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The government must reflect the different values these groups have.

4021You have to stay true to your values while destroying something as well.

2424They can standardize in a thousand more ways to a world economy, while maintaining their values, traditions, and distinctions.

103You behaved as becomes a man who values his honor, perhaps too hastily, but we won't go into that.

98To 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.

84His greatest and least mean hourly values and the hours of their occurrence are as follows: Gockel did not observe between 10 P.M.

86Table -Mean Values of a±.

86I And I_ Both Show A Considerable Range Of Values, Even At The Same Place During The Same Season Of The Year.

87The values of a +, a_ and a + also show large variations.

88The values of a +, a_ and a + also show large variations.

88You love your country's ideals, goals, values, and aspirations.

88The largest positive and negative values recorded are met with during disturbed weather.

63ft., but it is now fairly certain that these high values are erroneous, and due, not to the wind, but to faulty design of the anemometer.

53Like silicon and carbon, very varying values had been given for its specific heat, until H.

55It is a willing agreement to a set of values and procedures, and a standard of conduct.

55The 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:

55My 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.

42The following are the principal countries receiving the exports of France (special trade), with values for the same periods.

45There 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.

31At Midsummer The Extreme Hourly Values Were 0.91 And 1.45 For A, 0.94 And 1.60 For A_.

32These will suffice to give a general idea of the mean values met with.

32In individual cases widely different values of a_ or I + are associated with the same value of A.

32In our modern age, people disagree not just in terms of values they apply to knowledge, but they disagree on actual pieces of knowledge.

33The true method of science which he possessed forced him to condemn as useless the entire form which Schelling's and Hegel's expositions had adopted, especially the dialectic method of the latter, whilst his love of art and beauty, and his appreciation of moral purposes, revealed to him the existence of a transphenomenal world of values into which no exact science could penetrate.

34In the potential curves of the diagram the ordinates represent the hourly values expressed - as in Tables II.

34These are not differences of values but disagreements in terms of knowledge.

34"Kris values the Code and his duty more than he does anything," Jade said with some bitterness.

35As in every western city, particularly those in mining regions whose sites attained speculative values, Denver had grave problems with " squatters " or " landjumpers "in her early years; and there was the usual gambling and outlawry, sometimes extra-legally repressed by vigilantes.

35"Kris values the Code and his duty more than he does anything," Jade said with some bitterness.

35The former moves in a world of "values," and judges things as they are related to our "fundamental self-feeling."

21The former moves in a world of "values," and judges things as they are related to our "fundamental self-feeling."

21In England The Largest Values Of A Sufficiently Steady Character To Be Shown Correctly By An Ordinary Electrograph Occur During Winter Fogs.

22The hourly values are derived from smoothed curves, the object being to get the mean ordinate for a 60-minute period.

22Thus at Karasjok Simpson found for mean values: Temp. less than -20° - Io° to -5° Io° to 15° I + =0.18, I_=0.16 I + =0.36, I_=0.30 I + =0 '45, I_=0'43 Simpson found no clear influence of temperature on Q.

22At this station much lower values were found for A with sea breezes than with land breezes.

22We have created documents that enshrine our values as a method of articulating and preserving them.

22It will be noticed that the difference between the greatest and least hourly values is, in all but three winter months, actually larger than the mean value of the potential gradient for the day; it bears to the range of the regular diurnal inequality a ratio varying from 2.0 in May to 3.6 in November.

23Also, whilst the winter values of a i are fairly similar at the several stations the summer values are widely different.

23The values of a 2 at the various stations differ comparatively little, and show but little seasonal change.

23Now if the values of the rheostat and condenser are adjusted so as to make the rise and fall of the outgoing current through both windings of the relay exactly equal, then no effect is produced on the armature of the relay, as the two currents neutralize each other's magnetizing effect.

23Now if the values of the rheostat and condenser are adjusted so as to make the rise and fall of the outgoing current through both windings of the relay exactly equal, then no effect is produced on the armature of the relay, as the two currents neutralize each other's magnetizing effect.

