that is, to the ratio between the two corresponding tidal forces. This is what one would expect to find ...
— The North Pole - Its Discovery in 1909 under the auspices of the Peary Arctic Club • Robert E. Peary

... seaport. Nothing opposes this supposition. On one hand, it is a well-known fact that, owing to the conical motion of the earth, the waters retreat continually from the western coasts of America, which rise at a certain known ratio every century. On the other hand, the bank of oysters and other marine shells and debris, found on the slopes of the Andes to near their summits, obviously indicate that at some time or other ...
— The Mayas, the Sources of Their History / Dr. Le Plongeon in Yucatan, His Account of Discoveries • Stephen Salisbury, Jr.

... lightning has often been counted and for every fifty-four oaks struck, only one beech, or birch, or maple or alder is struck. Elms are fairly dangerous, being forty to the beech's one, and pines are less so, their ratio being fifteen. Not only this, boys, but a good deal depends on the way in which a tree is struck. An oak-tree may be riven into splinters, showing the terrible resistance that it gives to the stroke. A beech-tree, usually, ...
— The Boy with the U. S. Weather Men • Francis William Rolt-Wheeler

... employed by the brethren of Griqua Town, were greatly in their favor. Two natives had likewise been employed recently by the Kuruman Mission, and these had been highly efficient and successful. If the Directors would allow him to employ more of these, conversions would increase in a compound ratio, and regions not yet explored by Europeans would soon be supplied with the ...
— The Personal Life Of David Livingstone • William Garden Blaikie

... neighborhood of a hundred thousand dollars to one campaign fund and fifty thousand dollars to the campaign fund of the other side—and, I believe, made some further substantial contributions in the same ratio of two dollars to one side for every one dollar given to the other. The contributors were Democrats, and the big contributions went to the Democratic managers. The Republican was elected, and after ...
— Theodore Roosevelt - An Autobiography by Theodore Roosevelt • Theodore Roosevelt

... leaving Rio Janeiro we finally anchored in Corumb, an intensely sultry spot. Corumb is a town of 5,000 inhabitants, and often said to be one of the hottest in the world. It is an unhealthy place, as are most towns without drainage and water supply. In the hotter season of the year the ratio on a six months' average may be two deaths to one birth. It is a place where dogs at times seem more numerous than people, a town where justice is administered in ways new and strange. Does the reader wish an instance? ...
— Through Five Republics on Horseback • G. Whitfield Ray

... At the time of the departure for the South the proportion of sick in the whole company was under 5 per cent., the cases being mostly of a trivial nature. The following table, compiled from the monthly returns, will show how rapidly the ratio increased during ...
— History of Company E of the Sixth Minnesota Regiment of Volunteer Infantry • Alfred J. Hill

... "jus naturae" and "jus gentium" of the Roman lawyers are phrases of very different import from the modern phrases, "law of nature" and "law of nations." "Jus naturale," says Ulpian, "est quod natura omnia animalia docuit." D. I. I. I. 3. "Quod naturalis ratio inter omnes homines constituit, id que apud omnes peraeque custoditur vocaturque jus gentium." D. I. I. 9. But they sometimes neglect this subtle distinction—"Jure naturali quod appellatur jus gentium." I. 2. I. II. Jus feciale was the Roman term for our law of nations. ...
— A Discourse on the Study of the Law of Nature and Nations • James Mackintosh

... end of the final chapter:— The proportional intensity of sunlight to moonlight is subject to fluctuations, from many causes, and is therefore variously stated. The highest accepted ratio is 600,000 to 1.; the lowest 200,000 to 1. A constutional repugnance to anything savouring of effect prompted me to indicate the lower proportion. The error in the text ...
— Such is Life • Joseph Furphy

... thousands contribute, for generations upon generations; and under the consequences of which more thousands suffer for succeeding centuries. Yet public evils are what society suffer from most to-day, and must suffer from most in increasing ratio, as years pass. ...
— The Forerunner, Volume 1 (1909-1910) • Charlotte Perkins Gilman

... of the greatest controlling powers on earth, the sense of fame and estimation. The share of infamy, that is likely to fall to the lot of each individual in public acts, is small indeed; the operation of opinion being in the inverse ratio to the number of those who abuse power. Their own approbation of their own acts has to them the appearance of a public judgment in their favour. A perfect democracy is therefore the most shameless thing in the world. ...
— Selections from the Speeches and Writings of Edmund Burke. • Edmund Burke

