Values sentence example

values
  • The government must reflect the different values these groups have.
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  • You have to stay true to your values while destroying something as well.
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  • You love your country's ideals, goals, values, and aspirations.
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  • They can standardize in a thousand more ways to a world economy, while maintaining their values, traditions, and distinctions.
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  • You behaved as becomes a man who values his honor, perhaps too hastily, but we won't go into that.
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  • The largest positive and negative values recorded are met with during disturbed weather.
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  • To endow the universal substance with moral attributes, to maintain that it is more than the metaphysical ground of everything, to say it is the perfect realization of the holy, the beautiful and the good, can only have a meaning for him who feels within himself what real not imaginary values are clothed in those expressions.
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  • These will suffice to give a general idea of the mean values met with.
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  • There is no doubt that under average conditions of atmospheric density, the .005 should be replaced by 003, for many independent authorities using different methods have found values very close to this last figure.
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  • His greatest and least mean hourly values and the hours of their occurrence are as follows: Gockel did not observe between 10 P.M.
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  • The former moves in a world of "values," and judges things as they are related to our "fundamental self-feeling."
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  • Then by solving these equations, regarding the six elements as unknown quantities, the values of the latter may be computed.
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  • 1 Approximate values of the atomic weights are employed here.
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  • My purpose in this chapter will not be to persuade the reader of any political doctrine of trade; please apply your own political and social values as you see fit.
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  • These values are: Trimethylene.
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  • Nitrogen forms approximately 79% by volume (or 77% by weight) of the atmosphere; actual values are:% by volume-79.07 (Regnault), 79.20 (Dumas);% by weight76.87 (Regnault), 77.00 (Dumas), 77.002 (Lewy), 76.900 (Stas), 77.010 (Marignac).
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  • The French alphabet, written out with the same numerical values as the Hebrew, in which the first nine letters denote units and the others tens, will have the following significance:
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  • 2 But this appeal to " values " is only half of Lotze's constructive work.
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  • With what is specifically Christian we have nothing to do in the present article: but it is worth noticing that the appeal to " values, " aesthetic and still more moral, forms a substitute for that natural theology which Ritschl despised and professed to reject.
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  • When Otto Ritschl interprets values hedonistically - recoiling from Hegel's idealism the whole way to empiricism - he brings again to our minds the doubt whether hedonist ethics can serve as a foundation for any religious belief.
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  • But is the basis for religious belief to be constructed purely within the region of " values " ?
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  • Many varying values have been given for the atomic weight of molybdenum.
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  • This curve with the values reduced from metres to feet is reproduced below.
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  • Motors may be applied to every axle in the train, and their individual torques adjusted to values suitable to the weights naturally carried by the several axles.
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  • 17, four values of L being taken for formula (12) corresponding to trains of 5, 10, 15 and 20 bogie carriages.
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  • 17 gives values which must be regarded as only very approximate.
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  • - The combined engine and boiler efficiency has hitherto been taken to be o 06; actual values of the boiler efficiencies are given in Table XX.
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  • If h is the water heat at the lower temperature, h l the water heat at the higher temperature, and L the latent heat at the higher temperature, the heat supply per pound of steam is equal to h1 - h2+L1, which, from the steam tables, with the values of the temperatures given, is equal to 1013 B.Th.U.
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  • In a particular case where the boiler pressure was maintained constant at 130 lb per square inch, and the cut-off was approximately 20% of the stroke, the values c =55 and b=o 031 were deduced, from which it will be found that the value of the piston speed corresponding to the maximum horsepower is 887 ft.
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  • The Tonopah ores were richer in silver than in gold, the respective values in 1904 and 1905 being approximately in the proportion of three to one.
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  • This was followed by a reaction and a general collapse of inflated values until 1873, when the discovery of the Great Bonanza mine brought about a revival of industry and of speculation.
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  • In fact, the means of the best determinations of each of these quantities separately agree with one another more closely than do the various values of either.
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  • But since the elements cannot be converted one into the other, we are absolutely without knowledge of the relative values of their intrinsic energy.
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  • Personally he was not enthusiastic over the African enterprise, as it introduced new and, to him, unaccustomed and unwelcome values into Italian political life; but he realized that public opinion demanded it and he did not care to run counter to the current.
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  • St Petersburg, again, is connected with Greenwich by European systems of triangulation; and the Greenwich meridian is adopted by Russia as the zero for all her longitude values.
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  • But while we have yet to wait for that expansion of principal triangulation which will bring Asia into connexion with Europe by the direct process of earth measurement, a topobetween graphical connexion has been effected between Russian Russ/an and Indian surveys which sufficiently proves that the and deductive methods employed by both countries for the Indian determination of the co-ordinate values of fixed points so surveys.
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  • Other values are as follows: Prjevalsky, by his second and third explorations 94° 26' Krishna .
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  • He was one of the first to use oil-cake and bone-manure, to distinguish the feeding values of grasses, to appreciate to the full the beneficial effects of stock on light lands and to realize the value of long leases as an incentive to good farming.
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  • The general experience of the decade of the 'eighties was that of disappointing summers, harsh winters, falling prices, declining rents and the shrinkage of land values.
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  • The mean values at the foot of the table-they are not, strictly speaking, exact averages-indicate the average yields per acre in the United Kingdom to be about 31 bushels of wheat, 33 bushels of barley, 40 bushels of oats, 28 bushels of beans, 26 bushels of peas, 44 tons of potatoes, 134 tons of turnips and swedes, 184 tons of mangels, 32 cwt.
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  • This, indeed, is the practice in Ireland, and in order to incorporate the Irish figures with those for Great Britain so as to obtain average values for the United Kingdom, the Irish yields are calculated into bushels at the rate of 60 lb to the bushel of wheat, of beans and of peas, 50 lb to the bushel of barley and 39 lb to the bushel of oats.
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  • - Average Values of Fresh Meat, Bacon and Hams imported into the United Kingdom, 1891-1905 - per Cwt.
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  • But of course it was far less important than various other articles of trade in the aggregate values of commerce.
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  • It is well known that singly, doubly and trebly linked carbon atoms affect the physical properties of substances, such as the refractive index, specific volume, and the heat of combustion; and by determining these constants for many substances, fairly definite values can be assigned to these groupings.
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  • He applied himself more particularly to the oxygen compounds, and determined with a fair degree of accuracy the ratio of carbon to oxygen in carbon dioxide, but his values for the ratio of hydrogen to oxygen in water, and of phosphorus to oxygen in phosphoric acid, are only approximate; he introduced no new methods either for the estimation or separation of the metals.
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  • The most direct manner in which to test any property for additive relations is to determine the property for a number of elements, and then investigate whether these values hold for the elements in combination.
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  • These values, however, require modification in certain cases, for discrepancies occur which can be reconciled in some cases by assuming that the atomic value of a polyvalent element varies according to the distribution of its valencies.
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  • If, however, an amount of energy a is taken up in separating atoms, the ratio is expressible as C p /C„= (5+a)/(3-Fa), which is obviously smaller than 5/3, and decreases with increasing values of a.
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  • It therefore appears that the difference between the heats of combustion of two adjacent members of a series of homologous compounds is practically a constant, and that this constant has two average values, viz.
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  • Thomsen deduces the actual values of X, Y, Z to be 14.71, 13.27 and zero; the last value he considers to be in agreement with the labile equilibrium of acetylenic compounds.
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  • The thermal effects increase as one passes from primary to tertiary alcohols, the values deduced from propyl and isopropyl alcohols and trimethyl carbinol being: - primary =45 08, secondary = 50.39, tertiary = 60.98.
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  • The values are for the Ha line: The empirical formula (n2-I)/(n2-1-o 4)d apparently gives more constant values with change of temperature than the LorenzLorentz form.
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  • This is shown in the following table (the values are for Ha) Additive relations undoubtedly exist, but many discrepancies occur which may be assigned, as in the case of molecular volumes, to differences in constitution.
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  • Normal values of K were given by nitrogen peroxide, N204, sulphur chloride, S 2 C1 21 silicon tetrachloride, SiC1 4, phosphorus chloride, PC1 3, phosphoryl chloride, POC1 31 nickel carbonyl, Ni(CO) 4, carbon disulphide, benzene, pyridine, ether, methyl propyl ketone; association characterized many hydroxylic compounds: for ethyl alcohol the factor of association was 2.74-2.43, for n-propyl alcohol 2.86-2.72, acetic acid 3.62 -2.77, acetone 1 .
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  • To reduce these figures to a common standard, so that the volumes shall contain equal numbers of molecules, the notion of molecular volumes is introduced, the arbitrary values of the crystallographic axes (a, b, c) being replaced by the topic parameters' (x, ?i, w), which are such that, combined with the axial angles, they enclose volumes which contain equal numbers of molecules.
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  • The equivalent volumes and topic parameters are tabulated: From these figures it is obvious that the first three compounds form a morphotropic series; the equivalent volumes exhibit a regular progression; the values of x and t,t, corresponding to the a axes, are regularly increased, while the value of w, corresponding to the c axis, remains practically unchanged.
