# Values sentence example

The government must reflect the different

**values**these groups have.You have to stay true to your

**values**while destroying something as well.You love your country's ideals, goals,

**values**, and aspirations.The

**values**obtained are shown below.You behaved as becomes a man who

**values**his honor, perhaps too hastily, but we won't go into that.AdvertisementThey can standardize in a thousand more ways to a world economy, while maintaining their

**values**, traditions, and distinctions.The largest positive and negative

**values**recorded are met with during disturbed weather.These will suffice to give a general idea of the mean

**values**met with.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.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.AdvertisementMy 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.The former moves in a world of "

**values**," and judges things as they are related to our "fundamental self-feeling."Many varying

**values**have been given for the atomic weight of molybdenum.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.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.AdvertisementThen by solving these equations, regarding the six elements as unknown quantities, the

**values**of the latter may be computed.There are six ancient versions of various

**values**.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.But is the basis for religious belief to be constructed purely within the region of "

**values**" ?This curve with the

**values**reduced from metres to feet is reproduced below.AdvertisementMotors 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.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.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.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.But since the elements cannot be converted one into the other, we are absolutely without knowledge of the relative

**values**of their intrinsic energy.AdvertisementPersonally 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.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.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.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**.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.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.But of course it was far less important than various other articles of trade in the aggregate

**values**of commerce.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.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.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.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.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.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.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.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.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.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.The

**values**recognized in the great Hellenistic courts and the Greek world generally imposed their authority upon the dynasties of barbarian origin.Numerous determinations of the atomic weight of nitrogen have been made by different observers, the

**values**obtained varying somewhat according to the methods used.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.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.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.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.The numerical

**values**are, it is to be noted, exceedingly small.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.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**.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).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.Other " Galois " groups were defined whose substitution coefficients have fixed numerical

**values**, and are particularly associated with the theory of equations.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.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.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.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.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.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".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.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.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.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).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.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.Thus any desired number of corresponding

**values**of H and B can be easily and quickly found.**Values**of I are derived from (B -H)/477and of from B/H.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.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.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.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.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.The

**values**of the permeability corresponding to the highest and lowest temperatures are given in the following table.These high

**values**render hardened tungsten-steel particularly suitable for the manufacture of permanent magnets.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.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.The

**values**assigned to the atomic susceptibilities of most of the known elements are appended.His determination 2 of maximum and minimum

**values**for the slowly varying planetary eccentricities was the earliest attempt to deal with the problem.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.In this period the increase in the sterling equivalents would be proportionately greater than that of the currency

**values**.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.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.It is important to begin the study of graphics with concrete cases rather than with tracing

**values**of an algebraic function.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.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.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.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.Thus there appear to be discontinuities in the

**values**of y.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.The

**values**of x and y are different, unless V (qq o) = o.These

**values**are assumed to be independent, so we have 2n(n - I) derived units of the second species or order.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.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.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.The part corresponding to negative

**values**of u is similar, OA being a line of symmetry.When z has one of the

**values**thus determined, (z)=Jo(z).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.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 .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 .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.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.Primary, secondary and spurious bows were formed, and their radii measured; a comparison of these observations exhibited agreement with Airy's analytical

**values**.The total foreign trade in 1908 amounted to $9,778,810 imports and $14,560,830 exports, the

**values**being in U.S. gold.In the absence of statistical returns it is impossible to give the

**values**of this branch of trade.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.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.These

**values**may vary within certain limits for different specimens.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'.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.Sayce's phonetic

**values**and interpretations of determinatives are his best assured achievements.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.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.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.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.In its modern form the theorem, which is true for all

**values**of n, is written as (x +a) n -1+ I.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.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.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.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,..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.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.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.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.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.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".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'.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".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.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.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.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.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.Phonetic

**values**known, Assyrian was found to be a Semitic language cognate to Hebrew.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.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.This and the difficulty of obtaining accurate experimental results fully account for the differences inter se in the

**values**of the quantities calculated.Let us suppose that an infinite number of exactly similar systems start simultaneously from all possible

**values**of pi, q1,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).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.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**.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.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.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.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 +...This equation is found experimentally to be capable of representing the relation between p, v, and T over large ranges of

**values**.In the case of corporations realty and machinery are taxed generally by the local authorities, and stock

**values**by the commonwealth.Seubert (Ber., 1888, 21, p. 1839) from the analysis of potassium and ammonium osmichlorides, the

