approximation

The approximation was mutual.

395A much better approximation to the heat of combustion of such substances is obtained by deducting the oxygen together with the amount of carbon necessary to form C02, and then ascertaining the amount of heat produced by the residual carbon and hydrogen.

138Equation (44) shows that as a first approximation.

64The result is an approximation, for inequalities of the ground bounded by the two contours have not been considered.

50is approximately equal to -J(27rn).(nle) n; the approximation may be improved by Stirling's theorem log e 2 +log e 3 +...

55From these we may take 17.5 as a fair approximation.

55Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, &c., partitions, probabilities; "Linear Substitutions," with the topics determinants, &c., linear substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers.

41With sufficient approximation we may regard BQ and b as rectangular co-ordinates of Q.

42The correctness cf this hypothesis has long been under suspicion, but it has generally been accepted as the best simple approximation to the actual distribution of the motions that could be made.

30In the present work we have made an attempt to construct an accurate approximation to the functional for the exchange-correlation energy of density-functional theory.

301470 grains), which agrees well to the weight; but this was probably an approximation, and not derivative, as there is (14) a weight called shet of 4.70 or 4.95 uten, and this was perhaps the actual weight of a hon.

34A pair of cones having a semi-vertical angle of 45° were considered to combine high concentrative power with a sufficient approximation to uniformity of field.

36Specific Heat Of Mercury By Continuous Electric Method It Is Assumed As A First Approximation That The Heat Loss Is Proportional To The Rise Of Temperature Do, Provided That Do Is Nearly The Same In Both Cases, And That The Distribution Of Temperature In The Apparatus Is The Same For The Same Rise Of Temperature Whatever The Flow Of Liquid.

20Approximation of a discriminant function or regression function using a hyperplane.

20Subsequently to the floating off of the entosternite the approximation of the nerve cords took place in the prosoma, and thus they were able to take up a position below the entosternite.

21The approximation to square roots in Hero has been the subject of papers too numerous to mention.

21Probably the 25.0 is the best approximation.

21Mansi, Hardouin, Hefele and Dale are in substantial agreement upon 305 or 306, and this is probably the closest approximation possible in the present state of the evidence.

23In the article Crystallography the nature and behaviour of twinned crystals receives full treatment; here it is sufficient to say that when the planes and axes of twinning are planes and axes of symmetry, a twin would exhibit higher symmetry (but remain in the same crystal system) than the primary crystal; and, also, if a crystal approximates in its axial constants to 'a higher system, mimetic twinning would increase the approximation, and the crystal would be pseudo-symmetric.

25In the mesosoma the approximation had occurred before the entosternites were formed.

25In the same way we regard log l 02, not as a new kind of number, but as an approximation.

10This approximation between the two governments was happily followed by friendly feelings between the two nations, under the pressure of a common danger.

10Towards this goal of approximation to Cynicism the later Stoics had all along been tending.

10If the order of stratification differ from that of densities, we can show that each step of approximation to this order lowers the sum of tensions.

10The reistance represents an approximation of the amount of weight it replicates.

10They show again the closer approximation and better understanding with the Mahom.medans, which marks this Crusade.

11With increase of speeds this matter has become important as an element of comfort in passenger traffic. As a first approximation, the centre-line of a railway may be plotted out as a number of portions of circles, with intervening straight tangents connecting them, when the abruptness of the changes of direction will depend on the radii of the circular portions.

12Every hypothesis must be tested by an appeal to the facts of life, and modified or abandoned if it will not bear examination, unless we are convinced on genuine evidence that it may for a time be employed as a useful approximation, without prejudice to the later stages of the investigation we are conducting.

12In others there is an approximation of the lateral stems towards the median ventral line (Drepanophorus); in a genus of Heteronemertines (Langia), on the other hand, an arrangement occurs by which the longitudinal stems are no longer lateral, but have more or less approached each other dorsally.

12They were five-toed, bunodont Condylarthra, with a decided approximation to the perissodactyle type in the structure of the feet.

12Scelidotherium is another genus of large South American Pleistocene ground-sloths, characterized, among other features, by the elongation and slenderness of the skull, which thus makes a decided approximation to the anteater type, although retaining the full series of cheek-teeth, which were, of course, essential to an herbivorous animal.

