Ratios sentence example

ratios
  • In the former year the ratios were 40.2 and 41.5, in the latter 41-6 and 427%.
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  • He discovered that gases always combined in volumes having simple ratios, and that the volume of the product had a simple ratio to the volumes of the reacting gases.
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  • In the same preface is included (a) the famous problem known by Pappus's name, often enunciated thus: Having given a number of straight lines, to find the geometric locus of a point such that the lengths of the perpendiculars upon, or (more generally) the lines drawn from it obliquely at given inclinations to, the given lines satisfy the condition that the product of certain of them may bear a constant ratio to the product of the remaining ones; (Pappus does not express it in this form but by means of composition of ratios, saying that if the ratio is given which is compounded of the ratios of pairs - one of one set and one of another - of the lines so drawn, and of the ratio of the odd one, if any, to a given straight line, the point will lie on a curve given in position), (b) the theorems which were rediscovered by and named after Paul Guldin, but appear to have been discovered by Pappus himself.
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  • Hero's expressions for the areas of regular polygons of from 5 to 12 sides in terms of the squares of the sides show interesting approximations to the values of trigonometrical ratios.
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  • This is the case, for instance, with formulae which involve 7r or trigonometrical ratios.
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  • The earlier methods proposed were, like those of Briggs, purely arithmetical, and for a long time logarithms were regarded from the point of view indicated by their name, that is to say, as depending on the theory of compounded ratios.
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  • The oxygen and hydrogen, for example, into which water may be resolved are not in strictness indifferent one to the other, since both are members of an order regulated according to laws of combination in definite ratios.
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  • If now the assemblage be brought into any other position relative to the earth, without alteration of the mutual distances, this is equivalent to a rotation of the directions of the forces relatively to the assemblage, the ratios of the forces remaining unaltered.
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  • These may be, for instance, the five ratios f: ~: l: X: u v of the six quantities which specify an infinitesimal twist about the screw.
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  • The velocities referred to are the velocities of the various points of the body in any imagined motion of the body through the position in question; they obviously bear to one another the same ratios as the corresponding infinitesimal displacements.
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  • Hence these three forces will be concurrent, and their ratios wifi be given by a triangle of forces.
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  • Again, if G be the mass-centre of four particles a, $, 7, situate at the vertices of a tetrahedron ABCD, we find a: ~ :~: tet GBCD: tetUGCDA: tetGDAB: tetGABC, and by suitable determination of the ratios on the left hand we can make G assume any assigned position in space.
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  • In any general dynamical equation the dimensions of each term in the fundamental units must be the same, for a change of units would otherwise alter the various terms in different ratios.
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  • Eliminating~the flI ratios A1:AI: -.. :A~ we obtain the determinantal equation ~(u2)o, (6)
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  • For any particular root, the equations (5) determine the ratios of the quantities Af, A1,.
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  • The amplitudes of oscilla Ia tion of the various particles have definite ratios to one another, and the phases are in agreement, the absolute amplitude (depending on C) and the phase-constant () being alone arbitrary.
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  • If in (21) we imagine that x, y, I denote infinitesimal rotations of a solid free to turn about a fixed point in a given field of force, it appears that the three normal modes consist each of a rotation about one of the three diameters aforesaid, and that the values of in are proportional to the ratios of the lengths of corresponding diameters of the two quadrics.
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  • The following are some of the ratios of the modulus of stability to the depth of the joint which occur in practice :
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  • For the condition of equilibrium of forces not parallel is that they shall be represented in direction and magnitude by the sides and diagonals of certain parallelograms, and of parallel forces that they shall divide certain straight lines in certain ratios; and the parallel projection of a parallelogram is a parallelogram, and that of a straight line divided in a given ratio is a straight line divided in the same ratio.
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  • It is required to find the ratios of those angular velocities.
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  • The comparative motion of the first driver and last follower is obtained by combining the proportions expressing by their terms the velocity ratios and by their signs the directional relations of the several elementary combinations of which the train consists.