**values**obtained being approximately 191.Let KA and LB be the positions of NP corresponding to the extreme

**values**of x.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.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.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.The process is simplified by writing down the general formula first and then substituting the

**values**of u.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.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.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.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.Combining this with the first equation, we obtain the

**values**of P, Q, R, ..If we do not know

**values**of u outside the figure, we must use advancing or receding differences.Then, if the true moments are denoted by Pi, v 2, ..., their

**values**are given by vi ?Pl P2 - 11.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.The Euler-Maclaurin formula (§ 75) assumes that the bounding

**values**of u', u"',..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.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.Attention must be given to the possible accumulation of errors due to the small errors in the

**values**of u.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.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.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.**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.It may be noted that the elasticity E is only constant for small volume changes or for small

**values**of dy/dx.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.Substituting these

**values**and neglecting powerssof dy/dx above the second we get CU P= 17.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.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.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.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.Wohler's and Bauschinger's experiments give

**values**of t, u, and s, for some materials.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.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.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.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.The general question of food

**values**is discussed in the article Dietetics; see also Nutrition.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.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.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.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)].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)].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.The initial

**values**of T, S, D, I, A must be accepted as belonging to the anterior portion of the table.There are reasons to believe that these

**values**were considerably understated.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.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).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.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.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.The early observance of the relative

**values**may be inferred from Num.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.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.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.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.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.This equation defines log x for positive

**values**of x; if o the formula ceases to have any meaning.A connexion with the circular functions, however, appears later when the definition of log x is extended to complex

**values**of x.It is positive for all

**values**of y and increases steadily from o toward as y increases from -co towards + oo.The definitions of the logarithmic and exponential functions may be extended to complex

**values**of x.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.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.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.Corresponding to the argument log x it gives the

**values**of log (I -Fx - 1) and log (1+x).By means of these formulae Adams calculated the

**values**of log e 2, log e 3, log e s, and loge?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,.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.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.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).It is probable that this estimate is generous according to the

**values**of that time.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.The same conditions have made of importance general theories, such as the single tax theory of Henry George, for taxing landed

**values**.The following table gives the

**values**of this constant and several expressions involving it Useful fractional approximations are 22/7 and 355/113.Equating The Above Two

**Values**Of X, We Have 15 N' 3 =19 M' 16; Whence N' =M' 4'N1 13.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.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.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.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 ").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.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.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.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.The other method starts from the observed

**values**of the periods, and establishes a differential equation from which these periods may be derived.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.If we only assign positive

**values**to n and a, the band fades away from the head, the lines at first increasing in distance.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.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.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.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.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.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.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.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.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**.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.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.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.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.This separation causes a difference of potential, which can be calculated and is found to agree with the

**values**obtained experimentally.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.The relative

**values**of hand and machine work are often discussed.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.We arrive thus at two distinct and opposite uses and

**values**of fur.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**.**Values**have greatly increased, and the fur possessing good qualities as to colour and durability will doubtless always be in good request.This class of skin is the most expensive fur in the world, reckoning

**values**by a square foot unit.The

**values**given in the column headed " cooled " are those found by Mitchell with one end of the bar cooled.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.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.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**.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.The extreme divergence of the resulting

**values**of the diffusivity, including eight independent series of measurements on different days, was less than I %.This being inconvenient for comparison with sun-spots, use was made of his monthly

**values**to obtain corresponding data for years commencing with January.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.Westman, gives the

**values**4276.4 and 3913.5.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.The

**values**honoured by the rulers of the world must naturally impress themselves upon the subject multitudes.At the court a limited recognition might be given, as fashion veered, to the

**values**prevalent in the Hellenistic world.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.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.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.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.When finely rendered they are of great value to the student investigating the origins of their

**values**.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.Such measurements of fraternal correlation in the lower animal as Pearson and his pupils have at present made give

**values**very close to 2.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.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.Commerce.-A summary of import and export

**values**of trade in the Persian Gulf, excluding Mohammerah and Basra, is appended.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.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.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.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.The Absolute Value Of The Specific Heat Deduced Necessarily Depends On The Absolute

**Values**Of The Electrical Standards Employed In The Investigation.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.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.The following table of

**values**, calculated from these formulae, is taken from the Brit.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.This Would Indicate That Rowland'S Corrected

**Values**Should, If Anything, Be Lowered.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.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.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.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.Its specific gravity varies according to the method employed for its preparation, the extreme

**values**being 8.279 and 9.25.There are postage stamps of four

**values**.The give and take of thought had by a swift transformation of

**values**come by something more than its own.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.These cases are really included in the equation if we substitute the proper