12The Passalidae are a tropical family of beetles generally considered to be intermediate between stag-beetles and chafers, the enlarged segments of the feeler being capable of close approximation.

00- The total construction capital invested in the railways of the world in 1907 was estimated by the Archiv fur Eisenbahnwesen at £8,986,150,000; the figure is necessarily incomplete, though it serves as a rough approximation.

00He therefore abstained from determining for each case the specific heats of the solutions he employed, and contented himself with the above approximation.

00But the point which is important is that there was a certain approximation between the condition of the colonus and the slave which tended towards the fusion of both in a single class.

00The outcome has been that in the Church of England, and in many of her daughter Churches, there exists a bewildering variety of "uses," varying from that of Sarum and that of Rome down to the closest possible approximation to the Geneva model.

00In such experiments the narrowness of the zones renders necessary a pretty close approximation to the geometrical conditions.

00In spite of any inequality between p and p', the definition will be good to this order of approximation, provided a and y vanish.

00226) has shown that success may be attained by a variety of processes, including bichromated gelatin and the old bitumen process, and has investigated the effect of imperfect approximation during the exposure between the prepared plate and the original.

00If we write p = 27rR/A (6), we must regard p as a function of f, and we may take with sufficient approximation under any ordinary circumstances where p' denotes the value of p at 0, and is a constant, which is positive when the retarding plate is held at the side on which the blue of the spectrum is seen.

00Perhaps a closer approximation would be to rate the creole element (whites of European descent) at 10%, as in Colombia, and the mixed races at 70%, the remainder consisting of Africans, Indians and resident foreigners.

00The first step in this process is that of grinding the surface down until all projections are removed and a close approximation to a perfect plane is obtained.

00Estimates of the population of Arabia vary enormously, and the figures given in the following table can only be regarded as a very rough approximation: 4,825,000 Communications.

00It is found by experiment that the change of pv with pressure at moderate pressures is nearly proportional to the change of p, in other words that the coefficient d(pv)/dp is to a first approximation a function of the temperature only.

00Zeuner's formula for steam), but they cannot be made to represent with sufficient approximation the deviations from the ideal state at moderate pressures and generally lead to erroneous results.

00In working to a first approximation, the small term nc/V may be omitted in the expression for s.

00There must be considerable dissociation of molecules, and as a first approximation it may be taken that of io molecules of most of the components about 9 (or in the case of magnesium sulphate 5) have been separated into their ions, and that it is only during slow concentration as in a natural saline that the ions combine to produce the various salts in the proportions set out in the above table.

00While Gelocus exhibits a marked approximation to the Tragulidae, Prodremotherium comes nearer to the FIG 2.

00Thus, to within the degree of approximation to which our theory is accurate, the value of y for every gas ought to be one of this series.

00(iv) In order to find what formula may be applied, it is necessary to take the successive differences of u; and it is then just as easy, in most cases, to use a formula which directly involves these differences and therefore shows the degree of accuracy of the approximation.

00The vibrations of certain sources of sound may be represented, at least as a first approximation, as consisting of stationary waves, and from a consideration of the rate of propagation of waves along these sources we can deduce their frequency when we know their length.

00At the open end, as a first approximation to be corrected later, there are no pressure changes, for any tendency to excess can be relieved by immediate expansion into the outer air, and any tendency to defect can be filled up by an inrush from the outer air.

00the closest approximation of actual to theoretical dimensions of the parts.

00Comparing this time with the experimental value of the time occupied by the cordite in burning, a start is made for a fresh estimate and a closer approximation.

00Empirical formulas based on practical experience are employed for an approximation to the result.

0044-64 can thus be fixed with a fair approximation to certainty, it is unfortunately otherwise with the events of A.D.

00Besides this, all their evidence is but approximate, often only stating quantities to a half or quarter of the amount, and seldom nearer than 5 or 10%; hence they are entirely worthless for all the closer questions of the approximation or original identity of standards in different countries; and it is just in this line that the imagination of writers has led them into the greatest speculations, unchecked by accurate evidence of the original standards.