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  • These velocity ratios are known by the construction of the mechanism, and are independent of the absolute speed.
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  • Spherical aberration and changes of the sine ratios are often represented graphically as functions of the aperture, in the same way as the deviations of two astigmatic image surfaces of the image plane of the axis point are represented as functions of the angles of the field of view.
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  • Repeating this construction for all values of a between o° and 90°, we obtain a curve BPC, which can be used for determining the ratios of corresponding drums of cone pulleys or of conical drums for open belts.
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  • Also most fractions cannot be expressed exactly as decimals; and this is also the case for surds and logarithms, as well as for the numbers expressing certain ratios which arise out of geometrical relations.
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  • Divide SX internally at A and externally at A', so that the ratios SA/AX and SA'/A'X are each equal to the eccentricity.
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  • He needs to calculate the leverage ratios.
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  • Nitrogen and carbon isotope ratios in human bone collagen, for instance, tell us about diet.
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  • To get significantly higher compression ratios, a lossy compression method, such as JPEG, is required.
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  • The use of alloy brings thoughts of benefits from being able to run higher compression ratios.
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  • A future of controlled fertility and rapidly changing roles of women make projections of sex ratios highly conjectural.
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  • First old-age dependency ratios are misleading an aging society by definition has a much smaller proportion of children to support.
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  • Research projects typically involve interdisciplinary teams where we provide expertise in diatom analysis or the use of isotope ratios in diatom analysis or the use of isotope ratios in diatoms.
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  • In this article we use a simple framework to examine how these two ratios should behave in long-run equilibrium.
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  • The ratios greatly exceed findings around ' non-combustion ' urban sites.
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  • Compression ratios over 10.5:1 may create a detonation problem even with 93 octane premium gasoline.
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  • Prior to replacement I consider the possibility of changing the gear ratios: could you use a higher gear?
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  • A sports gearshift linkage for the Getrag 5-speed manual gearbox provides crisp, short throws between ratios.
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  • Hazard ratios were calculated using Cox proportional hazard ratios were calculated using Cox proportional hazards models that adjusted for potential confounders.
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  • Rechargeable electric cells offer a clue, but remain ludicrously inefficient in power to weight ratios when compared to the internal combustion engine.
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  • Observational studies have reported odds ratios for women with BV of between 1.4 and 6.9 for these adverse outcomes.
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  • Courses were heavily oversubscribed often with ratios of one to ten for each place.
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  • Confidence intervals are shown only on the graphs of standardized mortality ratios for deaths in the local areas.
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  • You should always consider what assistance you will need and adjust ratios as necessary, depending on your program and meeting place.
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  • Q: Aren't most of these things just gimmicks to mask the decline in staff-student ratios?
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  • Cost effectiveness will be assessed using incremental cost effectiveness ratios (ICERs) based on the additional costs incurred per additional informed choice offered.
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  • Continuous odds ratios for trend with proximity to sites were estimated.
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  • The study will focus on the use of stable isotope ratios to identify trophic positioning between species.
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  • The attached spreadsheet gives a list of the best ratios for the three room sizes tested.
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  • Beside the He-like triplets, Fe XXI line ratios are used to obtain plasma densities.
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  • They desired to assign simple whole numbers to everything -- and in particular they assigned ratios of numbers to musical intervals.
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  • If we compare Dalton's diagrams of the two oxides of carbon or of the three oxides of nitrogen that are given in the preceding table, we at once see the necessity of this law; for the more complex molecule has to be formed from the simpler one by the addition of one or more whole atoms. In the oxides of carbon the same weight of carbon must be combined with weights of oxygen that are as 2, and in the oxides of nitrogen a fixed weight of nitrogen must be in union with weights of oxygen that are as 1: 2: 2, which are the same ratios as 2: 4: r.
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  • The astonishing variety of ratios in which carbon and hydrogen combine was not at first realized.
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  • If a l, say, varies much throughout the year, or if the ratios of i c4, ...