**values**of n or m.The

**values**thus found agreed in the main with Raoult's law for dilute solutions (see Solutions).Taking the difference between the

**values**of H for any two temperatures 1 " Latent Heat of Steam," Phil.These observations give

**values**for S ranging from 0.30 to o 46, with a mean value 0.3778.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.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.**Values**calculated from these formulae are given in the table below.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.The

**values**so found are necessarily erroneous if formula (io) for the total heat is wrong.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.They give the following numerical

**values**The error of the formula for water is less than t mm.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.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.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.But in order to deduce the

**values**of c by the Joule-Thomson method, it is necessary to assume an empirical formula, and the type c=co(6019) n is chosen as being the simplest.The justification of this assumption lies in the fact that the

**values**of c found in this manner, when substituted in equation (25) for the saturation-pressure, give correct results for p within the probable limits of error of Regnault's experiments.The latent heat L (formula 9) is found by subtracting from H (equation 15) the

**values**of the heat of the liquid h given in the same article.The

**values**of the specific heat in the next column are calculated for a constant pressure equal to that of saturation by formula (16) to illustrate the increase of the specific heat with rise of pressure.The

**values**of the saturation-pressure given in the last column are calculated by formula (25), which agrees with Regnault's observations better than his own empirical formulae.The value of products in 1900 ($79.6 millions) was 44% of the total farm

**values**($181.4 millions).As a result of these improvements land and timber

**values**have markedly risen, and great impetus has been given to traffic on the rivers, which carry a large part of the cotton, lumber, coal, stone, hay and miscellaneous freights of the state.It is obvious that, both in its

**values**and in its measurements, the survey's reckoning is very crude.While thus the Greek philosophy furnished the dialectic and the mould for the characteristic Christian teaching, the doctrine of the Trinity preserved religious

**values**.The historic and religious

**values**of the doctrine of the Trinity may be illustrated by way of contrast.In the Mahayana gnosticism was triumphant, and the historic

**values**of Gautama's teaching and personality are lost.A magnetograph is an instrument for continuously recording the

**values**of the magnetic elements, the three universally chosen being the declination, the horizontal component and the vertical component.In each case the magnetograph only records the variation of the element, the absolute

**values**being determined by making observations in the neighbourhood with the unifilar magnetometer and inclinometer.The scale

**values**of the records given by the horizontal and vertical force magnetographs are determined by deflecting the respective needles, either by means of a magnet placed at a known distance or by passing an electric current through circular coils of large diameter surrounding the instruments.Of the foreign-born 4504 were ' Statistics for 1890 represent the value of all manufactures; those for 1900 (from this point) and 1905 show

**values**under the factory system, excluding neighbourhood industries and hand trades.For if the line in question be the axis of y, the first process gives us the

**values**of mx, and the second the value of 2(mx.x) or Z(mx2).From this point of view the equation is a mere truism, its real importance resting on the fact that by attributing suitable

**values**to the masses in, and by making simple assumptions as to the value of X in each case, we are able to frame adequate representations of whole classes of phenomena as they actually occur.If we take as rough

**values**a=21 X,o6 feet, g=32 foot-second units, we get a velocity of 36,500 feet, or about seven miles, per second.The motion being assumed to be small, the tensions of the two strings may be taken to have their statical

**values**Mgb/(a+b), Mga/(a+b), where a, b are the distances of G from the two threads.For given

**values**of n and 0 we have two possible**values**of i,l provided n exceed a certain limit.When, in any problem, the

**values**of u, v, w, p, q, r have been determined as functions of t, it still remains to connect the moving axes with some fixed frame of reference.It is easy ti construct in this connection a proof that the n

**values**of a2 an all real and positive.If in (21) we imagine that x, y, I denote infinitesimal rotations of a solid free to turn about a fixed point in a given field of force, it appears that the three normal modes consist each of a rotation about one of the three diameters aforesaid, and that the

**values**of in are proportional to the ratios of the lengths of corresponding diameters of the two quadrics.These limit the admissible

**values**of a-, which are in general determined by a transcendental equation corresponding to the determinantal equation (6).Since y must vanish at the upper end (x 1), the admissible

**values**of a are determined by o2=gz2/41, Jo(z)=o.The agreement between the observed and calculated

**values**of the critical speeds was in most cases quite remarkable.It implies a subsequent contribution, from all the parties concerned, rateably to the

**values**of their respective interests, to make good the loss thus occasioned.