# Numerical Sentence Examples

The

**numerical**values are, it is to be noted, exceedingly small.His treatise on

**numerical**divisions, weights and measures (Distributio) is extant, with the exception of the concluding portion.In 1905 the value of the wool export regained the £20,000,000 level, and with the rapid recovery of the

**numerical**II.Often the number with the biggest font will not have the largest

**numerical**value.The

**numerical**predominance of certain families or their absence affords criteria for marking out boundary lines and tracing relationships.AdvertisementIf, therefore, we take r i /(i+x) as equal to I -xdx2-...+ (-) r x r, there is an error whose

**numerical**magnitude is I xr+1/ (I +x) I; and, if I xConductivity.-Conductivity, whether thermic or electric, is very differently developed in different metals; and, as an exact knowledge of these conductivities is of great importance, much attention has been given to their

**numerical**determination (see Electric conduction; and Conduction Of Heat).The great

**numerical**superiority of the Federals enabled Sherman to press back the Confederates without a pitched battle, but the severity of the skirmishing may be judged from the casualties of the two armies (Sherman's about 26,000 men, Johnston's over io,000), and the obstinate steadiness of Johnston by the fact that his opponent hardly progressed more than one mile a day.A particular trick of his is also to divide his arguments after the manner of the preachers of his day into heads and subheads, with actual

**numerical**signs affixed to them.Coulomb proved the proportionality of electric surface force to density, but the above

**numerical**relation E= 42ra was first established by Poisson.AdvertisementThis assumption represents qualitatively the theoretical isothermal of James Thomson (see Vaporization) and the phenomena of the critical state (see Condensation Of Gases); but the

**numerical**results to which it leads differ so widely from experiment that it is necessary to suppose the constant, a, to be a function of the temperature.For such purely abstract purposes, the possibility of

**numerical**evaluation of the function is of secondary importance, and it is often possible to make qualitative deductions with regard to the general nature of a transformation without any knowledge of the actual form of the function.Thoughout, Ephraim played a distinctive and prominent part; it probably excelled Manasseh in

**numerical**strength, and the name became a synonym for the northern kingdom of Israel.The same result will be ob tained with a stationary fork and a movable glass plate; and, if the time occupied by the plate in moving through a given distance can be ascertained and the number of complete undulations exhibited on the plate for that distance, which is evidently the number of vibrations of the fork in that time, is reckoned, we shall have determined the

**numerical**vibration value of the note yielded by the fork.Mayer's real merit consists in the fact that, having for himself made out, on inadequate and even questionable grounds, the conservation of energy, and having obtained (though by inaccurate reasoning) a

**numerical**result correct so far as his data permitted, he applied the principle with great power and insight to the explanation of numerous physical phenomena.AdvertisementThe

**numerical**relations existing between the trunk series and the branch series make it somewhat difficult to believe that they belong to different vibrating systems. But while we should undoubtedly hesitate on this ground to adopt Fredenhagen's 3 view that the two branch series belong to the element itself and the trunk series to a process of oxidation, we cannot press the argument against the view of Lenard, because the addition or subtraction of an electron introduces two vibrating systems which are still connected with each other and some**numerical**relationship is probable.The

**numerical**results of the civil service examinations are reduced so as to conform to a certain symmetrical "frequency-curve," of which the abscissae represent percentages of marks between definite limits and the ordinates the number of candidates obtaining marks between those limits.He indulged in a great deal of speculation as to the existence of an extra-spatial unit, which was to furnish the raison d'etre of the

**numerical**part, and render the quaternion homogeneous as well as linear.We have also pioneered

**numerical**simulations of neutron star magnetospheres that helped to understand how pulsar winds are launched by neutron stars.All these measures work by setting up a set of

**numerical**recursion equations derived from the input clauses to the theorem prover.AdvertisementIt is a broad collection of

**numerical**and symbolic calculation and visualization tools with a familiar scratchpad interface.A general

**numerical**approach for limit and shakedown analyzes has been developed and applied to the engineering design of materials and structures.The two new chapters describe

**numerical**experiments on two- and three-dimensional rotors, and phase singularities in the heart wall.At the most obvious level, children were involved with tweaking

