# Approximation Sentence Examples

approximation
• The approximation was mutual.

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

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

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

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

• A 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.

• Under 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.

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

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

• The 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.

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

• The 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.

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

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

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

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

• The 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.

• But 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.

• The 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.

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

• The 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.

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

• Smith 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."

• It 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.

• But 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.

• Specific 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.

• Observing 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.

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

• In 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.

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

• With 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.

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

• Every 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.

• In 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.

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

• Subsequently 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.

• If 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.

• Perhaps 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.

• Scelidotherium 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.

• At 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.

• Probably the 25.0 is the best approximation.

• Maxwell 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.

• If 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.

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

• It 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.

• There 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.

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

• Thus, 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.

• Comparing 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.

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

• Besides 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.

• Found 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.

• A 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.

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

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

• 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 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.

• But, 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.

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

• Lyell 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."

• The 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.

• Under 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.

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

• If 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.

• Gomperz 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.

• Not 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.

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

• On 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.

• On 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.

• With 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.

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

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

• The 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.

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

• About 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."

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

• The 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.

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

• They 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.

• When 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.

• In 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.

• It 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.

• But 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.

• In 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.

• So 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.

• Of 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.

• The 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.

• Equation (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.

• Logarithms.-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.

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

• Although 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.

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

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

• Another 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• Theories 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.

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

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

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

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

• An approximation is proposed by truncating an infinite summation.

• It 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.

• In 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.

• If 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.

• Further, 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.

• Resuming 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.

• So 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.

• The 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.

• In 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 ??

• Generalized 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).

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

• Such " 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.

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

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

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

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

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

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

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

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

• A 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.

• Some 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.

• The 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).

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

• One 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.

• In 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.

• Their 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.

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

• Thus 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.

• A 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.

• The 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.

• Thus 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.

• But 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.

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

• Now 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.

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

• The 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.

• The 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.

• This 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.

• In 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.

• This 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.

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

• But 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.

• Although 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.

• When 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.

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

• Mansi, 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.

• In 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.

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

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