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  • Two cases then arise: (I) the properties may be expressed as linear functions of the composition, the terminal values being identical with those obtained for the individual components, and there being a break in the curve corresponding to the absence of mixed crystals; or (2) similar to (I) except that different values must be assigned to the terminal values in order to preserve collinearity.
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  • This arouses his spirit of contradiction; and he tells them that they might have won it from him by coaxing, but never by threats, and that he values his life no more than the stone he tosses away as he speaks to them.
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  • The values recognized in the great Hellenistic courts and the Greek world generally imposed their authority upon the dynasties of barbarian origin.
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  • The values obtained are shown below.
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  • Numerous determinations of the atomic weight of nitrogen have been made by different observers, the values obtained varying somewhat according to the methods used.
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  • The first class contains such revenues as the emlak verghi-si (duty on realty), `ashar (tithes), temettu (professional tax), &c. In all such cases the taxable values are fixed by a commission of experts, sometimes chosen by the tax-payers themselves, sometimes by the official authorities; in all cases both tax-payers and authorities are represented on the commissions, whose decisions may be appealed against, in last resort, to the council of state at Constantinople, whose decision is final.
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  • The economic effect of the railways upon the districts through which they run is apparent from the comparative values of the tithes in the regions traversed by the Anatolian railway in 1889 and 1898 in which years it so happened that prices were almost at exactly the same level, and again in 1908-1909, when they were only slightly higher.
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  • The heavy depreciation in silver causing large losses to the government, free coinage was suspended in 1880, and the nominal value of the mejidie was reduced by decree to 19 piastres (105.26 piastres thus = £T1), while in the same year the debased currencies were reduced, altilik, the 6-piastre piece to 5 piastres, the 3-piastre piece to 22 piastres, the 12-piastre piece to 14 piastre; beshlik, the 5-piastre piece to 22 piastres, the 22-piastre piece to 1;-piastre; metallik, the 1-piastre piece to 2 piastre, the 2-piastre piece to 4 piastre, the *-piastre piece to a piastre - these values representing approximately the intrinsic value of the silver, at mejidie standard, contained in the debased coins.
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  • In the Flos equations with negative values of the unknown quantity are also to be met with, and Leonardo perfectly understands the meaning of these negative solutions.
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  • The numerical values are, it is to be noted, exceedingly small.
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  • The plankton, both animal and vegetable, attains its minimal values and many of the larger forms of animal life pass into a kind of condition of hibernation.
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  • But when we pass to solutions of mineral salts and acids - to solutions of electrolytes in fact - we find that the observed values of the osmotic pressures and of the allied phenomena are greater than the normal values.
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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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  • Thus in the case of cyanacetic acid, while the volume V changed by doubling from 16 to 1024 litres, the values of k were 0.00 (37 6, 373, 374, 361, 362, 361, 368).
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  • The mean values of k for other common acids were - formic, 0.0000214; acetic, o 0000180; monochloracetic, 0.0.0155; dichloracetic, 0.051; trichloracetic, 1.21; propionic, 0.0000134.
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  • Other " Galois " groups were defined whose substitution coefficients have fixed numerical values, and are particularly associated with the theory of equations.
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  • For since A 11 A 22 -Ar 2 =,,a 33, with similar relations, we have a number of relations similar to A 11 A 22 =AM 2, and either Ars = +11 (A rr A ss) or - (A r .A ss) for all different values of r and s.
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  • =x� = o is the only solution; but if A vanishes the equations can be satisfied by a system of values other than zeros.
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  • We can prove that if the three equations be satisfied by a system of values of the variable, the same system will also satisfy the Jacobian or functional determinant.
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  • = 0, we find that, eliminating x, the resultant is a homogeneous function of y and z of degree mn; equating this to zero and solving for the ratio of y to z we obtain mn solutions; if values of y and z, given by any solution, be substituted in each of the two equations, they will possess a common factor which gives a value of x which, corn bined with the chosen values of y and z, yields a system of values which satisfies both equations.
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  • Hence in all there are mn such systems. If, therefore, we have a third equation, and we substitute each system of values in it successively and form the product of the mn expressions thus formed, we obtain a function which vanishes if any one system of values, common to the first two equations, also satisfies the third.
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  • Now by the theory of symmetric functions, any symmetric functions of the mn values which satisfy the two equations, can be expressed in terms of the coefficient of those equations.
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  • If m > n there are n +1 transvectants corresponding to the values o, t, 2,...
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  • In consequence of it, the values formerly found were systematically too small by an amount which even now it is difficult to estimate with precision.
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  • This last value agrees very closely with a determination made by Gill at the Cape of Good Hope, and most other recent determinations give values exceeding 20.50".
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  • The following may be taken as the most probable values of the solar parallax, as derived independently by the five methods we have described: From measures of parallax.
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  • Forces acting on a Small Body in the Magnetic Field.-If a small magnet of length ds and pole-strength m is brought into a magnetic field such that the values of the magnetic potential at the negative and positive poles respectively are V 1 and the work done upon the magnet, and therefore its potential energy, will be W =m(V2-Vi) =mdV, which may be written W =m d s- = M d v= - MHo = - vIHo, ds ds where M is the moment of the magnet, v the volume, I the magnetization, and Ho the magnetic force along ds.
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  • When a hysteresis curve is to be obtained, the procedure is as follows: The current is first adjusted by means of R to such a strength as will fit it to produce the greatest + and - values of the magnetizing force which it is intended to apply in the course of the cycle; then it is reversed several times, and when the range of the galvanometer throws has become constant, half the extent of an excursion indicates the induction corresponding to the extreme value of H, and gives the point a in the curve fig.
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  • In a similar manner, by giving different values to the resistance 4 F R, any desired number of points R= between a and c in the curve can FIG.
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  • Steinmetz's formula may be tested by taking a series of hysteresis curves between different limits of B,' measuring their areas by a pianimeter, and plotting the logarithms of these divided by 47r as ordinates against logarithms of the corresponding maximum values of B as abscissae.
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  • If H l and H2 be the values of 47rinll and 47ri' - 'Z/ l for the 2 2 same induction B, it can be shown that the true magnetizing force is H = H l - (H 2 - H 1).
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  • The values assigned to H were calculated from H= 2ni/r, and ranged from 3.9 to 585, but inasmuch as no account was taken of any 2 Since in most practicable experiments H 2 is negligible in comparison with B 2, the force may be taken as B 2 /87r without sensible= error.
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  • He showed that there was, on the whole, a fair agreement between the values determined ballistic ally and those given by the formula B = 871-F.
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  • Thus any desired number of corresponding values of H and B can be easily and quickly found.
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  • Values of I are derived from (B -H)/477and of from B/H.
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  • The annexed table gives the saturation values of I for the particular metals examined by Ewing and Low: Wrought iron .
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  • For fields of moderate intensity the first term of the expression is the more important, but when the value of H exceeds 12,000 or thereabouts, the second preponderates, and with the highest values that have been actually obtained, HI is several times greater than 21rI 2.
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  • Ann., 18 95, 54,655), who found the limiting values of to be 7.5 to 9.5 for iron, and 11.2 to 13.5 for steel, remaining constant up to H = 06; by P. Culmann (Elekt.
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  • The latter gives values of the constants a and b for different samples of iron and steel, some of which are shown in the following table :- K=a+bH For most samples of steel the straight-line law was found to hold approximately up to H=3; in the case of iron and of soft steel the approximation was less close.
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  • Further, if the alternations take place so slowly that the full maximum and minimum values of the magnetization are reached in the intervals between the reversals, there will again be no dissipation of energy.
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  • Honda subjected tubes of iron, steel and nickel to the simultaneous action of circular and longitudinal fields, and observed the changes of length when one of the fields was varied while the other remained constant at different successive values from zero upwards.
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  • The following table shows the values of I and H corresponding to the Villari critical point in some of Ewing's experiments: The effects of pulling stress may be observed either when the wire is stretched by a constant load while the magnetizing force is varied, or when the magnetizing force is kept constant while the load is varied.
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  • Bidwell 2 accordingly found upon trial that the Wiedemann twist of an iron wire vanished when the magnetizing force reached a certain high value, and was reversed when that value was exceeded; he also found that the vanishing point was reached with lower values of the magnetizing force when the wire was stretched by a weight.
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  • The values of the permeability corresponding to the highest and lowest temperatures are given in the following table.
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  • 8 The hysteresis of the soft annealed iron turned out to be sensibly the same for equal values of the induction at - 186° as at 15°, the loss in ergs per c. cm.
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  • These high values render hardened tungsten-steel particularly suitable for the manufacture of permanent magnets.
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  • The first column contains the symbols of the various elements which were added to the iron, and the second the percentage proportion in which each element was present; the sample containing 0.03% of carbon was a specimen of the best commercial iron, the values obtained for it being given for comparison.
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  • For H =11,500 the temperature of minimum resistance was about 50°; for much lower or higher values of H the actual minimum did not occur within the range of temperature dealt with.