23As we noted earlier, people no longer disagree simply about what values to apply to a set of facts—rather, they disagree as to the nature of the facts themselves.

23You view it as your duty to protest when people who do not hold to those values gain power.

23Specially large values of 1 + and I_ have been observed at high levels in balloon ascents.

11There is a difficulty in reconciling observed values of the ionization with the results obtained from balloon ascents as to the variation of the potential with altitude.

11The office of reason is to give a true and distinct appreciation of the values of goods and evils; or firm and determinate judgments touching the knowledge of good and evil are our proper arms against the influence of the passions.3 We are free, therefore, through knowledge: ex magna lute in intellectu sequitur magna propensio in voluntate, and omnis peccans est ignorans.

11The Domesday Survey contains a long account of the laws, customs and values of the salt-works at that period, which were by far the most profitable in Cheshire.

11There is a difficulty in reconciling observed values of the ionization with the results obtained from balloon ascents as to the variation of the potential with altitude.

11At any single station potential gradient has a wide range of values.

00Mean Values.

00These apparent relationships refer to mean values.

00It gives the real values in one column and tenth parts in another column of each of the benefices in the archdeaconry of Lothian.

002 But this appeal to " values " is only half of Lotze's constructive work.

00With 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.

00When 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.

00But is the basis for religious belief to be constructed purely within the region of " values " ?

00It might be argued that beauty bears witness against materialism, and moral values against pantheism; although such an anomalous type as ethical pantheism has its representatives - J.

00Many varying values have been given for the atomic weight of molybdenum.

00This curve with the values reduced from metres to feet is reproduced below.

00Motors 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.

0017, four values of L being taken for formula (12) corresponding to trains of 5, 10, 15 and 20 bogie carriages.

0017 gives values which must be regarded as only very approximate.

00per hour on a level straight road with the values of the resistances assumed.

00465)/32 = 28,720 ib, and the corresponding horse-power which must be developed in the cylinders is, from (20), f V/550, and this is with f and V equal to the above values, 1149.

005D, P=o 32D, p=o 22D, L=o 6D or o 9D, but not of intermediate values.

00- 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.

00If 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.

00In 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.

00The 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.

00This 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.

00In 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.

00But since the elements cannot be converted one into the other, we are absolutely without knowledge of the relative values of their intrinsic energy.

00Thus if we consider the energyequation C +02 = CO 2+943 00 cal., and replace the symbols by the values of the intrinsic energy, viz.

00Personally 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.

00St 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.

002 35 51.997 With these three independent values, all falling within a range of os.25, it is improbable that the mean value has an error as large as os.10.

00But 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.

00Other values are as follows: Prjevalsky, by his second and third explorations 94° 26' Krishna .

00would give negative, surd or imaginary values; Diophantus then traces how each element of the equation has arisen, and formulates the auxiliary problem of determining how the assumptions must be corrected so as to lead to an equation (in place of the "impossible" one) which can be solved rationally.

00He 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.

00The 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.

00The 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.

00This, 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.

00- Average Values of Fresh Meat, Bacon and Hams imported into the United Kingdom, 1891-1905 - per Cwt.

00Food - values and Early Maturity.

00But of course it was far less important than various other articles of trade in the aggregate values of commerce.

00The following table, summarized from the Handbook to the Imperial Institute Cotton Exhibition, 1905, giving the length of staple and value on one date (January 16, 1905), will serve to indicate the comparative values of some of the principal commercial cottons.

00was not misplaced, and that the pope had a true sense of religious values when he attacked Frederick.

00Then by solving these equations, regarding the six elements as unknown quantities, the values of the latter may be computed.

00Joly (Comptes rendus, 1889, 188, p. 946), who obtained the values 101.5 and 101 3.

00Gerhardt found that reactions could be best followed if one assumed the molecular weight of an element or compound to be that weight which occupied the same volume as two unit weights of hydrogen, and this assumption led him to double the equivalents accepted by Gmelin, making H= 1, 0 =16, and C = 12, thereby agreeing with Berzelius, and also to halve the values given by Berzelius to many metals.