00Found in Asia Minor and northern Greece, it does not appear unreasonable to connect it, as Hultsch does, with the Belgic foot of the Tungri, which was legalized (or perhaps introduced) by Drusus when governor, as 1/8 longer than the Roman foot, or 13.07; this statement was evidently an approximation by an increase of 2 digits, so that the small difference from 13.3 is not worth notice.

00Smith afterwards described Quesnay as a man "of the greatest modesty and simplicity," and declared his system of political economy to be, "with all its imperfections, the nearest approximation to truth that had yet been published on the principles of that science."

00A preliminary study of optics led to the publication, in 1604, of his Astronomiae pars optica, containing important discoveries in the theory of vision, and a notable approximation towards the true law of refraction.

00The last is the roughest approximation and would indicate a native mass of 50,000,000 in 1900, or a foreign contribution of approximately half.

002-}-cos B It is readily shown that the latter gives the best approximation to 0; but, while the former requires for its application a knowledge of the trigonometrical ratios of only one angle (in other words, the ratios of the sides of only one right-angled triangle), the latter requires the same for two angles, 0 and 3B.

00It has another characteristic which points to its being an early work of Aristotle, when he was still under the influence of Plato's style; namely its approximation to dialogue.

00The premolar is very small, thus showing an approximation to the Myoidea, although in other respects Petromys appears to approximate to the Hystricidae.

00As a first `approximation we may say that gases send out homogeneous 2 Wied.

00Rydberg favours the former view, but he does not attempt to obtain any very close approximation between the observed and calculated values of the frequencies.

00The fact that the addition of the term introduced by Ritz not only gives a more satisfactory representation of each series, but verifies the above relationship with a much closer degree of approximation, proves that Ritz's equation forms a marked step in the right direction.

00But, on the other hand, no one pretends to have found the rigorous expression for the law, and the appropriate approximation may take quite different forms when constants which are large in one case are small in the other.

00Larmor 7 developed the same idea, and arrived by a very simple method at an approximation estimate of the shift to be expected.

00The earth, which is commonly employed as a base for terrestrial motions, is not a very close approximation to being a Newtonian base.

00The following table, taken from the Manchester Guardian, gives in thousands of lb the amounts of cotton yarns exported from Great Britain during 1903, 1904 and 1905 respectively, according to the Board of Trade returns, together with the average value per lb for each of the countries: It should be understood, however, that in some cases the Board of Trade figures represent only an approximation to the ultimate distribution, as the exports are sometimes assigned to the intermediate country, and in particular it is understood that a considerable part of the yarn sent to the Netherlands is destined for Germany or Austria.

00There is actually :4, which is the nearest possible approximation with the number i 5.

00But from a study of Dalton's own MS. laboratory notebooks, discovered in the rooms of the Manchester society, Roscoe and Harden (A New View of the Origin of Dalton's Atomic Theor y, 1896) conclude that so far from Dalton being led to the idea that chemical combination consists in the approximation of atoms of definite and characteristic weight by his search for an explanation of the law of combination in multiple proportions, the idea of atomic structure arose in his mind as a purely physical conception, forced upon him by study of the physical properties of the atmosphere and other gases.

00Lyell concluded that, although no approximation can be given of the age of Etna, "its foundations were laid in the sea in the newer Pliocene period."

00The rough appearances of physical facts, their outlines, surfaces and so on, are the data of observation, and only by a method of approximation do we gradually come near to such propositions as are laid down in pure geometry.

00Under a rational system of institutions, the adaptation of numbers to the means available for their support is effected by the felt or anticipated pressure of circumstances and the fear of social degradation, within a tolerable degree of approximation to what is desirable.

00This condition can generally be satisfied with sufficient approximation with plates of reasonable dimensions.

00If the thickness of the glass is small compared with the diameter of the tube, say one-tenth, equation (1) may be applied with sufficient approximation, the area A being taken as the mean between the internal and external surfaces.

00Gomperz in his Herkulanische Studien, and in contributions to the Vienna Academy (Monatsberichte), has tried to evolve from the fragments more approximation to modern empiricism than they seem to contain.

00Not only has the development of the south differed from that of the north, and the west been subjected to other influences than those affecting the east, but even where the same influences have been at work the period of their operation has often varied widely in the different districts, so that in a general sketch of the whole country the chronology can only be a very rough approximation.