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  • 29 shows the variations of resistance in relation to temperature for fields of different constant values.
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  • Annexed are values of Io 6 K for the different salts examined, w being the weight of the salt per c.c. of the solution.
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  • The values assigned to the atomic susceptibilities of most of the known elements are appended.
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  • His determination 2 of maximum and minimum values for the slowly varying planetary eccentricities was the earliest attempt to deal with the problem.
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  • According to a summary for the six years 1901 to 1906, derived from official sources and published in the annual Retrospecto of the Jornal do Commercio, of Rio de Janeiro, the values of the imports and exports for those years (exclusive of coin), reduced to pounds sterling at the average rate of exchange (or value of one milreis) for each year, were as follows: - Nearly 761% of the exports of 1906 were of coffee and rubber, the official valuations of these being: coffee 2 45,474,5 2 5 milreis gold (27,615,884), and rubber (including manigoba and mangabeira), 12 4,941,433 milreis gold (£14,055,911).
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  • To illustrate the comparative productiveness and relationship of these sources of national wealth and industry, the following official returns of export for the years 1905 and 1906 are arranged in the four general classes previously discussed, the values being in Brazilian gold milreis, worth 2s.
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  • In this period the increase in the sterling equivalents would be proportionately greater than that of the currency values.
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  • 1 Merchandise passing the boundaries is subject to declaration; the respective values are stated by a special commission of experts residing in Budapest.
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  • Laplace published in 1779 the method of generating functions, the foundation of his theory of probabilities, and the first part of his Theorie analytique is devoted to the exposition of its principles, which in their simplest form consist in treating the successive values of any function as the coefficients in the expansion of another function with reference to a different variable.
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  • Bodin showed a more rational appreciation than many of his contemporaries of the causes of this revolution, and the relation of the variations in money to the market values of wares in general as well as to the wages of labour.
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  • - The calculation of the values of simple algebraical expressions for particular values of letters involved is a useful exercise, but its tediousness is apt to make the subject repulsive.
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  • It is important to begin the study of graphics with concrete cases rather than with tracing values of an algebraic function.
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  • In particular, the equality or inequality of values of two functions is more readily grasped by comparison of the lengths of the ordinates of the graphs than by inspection of the relative positions of their bounding lines.
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  • In the first class come equations in a single unknown; here the function which is equated to zero is the Y whose values for different values of X are traced, and the solution of the equation is the determination of the points where the ordinates of the graph are zero.
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  • It must, of course, be remembered (� 23) that this is a statement of arithmetical equality; we call the statement an " identity," but we do not mean that the expressions are the same, but that, whatever the numerical values of a, b and c may be, the expressions give the same numerical result.
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  • (vii.) In order to make the formula (5) hold for the extreme values n (o) and n (n) we must adopt the convention that o !
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  • (ix.) The position of the greatest term will depend on the relative values of A and a; if a/A is small, it will be near the beginning.
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  • The values of the first ten of Bernoulli's numbers are B1= t, B2= 1, B3 =412, B4 =30, B5 =6 = 6 9 1 B7 = l, B =3 =4 4 fl, IV.
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  • (vi.) It follows that, if two multinomials of the nth degree in x have equal values for more than n values of x, the corresponding coefficients are equal, so that the multinomials are equal for all values of x.
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  • (v.) The further extension to fractional values (positive or negative) of n depends in the first instance on the establishment of a method of algebraical evolution which bears the same relation to arithmetical evolution (calculation of a surd) that algebraical division bears to arithmetical division.
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  • Certain relations still hold, the most important being (22) of � 44 (ii.), which holds whatever the values of m and of n may be; r, of course, being a positive integer.
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  • (ix.) The extension of n (r), and therefore of n [r ], to negative and fractional values of n, enables us to extend the applicability of the binomial coefficients to the summation of series (� 46 (ii.)).
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  • Thus we arrive at the differential coefficient of f(x) as the limit of the ratio of f (x+8) - f (x) to 0 when 0 is made indefinitely small; and this gives an interpretation of nx n-1 as the derived function of xn (� 45)� This conception of a limit enables us to deal with algebraical expressions which assume such forms as -° o for particular values of the variable (� 39 (iii.)).
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  • We cannot, for instance, say that the fraction C _2 I is arithmetically equal to x+I when x= I, as well as for other values of x; but we can say that the limit of the ratio of x 2 - I to x - I when x becomes indefinitely nearly equal to I is the same as the limit of x+ On the other hand, if f(y) has a definite and finite value for y = x, it must not be supposed that this is necessarily the same as the limit which f (y) approaches when y approaches the value x, though this is the case with the functions with which we are usually concerned.
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  • Thus there appear to be discontinuities in the values of y.
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  • It could not escape notice that one and the same symbol, such as -1 (a - b), or even (a - b), sometimes did and sometimes did not admit of arithmetical interpretation, according to the values attributed to the letters involved.
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  • The values of x and y are different, unless V (qq o) = o.
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  • These values are assumed to be independent, so we have 2n(n - I) derived units of the second species or order.
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  • Even in this case the series converges sufficiently to give the value of the root with considerable accuracy, while for higher values of m it is all that could be desired.
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  • Since the maxima occur when u = (m +1)7r it nearly, the successive values are not very different from 4 4 4 &c The application of these results to (3) shows that the field is brightest at the centre =o, =0, viz.
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  • From the general formula (2), if A be the area of aperture, 102 = A2 / x2 f (7) The formation of a sharp image of the radiant point requires that the illumination become insignificant when, n attain small values, and this insignificance can only arise as a consequence of discrepancies of phase among the secondary waves from various parts of the aperture.
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  • The part corresponding to negative values of u is similar, OA being a line of symmetry.
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  • The following table gives the actual values: - In both cases the image of a mathematical point is thus a symmetrical ring system.
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  • When z has one of the values thus determined, (z)=Jo(z).
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  • The accompanying table is given by Lommel, in which the first column gives the roots of J2(z) =o, and the second and third columns the corresponding values of the functions specified.
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  • If we put for shortness 7 for the quantity under the last circular function in (I), the expressions (i), (2) may be put under the forms u sin T, v sin (T - a) respectively; and, if I be the intensity, I will be measured by the sum of the squares of the coefficients of sin T and cos T in the expression u sin T +v sin (T - a), so that I =u 2 +v 2 +2uv cos a, which becomes on putting for u, v, and a their values, and putting f =Q .
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  • By separation of real and imaginary parts, C =M cos 27rv 2 +N sin 27rv2 1 S =M sin 27rv 2 - N cos 27rv2 where 35+357.9 N _ 7rv 3 7r 3 v 7 + 1.3 1.3.5.7 1.3.5.7.9.11 These series are convergent for all values of v, but are practically useful only when v is small .
    0
    0
  • Taking the refractive index of water for the red rays as 0;, and for the violet rays as 1 r, we can calculate the following values for the minimum deviations corresponding to certain assigned values of n.
    0
    0
  • It may be readily deduced that the directions of minimum deviation for a pencil of parallel rays lie on the surface of cones, the semi-vertical angles of which are equal to the values given in the above table.
    0
    0
  • Primary, secondary and spurious bows were formed, and their radii measured; a comparison of these observations exhibited agreement with Airy's analytical values.
    0
    0
  • The total foreign trade in 1908 amounted to $9,778,810 imports and $14,560,830 exports, the values being in U.S. gold.
    0
    0
  • In the absence of statistical returns it is impossible to give the values of this branch of trade.
    0
    0
  • 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.
    0
    0
  • All metals are elastic to this extent that a change of form, brought about by stresses not exceeding certain limit values, will disappear on the stress being removed.
    0
    0
  • These values may vary within certain limits for different specimens.
    0
    0
  • (7) Interchanging these values =m log r, 4, = mO, 4,+4,i =m log rei e (8) gives a state of vortex motion, circulating round Oz, called a straight or columnar vortex.
    0
    0
  • Negative values of n must be interpreted by a streaming motion on a parallel plane at a level slightly different, as on a double Riemann sheet, the stream passing from one sheet to the other across a cut SS' joining the foci S, S'.
    0
    0
  • In the case of texts from the oldest historical periods we encounter hundreds of names that are genuinely Sumerian, and here in view of the multiplicity of the phonetic values attaching to the signs used it is frequently difficult definitely to determine the reading of the names.
    0
    0
  • Sayce's phonetic values and interpretations of determinatives are his best assured achievements.
    0
    0
  • The coinage began before the Roman conquest was completed; the monetary system resembles that of the Roman republic, with values analogous to denarii and quinarii.
    0
    0
  • The values of the coinage are pieces of 5 and 10 centimes in bronze, of 50 centimes, 1 franc and 2 francs in silver, of 10 francs and 20 francs in gold.
    0
    0
  • In some foreign words like cicala the ch- (tsh) value is given to c. In the transliteration of foreign languages also it receives different values, having that of tsh in the transliteration of Sanskrit and of is in various Slavonic dialects.