**numerical**parameters of robots, a non-trivial exercise.Discrete

**numerical**variates have only a fixed set of possible values - typically integer values, arising from counting things.AdvertisementStar Wishing, in business since 1992, catalogs all stars with the Millennium Chronicle, an online catalog that includes over 10,000 stars with

**numerical**designations.Small laptops may not have the

**numerical**keyboard to the right of the letter keyboard.On the other hand, if you use Excel or other math programs frequently, a full size keyboard with a

**numerical**keypad will be a necessity.You can also alter the properties of the furniture and resize/rotate by increasing/decreasing the

**numerical**value.This can help people to better retain

**numerical**information, remember words they have read or heard, recall directions and just function better in their day to day lives.When you input these numbers into a mulch calculator, the

**numerical**answer is the number of cubic feet of mulch you will need to cover the area at the depth indicated.The overall

**numerical**reviews are averaged so you can see what people think of the guitar with a quick glance.After 1924, all serial numbers were assigned a two-letter prefix before the

**numerical**portion.On the downside, there is no QWERTY keyboard (only a regular

**numerical**keypad), so inputting text in the case of emails, schedule events, and SMS text messages can be more difficult than on other smartphones or on PDA phones.Thus there is no

**numerical**score or scale for the test.Psychometric tests convert an individual's psychological traits and attributes into a

**numerical**estimation or evaluation.The results of quantifiable psychological tests can be translated into

**numerical**values, or scores.Karyotype-A standard arrangement of photographic or computer-generated images of chromosome pairs from a cell in ascending

**numerical**order, from largest to smallest.Children with mathematical disorders are often unable to count in the correct sequence, to name numbers, and to understand

**numerical**concepts.Couples should not feel obligated to choose one diamond over another they prefer simply based on

**numerical**values.Understanding the intricacies of the history of carat weights and how they apply to engagement rings can help couples find the perfect ring for their budget and style preferences without being fooled by its

**numerical**values.Use symbols instead of letters, or write a

**numerical**code.Parents who want more information about films before they make decisions about whether or not their children can watch them can obtain categorized

**numerical**ratings from Kids-in-Mind.com.Extra wide women's shoes are expressed in a combination of

**numerical**and alphabetical figures.The index is a formula that uses weight and height to come up with a

**numerical**measure of whether a person is overweight.The point value system assigns a

**numerical**value to all foods and drinks.That's it - columns with headings, rows of data, all in

**numerical**or text form.The following example shows how to search the XML file using

**numerical**expressions.He is notorious for his wilful exaggeration, both in narrative and

**numerical**statements.When a character is said to be transmitted, or to be correlated with another character, the biometricist declares the statement valueless without

**numerical**estimations of the inheritance or correlation.The ultimate value of

**numerical**inquiries must depend on the equivalence of the units on which they are based.The nature of this problem is illustrated by the

**numerical**example in § g.Owing to the existence of a strong Mussulman minority among its inhabitants, the warlike character of the natives, and the mountainous configuration of the country, which enabled a portion of the Christian population to maintain itself in a state of partial independence, the island has constantly been the scene of prolonged and sanguinary struggles in which the

**numerical**superiority of the Christians was counterbalanced by the aid rendered to the Moslems by the Ottoman troops.Its symbolic expression, to a

**numerical**factor pres, is (Hbc) (Hbd) (Hcd) (bcd), and it is clearly of degree 6.Of these thirteen sections, the first contains a simple description of the more prominent phenomena, without mathematical symbols or

**numerical**data.We disregard

**numerical**coefficients, so that by the H.C.F.In order that

**numerical**results obtained by summing the first few terms of a series may be of any value, it is usually necessary that the series should converge to a limit; but there are exceptions to this rule.Then a+a = as = a; hence

**numerical**coefficients and indices are not required.A point A in space may be associated with a (real, positive, or negative)

**numerical**quantity a, called its weight, and denoted by the symbol aA.In the applications of the calculus the co-ordinates of a quaternion are usually assumed to be

**numerical**; when they are complex, the quaternion is further distinguished by Hamilton as a biquaternion.The Greeks had succeeded in solving an isolated example; the Arabs accomplished the general solution of

**numerical**equations.The component vibrations at P due to the successive zones are thus nearly equal in amplitude and opposite in phase (the phase of each corresponding to that of the infinitesimal circle midway between the boundaries), and the series which we have to sum is one in which the terms are alternately opposite in sign and, while at first nearly constant in