... man to-day, plus twenty years of experience. The figure is still the figure of his youth, the hickory a little better seasoned, perhaps, and the steel and whalebone a little harder, but they have lost none of their spring and vitality. The ratio of promotion has also been kept up. That he should now rank as the most expert pilot on the station was quite to be expected. He could have filled as well a commander's place on the bridge, had he chosen to work ...
— The Underdog • F. Hopkinson Smith

... desert soil, that is now utterly worthless, would become of great value; and the taxes upon the increased produce would not only cover the first outlay of the irrigation works, but would increase the revenue in the ratio proportionate to the increased surface of fertility. A dam across the Atbara would irrigate the entire country from Gozerajup to Berber, a distance of upwards of 200 miles; and the same system upon the Nile would carry the ...
— The Nile Tributaries of Abyssinia • Samuel W. Baker

... whites during the rest of the colonial period the proportion of the negroes was steadily maintained at about one-seventh of the whole. They became fairly numerous in all districts except the extreme frontier, but in the counties fronting New York Harbor their ratio was somewhat above the average.[33] In 1755 a special census was taken of slaves older than fourteen years, and a large part of its detailed returns has been preserved. These reports from some two-score scattered localities ...
— American Negro Slavery - A Survey of the Supply, Employment and Control of Negro Labor as Determined by the Plantation Regime • Ulrich Bonnell Phillips

... of the moment, I could but indistinctly learn, and cannot now remember. As midnight approached, our old friend the fog gathered density, and effectually deprived us of the slightest glimpse of the light; and we retired to rest ill at ease, plunged into the vale of anxiety in the same ratio as we had been exalted on the peaks of expectation ...
— A Yacht Voyage to Norway, Denmark, and Sweden - 2nd edition • W. A. Ross

... to be enlisted by the admirable description of an interior or a character in one of their novels, to find the plot which embodies them an absurd melodrama! Evanescence is the law of Parisian felicities,—selfishness the background of French politeness,—sociability flourishes in an inverse ratio to attachment; we become skeptical almost in proportion as we are attracted. If we ask the way, we are graciously directed; but if we demand the least sacrifice, we must accept volubility for service. Thus the perpetual flowering in manners, in philosophy, ...
— The Atlantic Monthly, Volume V, Number 29, March, 1860 - A Magazine Of Literature, Art, And Politics • Various

... subject matter is one which demands for its effective apprehension either intellectual effort or emotional insight. When both these variables are demanded, the gulf widens and deepens at a ratio which is "geometrical" rather than "arithmetical"; and when a high degree of each is demanded, the separation between ...
— What Is and What Might Be - A Study of Education in General and Elementary Education in Particular • Edmond Holmes

... suggest that if any fund be dedicated to this purpose it may be wisely distributed in the different States according to the ratio of illiteracy, as by this means those localities which are most in need of such assistance will reap its ...
— A Compilation of the Messages and Papers of the Presidents - Section 2 (of 2) of Volume 8: Chester A. Arthur • James D. Richardson

... will be paid out of profits, and all increase of profits out of wages. I shall now, however, extort a sufficient defence of Mr. Ricardo from your own concessions. For you acknowledge that the same cause which raises the wages of the hatter will raise wages universally, and in the same ratio—that is, by twenty-five per cent. And, if such a rise in wages could raise the price of hats by sixteen and one half per cent., it must raise all other commodities whatsoever by sixteen and one half per cent. Now, ...
— Memorials and Other Papers • Thomas de Quincey

... remembered that the enemy had but three corps, while the Union army had seven. Each of their corps represented a third, and each of ours a seventh, of our total force. The same ratio extended ...
— Chancellorsville and Gettysburg - Campaigns of the Civil War - VI • Abner Doubleday

... surplus revenue, after the debt shall have been paid off, should be portioned out to the different states, in proportion to their ratio of representation; which appears to be judicious, as the question of congressional power to appropriate money to road-making, &c., although of a general character, involves also the right of jurisdiction; ...
— A Ramble of Six Thousand Miles through the United States of America • S. A. Ferrall