    0
    0
  • So perfectly does the modern Japanese embroiderer elaborate his scheme of values that all the essential elements of pictorial effects chiaroscuro, aerial perspective and atmosphere are present in his work.
    0
    0
  • In its modern form the theorem, which is true for all values of n, is written as (x +a) n -1+ I.
    0
    0
  • Newton gave no proof, and it was in the Ars Conjectandi (1713) that James Bernoulli's proof for positive integral values of the exponent was first published, although Bernoulli must have discovered it many years previously.
    0
    0
  • A rigorous demonstration was wanting for many years, Leonhard Euler's proof for negative and fractional values being faulty, and was finally given by Niels Heinrik Abel.
    0
    0
  • There are very considerable differences between the values assigned by different observers, sometimes no doubt due to differences in method, but in most cases unquestionably depending on variations in the quality of the specimens examined.
    0
    0
  • 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,..
    0
    0
  • (9) These must be expressed as functions of v and 0, which is theoretically possible if the values of s, p, and dp/do are known.
    0
    0
  • To find the total heat of a substance in any given state defined by the values of p and 0, starting from any convenient zero of temperature, it is sufficient to measure the total heat required to raise the substance to the final temperature under a constant pressure equal to p. For instance, in the boiler of a steam engine the feed water is pumped into the boiler against the final pressure of the steam, and is heated under this constant pressure up to the temperature of the steam.
    0
    0
  • The values of the partial differential coefficients in terms of n and c are as follows: - Substituting these values in equations already given, we find, from (6) S - s =R(I +nc/V)2 (24) „ (9) dE/dv (o const) =ncp/V .
    0
    0
  • We may therefore reasonably assume that the limiting values of the specific heats at zero pressure do not vary with the temperature, provided that the molecule is stable and there is no dissociation.
    0
    0
  • Denoting by So, so, these constant limiting values at p=o, we may obtain the values at any pressure by integrating the expressions (27) and (28) from co to v and from o to p respectively.
    0
    0
  • The expression for the change of intrinsic energy E between any given limits poOo to po is readily found by substituting these values of the specific heats in equations (II) or (13), and integrating between the given limits.
    0
    0
  • If J', J" represent the values of the function for unit mass of the substance of specific volumes v' and v" in the two states at temperature 0 and pressure and if a mass m is in the state v', and 1-m in the.
    0
    0
  • If G' and G" are the values of the function G for the two states in equilibrium at the same pressure and temperature, we must have G' =G".
    0
    0
  • The values of the corresponding functions for the liquid or solid cannot be accurately expressed, as the theoretical variation of the specific heat is unknown, but if we take the specific heat at constant pressure s to be approximately constant, and observe the small residual variation dh of the total heat, we may write F'=s'D+dh+B'.
    0
    0
  • To find the border curve of equilibrium between the two states, giving the saturation pressure as a function of the temperature, we have merely to equate the values of G and G".
    0
    0
  • The annual output of Victoria declined until the year 1892, when it began to increase rapidly, but not to its former level, the values for 1900 and 1905 being £3,142,000 and £3,138,000.
    0
    0
  • Halting just short of this analysis, the Assyrian ascribed syllabic values to the characters of his script, and hence, instead of finding twenty odd characters sufficient, he required about five hundred.
    0
    0
  • There was a further complication in that each one of these characters had at least two different phonetic values; and there were other intricacies of usage which, had they been foreknown by inquirers in the middle of the 19th century, might well have made the problem of decipherment seem an utterly hopeless one.
    0
    0
  • Working with some inscriptions from Persepolis which were found to contain references to Darius and Xerxes, Grotefend had established the phonetic values of certain of the Persian characters, and his successors were perfecting the discovery just about the time when the new Assyrian finds were made.
    0
    0
  • Assuming, then, that the proper names found in the Persian portion of the Behistun inscription occurred also in the Assyrian portion, retaining virtually the same sound in each, a clue to the phonetic values of a large number of the Assyrian characters was obviously at hand.
    0
    0
  • Phonetic values known, Assyrian was found to be a Semitic language cognate to Hebrew.
    0
    0
  • During the three centuries that have elapsed between Vieta's day and our own several changes of opinion have taken place on this subject, till the principle has at last proved so far victorious that modern mathematicians like to make homogeneous such equations as are not so from the beginning, in order to get values of a symmetrical shape.
    0
    0
  • Jupiter was measured on eleven nights in the months of June and July 1794; from these measures Schur derives the values 35"39 and 37".94 for the polar and equatorial diameter respectively, at mean distance, corresponding with a compression 1/14.44.
    0
    0
  • There are six ancient versions of various values.
    0
    0
  • Slightly higher values have been obtained, but 240 may be taken as the average value under these conditions.
    0
    0
  • The values of the principal catches in 1902 were: red snapper, $103,398; oysters, $100,359; squeteague, $49,577, and channel bass, $39,525.1 Minerals.-The total value of the mineral products of Texas in 1890 was $1,986,679; in 1902, $6,981,532; in 1907, $19,806,458, and in 1908, $15,212,929-the valuations for the two years last named being those of the United States Geological Survey.
    0
    0
  • The values of other products in 1905 were as follows: slaughtering and meat packing (wholesale), $15,620,931; lumber and timber products (which employed the largest average number of wage-earners-13,332, or 27.2 per cent.), $16,278,240; cars and general shop construction and repairs by steam railway companies, $10,472,742; printing and publishing, $7,782,247; foundry and machine shop products, 1905, $4,952,827; malt liquors, $4,153,938; saddlery and harness, 1905, $3,251,525.
    0
    0
  • In the following table are given the values of the diameters of the molecules of six substances with which it is easy to experiment in the gaseous state, these values being calculated in different ways from formulae supplied by the kinetic theory.
    0
    0
  • The agreement of the values obtained for the same quantity by different methods provides valuable confirmation of the truth of the molecular theory and of the validity of the methods of the kinetic theory of gases.
    0
    0
  • This and the difficulty of obtaining accurate experimental results fully account for the differences inter se in the values of the quantities calculated.
    0
    0
  • Let us suppose that an infinite number of exactly similar systems start simultaneously from all possible values of pi, q1,
    0
    0
  • Let us confine our attention to those systems for which the initial values of pi, qi, ...
    0
    0
  • Thus after a time dt the values of the coordinates and momenta of the small group of systems under consideration will lie within a range such that pi is between pi +pidt and pi +dp,+(pi+ap?dpi) dt „ qi +gidt „ qi+dqi+ (qi +agLdgi) dt, Thus the extension of the range after the interval dt is dp i (i +aidt) dq i (I +?gidt).
    0
    0
  • Since the values of the co-ordinates and momenta at any instant during the motion may be treated as " initial " values, it is clear that the " extension " of the range must remain constant throughout the whole motion.
    0
    0
  • This result at once disposes of the possibility of all the systems acquiring any common characteristic in the course of their motion through a tendency for their co-ordinates or momenta to concentrate about any particular set, or series of sets, of values.
    0
    0
  • Let us imagine that the systems had the initial values of their co-ordinates and momenta so arranged that the number of systems for which the co-ordinates and momenta were within a given range was proportional simply to the extension of the range.
    0
    0
  • Then the result proves that the values of the coordinates and momenta remain distributed in this way throughout the whole motion of the systems. Thus, if there is any characteristic which is common to all the systems after the motion has been in progress for any interval of time, this same characteristic must equally have been common to all the systems initially.
    0
    0
  • Thus the contribution to the total impulsive pressure exerted on the area dS in time dt from this cause is mu X udtdS X (11 3 m 3 /,r 3)e hm (u2+v2+w2 )dudvdw (I o) The total pressure exerted in bringing the centres of gravity of all the colliding molecules to rest normally to the boundary is obtained by first integrating this expression with respect to u, v, w, the limits being all values for which collisions are possible (namely from - co too for u, and from - oo to + oo for v and w), and then summing for all kinds of molecules in the gas.
    0
    0
  • Clearly the integral is the sum of the values of mu g for all the molecules of the first kind in unit volume, thus p=v mu l +v'm'u 2 +...
    0
    0
  • This equation is found experimentally to be capable of representing the relation between p, v, and T over large ranges of values.
    0
    0
  • (20) By division of the values of C, and C„ we find for -y, the ratio of the specific heats.
    0
    0
  • On giving different values to n in formula (21), we obtain the values for y: n = o, 1, 2, 3, 4, 5, y = 1.66, 1.5, 1.4, 1.33, 1.28, 1.25, &c.
    0
    0
  • The following are the values of y for gases for which y can be observed with some accuracy: Mercury..
    0
    0
  • In the case of corporations realty and machinery are taxed generally by the local authorities, and stock values by the commonwealth.
    0
    0
  • Seubert (Ber., 1888, 21, p. 1839) from the analysis of potassium and ammonium osmichlorides, the values obtained being approximately 191.
    0
    0
  • Let KA and LB be the positions of NP corresponding to the extreme values of x.