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  • A point of high practical interest is the ratio of carcase weight to fasted live weight, and in the case of prizewinning carcases these ratios usually fluctuate within very narrow limits.
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  • The answer is that though the ratios between the prices of the various grades alter, the prices of all of them move generally together, and that the " futures " of the Exchange at least provide a hedge against the latter movements.
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  • The actual values of the topic parameters can then readily be expressed in terms of the elements of the crystals (the axial ratios and angles), the density, and the molecular weight (see Groth, Physikalische Krystallographie, or Chemical Crystallography).
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  • We can solve these, assuming them independent, for the - i ratios yl, y2,...yn-i� Now a21A11 +a22Al2 � � � = 0 a31A11+a32Al2 +� �� +a3nAln = 0 an1Al1+an2Al2 +���+annAln =0, and therefore, by comparison with the given equations, x i = pA11, where p is an arbitrary factor which remains constant as i varies.
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  • The validity of his fundamental position was impaired by the absence of a well-constituted theory of series; the notation employed was inconvenient, and was abandoned by its inventor in the second edition of his Mecanique; while his scruples as to the admission into analytical investigations of the idea of limits or vanishing ratios have long since been laid aside as idle.
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  • A ratio of 48 to is the minimum allowable; better 60 to 75 to 1, and for highly tempered steel ropes ratios of 150 to i or more are desirable.
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  • The osculating plane of a stream line in steady motion contains the resultant acceleration, the direction ratios of which are du du, du d i g d g 2 _ dH dx +v dy + dz - 2v?
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  • This inexactness may, however, be ignored, since the numbers or ratios in question can generally be obtained to a greater degree of accuracy than the other numbers involved in the calculation (see (ii) (b) below).
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  • In the first series of circles, reckoning from the centre the openings are so made as to divide the respective circumferences, on which they are found, in aliquot parts bearing to each other the ratios of the numbers 2, 4, 5, 6, 8, 10, 12, 16, 20,.
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  • These results are for the centre deflections of main girders, but Stone infers that the augmentation of stress for any member, due to causes included in impact allowance, will be the same percentage for the same ratios of live to dead load stresses.
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  • Repeating this construction for all values of a between o° and 90°, we obtain a curve BPC, which can be used for determining the ratios of corresponding drums of cone pulleys or of conical drums for open belts.
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  • (See Diffusion.) He further studied the passage of gases by transpiration through fine tubes, and by effusion through a minute hole in a platinum disk, and was enabled to show that gas may enter a vacuum in three different ways: (i) by the molecular movement of diffusion, in virtue of which a gas penetrates through the pores of a disk of compressed graphite; (2) by effusion through an orifice of sensible dimensions in a platinum disk the relative times of the effusion of gases in mass being similar to those of the molecular diffusion, although a gas is usually carried by the former kind of impulse with a velocity many thousand times as great as is demonstrable by the latter; and (3) by the peculiar rate of passage due to transpiration through fine tubes, in which the ratios appear to be in direct relation with no other known property of the same gases - thus hydrogen has exactly double the transpiration rate of nitrogen, the relation of those gases as to density being as 1 :14.
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  • However, it uses lower quartile house price figures rather than the mean prices used in the ratios analysis.
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  • Q: Are n't most of these things just gimmicks to mask the decline in staff-student ratios?
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  • There is a choice of four final-drive ratios for the Meritor rear axle, two for each gearbox.
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  • When a solution solidifies, alloys of metals which have a limited mutual solubility may form new phases at certain ratios.
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  • Solidity ratios from 0 to 1.0 are in general catered for.
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  • In the next section we will consider the longer term solvency ratios.
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  • Figure 2. Strontium isotope ratios (87 Sr / 86 Sr) in teeth from three different cows from Vaihingen.
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  • The smaller " fluffy " ones however, will often survive entry intact because of their large surface to mass ratios.
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  • The ratios of different taxa within the context classes are given in Figs.
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  • Adult to Child Ratios - Usually varies by age range of group, more adults are expected per child for the younger ages.