**numerical**magnitude, gradually diminish to zero.If, on the other hand, the point be well immersed in the geometrical shadow, the earlier zones are altogether missing, and, instead of a series of terms beginning with finite

**numerical**magnitude and gradually diminishing to zero, we have now to deal with one of which the terms diminish to zero at both ends.The denominator sin a is the quantity well known (after Abbe) as the "

**numerical**aperture."Descending series of the semi-convergent class, available for

**numerical**calculation when u is moderately large, can be obtained from (12) by writing x=uy, and expanding the denominator in powers of y.In another respect also he aided in establishing an exact science of medicine by the introduction of the

**numerical**or statistical method.The great

**numerical**superiority which they had at first possessed was gone by the 9th, and their task had come to be the ejection of an almost equal enemy from a naturally formidable position.The Turks, therefore, now possessed a huge

**numerical**preponderance in the theatre of war.The absolute unit of force is employed here, and not the gravitation unit of hydrostatics; in a

**numerical**application it is assumed that C.G.S.In other species there is a definite arrangement of the leaves, some with and others without tendrils opposite to them, the

**numerical**order remaining constant or nearly so.When it was over the Liberal party was just short of the

**numerical**strength which was requisite to defeat the combination of Tories and Parnellites.Since the establishment of the privileged province they have lost the Ottoman support which used to compensate for their

**numerical**inferiority as compared with the Christians; and they are fast losing also their old habits and distinctiveness.The foreign-born are more numerously represented among the criminal, defective and dependent classes than their

**numerical**strength would justify.The results coincide with Maxwell's so far as above stated, though the

**numerical**coefficients do not agree.He devised an approximate

**numerical**solution of equations of the second and third degrees, wherein Leonardo of Pisa must have preceded him, but by a method every vestige of which is completely lost.In the

**numerical**expression of absolute densities it is necessary to specify the units of mass and volume employed; while in the case of relative densities, it is only necessary to specify the standard substance, since the result is a mere number.The latter's enormous

**numerical**superiority was neutralized by Sulla's judicious choice of ground and the steadiness of his legionaries; the Asiatics after the failure of their attack were worn down and almost annihilated.The attempt to apply

**numerical**methods to the comparison of geometrical quantities led to the doctrine of incommensurables, and to that of the infinite divisibility of space.From this point of view the atomic doctrine might be regarded as a relic of the old

**numerical**way of conceiving magnitude, and the opposite doctrine of the infinite divisibility of matter might appear for a time the most scientific. The atomists, on the other hand, asserted very strongly the distinction between matter and space.Idealism has, of course, no quarrel with

**numerical**difference.He might thus compensate for his

**numerical**inferiority by superior mobility and superior leadership.Here they would be in contact, and ready to act united against Napoleon with a

**numerical**superiority of two to one.He had to delay the French advance for 24 hours and give time for Blucher's concentration, at the same time retaining his own freedom of manoeuvre, and this in spite of the great length of the summer day, the short distance that he lay 'in front of Fleurus, the tremendous

**numerical**superiority of the French and Napoleon's personal presence at their head.The measurement is

**numerical**, i.e.It might, therefore, be described as that branch of mathematics which deals with formulae for calculating the

**numerical**measurements of curved lengths, areas and volumes, in terms of**numerical**data which determine these measurements.Mensuration, then, is mainly concerned with quadratureformulae and cubature formulae, and, to a not very clearly defined extent, with the methods of obtaining such formulae; a quadrature-formula being a formula for calculating the

**numerical**representation of an area, and a cubature-formula being a formula for calculating the**numerical**representation of a volume, in terms, in each case, of the**numerical**representations of particular data which determine the area or the volume.On the other hand, it is worth noticing that the words " quadrature " and " cubature " are originally due to geometrical rather than

**numerical**considerations; the former implying the construction of a square whose area shall be equal to that of a given surface, and the latter the construction of a cube whose volume shall be equal to that of a given solid.The failure seems (§ 2) to be due to difficulty in realizing the

**numerical**expression of an area or a solid in terms of a specified unit, while the same difficulty does not arise in the case of linear measure or liquid measure, where the number of units can be ascertained by direct counting.The main object to be aimed at, therefore, in the study of elementary mensuration, is that the student should realize the possibility of the