    0
    0
  • If the planes of one set divide it into m slabs of thickness h, and those of the other into n slabs of thickness k, so that H =mh, K = nk, then the values of x and of y for any ordinate may be denoted by xo+Oh and yo+Ok, and the length of the ordinate by uo, 0.
    0
    0
  • Generally, if the area of a trapezette for which u is an algebraical function of x of degree 2n is given correctly by an expression which is a linear function of values of u representing ordinates placed symmetrically about the mid-ordinate of the trapezette (with or without this mid-ordinate), the same expression will give the area of a trapezette for which u is an algebraical function of x of degree 2n + 1.
    0
    0
  • In the case of the sphere, for instance, whose radius is R, the area of the section at distance x from the centre is lr(R 2 -x 2), which is a quadratic function of x; the values of So, Si, and S2 are respectively o, 7rR 2, and o, and the volume is therefore s.
    0
    0
  • The process is simplified by writing down the general formula first and then substituting the values of u.
    0
    0
  • In the case of a trapezette, for instance, the data are the magnitudes of certain ordinates; the problem of interpolation is to determine the values of intermediate ordinates, while that of mensuration is to determine the area of the figure of which these are the ordinates.
    0
    0
  • In what follows it will be assumed that the conditions of continuity (which imply the continuity not only of u but also of some of its differential coefficients) are satisfied, subject to the small errors in the values of u actually given; the limits of these errors being known.
    0
    0
  • It is only necessary to consider the trapezette and the briquette, since the cases which occur in practice can be reduced to one or other of these forms. In each case the data are the values of certain equidistant ordinates, as described in §§ 43-45.
    0
    0
  • The second consists in taking a comparatively simple expression obtained in this way, and introducing corrections which involve the values of ordinates at or near the boundaries of the figure.
    0
    0
  • Combining this with the first equation, we obtain the values of P, Q, R, ..
    0
    0
  • (iii) Different formulae have to be adopted for different values of m; the method is therefore unsuitable for the construction of a table giving successive values of the area up to successive ordinates.
    0
    0
  • If we do not know values of u outside the figure, we must use advancing or receding differences.
    0
    0
  • Then, if the true moments are denoted by Pi, v 2, ..., their values are given by vi ?Pl P2 - 11.
    0
    0
  • The expressions in square brackets are in each case to be taken as relating to the extreme values x =xo and x=xm, as in §§ 75 and 76.
    0
    0
  • The Euler-Maclaurin formula (§ 75) assumes that the bounding values of u', u"',..
    0
    0
  • One method is to construct a table for interpolation of x in terms of u, and from this table to calculate values of x corresponding to values of u, proceeding by equal intervals; a quadrature-formula can then be applied.
    0
    0
  • Even where u is an explicit function of x, so that f x udx may be expressed in terms of x, it is often more convenient, for construction of a table of values of such an integral, to use finite-difference formulae.
    0
    0
  • Attention must be given to the possible accumulation of errors due to the small errors in the values of u.
    0
    0
  • The use of quadrature-formulae is important in actuarial work, where the fundamental tables are based on experience, and the formulae applying these tables involve the use of the tabulated values and their differences.
    0
    0
  • Among the incidental operations are (a) the valuation of the bullion by weighing and assaying it; (b) " rating" the bullion, or calculating the amount of copper to be added to make up the standard alloy; (c) recovering the values from ground-up crucibles, ashes and floor sweepings (the Mint " sweep "); (d) assaying the melted bars; (e) " pyxing " the finished coin or selecting specimens to be weighed and assayed; (f) " telling " or counting the coin.
    0
    0
  • In 1896 municipal and rural local bodies were allowed to levy rates upon unimproved land values if authorized to do so by a vote of their electors, and by the end of 1901 some sixty bodies, amongst them the city of Wellington, had made use:of this permission.
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  • Undoubtedly also commercial confidence was restored by the reconstruction in 1895 of the Bank of New Zealand, and activity has been stimulated by large public loans, while more cautious banking and the systems of taxation and rating on land values, adopted in 1891 and 1896, have done something to check land speculation.
    0
    0
  • Values can therefore be accumulated only by being reproduced in the course or, as often happens, by the very act of consumption; hence his distinction between reproductive and unproductive consumption.
    0
    0
  • Personal property is exempt from execution or attachment as follows: all wearing apparel of every person and family; private libraries to the value of $500; all family pictures; household goods to the value of $500; certain domestic animals or $250 worth of other property chosen instead; firearms kept for the use of a person or family; certain articles (within specified values) necessary to the occupations of farmers, physicians, and other professional men, teamsters, lightermen, &c., and the proceeds of all life and accident insurance.
    0
    0
  • It may be noted that the elasticity E is only constant for small volume changes or for small values of dy/dx.
    0
    0
  • At 0° C.: we have Uo =1/ (yk), and hence U t = Uolt (I +at) =U 0 (I+-o o0184t) (for small values of t).
    0
    0
  • But the values of 2 which occur successively during the second at AB exist simultaneously at the beginning of the second over the distance U behind AB.
    0
    0
  • Substituting these values and neglecting powerssof dy/dx above the second we get CU P= 17.
    0
    0
  • If the train of waves is reflected, the value of p at AB will be the sum of the values for the two trains, and will, on the average, be doubled.
    0
    0
  • Now we may resolve these trains by Fourier's theorem into harmonics of wave-lengths X, 2X, 3A, &c., where X=2AB and the conditions as to the values of y can be shown to require that the harmonics shall all have nodes, coinciding with the nodes of the fundamental curve.
    0
    0
  • Each section then vibrates, and its amplitude goes through all its values in time given by 21rUT/A =2r, or T =A/U, and the frequency is U/A.
    0
    0
  • If L 1 is the internodal distance and U 1 the velocity in a gas, L and U being the corresponding values for air, we have U 1 /U =L1/L.
    0
    0
  • Wohler's and Bauschinger's experiments give values of t, u, and s, for some materials.
    0
    0
  • Putting the values of F in (1) and solving for f max ., we get for the breaking stress of a bar subjected to repetition of varying stress, f max.
    0
    0
  • The following table gives values of the working stress calculated by these equations: Working Stress for Tension or Thrust by Launhardt and Weyrauch Formula.
    0
    0
  • But if the load is distributed to the bracing intersections by rail and cross girders, then the shear at C' will be greatest when the load extends to N, and will have the values wXADN and -wXNEB.
    0
    0
  • Professor Claxton Fidler (Treatise on Bridge Construction, 1887) has made a very careful theoretical analysis of the weights of bridges of different types, and has obtained the following values for the limiting spans.
    0
    0
  • There is a want of depth in Christian experience, in the power of realizing relative spiritual values in the light of the master principle involved in the distinctively Christian consciousness, such as could raise Clement above a verbal eclecticism, rather than comprehensiveness, in the use of Apostolic language.
    0
    0
  • The general question of food values is discussed in the article Dietetics; see also Nutrition.
    0
    0
  • The second volume (1817) relates to the Eulerian integrals, and to various integrals and series, developments, mechanical problems, &c., connected with the integral calculus; this volume contains also a numerical table of the values of the gamma function.
    0
    0
  • Starting with the experimental values of p, for a standard projectile, fired under standard conditions in air of standard density, we proceed to the construction of the ballistic table.
    0
    0
  • Denoting the value of T at any velocity v by T (v), then (8) T(v) = sum of all the preceding values of AT plus an arbitrary constant, expressed by the notation (9) T(v) =Z(Av)/gp+ a constant, or fdv/gp+ a constant, in which p is supposed known as a function of v.
    0
    0
  • The constant may be any arbitrary number, as in using the table the difference only is required of two tabular values for an initial velocity V and final velocity v; and thus (to) T(V) - T(v) = Ev Ov/gp or fvdv/gp; and for a shot whose ballistic coefficient is C (II) t=C[T(V) - T(v)].
    0
    0
  • Denoting by S(v) the sum of all the values of AS up to any assigned velocity v, (is) S(v) =E(OS)+ a constant, by which S(v) is calculated from AS, and then between two assigned velocities V and v, V AT, = vAv or rvvdv vgp gp' and if s feet is the advance of a shot whose ballistic coefficient is C, (17) s=C[S(V) - S(v)].
    0
    0
  • The differences OD and DI are thus calculated, while the values of D(v) and I (v) are obtained by summation with the arithmometer, and entered in their respective columns.
    0
    0
  • The initial values of T, S, D, I, A must be accepted as belonging to the anterior portion of the table.
    0
    0
  • There are reasons to believe that these values were considerably understated.
    0
    0
  • Heinrich Eduard Heine has shown that the functions of higher orders may be considered as limiting values of the associated functions; this relation was discussed independently, in 1878, by Lord Rayleigh.