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  • Also keep in mind that your waist, hip and thigh ratios can effect the fit of boy shorts.
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  • This type of technology offers higher contrast ratios, which give you a larger range of colors.
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  • If the bag doesn't list the ratios, you can phone the company and get more details.
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  • Adjustments of the ingredient ratios to match personal preferences are encouraged.
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  • She experimented with different ratios of the four herbs until she came up with a mixture that worked best.
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  • In some school districts with high student-teacher ratios in classrooms, finding the opportunity to cheat is there, not only for one student but sometimes the entire class.
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  • Smaller student to teacher ratios indicate more personalized education time with teachers and greater potential for access to an educator.
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  • The college system offers over 200 degree and certificate programs, with small student-to-teacher ratios for increased learning opportunities.
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  • New quality control methods include testing every thirty minutes during the production process and random sampling of formula ratios.
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  • It is a good idea to mix a few drops of each of your chosen oils in different ratios to see which you like the best.
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  • Some people just want to dive right in and race without worrying about drag, suspension ratios, and what tires go with what racing surface.
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  • So much for the numbers and ratios, I'm beginning to sound like a tour guide or an automaton server; let's get serious.
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  • Staffing ratios and qualifications are established in federal guidelines and are checked by local boards or state department.
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  • Nadkarni. "Optimizing chest compression to rescue ventilation ratios during one-rescuer CPR by professionals and lay persons: children are not just little adults."
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  • There are also major population differences in skeletal proportions and bone sizes and ratios.
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  • The Greek Parthenon is a true example of endless Golden Rectangles that create many Golden Ratios.
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  • Debt to Income Ratios: In an effort to protect borrowers against purchasing a mortgage that is not affordable, new debt to income ratio guidelines have been established.
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  • There are two different ratios that are calculated.
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  • If you cook specialty rice each will come with specific cooking instructions, such as water and rice ratios, rinsing and cooking times.
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  • Making ice cream to your desired consistency and with the proper ratios of additives takes practice.
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  • If they don't have what you need, check with other published sources like Dun & Bradstreet's Industry Norms and Key Business Ratios.
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  • By consuming foods in their natural state, you eat the fiber, vitamins, minerals, proteins and fats in proper ratios.
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  • The question is: Do people lose weight because of the ratios of protein, carbs and fat, or perhaps because they are eating less and making healthier choices?
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  • A study cited in an article published in the American College of Nutrition claims there is no evidence that the ratios have any influence on reducing insulin response.
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  • While the exact ratios are different from one state to another, the ratio means the same thing.
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  • To understand these ratios, assume you hit a car that contained three people.
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  • A Klingon security officer and a blind engineer increased the crew's 'diversity ratios'.
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  • He maintained that, under varying conditions, two substances could combine in an indefinitely large number of different ratios, that there could in fact be a continuous variation in the combining ratio.
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  • Berzelius, who, fired with enthusiasm by the original theory of Dalton and the law of multiple proportions, determined the equivalents of combining ratios of many elements in an enormous number of compounds.2 He prosecuted his labours in this field for thirty years; as proof of his industry it may be mentioned that as early as 1818 he had determined the combining ratios of about two thousand simple and compound substances.
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  • We can solve these, assuming them independent, for the - i ratios yl, y2,...yn-i� Now a21A11 +a22Al2 � � � = 0 a31A11+a32Al2 +� �� +a3nAln = 0 an1Al1+an2Al2 +���+annAln =0, and therefore, by comparison with the given equations, x i = pA11, where p is an arbitrary factor which remains constant as i varies.
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  • Dividing by (0' - e"), and writing dp/do and dL/do for the limiting values of !the ratios (p' - p")/(o' - o") and (L' - L")/(o' - o"), we obtain the important relations s' - s"+dL/do= (v" - v')dp/do=L/o,..