**numerical**expression of areas and volumes.The

**numerical**result obtained by applying a formula to particular data will generally not be exact.The general principle is that the

**numerical**data from which a particular result is to be deduced are in general not exact, but are given only to a certain degree of accuracy.In the case of mathematical functions certain conditions of continuity are satisfied, and the extent to which the value given by any particular formula differs from the true value may be estimated within certain limits; the main inaccuracy, in favourable cases, being due to the fact that the

**numerical**data are not absolutely exact.On the other hand, the

**numerical**increase had not kept pace with the increase of population.When war broke out the Ottoman forces in Europe numbered less than 250,000 men, dispersed over Macedonia and Thrace; they were thus at great

**numerical**disadvantage.His strong opposition to "dissenting churches" was nowhere so clearly shown as in a pamphlet published in 1816 to dissuade all Episcopalians from joining the American Bible Society, which he thought the Protestant Episcopal Church had not the

**numerical**or the financial strength to control.The second volume (1817) relates to the Eulerian integrals, and to various integrals and series, developments, mechanical problems, &c., connected with the integral calculus; this volume contains also a

**numerical**table of the values of the gamma function.Under these circumstances, and also because of their

**numerical**weakness and the rigour of the weather, the Germans advanced but slowly.The equations (66) - (71) are Siacci's, slightly modified by General Mayevski; and now in the

**numerical**applications to high angle fire we can still employ the ballistic table for direct fire.It has been said that the blockade of the Confederate coast became in the end practically impenetrable, and that every attempt of the Confederate naval forces to break out was checked at once by crushing

**numerical**preponderance.For engineering and manufacturing purposes the more important linear gauges are, however, now used, adjusted to some fundamental unit of measure as the inch; although in certain trades, as for wires and flat metals, gauges continue to be used of arbitrary scales and of merely

**numerical**sizes, having no reference to a legal unit of measure; and such are rarely accurate.The

**numerical**value of this modulus is o 4342944 81 9 03251 82765 11289..The quantity denoted by e is the series, I I I+ I + i.2 +1.2.3+1.2.3.4 + the

**numerical**value of which is, 2.71828 18284 59 0 45 2 353 6 02874.One of the chief deductions is that there are special dangers in

**numerical**diminution of herds, which may arise from a chief or original cause and be followed by a conspiracy of other causes which are cumulative in effect.In Great Britain, whither they began to straggle over during the revolutionary troubles at the close of the 18th century, and where, practically unaffected by the clause directed against them in the Emancipation Act of 1829, their chief settlement has been at Stonyhurst in Lancashire, an estate conferred on them by Thomas Weld in 1795, they have been unmolested; but there has been little affinity to the order in the British temperament, and the English province has consequently never risen to

**numerical**or intellectual importance in the Society.The arrival of a Spanish squadron of twelve ships of the line in June gave a great

**numerical**superiority to the allies, and Rodney retired to Gros Islet Bay in Santa Lucia.He became secretary of the American Oriental Society and editor of its Journal, to which he contributed many valuable papers, especially on

**numerical**and temporal categories in early Sanskrit literature.The representatives of the extreme monotheistic view, which while regarding Christ as Redeemer, clung tenaciously to the

**numerical**unity of the Deity, were called Monarchians, a term brought into general use by Tertuliian.Various chemists had traced

**numerical**sequences among the atomic weights of some of the elements and noted connexions between them and the properties of the different substances; but it was left to him to give a full expression to the generalization, and to treat it not merely as a system of classifying the elements according to certan observed facts, but as a "law of nature" which could be relied upon to predict new facts and to disclose errors in what were supposed to be old facts.In character the Indians are, as a rule, peaceable, though conscious of their

**numerical**superiority and at times driven to join in the revolutions which so often disturb the course of local politics; they are often intensely religious, but with a few exceptions are thriftless, indolent and inveterate gamblers.Thus the

**numerical**superiority of the Baptists and Methodists in the two Southern divisions is complementary to that of the Roman Catholics in the other three divisions of the country.This correlative

**numerical**problem and the two purely geometrical problems are inseparably connected historically.In his earlier years he devoted himself to chemistry, both theoretical and applied, publishing papers on the preparation of gold and platinum,