    0
    0
  • Other important manufactures, with their product values in 1900 and in 1905, are iron and steel ($5,004,572 in 1900; $6,167,542 in 1905); railway cars ($4,248,029 in 1900; $5,739,071 in 1905); packed meats ($5, 1 77, 16 7 in 1900; $5, 6 93,73 1 in 1905); foundry and machine shop products ($4,434,610 in 1900; $4, 6 99,559 in 1905); planing mill products, including sash, doors and blinds ($1,891,517 in 1900; $4,593, 2 5 1 in 1905-an increase already remarked); carriages and wagons ($2,849,713 in 1900; $4,059,438 in 1905); tanned and curried leather ($3,757,016 in 1900; $3,952,277 in 1905); and malt liquors ($3,186,627 in 1900; $3,673,678 in 1905).
    0
    0
  • In 1898 there began an increased activity in the mining of fluorspar, and Crittenden, Fayette and Livingston counties produced in 1902, 29,030 tons (valued at $143,410) of this mineral, in 1903 30,835 tons (valued at $153,960) and in 1904 19,096 tons (valued at $111,499), amounts (and values) exceeding those produced in any other state for these years; but in 1907 the quantity (21,058 tons) was less than the output of Illinois.
    0
    0
  • (Note: these figures refer to the authorities at the end of this section.) It is above all desirable to make allowances for the changes which weights have undergone; and, as this has only been done for the above Egyptian collections and that of the British Museum, conclusions as to the accurate values of different standards will here be drawn from these rather than continental sources.
    0
    0
  • Altogether, we see that weights have descended from original varieties with so little intercomparison that no rectification of their values has been made, and hence there is as much variety in any one place and time as in all together.
    0
    0
  • It should be borne in mind that in early times the larger values, such as minae, would be transmitted by commerce, while after the introduction of coinage the lesser values of shekels and drachmae would be the units; and this needs notice, because usually a borrowed unit was multiplied or divided according to the ideas of the borrowers, and strange modifications thus arose.
    0
    0
  • The early observance of the relative values may be inferred from Num.
    0
    0
  • The values here given are from some Persian buildings (25), which indicate 21.4, or slightly less; Oppert's value, on less certain data, is 21.52.
    0
    0
  • There is great uncertainty as to the exact values of all ancient standards of volume -- the only precise data being those resulting from the theories of volumes derived from the cubes of feet and cubits.
    0
    0
  • The values are 1.5 times the Attic (Athenaeus, Theophrastus, &c.) (2, 18), or more closely 11 to 12 times (1/8)th of Attic. Hence, the Attic cotyle being 17.5 cub.
    0
    0
  • In actual use this unit varied greatly: at Naucratis (29) there are groups of it at 231, 223 and others down to 208; this is the earliest form in which we can study it, and the corresponding values to these are 130 and 126, or the gold and trade varieties of the Babylonian, while the lower tail down to 208 corresponds to the shekel down to 118, which is just what is found.
    0
    0
  • Hultsch reckons on a ratio of 24:25 between them, and this is very near the true values; the full Attic being 67.3, the Assyrian should be 129.2, and this is just the full gold coinage weight.
    0
    0
  • Turning now to its usual trade values in Greece (44), the mean of 113 gives 67.15; but they vary more than the Egyptian examples, having a sub-variety both above and below the main body, which itself exactly coincides with the Egyptian weights.
    0
    0
  • For the purpose of thus simplifying the operations of arithmetic, the base is taken to be Io, and use is made of tables of logarithms in which the values of x, the logarithm, corresponding to values of m, the number, are tabulated.
    0
    0
  • This equation defines log x for positive values of x; if o the formula ceases to have any meaning.
    0
    0
  • A connexion with the circular functions, however, appears later when the definition of log x is extended to complex values of x.
    0
    0
  • It is positive for all values of y and increases steadily from o toward as y increases from -co towards + oo.
    0
    0
  • The definitions of the logarithmic and exponential functions may be extended to complex values of x.
    0
    0
  • Thus even when the argument is real log x has an infinite number of values; for putting 71 =o and taking positive, in which case a = o, we obtain for log the infinite system of values log +2n7ri.
    0
    0
  • It follows from this property of the function that we cannot have for log x a series which shall be convergent for all values of x, as is the case with sin x and cos x, for such a series could only represent a uniform function, and in fact the equation log(I +x) =x -",, x2 +3x 3 -4x 4 + is true only when the analytical modulus of x is less than unity.
    0
    0
  • The exponential function, which may still be defined as the inverse of the logarithmic function, is, on the other hand, a uniform function of x, and its fundamental properties may be stated in the same form as for real values of x.
    0
    0
  • Corresponding to the argument log x it gives the values of log (I -Fx - 1) and log (1+x).
    0
    0
  • By means of these formulae Adams calculated the values of log e 2, log e 3, log e s, and loge?
    0
    0
  • In 1846 Peter Gray constructed a new table to 12 places, in which the factors were of the form I - (oi) r n, so that n had the values I, 2,.
    0
    0
  • If suitable values are chosen for these constants, the formula can be made to represent the dispersion of ordinary transparent media within the visible spectrum very well, but when extended to the infra-red region it often departs considerably from the truth, and it fails altogether in cases of anomalous dispersion.
    0
    0
  • As A m is a wave-length corresponding to an absorption band, this formula can be used to find values of A m which satisfy the observed values of n within the region of transparency, and so to determine where the absorption bands are situated.
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  • Thus, the density of air being taken as unity, Victor Meyer found the following values for the density of iodine vapour at different temperatures: T° C...
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  • Aeuer (Ber., 1904, 37, p. 2 53 6; Ann., 1904, 337, p. 362), who converted pure ethyl iodide into hydriodic acid and subsequently into silver iodide, which they then analysed, obtained the value 126.026 (H =1); a discussion of this and other values gave as a mean 126.97 (0=16).
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  • It is probable that this estimate is generous according to the values of that time.
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  • But even supposing $1,000,000,000 to be a juster estimate according to present-day values, it is probable that the increase of this since 1790 has been more than a hundredfold and since 1850 (since when such data have been gathered by the census) about fifteenfold.
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  • The same conditions have made of importance general theories, such as the single tax theory of Henry George, for taxing landed values.
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  • The following table gives the values of this constant and several expressions involving it Useful fractional approximations are 22/7 and 355/113.
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  • Equating The Above Two Values Of X, We Have 15 N' 3 =19 M' 16; Whence N' =M' 4'N1 13.
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  • In Consequence Of The Solar And Lunar Equations, It Is Evident That The Epact Or Moon'S Age At The Beginning Of The Year, Must, In The Course Of Centuries, Have All Different Values From One To Thirty Inclusive, Corresponding To The Days In A Full Lunar Month.
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  • P= 54 E 1=57 E, Or (57 E) 7 R' By Substituting One Or Other Of These Values Of P And 1, According A; The Case May Be, In The Formula P = P (L L), We Shall Have P, Orthe Number Of Days From The 21St Of March To Easter Sunday.
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  • So That J W=6 (Y) R 3 (113 0 3) R (Rejecting Sevens), The Values Of Which Obviously Circulate In A Period Of 7 Times 30 Or 210 Years.
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  • In 1906, according to the Year-Book of the Department of Agriculture, the following were the acreages, yields and values of Alabama's more important crops (excepting cotton): - Indian corn, 2,990,387 acres, 47, 8 49,39 2 bushels, $30,623,611; wheat, 98,639 acres, 1,085,029 bushels, $1,019,927; oats, 184,179 acres, 3,167,879 bushels, $1,615,618; hay, 5 6, 35 o acres, 109,882 tons, $1,461,431.
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  • Great importance was attached to the mystical values of letters and numbers, especially the numbers 18 and 19 (" the number of the unity ") and 19 2 = 361 (" the number of all things ").
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  • " In the paper quoted the numerical values of p are given for different widths of slit, and a table shows to what extent the loss of purity due to a widening of the slit is accompanied by a gain in luminosity.
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  • He finds a remarkable agreement between the theoretical and experimental values, which it would be important to confirm with the more suitable instruments which are now at our disposal, as we might in this way get an estimate of the energy of translatory motion of the luminous molecules.
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  • Balmer, who showed that the four hydrogen lines in the visible part of the spectrum may be represented by the equation n = A(i - 4/s2), where n is the reciprocal of the wave-length and therefore proportional to the wave frequency, and s successively takes the values 3, 4, 5, 6.
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  • Rydberg favours the former view, but he does not attempt to obtain any very close approximation between the observed and calculated values of the frequencies.
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  • The present writer, therefore, in his Theory of Optics, adopted different names, and called the series respectively the " Trunk," the " Main Branch " and the " Side Branch," the main branch being identical with the second subordinate series; the limit of frequency for high values of s is called the " root " of the series, and it is found in all cases that the two branches have a common root at some point in the trunk.
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  • The other method starts from the observed values of the periods, and establishes a differential equation from which these periods may be derived.
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  • If this is the case it is obvious that an equation of the form n=A - +a does, for small values of s, becomes identical with Deslandres' equation, a representing a constant which is large compared with unity.
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  • If we only assign positive values to n and a, the band fades away from the head, the lines at first increasing in distance.
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  • If we adopt Thiele's view that each band is accompanied by a second branch for which s has negative values the complication is still further increased, but there does not seem to be sufficient reason to adopt this view.