001 Approximate values of the atomic weights are employed here.

00Considerable uncertainty existed as to the atomic weights of these metals, the values obtained by Berzelius being doubtful.

00The values in other cases are calculable from the formula RI 09° 28' - a), where a is the internal angle of the regular polygon contained by sides equal in number to the number of the carbon atoms composing the ring.

00These values are: Trimethylene.

00It 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.

00He 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.

00The 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.

00These values hold fairly well when compared with the experimental values determined from other compounds, and also with the molecular volumes of the elements themselves.

00These 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.

00If, 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.

00This ratio, termed by Guye the critical coefficient, has the following approximate values: C. H.

00It 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.

00Thomsen 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.

00The 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.

00The 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.

00The values are for the D line: Landolt and Gladstone, and at a later date J.

00This 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.

00Normal 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 .

00To 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.

00The 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.

00Two 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.

00This 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.

00The values recognized in the great Hellenistic courts and the Greek world generally imposed their authority upon the dynasties of barbarian origin.

00Nitrogen 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).

00The values obtained are shown below.

00Numerous determinations of the atomic weight of nitrogen have been made by different observers, the values obtained varying somewhat according to the methods used.

00The 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.

00The 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.

00The 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.

00In 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.

00The numerical values are, it is to be noted, exceedingly small.

00The 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.

00But 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.

00The 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.

00Thus 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).

00The 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.

00Thus the values of the expressions a 2 /(i - a /V) (Rudolphi, Zeits.

00The heats of formation thus obtained may be either positive or negative, and by using them to supplement the heat of formation of water, Arrhenius calculated the total heats of neutralization of soda by different acids, some of them only slightly dissociated, and found values agreeing well with observation (Zeus.

00Other " Galois " groups were defined whose substitution coefficients have fixed numerical values, and are particularly associated with the theory of equations.

00For 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.

00=o and ars=-asr for all values of r and s.

00= b11EE1 + b12 EE t 2 + b133 + ï¿½ï¿½ï¿½, X2 = b21E1 + b 22E2 + b 23E3 + ï¿½ï¿½ï¿½, X1 = b11E1+b21}5.2+b3,5tt3 +ï¿½ï¿½ï¿½ X2 = b12E1+b2'_S2+ b 3253 +ï¿½ï¿½ï¿½ where b rr = I and b rs = - b sr for all values of r and s.

00=xï¿½ = o is the only solution; but if A vanishes the equations can be satisfied by a system of values other than zeros.

00each of them satisfied by a common system of values; hence the equation R =o is derived on this supposition, and the vanishing of R expresses the condition that the equations can be satisfied by a common system of values assigned to the variables.

00We 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.

00aj Hence the system of values also causes to vanish in this case; dx and by symmetry aj and Fz also vanish.

00CY The proof being of general application we may state that a system of values which causes the vanishing of k polynomials in k variables causes also the vanishing of the Jacobian, and in particular, when the forms are of the same degree, the vanishing also of the differential coefficients of the Jacobian in regard to each of the variables.

00= 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.

00Hence 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.

00Now 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.

00If m > n there are n +1 transvectants corresponding to the values o, t, 2,...

00n of k; if k = o we have the product of the two forms, and for all values of k>n the transvectants vanish.

00Now D A xA k = (n - k) A k; Aï¿½ A k = k A?1; D ï¿½A A k = (n - k) A k+1;D mï¿½ A k = kA k; (n - k)A ka - w Ak - 1 aA k = O; a _ J (n - k) A k +l A k = O; kA k Ak = wJ; equations which are valid when X 1, X 2, ï¿½ 1, ï¿½2 have arbitrary values, and therefore when the values are such that J =j, A k =akï¿½ Hence °a-do +(n -1)71 (a2aa-+...

00A binary form of order n contains n independent constants, three of which by linear transformation can be given determinate values; the remaining n-3 coefficients, together with the determinant of transformation, give us n -2 parameters, and in consequence one relation must exist between any n - I invariants of the form, and fixing upon n-2 invariants every other invariant is a rational function of its members.