... phenomenon. Suppose that the application of a certain quantity of heat to a body merely increases its bulk, that a double quantity melts it, and a triple quantity decomposes it: these three effects being heterogeneous, no ratio, whether corresponding or not to that of the quantities of heat applied, can be established between them. Thus the supposed axiom of the proportionality of effects to their causes fails at the precise point where the principle of the Composition of Causes also ...
— A System Of Logic, Ratiocinative And Inductive • John Stuart Mill

... own times that the rate of progress in the arts and sciences proceeds in a geometrical ratio as knowledge increases, and so when we carry back our retrospect into the past, we must be prepared to find the signs of retardation augmenting in a like geometrical ratio; so that the progress of a thousand years at a remote period may ...
— The Antiquity of Man • Charles Lyell

... wing surface of a gnat is forty-nine units of area to every one of weight. In graphic contrast to that, a condor (Sarcorhamphus gryphus) which weighed 16.52 pounds had a wing surface of 9.80 square feet. In other words, though the gnat needs wing surface in a ratio of forty-nine square feet per pound of weight, a great condor manages to sail along majestically with .59 of a square foot to at least a pound of weight. The unexplained phenomenon persists consistently throughout the whole domain of entomology and ornithology. Going up the scale ...
— Our Bird Comrades • Leander S. (Leander Sylvester) Keyser

... of arts and inventions has been, in modern days, in such increased ratio to the increase of capital that it has created so great a demand that a monopoly has been made of it; more is paid for the use of it than its real worth, so that wealth, even in this democratic country, is piling up in colossal fortunes by being drawn from the great body of society. ...
— Brook Farm • John Thomas Codman

... advancing culture, and people are able to appropriate to themselves more of the various forms of art, the artist himself attains to greater power, his abilities increase in direct ratio with the progress in culture made by the people and their ability to comprehend him. When one side or phase of an art comes to be received, new and more difficult problems are invariably presented, the elucidation of which can only be effected by a higher development of the faculties. There ...
— Beethoven • George Alexander Fischer

... Riddle thinks the "developmental energy" of the eggs is in an inverse ratio to their size. The last and largest eggs of the season develop least and produce most females. The second egg of a clutch is larger than the first, but develops less and the bird produced is shorter-lived. Overworking and ...
— Taboo and Genetics • Melvin Moses Knight, Iva Lowther Peters, and Phyllis Mary Blanchard

... jealous for the actors who pleased my youth,' he says elsewhere. And again: 'For me, I do not know whether a constitutional imbecility does not incline me too obstinately to cling to the remembrances of childhood; in an inverted ratio to the usual sentiment of mankind, nothing that I have been engaged in since seems of any value or importance compared to the colours which imagination gave to everything then.' In Lamb this love of old things, ...
— Figures of Several Centuries • Arthur Symons

... sort, a part of the programme of the day, the fear had seized them that they might be forced to execute it faithfully, and they had fled far from the scene at the instant when the balloon was being filled. Their courage was evidently the inverse ratio of ...
— A Winter Amid the Ice - and Other Thrilling Stories • Jules Verne

... cultivated parents will have, by born nervous organisation, a greater aptitude for cultivation than the descendants of such as are not cultivated; and that this tendency augments, in some enhanced ratio, for many generations. ...
— Physics and Politics, or, Thoughts on the application of the principles of "natural selection" and "inheritance" to political society • Walter Bagehot

... whole, the stars which we call faint are farther from us than the brighter ones; and, on the whole, the brilliancy of our brightest and nearest stars is not very far from the brilliancy of the average star in space. We cannot yet define the word very by a numerical ratio. ...
— Sir William Herschel: His Life and Works • Edward Singleton Holden

... perhaps, easy to give any distinct reason why they should be so, since theological disputes in general could scarce be considered as interesting to them. But zeal, amongst the lower orders at least, is often in an inverse ratio to knowledge; and sailors were not probably the less earnest and devoted Protestants, that they did not understand the controversy between the Churches. As for the merchants, they were almost necessarily ...
— Peveril of the Peak • Sir Walter Scott

... German word Verhaltnis as used in the arithmetic lesson means ratio, proportion. The word is in common use in Germany for a love intimacy or ...
— A Young Girl's Diary • An Anonymous Young Girl