00Bismarck was their national hero, the anniversary of Sedan their political festival, and approximation to Germany was dearer to them than the maintenance of Austria.

00On the other hand, Palaeosyops is connected with Titanotherium by means of Telmatotherium of the upper Bridger and Washakia Eocene, a larger animal, with a longer and flatter skull, showing rudiments of horn-cores, only two pairs of lower incisors, and a general approximation in dental character to Titanotherium.

00caribou), which is a larger animal with shorter and more massive antlers, in which the great terminal expansions are in approximation to the brow-tine owing to the shortness of the beam.

00On the other hand, the comparison we are now able to make between the canonical books of the older Buddhism and the later texts of the following centuries, shows a continual decline from the old standpoint, a continual approximation of the Buddhist views to those of the other philosophies and religions of India.

00With Die Braut von Messina (1803) he experimented with a tragedy on purely Greek lines, this drama being as close an approximation to ancient tragedy as its medieval and Christian milieu permitted of.

00Consider the rational-real in the unity that must be, and this is the way of it, or an approximation to the way of it!

00Observing that this rate of diminution is approximately as the square of the reciprocal of the absolute temperature, we see that the almost equally simple formula log p=A+B/0 represents a much closer approximation to experiment.

00The specific volumes of superheated vapours may, however, (19) be measured with a satisfactory degree of approximation.

00.q,, that they shall vanish in the configuration in question: The potential energy is then given with sufficient approximation by an expression of the form 2V=ciiqi1+clzqii+...

00The area and population of the world, as a whole, have been the subject of many estimates in scientific works for the last three centuries and are still to a considerable extent matters of rough approximation.

00Maxwell made a comparison between the optical refractive index and the dielectric constant of paraffin wax, and the approximation between the numerical values of the square of the first and that of the last was sufficient to show that there was a basis for further work.

00In his religious views Renouvier makes a considerable approximation to Leibnitz.

00About this time, indeed, there was in Scotland a remarkable approximation to that solution of the toleration difficulty which later ages have approved; for the regent was understood to favour the demand of the "congregation" that at least the penal statutes against heretics "be suspended and abrogated," and "that it be lawful to us to use ourselves in matters of religion and conscience as we must answer to God."

00The problem of finding a system which reproduces a given object upon a given plane with given magnification (in so far as aberrations must be taken into account) could be dealt with by means of the approximation theory; in most cases, however, the analytical difficulties are too great.

00The analytical approximation theory is often employed provisionally, since its accuracy does not generally suffice.

00The Gaussian theory is only an approximation; monochromatic or spherical aberrations still occur, which will be different for different colours; and should they be compensated for one colour, the image of another colour would prove disturbing.

00Every convergent is a nearer approximation to the value of the whole fraction than any fraction whose denominator is less than that of the convergent.

00The chief practical use of the simple continued fraction is that by means of it we can obtain rational fractions which approximate to any quantity, and we can also estimate the error of our b4 as a4 b5 approximation.

00Huygens (Descriptio automati planetarii, 1703) uses the simple continued fraction for the purpose of approximation when designing the toothed wheels of his Planetarium.

00This was a serious departure from the principles of the system, facilitating a return of later Stoicism to the dualism of God and the world, reason and the irrational part in man, which Chrysippus had striven to surmount.3 Yet in the general approximation and fusion of opposing views which had set in, the Stoics fared far better than rival schools.

00They testify to the restriction of philosophy to the practical side, and to the increasing tendency, ever since Panaetius, towards a relaxation of the rigorous ethical doctrine and its approximation to the form of religious conviction.

00Since the plates are very near one another we may use the following equation of the surface as an approximation: y= h1+Ax+Bx 2, h2=h1+Aa+Ba2, whence cot a 1 = - A, cot a 2 =A+2Ba T(cos a i +cos a 2) = +3Ba2), whence we obtain h, = g (cos a, +cos a 2) +6 (2 cot a, - cot a2) h 2 = - T (cos a,+cos a 2) +6 cot a2 - cot al) Let X be the force which must be applied in a horizontal direction to either plate to keep it from approaching the other, then the forces acting on the first plate are T+X in the negative direction, and T sin a t + 2gph 1 2 in the positive direction.