00(1-20) The actual form of a perpetuant of degree 0 has been shown by MacMahon to be +1 K0_1+1 K 3+20-4 K2, 01, 0-2, 0-3, ...3, 2), K 0, Ke -1, ...K 2 being given any zero or positive integer values.

00t (22P11),; X 1 and 12 each assuming all integer (including zero) values.

00The photographic right ascensions gave the values 8.80" -}- 0.007" -}- 0.0027" (Hinks) and 8.80" + 0 .

00In consequence of it, the values formerly found were systematically too small by an amount which even now it is difficult to estimate with precision.

00This 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".

00The 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.

00These, together with values of nt 2 N for cylindrical rods, and of N and m 2 N for ellipsoids of revolution, are given in the following useful table (loc. cit.

00Forces 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.

00We then have approximately for the field at M due to the rod 4 HP= (dm1)2 (d + 1) = m (d 2 _ M Therefore 2m1= = (d2 - 12)2Ht, - (d2-12)2HEtan 0 2d 2d (44) M (d2-12)2HE (45) And I = v - 2dv tan 0, whence we can find the values of I which correspond to different angles of deflection.

00II, S is kept permanently closed, and corresponding values of H and B are determined by one of the two methods already described, the strength of the battery-current being varied by means of the adjustable resistance R.

00When 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.

00In 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.

00Steinmetz'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.

00The values of this ratio for different values of B, as given by Fleming (Phil.

001888, p. 274), and that the values which he assigned to H are consequently somewhat too high.

00If 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).

00The 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.

00Below is given a selection from Bidwell's tables, showing corresponding values of magnetizing force, weight supported, magnetization, induction, susceptibility and permeability: - A few months later R.

00He 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.

00Taylor Jones subsequently found a good agreement between the theoretical and the observed values of the tractive force in fields ranging up to very high intensities (Phil.

00Thus any desired number of corresponding values of H and B can be easily and quickly found.

00Values of I are derived from (B -H)/477and of from B/H.

00The annexed table gives the saturation values of I for the particular metals examined by Ewing and Low: Wrought iron .

00H(= B -47rI) was calculated from corresponding values of I and B.

00For 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.

00Ann., 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.

00The 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.

00Further, 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.

00Honda 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.

00The 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.

00Bidwell 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.

00no evidence of hysteresis could [[[Temperature And Magnetization]] found to be 780°, 360° and 1090° respectively, but these values are not quite independent of the magnetizing force.

00The values of the permeability corresponding to the highest and lowest temperatures are given in the following table.

008 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.

00These high values render hardened tungsten-steel particularly suitable for the manufacture of permanent magnets.

00The 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.

00For 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.

0029 shows the variations of resistance in relation to temperature for fields of different constant values.

00The following values of K for different metals are given by E.

00Annexed are values of Io 6 K for the different salts examined, w being the weight of the salt per c.c. of the solution.

00The values assigned to the atomic susceptibilities of most of the known elements are appended.

00His determination 2 of maximum and minimum values for the slowly varying planetary eccentricities was the earliest attempt to deal with the problem.

00According 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).

00To 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.

00In this period the increase in the sterling equivalents would be proportionately greater than that of the currency values.

001 Merchandise passing the boundaries is subject to declaration; the respective values are stated by a special commission of experts residing in Budapest.

00Laplace 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.

00Bodin 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.

00- 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.

00It is important to begin the study of graphics with concrete cases rather than with tracing values of an algebraic function.

00In 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.

00This, however, applies mainly to the representation of values of Y.

00"), that the graphic method leads without arithmetical reasoning to the properties of negative values.

00In 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.

00It must, of course, be remembered (ï¿½ 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.

00is then an expression of the form a p b e c r d s, where p, q, r, s have the greatest possible values consistent with the condition that each of the given expressions shall be divisible by a p b e c r d s .

00is of the form a p b e c r d s, where p, q, r, s have the least possible values consistent with the condition that a P PC'd s shall be divisible by each of the given expressions.

00if B and C are expressions involving x which are different in form but are arithmetically equal for all values of x), then the statement A = C is an equation which is true for the same value of x for which A = B is true.

00(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 !

00(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.

00The 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.