... Florin, show at one view the amount of duty at the various rates fixed by the late act, and are accompanied by a variety of statistical information, tending to show that the wealth of the nation has increased in as great, if not a greater, ratio, than the population. The price at which the work is issued serves to lead our attention to a little pamphlet, published at sixpence, or 25 mils, by Mr. Robert Mears, entitled Decimal Coinage Tables for simplifying and facilitating the Introduction ...
— Notes and Queries, Number 213, November 26, 1853 • Various

... if these latter considerations were of little importance, the first was of great weight. According to all probability, it was too soon for any serious attack. Without being beautiful, she pleased much and many; a second obstacle, since sensibility in women is almost always developed in inverse ratio to their success. She had brains; she was wonderfully aristocratic in ...
— Gerfaut, Complete • Charles de Bernard

... of remarking on the well-known hereditary character of colour blindness in connection with the fact, that it is nearly twice as prevalent among the Quakers as among the rest of the community, the proportions being as 5.9 to 3.5 per cent. [1] We might have expected an even larger ratio. Nearly every Quaker is descended on both sides solely from members of a group of men and women who segregated themselves from the rest of the world five or six generations ago; one of their strongest opinions ...
— Inquiries into Human Faculty and Its Development • Francis Galton

... in the care of others has been harshly criticized. But there is one phase of the subject that I have never seen commented upon—and that is that a mother's love for her offspring bears a certain ratio to the love she bore their father. Had Madame Guyon ever carried in her arms a love-child, I can not conceive of her allowing this child to be cared for by others—no matter ...
— Little Journeys to the Homes of the Great, Vol. 2 of 14 - Little Journeys To the Homes of Famous Women • Elbert Hubbard

... computed to be required for a seventy-four. Now, reckoning fifty oaks to the acre, of 100 years' standing, and the quantity in each tree to be a load and a half, it would require forty acres of oak forest to build one seventy-four; and the quantity increases in a great ratio, for the largest class of line of battle ships. The average duration of these vast machines, when employed, is computed to be fourteen years. It is supposed, that all the full grown oaks now in Scotland would not build two ...
— The Mirror of Literature, Amusement, and Instruction, Vol. 17, - Issue 479, March 5, 1831 • Various

... a larger law which perhaps comprehends these facts. It is this. The rapidity with which ideas grow old in our memories is in a direct ratio to the squares of their importance. Their apparent age runs up miraculously, like the value of diamonds, as they increase in magnitude. A great calamity, for instance, is as old as the trilobites an hour after it has happened. It stains backward ...
— The Autocrat of the Breakfast-Table • Oliver Wendell Holmes, Sr. (The Physician and Poet not the Jurist)

... (as I didn't mention) sat next to me at school: Sometimes I had to show her the way to work the rule Of Ratio and Proportion, and do upon her slate Those long, hard sums that ...
— Our Young Folks, Vol 1, No. 1 - An Illustrated Magazine • Various

... expect the same profit from supplying necessity and from adding to abundance, they multiply their trading-fleets and double their investments. Is it not evident that if their shipments are in excess, their profits must fall short, and that the ratio between the two cannot be equal to what it was before? Let the records of the customs duties belonging to your Majesty be examined, where those who profit and those who lose pay on account of what they produce; and they will tell how not only the commerce has not declined, but ...
— The Philippine Islands, 1493-1898: Volume XVII, 1609-1616 • Various

... ratio of increase in population is not greater in Minnesota than in some of her adjoining sister States, notwithstanding her superior attractions of climate and scenery. Yet, if this be true, it is readily accounted for in that the majority of the people ...
— Minnesota; Its Character and Climate • Ledyard Bill

... anyhow, as most of us know. There's my own case, for example. I'm supposed to be a gentleman of leisure and means. Leisure, certainly, but the means are slender enough, and proceeding in a diminishing ratio. That's the penalty of having been born a rich man's son and educated chiefly in the arts of riding off at polo and thrashing a single-sticker to windward in a Cape Cod squall. But I sha'n't say a word against the governor, God bless him! He gave me what I thought I wanted, and it wasn't his ...
— The Gates of Chance • Van Tassel Sutphen

... for which there were other forms of punishment, the strap was regarded at Vendome as the ultima ratio Patrum. Exercises forgotten, lessons ill learned, common ill behavior were sufficiently punished by an imposition, but offended dignity spoke in the master through the strap. Of all the physical torments to which we were exposed, certainly the ...
— Louis Lambert • Honore de Balzac