00When the stream consists of drops following one another in single file, no such increase of section is possible; and then the constancy of the total stream requires a gradual approximation of the drops, which in the case of a nearly vertical direction of motion cannot stop short of actual contact.

00In the earlier stages of approximation the obstacle thus arising may not be important; but when the thickness of the layer of air is reduced to the point at which the colours of thin plates are visible, the approximation must be sensibly resisted by the viscosity of the air which still remains to be got rid of.

00W.) having given up the specializations of func tion impressed on them during evolution and simply carrying out the fundamental functions of nutrition, growth, and multiplication which mark the generalized activities of the bacterial cell, and at the same time rendered as accessible to the environment by isolation and consequent extension of surface, we should doubtless find them exerting changes in the fermentable fluids necessary to their life similar to those exerted by an equal mass of bacteria, and that in proportion to their approximation in size to the latter.

00It is highly probable, however, that the biramous limb is a simplification of a more complex primitive type, to which the Phyllopod limb is a more or less close approximation.

00But given the imperfect medium for investigation and the absence of an archaeological basis for criticism, the work of Herodotus remains a scientific achievement, as remarkable for its approximation to truth as for the vastness of its scope.

00In the same year the changes which had occurred in the policy, or rather the caprice, of Queen Anne, brought about an approximation between England and France, and put an end to the influence which Marlborough had hitherto possessed.

00So far as the course of universal history can be truly represented as an approximation to this reconciliation by a widening and deepening of both the elements, we may claim to possess a philosophy of history.

00Of his extensive investigations into the solution (especially by numerical approximation) of certain classes of differential equations which constantly occur in the treatment of physical questions, only a few items have been published, at intervals, in the Philosophical Magazine.

00The conditions which enable a pulley tackle to sustain a weight when the effort is removed may be examined, to a first approximation, if we assume that the internal friction acts in such a way as virtually to diminish FIG.

00Equation (I) becomes E/R= (I - b - c - M/R)/(i - a), and hence b+c +M /R is equal to or greater than unity when the load is self-sustained, and we thus obtain a relation between R and E in the form i - a/2 - c, which shows to a first approximation, that as c approaches unity a high efficiency is obtainable, while the self-sustaining power of the tackle is retained.

00the impossibility, outside a certain limited range of subjects, of ever obtaining absolute accuracy, and the consequent importance of not wasting time in attempting to obtain results beyond a certain degree of approximation.

00Logarithms.-Multiplication, division, involution and evolution, when the results cannot be exact, are usually most simply performed, at any rate to a first approximation, by means of a table of logarithms. Thus, to find the square root of 2, we have log A /2 = log (21)=1 log 2.

00When a first approximation has been obtained in this way, further approximations can be obtained in various ways.

00Although the present article does not discuss mammalian osteology in general (for which see Vertebrata), it is interesting to notice in this connexion that the primitive condition of the mammalian tympanum apparently consisted merely of a small and incomplete bony ring, with, at most, an imperfect ventral wall to the tympanic cavity, and that a close approximation to this original condition still persists in the monotremes, especially Ornithorhynchus.

00In this case, the problem can be attacked only by methods of approximation, devised so as to meet the special conditions of each case.

00The special conditions which obtain in the solar system are such as to make the necessary approximation theoretically possible however complex the process may be.

00Another approximation is, therefore, to be made, when necessary, by correcting the expression of the pull through taking account of the variations of the elements already determined, which will give a yet nearer approximation to the truth.

00In theory these successive approximations may be carried as far as we please, but in practice the labour of executing each approximation is so great that we are obliged to stop when the solution is so near the truth that the outstanding error is less than that of the best observations.

00An approximation to such an attempt is that of F.

00The numerical computations were worked out by Hill only for the first approximation.

00But Adams in 1853 1 showed that the previous computations of the acceleration were only a rude first approximation, and that a more rigorous computation reduced the result to about one-half.

00Although St Patrick endeavoured to organize the Irish church on regular diocesan lines, after his death an approximation to the lay system was under the circumstances almost inevitable.

00When light from an extended source is made to converge upon the crystal, the phenomenon of rings and brushes localized at infinity is obtained.The exact calculation of the intensity in this case is very complicated and the resulting expression is too unwieldy to be of any use, but as an approximation the formula for the case of a parallel beam may be employed, the quantities and p therein occurring being regarded as functions of the angle and plane of incidence and consequently as variables.

