# Ratios Sentence Examples

- In the former year the
**ratios**were 40.2 and 41.5, in the latter 41-6 and 427%. - 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. - 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. - Equal changes in temperature and pressure occasion equal changes in equal volumes of all gases and vapours - Avogadro deduced the law: Under the same conditions of temperature and pressure, equal volumes of gases contain equal numbers of molecules; and he showed that the relative weights of the molecules are determined as the
**ratios**of the weights of equal volumes, or densities. - 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. - 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. - Molecular weight, is constant for isomers, and that two atoms of hydrogen were equal to one of carbon, three to one of oxygen, and seven to one of chlorine; but these
**ratios**were by no means constant, and afforded practically no criteria as to the molecular weight of any substance. - 2 7, p. 45 2), assuming that two liquids may be compared when the
**ratios**of the volumes of the liquids to the volumes of the saturated vapours are the same, deduced that yV 3 (where y is the surface tension, and V the molecular volume of the liquid) causes all liquids to have the same temperature coefficients. - 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. - 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. - 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. - 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. - 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. - 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. - We can solve these, assuming them independent, for the - i
**ratios**yl, y2,...yn-iï¿½ Now a21A11 +a22Al2 ï¿½ ï¿½ ï¿½ = 0 a31A11+a32Al2 +ï¿½ ï¿½ï¿½ +a3nAln = 0 an1Al1+an2Al2 +ï¿½ï¿½ï¿½+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. - Be immediately derived, because the
**ratios**of distances in the solar system are known with the last degree of of precision. - 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,.. - 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. - 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. - 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. - 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. - The frequencies are nearly in the
**ratios**3 2 :5 2 :7 2 .... - The frequencies are nearly in the
**ratios**1: 6.25:17.5. - From
**ratios**stated before Greek times (35) the series of multiples was -- - 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). - 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. - 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. - 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. **Ratios**of 1900 and 2000, and reinforce the suggestions of various other facts that the social, as well as the economic, conditions in colonial times were practically constant.- 2-}-cos B It is readily shown that the latter gives the best approximation to 0; but, while the former requires for its application a knowledge of the trigonometrical
**ratios**of only one angle (in other words, the**ratios**of the sides of only one right-angled triangle), the latter requires the same for two angles, 0 and 3B. - Of less interest nowadays are Robins's more purely mathematical writings, such as his Discourse concerning the Nature and Certainty of Sir Isaac Newton's Methods of Fluxions and of Prime and Ultimate
**Ratios**(1735), "A Demonstration of the Eleventh Proposition of Sir Isaac Newton's Treatise of Quadratures" (Phil. - 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. - 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. - 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. - 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. - "It appears like the mystical
**ratios**of Kepler which Newton so happily elucidated." - 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. - 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. - The "Essay on Quantity, occasioned by reading a Treatise in which Simple and Compound
**Ratios**are applied to Virtue and Merit," denies the possibility of a mathematical treatment of moral subjects. - Chem-., 1905, 47, p. 1 45), who, by estimating the
**ratios**of strontium bromide and chloride to silver, obtained the values 87.663 and 87.661. - 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. - (a) The formula may involve numbers or
**ratios**which cannot be expressed exactly in the ordinary notation. - If the data for any of these figures are other than those given above, trigonometrical
**ratios**will usually be involved. - The calculation of this last expression is simplified by noticing that we are only concerned with the mutual
**ratios**of Xo, X 1, ... - 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. - 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 }. - 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. - 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). - 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. - 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. - 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. - 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. - 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.