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  • If K has a value nearly equal to unity, the pressure shift is z k2 " +3 (K- 1 - 1); and it is significant that for different values of n, the shifts should be in geometric ratio, because as stated above, the ratio occurring in the amounts observed with different lines of the same element are as 1: 2: 4.
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  • Close to and on either side of the absorptive band µ 2 has large positive and negative values, and if the above expression remains correct the change of frequency would, close to the centre of absorption, be 2 k-2"+3, which for n =3 and k= Io is 1/2000, or 500 times greater than the observed shifts, but this represents now the maximum displacement and not the displacement of the most intense portion of the radiation.
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  • Within this essential co-ordination he distinguished three values: R-values of the environment as stimulus; C-values of the central nervous system; and E-values of human statements - the latter being characterized by that which at the time of its existence for the individual admits of being named, and including what we call sensations, &c., which depend indirectly on the environment and directly on the central nervous system, but are not, as the materialist supposes, in any way reducible to possessions of the brain or any other part of that system.
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  • This division of values brings us to the second point in his philosophy, his theory of what he called " vital series," by which he assayed to explain all life, action and thought.
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  • In 1769, in a letter to Dr Franklin, he wrote some observations on the expectation of lives, the increase of mankind, and the population of London, which were published in the Philosophical Transactions of that year; in May 1770 he communicated to the Royal Society a paper on the proper method of calculating the values of contingent reversions.
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  • Following the first chart of lines of equal variation compiled by Edmund Halley in 1700, charts of similar type have been published from time to time embodying recent observations and corrected for the secular change, thus providing seamen with values of the variation accurate to about 30' of arc. Possessing these data, it is easy to ascertain by observation the effects of the iron in a ship in disturbing the compass, and it will be found for the most part in every vessel that the needle is deflected from the magnetic meridian by a horizontal angle called the deviation of the compass; in some directions of the ship's head adding to the known variation of the place, in other directions subtracting from it.
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  • If, instead of one phase, we have r phases, we must find out the values of r(n - I) quantities before we know the composition of the whole system.
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  • Substituting these values, we find that the relative lowering of vapour pressure in a very dilute solution is equal to the ratio of the numbers of solute and solvent molecules, or (p - p')/p = n/N.
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  • Although even good membranes of copper ferrocyanide are rarely perfectly semi-permeable, and in other membranes such as indiarubber, &c., which have been used, the defects from the theoretical values of the equilibrium pressure are very great, yet, in the light of the exact verification of theory given by the experiments described above, it is evident that such failures to reach the limiting value in no wise invalidate the theory of osmotic equilibrium.
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  • Dilute solutions of substances such as cane-sugar, as we have seen, give experimental values for the connected osmotic properties - pressure, freezing point and vapour pressure - in conformity with the theoretical values.
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  • The osmotic pressure (defined as the difference in the hydrostatic pressures of the solution and solvent when their vapour pressures are equal and they are consequently in equilibrium through a perfect semi-permeable membrane) may also depend on the absolute values of the hydrostatic pressures, as may the vapour pressure of the liquids.
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  • The probable error in neglecting any variation of specific heat is small, and we may calculate L from the values of Lo - (s - s') (To - T), where s - s' is about 0.5 calories.
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  • Putting in these values and integrating we have, neglecting terms involving 0', P=12.06 0-0.021 O s where P is the osmotic pressure in atmospheres.
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  • In the limit of dilution when n is very small compared with N this gives Raoult's experimental law that the relative lowering is n/N, which we deduced from the osmotic law, and conversely from which the osmotic law follows, while for more concentrated solutions agreement is obtained by assigning arbitrary values to a, which, as we have seen, is 5 in the case of cane-sugar.
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  • This separation causes a difference of potential, which can be calculated and is found to agree with the values obtained experimentally.
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  • If a more dilute acid than this be distilled, water passes over in excess and the residue in the retort reaches the above composition and boiling point; on distillation of a stronger acid, excess of acid passes into the distillate and the boiling point rises until the values of the constant boiling mixture are reached.
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  • The relative values of hand and machine work are often discussed.
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  • The different values of the angle of minimum deviation for rays of different refrangibilities give rise to spectral colours, the red being nearest the sun, while farther away the overlapping of the spectra forms a flaming colourless tail sometimes extending over as much as ro° to 20 °.
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  • These are (1) the origin of the cuneiform signs, (2) the etymology of the phonetic values, and (3) the elucidation of the many and varied primitive sign-meanings.
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  • We arrive thus at two distinct and opposite uses and values of fur.
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  • The Hudson's Bay Co.'s sales take place before the others, and, as no reserves are placed on any lot, the results are taken as exactly indicating current values.
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  • Values have greatly increased, and the fur possessing good qualities as to colour and durability will doubtless always be in good request.
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  • This class of skin is the most expensive fur in the world, reckoning values by a square foot unit.
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  • The values for the five years1904-1908were: - Of the imports into Paraguay, 29% came from Germany in 1908, 21% from the United Kingdom and 19% from Argentina.
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  • (2) If k is constant the solution is evidently B =a log r+b, where a= and b and k are determined from the known values of the temperatures observed at any two distances from the axis.
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  • This is not very surprising, if the values in the following table are compared :- Conductivity of Forbes's Iron Bar D - (1 25 inches square).
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  • The values given in the column headed " cooled " are those found by Mitchell with one end of the bar cooled.
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  • On some occasions, owing to the sudden melting of a surface layer of ice and snow, a large quantity of cold water, percolating rapidly, gave for a short time values of the diffusivity as high as.
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  • The values obtained in this way for waves having a period of one second and a wave-length of half an inch agreed very well with those obtained in the same cast-iron by Angstrom's method (see below), with waves having a period of i hour and a length of 30 in.
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  • An additional difficulty arises in the case of observations made with long mercury thermometers buried in vertical holes, that the correction for the expansion of the liquid in the long stems is uncertain, and that the holes may serve as channels for percolation, and thus lead to exceptionally high values.
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  • In any case results deduced from the annual wave must be expected to vary in different years according to the distribution of the rainfall, as the values represent averages depending chiefly on the diffusion of heat by percolating water.
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  • The following are a few typical values for sand or gravel deduced from the annual wave in different localities: - [[Table Ii]].
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  • The extreme divergence of the resulting values of the diffusivity, including eight independent series of measurements on different days, was less than I %.
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  • The values found for the conductivity of air at o° C. range from 000048 to.
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  • This being inconvenient for comparison with sun-spots, use was made of his monthly values to obtain corresponding data for years commencing with January.
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  • Even smaller mean values have been found for the angle between the auroral and magnetic " zeniths " - as the two directions have been called - e.g.
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  • Westman, gives the values 4276.4 and 3913.5.
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  • The values recognized at the court would naturally be recognized in noble families generally, and Philip chose Aristotle to be the educator of his son.
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  • The values honoured by the rulers of the world must naturally impress themselves upon the subject multitudes.
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  • At the court a limited recognition might be given, as fashion veered, to the values prevalent in the Hellenistic world.
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  • At Assuan the mean value for the year is only 38%, that for the summer being 29%, and for the winter 51%; while for Wadi Haifa the mean is 32%, and 20% and 42% are the mean values for summer and winter respectively.
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  • Yet, while the values of the signs were for the most part well ascertained, and the meanings of most works fixed with some degree of accuracy, few grammatical rules had as yet been established, the varieties of the language at different periods had not been.
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  • Although a picture sign may at times have embarrassed the skilled native reader by offering a choice of fixed values or functions, it was never intended to convey merely an idea, so as to leave to him the task of putting the idea into his own words.
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  • Thus ~ is lir, face;, a vase of ointment, is mrii.t, ointment; ~ is wdb, turn, Much investigation is still required to establish the origins of the values of the signs; in some cases the connection between the pictures and the primary values seems to be curiously remote.
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  • The phonetic values of the signs are derived from their word-sign values and consist usually of the bare root, though there are rare examples of the retention of a flexional ending; they often ignore also the weaker consonants of the root, and on the same principle reduce a repeated consonant to a single one, as when the hoe ~, tinn, has the phonetic value bn.
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  • The history of some of the alphabetic signs is still very obscure but a sufficient number of them have been explained to make it nearly certain that the values of all were obtained on the same principles.i Some of the ancient words from which the phonetic values were derived probably fell very early into disuse, and may, never be discoverable in the texts that have come down to us.
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  • Flexional consonants are almost always marked by phonograms, except in very early times; as when the feminine word z.t, cobra, is spelled ~ Also, if a sign had more than one value, a phonogram would be added to indicate which of its values was intended:
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  • When finely rendered they are of great value to the student investigating the origins of their values.
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  • The only native work on the writing that has come to light as yet is a fragmentary papyrus of Roman date which has a table in parallel bite, &c. columns of hieroglyphic signs, with their hieratic equivalents and words written in hieratic de d ~ scribing them or giving their values or mean- woo ree ings.
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  • In spite of this difficulty, however, the values of the correlation coefficients so far obtained cluster fairly well round the mean value of all of them, which is almost exactly 2.