00From 2412 to 1479 the separation lasted with a growing approximation of the two states whose interests touched one afiother so closely.

00We now use matrix perturbation theory to compute the covariance of based on this zero approximation.

00adiabatic nuclei approximation.

00angular momentum DWBA (Distorted Wave Born Approximation) cross sections for a range of transferred angular momenta.

00approximation of laws are recognized as two parallel means of implementing policies.

00The structure function project will be carried out in the quenched approximation first.

00A demonstration of this relationship is given for a simplified approximation to a single Taylor screen atmosphere in Appendix A.

00The score functions of the individual versions were combined to derive an approximation of the difficulty function.

00approximation obtained by just using the first ten terms is, to.

00We also investigate the effect of self-consistency in the self-energy within the GW approximation on the spectral function and total energy.

00To get a rough approximation of how much sums in the 1890s would be in today's terms we multiply by 60.

00The above approximation for the error bars rests on a gaussian approximation which assumes that the Hessian A is positive definite.

00These are automatically computed by finite difference approximation (either forward or central differences ).

00approximation algorithms for the problem.

00approximation theory.

00The results are compared with the widely-used local-density approximation (LDA ).

00Convergence of the scattering amplitudes with the number of partial waves is improved by using a procedure which is related to the Pade approximation.

00Bayesian inference for stochastic kinetic models using a diffusion approximation.

00The local density approximation (LDA) is shown to be inadequate for calculating the band-gap narrowing.

00Following a section on normed linear spaces, we will consider periodic approximation using classical Fourier series.

00diffusion approximation.

00Approximation of the Beta function The asymptotic expansion for the T score, equation 31, requires the value of.

00This is suitable when the bounds of the approximation are known not to change, as staggered fermions.

00Theories of halo nucleus scattering often use an approximation in which the halo nucleus scattering often use an approximation in which the halo is appeared frozen during the collision.

00impingelectric approximation is used to characterize the response of the target material to the long-ranged coulomb field of the impinging electrons.

00Restrictions: In the Born approximation angular momenta lar momenta l 10 are used.

00Restrictions: In the Born approximation angular momenta lass="ex">angular momenta l 10 are used.

00The generic approximation lemma (pdf, ps, bibtex) Graham Hutton and Jeremy Gibbons.

00magnitude estimation data are offline data that only represent a rough approximation of processing difficulty.

00Theories of halo nucleus scattering often use an approximation in which the halo is appeared frozen during the collision.

00numerical approximation.

00One of these is that efficient approximation algorithms exist that yield nearly optimal solutions to NP-hard optimization problems.

00The density of states at the surface is calculated within the GW approximation of many-body perturbation theory.

00polynomial approximation on compact manifolds.

00The Poisson approximation would be acceptable (q small and k q small ).

00quenched approximation first.

00reactance x s is to a good approximation proportional to f.

00scattering amplitudes with the number of partial waves is improved by using a procedure which is related to the Pade approximation.

00semiclassical approximation because its validity lies somewhere between that of classical and quantum physics.

00This does not indicate that Newtonian space-time is only a useful approximation to reality and nothing more.

00sparse polyhedral approximation to the original shape surfaces.

00spur of that hill is named Uamh Mhor, a possible approximation to Uam Var.

00An approximation is proposed by truncating an infinite summation.

00whiny voice, which at times seemed to have just an approximation to pitch.

00It appears, therefore, that to the order of approximation afforded by (3), the effect of the particles in dx is to modify the phase, but not the intensity, of the light which passes them.

00In the case, however, of many observatories, especially as regards the older records, no data for reduction exist; further, the reduction to the open is at best only an approximation, the success attending which probably varies considerably at different stations.

00If the mean of the gradients observed at the ground and at 1500 metres be taken as an approximation to the mean value of the gradient throughout the lowest 1500 metres of the atmosphere, we find for the potential at 1500 metres level 112,500 volts.

00Further, the preliminary survey over the proposed route, necessary for deciding the length and types of cable required, can afford merely an approximation to the depth in which the cable actually lies, since accidents of wind and weather, or lack of observations for determining the position, cause deviations, often of considerable importance, from the proposed route.