... women, more amiable women, but none of them had affected me like Audrey. The problem was inexplicable. Any idea that we might be affinities, soul-mates destined for each other from the beginning of time, was disposed of by the fact that my attraction for her was apparently in inverse ratio to hers for me. For possibly the millionth time in the past five years I tried to picture in my mind the man Sheridan, that shadowy wooer to whom she had yielded so readily. What quality had he possessed that I did not? Wherein lay ...
— The Little Nugget • P.G. Wodehouse

... deemed inexpedient to provoke its renewal by any hostile demonstration on the part of the Crown; while, moreover, the popularity of Conde was so notorious that no doubt could be entertained of his success should the ultima ratio regum be adopted. His influence was alike powerful with all classes; the people were unanimous in his cause; the Princes and great nobles were his zealous adherents; and since his entrance into the Council ...
— The Life of Marie de Medicis, Vol. 2 (of 3) • Julia Pardoe

... to the ground for desired cutting heights, and it can be lifted and fastened in an upright position for transport to and from the field. Mowers cut more rapidly and lower than did reapers, and thus they used a different gear ratio; however, farmers sometimes used reapers for mowing. Gift of New York Historical Association, Cooperstown, ...
— Agricultural Implements and Machines in the Collection of the National Museum of History and Technology • John T. Schlebecker

... salary to a thousand dollars only made him less careful of his money. Before, he lived as freely as if his income had been one-third above what it was; now, he increased his expenses in a like ratio. It was a pleasure to him to spend his money—not for himself alone, but among ...
— Words for the Wise • T. S. Arthur

... publishing the grammatical treatises of Grocyn, Linacre, Stanbridge, Lilye, Holte, Whittington, and others—for the benefit, as well of the public, as of his own particular circle. I take it, his library must have been both choice and copious; for books now began to be multiplied in an immense ratio, and scholars and men of rank thought a Study, or Library, of some importance to their mansions. What would we not give for an authenticated representation of Dean Colet in his library,[295] surrounded with books? You, Lisardo, would ...
— Bibliomania; or Book-Madness - A Bibliographical Romance • Thomas Frognall Dibdin

... to get any supper but eggs and bread, and having to sleep on the supper-table afterwards, confirmed us in the theory we were beginning to adopt, that nature and mankind vary in an inverse ratio; and we were off at daybreak, delighted to get into the forest again. We rode over hill and dale for four or five hours, and then along the edge of a barranca for the rest of the day. This was one of the grandest chasms we had ever seen, even ...
— Anahuac • Edward Burnett Tylor

... is in ratio with their passion for each other. These two loved with complete abandon, consequently each could wound the ...
— The Fur Bringers - A Story of the Canadian Northwest • Hulbert Footner

... intervenes. The work, at first of some worth, is ill done, and becomes of less worth and of ever less, and finally of none: the worthless work can now afford to be ill done; and Human Stupidity, at a double geometrical ratio, with frightful expansion ...
— Latter-Day Pamphlets • Thomas Carlyle

... cabbages{266}) of our domestic plants and animals. If we admit that every organism maintains its place by an almost periodically recurrent struggle; and how can we doubt it,—when we know that all beings tend to increase in a geometrical ratio (as is instantly seen when the conditions become for a time more favourable); whereas on an average the amount of food must remain constant, if so, there will be a natural means of selection, tending to preserve those individuals ...
— The Foundations of the Origin of Species - Two Essays written in 1842 and 1844 • Charles Darwin

... and axis of the beam formed one and the same straight line—the tension on the beam would be 2000 lbs. But, if the beam were inclined, and the force acted in a vertical direction, then the strain would be increased in the ratio of the increase of the diagonal of inclination over the vertical;—suppose the beam is 20 ft. long and inclined at an angle of 45 deg.—and let 2000 lbs., as before, be suspended from its lower end. Now the diagonal being 20 deg.,—the ...
— Instructions on Modern American Bridge Building • G. B. N. Tower

... lawyer who is a businessman and who will keep people out of trouble instead of getting them in. And we also have a few physicians who are big enough to tell a man there is nothing the matter with him, if they think so, and then charge him accordingly—in inverse ratio to ...
— Little Journeys to the Homes of the Great Philosophers, Volume 8 • Elbert Hubbard