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  • Such measurements of fraternal correlation in the lower animal as Pearson and his pupils have at present made give values very close to 2.
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  • Variation provides the material for selection, and although opinions may differ as to the nature of that material, the modes by which it comes into existence and their relative values and permanences, there is an increasingly wide consensus of opinion that all such material has to pass through the sieve of natural selection and that the sifted products form new varieties and species, and new adaptations.
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  • In 1900 about nine-tenths of the total land area was inclosed in farms; the value of farm property ($2,004,316,897) was greater than that of any other state; as regards the total value of farm products in 1899 Illinois was surpassed only by Iowa; in the value of crops Illinois led all the states, and the values of property and of products were respectively 35.6% and 87.1% greater than at the end of the preceding decade.
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  • The Federal government completed in October 1907 the construction of a 1 According to the report of the State Geological Survey, the value of the total mineral product in the state for 1907 was $152,122,648, the values of the different minerals being as follows: coal, $54,687,382; pig iron, about $52,228,000; petroleum, $ 16, 43 2, 947; clay and clay products, $13,351,362; zinc, $6,614,608; limestone, $4,333,651; Portland cement, $2,632,576; sand and gravel, $1,367,653; natural slag, $174,282; fluorspar, $141,971; mineral waters, $91,700; lead ore, $45,760; sandstone, $14,996; and pyrite, $5700.
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  • Commerce.-A summary of import and export values of trade in the Persian Gulf, excluding Mohammerah and Basra, is appended.
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  • Bushire, Hanjam, Bahrein, Abadan and Basra Summary showing Import and Export Values of Trade in the Persian Gulf (excluding Iraq and Arabistan) in two pre-war years and in the latest post-war year available.
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  • This is generally calculated by assuming values for the specific heats of the materials obtained by experiment between loo° C. and 20° C. Since the specific heats of most metals increase rapidly with rise of temperature, the values so obtained are generally too high.
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  • The following are some of the values deduced by well-known experimentalists for the latent heat of fusion: - Regnault, 79.06 to 79.24 calories, corrected by Person to 79.43; Person, 79.99 calories; Hess, 80.34 calories; Bunsen, 80.025 calories.
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  • If such variations of density exist, they may introduce some uncertainty in the absolute values of results obtained with the ice calorimeter, and may account for some of the discrepancies above enumerated.
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  • Thus Corrected His Values Are As Follows: Temperature.
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  • The Values Deduced In This Manner For The Equivalent Agreed As Closely As Could Be Expected Considering The Impossibility Of Regulating The External Condition Of Temperature And Moisture With Any Certainty In An Engine Room.
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  • The Heat Loss Hdo Is Determined And Eliminated By Varying The Flow Of Liquid And The Electric Current Simultaneously, In Such A Manner As To Secure Approximately The Same Rise Of Temperature For Two Or More Widely Different Values Of The Flow Of Liquid.
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  • The Absolute Value Of The Specific Heat Deduced Necessarily Depends On The Absolute Values Of The Electrical Standards Employed In The Investigation.
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  • But For The Determination Of Relative Values Of Specific Heats In Terms Of A Standard Liquid, Or Of The Variations Of Specific Heat Of A Liquid, The Method Depends Only On The Constancy Of The Standards, Which Can Be Readily And Accurately Tested.
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  • We May Probably Take The Tabulated Values As Showing Correctly The Rate Of Variation Between 110° And 190° C., But The Values In Terms Of Any Particular Thermal Unit Must Remain Uncertain To At Least 0.5% Owing To The Uncertainties Of The Thermometry.
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  • Bosscha From An Independent Reduction Of Regnault'S Experiments Is Probably Within The Limits Of Accuracy Between Ioo° And Zoo° C., So Far As The Mean Rate Of Variation Is Concerned, But The Absolute Values Require Reduction.
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  • 6, Show A Minimum At 25° C., And A Maximum At 87° C., The Values Being 9935 And 1.0075 Respectively In Terms Of The Mean Specific Heat Between O° And 100° C. He Paid Great Attention To The Thermometry, And The Discrepancies Of Individual Measurements At Any One Point Nowhere Exceed O 3%, But He Did Not Vary The Conditions Of The Experiments Materially, And It Does Not Appear That The Well Known Constant Errors Of The Method Could Have Been Completely Eliminated By The Devices Which He Adopted.
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  • It Appears Probable That His Values For Higher Temperatures May Be Adopted With This Reduction, Which Is Further Confirmed By The Results Of Reynolds And Moorby, And By Those Of Liidin.
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  • Above 60° C. Regnault'S Formula Is Adopted, The Absolute Values Being Simply Diminished By A Constant Quantity O O056 To Allow For The Probable Errors Of His Thermometry.
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  • The following table of values, calculated from these formulae, is taken from the Brit.
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  • Assoc. Report, 1899, with a slight modification Specific Heat Of Water In Terms Of Unit At 20° C. 4.180 Joules to allow for the increase in the specific heat below 20° C. This was estimated in 1899 as being equivalent to the addition of the constant quantity 0.020 to the values of the total heat h of the liquid as reckoned by the parabolic formula (5).
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  • This quantity is now, as the result of further experiments, added to the values of h, and also represented in the formula for the specific heat itself by the cubic term.
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  • This Would Indicate That Rowland'S Corrected Values Should, If Anything, Be Lowered.
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  • The Mean Specific Heat, Over Any Range Of Temperature, May Be Obtained By Integrating The Formulae Between The Limits Required, Or By Taking The Difference Of The Corresponding Values Of The Total Heat H, And Dividing By The Range Of Temperature.
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  • It May Be Remarked That Starting From The Same Value At 5°, For The Sake Of Comparison, Rowland'S Values Of The Total Heat Agree To I In 5000 With Those Calculated From The Formulae.
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  • The Values Of The Total Heat Observed By Regnault, As Reduced By Shaw, Also Show A Very Fair Agreement, Considering The Uncertainty Of The Units.
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  • Since Much Smaller Values Are Found For More Complex Molecules, We May Suppose That, In These Cases, The Energy Of Rotation Of A Polyatomic Molecule May Be Greater Than Its Energy Of Translation, Or Else That Heat Is Expended In Splitting Up Molecular Aggregates, And Increasing Energy Of Vibration.
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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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  • Its specific gravity varies according to the method employed for its preparation, the extreme values being 8.279 and 9.25.
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  • There are postage stamps of four values.
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  • The give and take of thought had by a swift transformation of values come by something more than its own.
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  • Argand had been led to deny that such an expression as i 2 could be expressed in the form A+Bi, - although, as is well known, Euler showed that one of its values is a real quantity, the exponential function of --7112.
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  • These cases are really included in the equation if we substitute the proper values of n or m.
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  • The values thus found agreed in the main with Raoult's law for dilute solutions (see Solutions).
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  • Taking the difference between the values of H for any two temperatures 1 " Latent Heat of Steam," Phil.
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  • These observations give values for S ranging from 0.30 to o 46, with a mean value 0.3778.
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  • This method is logically consistent, and gives values ranging from 0.305 at o° to 0.345 at Ioo° C. and 0.464 at 210° C., but the difference from Regnault's S = 0.475 cannot easily be explained.
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  • It is evident that this is a very delicate method of determining the wetness z, but, since with dry saturated steam at low pressures this formula always gives negative values of the wetness, it is clear that Regnault's numerical coefficients must be wrong.
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  • Employing the values of S calculated from dH/d0 = 0.305, he found that the product SQ was independent of both pressure and temperature for the range of his experiments.
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  • The introduction of this correction into the calculations would slightly improve the agreement with Regnault's values of the specific heat and total heat between 100° and 200° C., where they are most trustworthy, but would not materially affect the general nature of the results.
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  • Values calculated from these formulae are given in the table below.
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  • The values of the saturation-pressure have been ver y accurately determined for the majority of stable substances, and a large number of empirical formulae have been proposed to represent the relation between pressure and temperature.
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  • The values so found are necessarily erroneous if formula (io) for the total heat is wrong.
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  • He proceeds to calculate from this expression the difference of vapour-pressures of ice and water in the immediate neighbourhood of the melting-point, but does not observe that the vapour-pressures themselves may be more accurately calculated for a considerable interval of temperature by means of formula (23), by substituting the appropriate values of the latent heats and specific heats.
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  • They give the following numerical values The error of the formula for water is less than t mm.
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  • It is generally called Dupre's formula in continental text-books, but he did not give the values of the coefficients in terms of the difference of specific heats of the liquid and vapour.
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  • It was employed as a purely empirical formula by Bertrand and Barus, who calculated the values of the coefficients for several substances, so as to obtain the best general agreement with the results of observation over a wide range, at high as well as low pressures.
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  • It is easy, however, to correct the formula for these deviations, and to make it thermodynamically consistent with the characteristic equation (13) by substituting the appropriate values of (v-w) and L =H -h from equations (13) and (is) in formula (21) before integrating.
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  • (25) The values of the coefficients B and C remain practically as before.
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