00He found on both sides an unreadiness for approximation: the Jews had sunk into apathy and degeneration, the Christians were still moved by hereditary antipathy.

00A pair of cones having a semi-vertical angle of 45Ã‚° were considered to combine high concentrative power with a sufficient approximation to uniformity of field.

00Resuming the inquiry into the invariability of mean motions, Poisson carried the approximation, with Lagrange's formulae, as far as the squares of the disturbing forces, hitherto neglected, with the same result as to the stability of the system.

00So long as he held aloof from Ledru-Rollin and the more radical of his colleagues, the disunion resulting weakened the government; as soon as he effected an approximation to them the middle classes fell off from him.

00The parallel motion known by his name is a three-bar linkage, which gives a very close approximation to exact rectilinear motion, but in spite of all his efforts he failed to devise one that produced absolutely true rectilinear motion.

00HOLY, sacred, devoted or set apart for religious worship or observance; a term characteristic of the attributes of perfection and sinlessness of the Persons of the Trinity, as the objects of human worship and reverence, and hence transferred to those human persons who, either by their devotion to a spiritual ascetic life or by their approximation to moral perfection, are considered worthy of reverence.

00In the application of Siacci's method to the calculation of a trajectory in high angle fire by successive arcs of small curvature, starting at the beginning of an arc at an angle 4) with velocity v4), the curvature of the arc 4-8 is first settled upon, and now (80) n=1(0+0) is a good first approximation for n.

00(See River -HoG.) The recently discovered Hylochoerus of the equatorial forestdistricts of Africa comes nearest to the under-mentioned warthogs, but the skull is of a much less specialized type, while the upper tusks are much smaller although they have the same general curvature and direction, and the cheek-teeth lack the peculiar characteristics of those of Phacochoerus, although they present a certain approximation thereto.

008), joined A and B with 0 the centre, bisected the angle AOB by OD, so that BD became the semi-side of a circumscribed regular 12-gon; then as AB :BO: OA :: I: d 3: 2 he sought an approximation to X 1 3 and found that AB: BO >153:265.

00In refutation of Duchesne(Van der Eycke), he showed that the ratio was 3-, %-, and thence made the exceedingly lucky step of taking a mean between the two by the quite unjustifiable process of halving the sum of the two numerators for a new numerator and halving the sum of the two denominators for a new denominator, thus arriving at the now well-known approximation 3 6 3 - or ??

00Generalized features are also displayed by the Oligocene Hypisodus, which in its short skull and large orbits presents a curious approximation to the African dik-dik antelopes of the genus Madoqua (see Antelope).

00(1827), &c. In the first of these memoirs Poisson discusses the famous question of the stability of the planetary orbits, which had already been settled by Lagrange to the first degree of approximation for the disturbing forces.

00Poisson showed that the result could be extended to a second approximation, and thus made an important advance in the planetary theory.

00The work on its appearance created an immense sensation among scholars, and was vehemently attacked in many quarters, but on the whole it was received as being much the nearest approximation yet made to the original text of the New Testament (see Bible: New Testament, " Textual Criticism").

00Such " psychological certainty " was denied by their agnostic opponents, and in the history of Stoicism we have apparently a modification of the doctrine of 4avra rta KaraXnirnici with a view to meet the critics, an approximation to a recognition that the primary conviction might meet with a counter-conviction, and must then persist undissipated in face of the challenge and in the last resort find verification in the haphazard instance, under varying conditions, in actual working.

00with each degree of approximation to reality (to finite objects and apertures), a certain number of aberrations is associated.

00There are several approximation formulae: - S = (a ±b) makes the perimeter about 1/tooth too small; s = 7r-V (a 2 +b 2) about 1 /tooth too great; 2s=1r(a+b)+7r'I (a 2 +b 2) is within 1/30,000 of the truth.

00The Poisson approximation would be acceptable (q small and k q small).

00Also the surface reactance X s is to a good approximation proportional to f.

00This is known as the semiclassical approximation because its validity lies somewhere between that of classical and quantum physics.

00These patches represent the triangles of the sparse polyhedral approximation to the original shape surfaces.

00The southwest spur of that hill is named Uamh Mhor, a possible approximation to Uam Var.