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  • The ultimate term of bacterial activity seems to be the production of ulmic acid, containing carbon 65.31 and hydrogen 3.85%, which is a powerful antiseptic. By the progressive elimination of oxygen and hydrogen, partly as water and partly as carbon dioxide and marsh gas, the ratios of carbon to oxygen and hydrogen in the rendered product increase in the following manner: The resulting product is a brown pasty or gelatinous substance which binds the more resisting parts of the plants into a compact mass.
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  • The frequencies are nearly in the ratios 3 2 :5 2 :7 2 ....
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  • The name logarithm is derived from the words X6 7 wv hp426s, the number of the ratios, and the way of regarding a logarithm which justifies the name may be explained as follows.
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  • Stas, from the analysis of pure silver iodate, and by C. Marignac from the determinations of the ratios of silver to iodine, and of silver iodide to iodine; the mean value obtained for the atomic weight being 126.53.
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  • Henry Cavendish had before 1773 discovered that glass, wax, rosin and shellac have higher specific inductive capacities than air, and had actually determined the numerical ratios of these capacities, but this was unknown both to Faraday and to all other electricians of his time, since Cavendish's Electrical Researches remained unpublished till 1879.
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  • The volume contains also dissertations on Logarithms and on the Limits of Quantities and Ratios, and a few problems illustrative of the ancient geometrical analysis.
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  • In these solid solutions, as in aqueous ones, the ratios in which the different chemical substances are present are not fixed or definite, but vary from case to case, not per saltum as between definite chemical compounds, but by infinitesimal steps.
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  • The mean values of the relative coagulative powers of sulphates of mono-, di-, and tri-valent metals have been shown experimentally to be approximately in the ratios 1 :35:1023.
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  • In the scale of C the intervals from the key-note, the frequency ratios with the key-note, the successive frequency ratios and the successive intervals are as follows: - If we pass through two intervals in succession, as, for instance, if we ascend through a fourth from C to F and then through a third from F to A, the frequency ratio of A to C is a, which is the product of the ratios for a fourth 4, and a third I That is, if we add intervals we must multiply frequency ratios to obtain the frequency ratio for the interval which is the sum of the two.
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  • The frequency ratios in the diatonic scale are all expressible either as fractions, with i, 2, 3 or 5 as numerator and denominator, or as products of such fractions; and it may be shown that for a given note the numerator and denominator are smaller than any other numbers which would give us a note in the immediate neighbourhood.
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  • If we write down the eight notes from G to g in the key of C, their frequency ratios to C, the frequency ratios required by the diatonic scale for G, we get the frequency ratios required in the last line: - We see that all but two notes coincidewith notes on the scale of C. But instead of A = we have n, and instead of f= 4 we have 4 b.
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  • In the North there was little difference in 1900 in the ratios shown by city and country districts, but in the South the ratio in the latter was almost twice that reported for the former.
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  • Some corroboration of the simple law was apparently found by Johnstone Stoney, who first noted that the frequencies of three out of the four visible hydrogen lines are in the ratios 20: 27: 32.
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  • We can calculate, by the help of the kinetic theory and the theory of chances, the frequency with which the necessary conjunctions of ions will occur, and show that the general law will be that the coagulative powers should be in the ratios of 1: x: x 2.
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  • This Gives A Series Of Ratios 5/3, 7/5, 9/7, Ii/9, &C., For I, 2, 3, 4, &C., Atoms In The Molecule, Values Which Fall Within The Limits Of Experimental Error In Many Cases.
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  • In most questions of pure statics we are concerned only with the ratios of the various forces which enter into the problem, so that it is indifferent what unit of force is adopted.
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  • Again, the expression (22) will also have a least value when the ratios x: y: 1 are subject to the conditton av ~v av x1~+y1~----+z1~- ~O; (24)
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  • "It appears like the mystical ratios of Kepler which Newton so happily elucidated."
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  • The totals of passengers killed and injured in train accidents are not separated from those killed and injured from other causes, but ratios are given showing that for four years no passengers were killed in this class.
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  • Lines representing efficiency ratios of o 6, 0.5 and 0.4 are plotted on the diagram, so that the efficiency ratios corresponding to the various experiments plotted may be readily read off.