... punishment. It is true that she was still inferior and this distinction was recognized and emphasized by the difference in the penalties imposed for the commission of the same crimes, these penalties being in inverse ratio to ...
— Legal Status Of Women In Iowa • Jennie Lansley Wilson

... other words, the ratio of angular motion of two mobiles acting on each must be in the same ratio as the length of their radii at the point of contact. If we desire to give the jewel pin, or, in ordinary horological phraseology, have a greater arc of roller action, we would extend the length ...
— Watch and Clock Escapements • Anonymous

... very simple numbers there is no need of this. For instance, one, two, three, being given, everyone can see that the fourth proportional is six; and this is much clearer, because we infer the fourth number from an intuitive grasping of the ratio, which the ...
— The Ethics • Benedict de Spinoza

... good shears, a couple of punches, and a leaden anvil of two or three pounds weight. Will you inquire how the goldsmiths put in their plugs?" The Confederation, upon Jefferson's report, July 6, 1785, adopted the dollar as its unit, and provided for a decimal ratio; but a few tons of copper cents made up the only national currency ...
— Formation of the Union • Albert Bushnell Hart

... arts. The reconciliation between the royalties is finished, and fifty thousand pounds a-year more added to the heir apparent's revenue. He will have money now to tune up Glover, and Thomson, and Dodsley again: Et spes et ratio ...
— The Letters of Horace Walpole, Volume 1 • Horace Walpole

... the pay of his chief foreman it would have changed the ratio between that and the wages of the others, unless theirs, too, was increased. In that event, a reproof was likely to come from the directors, and he would find it ...
— The Jungle Fugitives • Edward S. Ellis

... domestication should not have acted under nature. In the preservation of favoured individuals and races, during the constantly-recurrent Struggle for Existence, we see the most powerful and ever-acting means of selection. The struggle for existence inevitably follows from the high geometrical ratio of increase which is common to all organic beings. This high rate of increase is proved by calculation,—by the rapid increase of many animals and plants during a succession of peculiar seasons, or when naturalised in a new country. More individuals are born than can possibly survive. ...
— On the Origin of Species by Means of Natural Selection • Charles Darwin

... page illustrate motors of each make. The weight of one make complete, with gear and gear case, is 5,900 pounds. The corresponding weight of the other is 5,750 pounds. The ratio of gear reduction used with one motor is 19 to 63, and with the ...
— The New York Subway - Its Construction and Equipment • Anonymous

... the night before. He was just ending his vacation, and he thought he recalled having a final farewell party for two or three lovely female types he had chanced to meet in what was still the world's finest City of Opportunity, Washington, D.C. (latest female-to-male ratio, five-and-a-half to one). The party had been a classic of its kind, complete with hot and cold running ideas of all sorts, and lots and lots ...
— Brain Twister • Gordon Randall Garrett

... this, however, we had each in succession spoken the launch, reporting the distance that we had traversed up to sunset. And, with the data thus supplied, the master had gone to work upon a calculation which formed the basis of a sort of table showing the ratio of the speeds of the several boats, with the aid of which the officer in charge of each boat could estimate with a moderate degree of accuracy the position of each of the other boats at any given moment—so long, that is to say, as the wind held fair enough to allow the boats ...
— A Pirate of the Caribbees • Harry Collingwood

... to light at Pompeii suggest the hypothesis that at the commencement of the imperial period alongside of the Roman pound the Attic mina (presumably in the ratio of 3: 4) passed current as a second imperial weight (Hermes, ...
— The History of Rome (Volumes 1-5) • Theodor Mommsen

... influence of man, decreasing. Fluctuations there may be; but permanent increase, except in restricted localities, is almost impossible. For example, our own observation must convince us that birds do not go on increasing every year in a geometrical ratio, as they would do, were there not some powerful check to their natural increase. Very few birds produce less than two young ones each year, while many have six, eight, or ten; four will certainly be below the average; ...
— Contributions to the Theory of Natural Selection - A Series of Essays • Alfred Russel Wallace

... Coketown working-people had been for scores of years, deliberately set at nought? That there was any Fancy in them demanding to be brought into healthy existence instead of struggling on in convulsions? That exactly in the ratio as they worked long and monotonously, the craving grew within them for some physical relief - some relaxation, encouraging good humour and good spirits, and giving them a vent - some recognized holiday, though ...
— Hard Times • Charles Dickens*