00We now use matrix perturbation theory [7] to compute the covariance of based on this zero approximation.

00We examine our invariant measure approximation in more detail, and include encouraging numerical examples for the HÃ©non system and a nonlinear torus map.

00OPTIONS -a Generate an ASCII approximation of the typeset output.

00A very whiny voice, which at times seemed to have just an approximation to pitch.

00You'll be able to see boundaries and an approximation of how large a city is, but nothing more.

00Use this approximation when deciding how much TVP to include in your curry recipe.

00A fishnet chemise is not something you buy for an exact fit, since it's really fantasy lingerie, so you just need an approximation and don't have to worry about trying on.

00Some online mortgage calculators will estimate the total cost of your PITI payment by presenting an approximation of tax and insurance charges within the geographical area in which you plan to buy a home.

00The easiest option is to choose the identical shape to what is used in the ring, or to choose the closest approximation (princess cut earrings can complement emerald cut engagement rings, for example).

00Airbrush tattoos are more realistic and last longer than traditional temporary tattoos do, giving a better approximation of the real thing.

00One way to make sure that your drum majorette uniforms will be up to the task is to wear them (or an approximation of them) for rehearsals.

00In order to render an 'account of Tyndall's "residual blue" it is necessary to pursue the approximation further, taking for simplicity the case of spherical shape.

01Their form, however, is not sufficiently characteristic to warrant this identification, though it may be noted that the nearest approximation to phallic worship is found amongst the most typical of African peoples, viz.

01The Arab astronomers measured a degree on the plains of Mesopotamia, thereby deducing a fair approximation to the size of the earth.

01Thus the best approximation to the average depth of the ocean is little more than an expert guess; yet a fair approximation is probable for the features of sub-oceanic relief are so much more uniform than those of the land that a smaller number of fixed points is required to determine them.

01A mean degree of the meridian being assumed to be 69-09 statute miles of 5280 ft., the nautical mile (A l b - degree) is taken as 6080 ft., which is a sufficiently close approximation for practical purposes, and the distances between the knots are made to bear the same relation to 6080 ft.

01They are not exact, but may be taken as representing an approximation correct within one per cent.

01The people, though remarkable for their intelligence whilst Europe was in a state of barbarism, made no approximation to the mechanical operations of modern times, nor was the cultivation of cotton either improved or considerably extended.

01Thus the prominent school of criticism which appraised Wagner in the 10th century by his approximation to Darwin and Herbert Spencer, appraises him in the aoth by his approximation to Bernard Shaw; with the absurd result that Gatterdammerung is ruled out as a reactionary failure.

01But though a formula of this type has no physical significance, and cannot be accepted as an equation to the actual curve of W and B, it is, nevertheless, the case that by making the index e =1.6, and assigning a suitable value to r t, a formula may be obtained giving an approximation to the truth which is sufficiently close for the ordinary purposes of electrical engineers, especially when the limiting value of B is neither very great nor very small.

01The 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.

01Substituting this, we find cot y = U-y, whence 5 7 y U(1+/-1-2:-+2...) - y3 -15-315' This equation is to be solved by successive approximation.

01(17) in which c is a small quantity (expressing the defect from the ideal volume V =Re/p due to co-aggregation of the molecules) which varies inversely as the nth power of 0, but is independent of p to a first approximation at moderate pressures.

012) differ from the corresponding organs of allied species in great breadth of the crown as compared with the length, the narrowness and crowding or close approximation of the ridges, the thinness of the enamel, and its straightness, parallelism and absence of " crimping," as seen on the worn surface or in a horizontal section of the tooth.

01Now µx 2 is very small compared with Ax, so that x is nearly equal to F/X, and as an approximation, F=Ax+µF 2 /A 2, or x=F/A - µF 2 /A 3.

01This is a very close approximation to the truth, if the length of the unit employed has been correctly assigned.2 Among the astronomers of antiquity, two great men stand out with unchallenged pre-eminence.

01A nitrogen molecule is thus a good approximation to a harmonic oscillator.

01And without considering the multiplicity and complexity of the conditions any one of which taken separately may seem to be the cause, he snatches at the first approximation to a cause that seems to him intelligible and says: "This is the cause!"

01

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