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  • The treatment of an angle as generated by rotation, the investigation of the relations between trigonometrical ratios and circular measure, the application of interpolation to trigonometrical tables, and the general use of graphical methods to represent continuous variation, all imply an analytical onlook, and must therefore be deferred to this stage.
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  • (a) The formula may involve numbers or ratios which cannot be expressed exactly in the ordinary notation.
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  • If the data for any of these figures are other than those given above, trigonometrical ratios will usually be involved.
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  • The calculation of this last expression is simplified by noticing that we are only concerned with the mutual ratios of Xo, X 1, ...
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  • Here it is sufficient to say that the frequencies of a note, its major third, its fifth and its octave, are in the ratios of 4: 5: 6: 8.
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  • Comparing the velocities of sound U i and U2 in two different gases with densities and at the same temperature and pressure, and with ratios of specific heats 'yl, 72, theory gives Ui/U2 = 1/ {71 p 2/72 p i }.
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  • If, for the single toothed wheel, be substituted a set of four with a common axis, in which the teeth are in the ratios 4: 5: 6: 8, and if the card be rapidly passed along their edges, we shall hear distinctly produced the fundamental chord C, E, G, C 1 and shall thus satisfy ourselves that the intervals C, E; C, G and C, C 1 are, 2 and 2 respectively.
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  • Thus may be obtained, either separately or in various combinations, the four notes whose vibrations are in the ratios of the above numbers, and which therefore form the fundamental chord (Cegc 1).
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  • The frequencies are nearly in the ratios 1: 6.25:17.5.
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  • From ratios stated before Greek times (35) the series of multiples was --
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  • I „ Logarithms of the ratios of arcs to sines from 04 00000 to 0 4.05000, and log sines throughout the quadrant 4 „ Logarithms of the ratios of arcs to tangents from 0 4 00000 to 0 4.05000, and log tangents throughout the quadrant 4 The trigonometrical results are given for every hundred-thousandth of the quadrant (to" centesimal or 3" 24 sexagesimal).
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  • Logistic or Proportional Logarithms. - The old name for what are now called ratios or fractions are logistic numbers, so that a table of log (a/x) where x is the argument and a a constant is called a table of logistic or proportional logarithms; and since log (a/x) =log a-log x it is clear that the tabular results differ from those given in an ordinary table of logarithms only by the subtraction of a constant and a change of sign.
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  • In crystallography, the regular or ordinary dodecahedron is an impossible form since the faces cut the axes in irrational ratios; the "pentagonal dodecahedron" of crystallographers has irregular pentagons for faces, while the geometrical solid, on the other hand, has regular ones.
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  • Hence P is equivalent to three forces P1, Pm, Pu acting Ff0- 5 along Ox, Oy, Oz, respectively, ~ where 1, m, n, are the direction- ratios of OH.
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  • In other spectra such " harmonic " ratios were also discovered, but their search was abandoned when it was found that their number did not exceed that calculated by the laws of probability on the supposition of a chance distribution.
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  • He was undoubtedly a clear-sighted and able mathematician, who handled admirably the severe geometrical method, and who in his Method of Tangents approximated to the course of reasoning by which Newton was afterwards led to the doctrine of ultimate ratios; but his substantial contributions to the science are of no great importance, and his lectures upon elementary principles do not throw much light on the difficulties surrounding the border-land between mathematics and philosophy.
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  • Suppose that the ratio of 10, or any other particular number, to i is compounded of a very great number of equal ratios, as, for example, 1,000,000, then it can be shown that the ratio of 2 to i is very nearly equal to a ratio compounded of 301,030 of these small ratios, or ratiunculae, that the ratio of 3 to I is very nearly equal to a ratio compounded of 477,121 of them, and so on.
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  • The ratios of the coagulative powers can thus be calculated to be i: x: x 2, and putting x =32 we get I: 32: 1024, a satisfactory agreement with the numbers observed.4 The question of the application of the dissociation theory to the case of fused salts remains.
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