... a change of base, and he estimates its value in comparison with that of his subsequent operations in the ratio of one to ten. But why those subsequent operations, or a change of base with a view to any such ulterior purpose? Grant had not at that time even suggested the need of Sherman's aid against Lee, ...
— Forty-Six Years in the Army • John M. Schofield

... the details of the horrors of the French revolution to be fully impressed with this fact. Where was patriotism then? and was not Napoleon the real patriot when he said, "two or three six-pounders would have settled the canaille of Paris!" I by no means advocate the ultima ratio regum being resorted to in popular commotions, in saying this; but France would have been happier had the little corporal been permitted to use his artillerymen. It has often surprised me, in reading the ...
— Canada and the Canadians, Vol. 2 • Richard Henry Bonnycastle

... Highlanders must have sent messages home not altogether unfavorable, for they were the pioneers of a multitude whose coming in successive years were to add strength and thrift and intelligence beyond the ratio of their numbers to the communities in which they set up their homes." Many Scottish immigrants settled in the vicinity of Goshen, Orange County, in 1720, and by 1729 had organized and built two churches. A second colony arrived from the north of Ireland in 1731. At ...
— Scotland's Mark on America • George Fraser Black

... world, and the "interpreter of nature": that famous expression of Bacon's really belongs to Pico. Tritum est in scholis, he says, esse hominem minorem mundum, in quo mixtum ex elementis corpus et spiritus coelestis et plantarum anima vegetalis et brutorum sensus et ratio et angelica mens et Dei similitudo conspicitur.—"It is a commonplace of the schools that man is a little world, in which we may discern a body mingled of earthy elements, and ethereal breath, and the vegetable life of plants, and the senses of the ...
— The Renaissance - Studies in Art and Poetry • Walter Pater

... pass on to l m, and subsequently in the direction of the arrow. The refraction of the beam is thus completely accounted for; and it is, moreover, based upon actual experiment, which proves that the ratio of the velocity of light in glass to its velocity in air is that here mentioned. It is plain that if the change of velocity on entering the glass were greater, the refraction also ...
— Six Lectures on Light - Delivered In The United States In 1872-1873 • John Tyndall

... working classes to those who do not work; that the pyramid of the social edifice seems to be reconstructed in such fashion that the foundation stones are carried to the apex, and the swiftness of this transfer is increasing in a sort of geometrical ratio. I see that the result of this is something like that which would take place in an ant-heap if the community of ants were to lose their sense of the common law, if some ants were to begin to draw the products of labor from ...
— The Moscow Census - From "What to do?" • Lyof N. Tolstoi

... I have had opportunity of observing the great difference in the quantity of cattle brought to one of our largest beast-markets in the south of England; and it is well known that this has increased in a ratio of more than double; and I am informed by a worthy and truly honourable prelate, who has observed the same for twenty-five years previously, that it has nearly quadrupled. I have also made it my business, as a subject of curiosity, to inquire if the ...
— The Botanist's Companion, Vol. II • William Salisbury

... a marked increase in the consumption of tea and coffee during the same period, the ratio of increase fell far below that of cocoa. It is evident that the coming American is going to be less of a tea and coffee drinker, and more of a cocoa and chocolate drinker. This is the natural result of a better knowledge of the laws ...
— Chocolate and Cocoa Recipes and Home Made Candy Recipes • Miss Parloa

... for it must be remembered that the poor cock who undergoes all this plucking and mangling is a living bird! It is doubtful whether a thought of the cruelty ever entered the mind of a New Mexican. If so, it must have been a New Mexican woman; for the humanity of these is in an inverse ratio to that of their lords. For the women it may be urged that the sport is a custom of the country; and what country is without its cruel sports? Is it rational or consistent to weep over the sufferings of Chanticleer, ...
— The White Chief - A Legend of Northern Mexico • Mayne Reid

... kilometer radius is ample. By increasing the initial pressure of the air, much better results can be obtained, and future attention in practice should be devoted to this point. The amount of work required to compress air does not increase in the same ratio as the pressure, and for this reason considerable economy can be effected at the first stage, and the loss in ...
— Scientific American Supplement, No. 803, May 23, 1891 • Various



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