00(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.

00(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.

00(vi.) The definition of no.), which has already been extended in (iv.) above, has to be further extended so as to cover fractional values of n, positive or negative.

00Certain relations still hold, the most important being (22) of ï¿½ 44 (ii.), which holds whatever the values of m and of n may be; r, of course, being a positive integer.

00(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 (ï¿½ 46 (ii.)).

00to consider the relations between the coefficients of powers of x, rather than the values of the terms themselves.

00a succession of numbers corresponding to the numbers I, 2, 3, ...) which possesses the property that, by starting far enough in the sequence, the range of variation of all subsequent terms can be made as small as we please, but (x+h) n always lies between the two values determining the range.

00Thus 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 (ï¿½ 45)ï¿½ This conception of a limit enables us to deal with algebraical expressions which assume such forms as -° o for particular values of the variable (ï¿½ 39 (iii.)).

00We 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.

00Thus there appear to be discontinuities in the values of y.

00It 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.

00The values of x and y are different, unless V (qq o) = o.

00a n are scalars, and in particular applications may be restricted to real or complex numerical values.

001n(n - I) distinct values, exclusive of zero.

00These values are assumed to be independent, so we have 2n(n - I) derived units of the second species or order.

00His method for determining approximate values of the roots of equations is far in advance of the Hindu method as applied by Cardan, and is identical in principle with the methods of Sir Isaac Newton and W.

00Even 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.

00The actual values of u/zr (calculated in another manner by F.

00Since 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.

00From 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.

00The part corresponding to negative values of u is similar, OA being a line of symmetry.

00The following table gives the actual values: - In both cases the image of a mathematical point is thus a symmetrical ring system.

00When z has one of the values thus determined, (z)=Jo(z).

00The 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.

00This disposition is adopted in Rowland's instrument; only, in addition to the central image formed at the angle 4' =4), there are a series of spectra with various values of 4', but all disposed upon the same circle.

00If 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 .

00By 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 .

007rv 7rt 5 7r 5 v 9 The corresponding values of C and S were originally derived by A.

00Taking 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.

00It 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.

00Primary, secondary and spurious bows were formed, and their radii measured; a comparison of these observations exhibited agreement with Airy's analytical values.

00Soc., 1901, 23, p. 527), who, assuming the formula C24H4 6 O 20 for cellulose, showed how the nitrocelluloses described by different chemists may be expressed by the formula C24H4,..-z020(N02)s, where x has the values 4, 5, 6, ...

00The total foreign trade in 1908 amounted to $9,778,810 imports and $14,560,830 exports, the values being in U.S. gold.

00In the absence of statistical returns it is impossible to give the values of this branch of trade.

00Hero'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.

00The following values are due to Rubens and Hagen (Ann.

00the contraction along a given straight line will in general have different values in any two neighbouring crystals, and the crystals consequently become slightly detached from one another.

00All 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.

00These values may vary within certain limits for different specimens.

00(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.

00Negative 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'.

00.) = (X-jfidp) +m (Y-dy) +n (Zp 2), for all values of 1, m, n, leading to the equations of motion with moving axes.

00These equations are proved by taking a line fixed in space, whose direction cosines are 1, then dt=mR-nQ,' d'-t = nP =lQ-mP. (5) If P denotes the resultant linear impulse or momentum in this direction P =lxl+mx2+nx3, ' dP dt xl+, d y t x2' x3 +1 dtl dt 2 +n dt3, =1 ('+m (dt2-x3P+x1R) ' +n ('-x1Q-{-x2P) ' '= IX +mY+nZ, / (7) for all values of 1, Next, taking a fixed origin and axes parallel to Ox, Oy, Oz through 0, and denoting by x, y, z the coordinates of 0, and by G the component angular momentum about 1"2 in the direction (1, G =1(yi-x2z+x3y) m 2-+xlz) n(y(y 3x 1 x3x y + x 2 x) (8) Differentiating with respect to t, and afterwards moving the fixed.

003 - y1Q+y2P-x1V+x2U =1L+mM+nN, (9) for all values of 1, m, n.

00

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