**numerical**relations between the atomic weights of analogous elements, the formation of aventurine glass, the manufacture of illuminating gas from wood, the preservation of oil-paintings, &c. The reaction known by his name for the detection of bile acids was published in 1844.The efforts which were consequently made in the early days of spectroscopy to discover some

**numerical**relationship between the different wave lengths of the lines belonging to the same spectrum rather disregard the fact that even in acoustics the relationship of integer numbers holds only in special and very simple cases.These forms all agree in making the frequency negative when s falls below a certain value sp. Rydberg's second law states that if the main branch series is taken, the

**numerical**value of np_I corresponding to sp_ I is equal.Down to 1848, and even still later, " Democracy " was used to cover the whole mass of the people, pre-eminently represented by the broad strata of the bourgeoisie; in 1900 the Democratic party itself meant by this term the rule of the labouring class organized as a nation, which, by its

**numerical**superiority, thrust aside all other classes, including the bourgeoisie, -and excluded them from participation in its rule.Henry Cavendish had before 1773 discovered that glass, wax, rosin and shellac have higher specific inductive capacities than air, and had actually determined the

**numerical**ratios of these capacities, but this was unknown both to Faraday and to all other electricians of his time, since Cavendish's Electrical Researches remained unpublished till 1879.It is found that this gives a consistent result; that is to say, if by an experiment with two particles A and B we get the ratio of their masses, and by an experiment with B and a third particle C we get the ratio of the masses of B and C, and thus the ratio of the masses of A and C, we should get the same ratio by a direct experiment with A and C. For the

**numerical**measure of mass that of some standard body is chosen as a unit, and the masses of other bodies are obtained by comparison with this.Before the Seven Years' War the Quakers dominated the government, but from that time until the failure of the Whisky Insurrection (17g4) the more belligerent Scotch-Irish (mostly Presbyterians) were usually in the ascendancy, the reasons being the growing

**numerical**strength of the Scotch-Irish and the increasing dissatisfaction with Quaker neglect of means of defending the province.The physical investigation of osmotic pressure, and its correlation by Van't Hoff with the pressure of a gas, brought forward a new aspect of the phenomena, and suggested an identity of physical modus operandi as well as of

**numerical**value.If we were to say that on his view the essential step must be the establishment of identities or equivalences, we should probably be doing justice to his doctrine of

**numerical**reasoning, but should have some difficulty in showing the application of the method to geometrical reasoning.Ang3trom's value for iron, when corrected for obvious

**numerical**errors, and for the probable variation of c, becomes Iron, k =0.164 (1-0.0013 0), but this is very doubtful as c was not measured.Since the plebeian element in the state had an immense

**numerical**preponderance over the patrician these disabilities were not widely spread, and seem generally to have been cheerfully borne as the price of belonging to the families still recognized as the oldest and noblest in Rome.At Cambridge,

**numerical**marks are used.The advantage of

**numerical**marks is that they are more easily manipulated than symbols; the disadvantage, that they produce the false impression that merit can be estimated with mathematical accuracy.The element of chance, which prevails in the region on either side of the border between pass and failure, obviously prevails equally on either side of the border between " classes," where candidates are classified; it has been suggested by Dr Schuster that

**numerical**order should accompany classification so as to avoid the creation of an artificial gap between the last candidate in one class and the highest in the next.Latham (The Action of Examinations, 1877, p. 490) describes other

**numerical**adjustments used to meet this difficulty, especially that used in English civil service examinations.For while Hegel, depending on a

**numerical**proportion suggested by Plato, hinted in a single sentence that it might be a mistake to look for a planet between Mars and Jupiter, Giuseppe Piazzi (q.v.) had already discovered the first of the asteroids (Ceres) on the ist of January 1801.The

**numerical**preponderance of the works of Philodemus led some people to believe that this had been the library of that philosopher.The

**numerical**value of the mechanical equivalent necessarily depends on the particular units of heat and work employed in the comparison.This appears to be the explanation of Stumpe's and Porter's results; they both divided their proper motions into groups according to their

**numerical**amount, and found that the declination of the solar apex progressively increased as the size of the motions used diminished.The ideal is progressively to determine a universe of discourse till true infimae species are reached, when no further distinction in the determinate many is possible, though there is still the

**numerical**difference of the indefinite plurality of particulars.Owing to the variation in the value of the dielectric constant of glass with the temperature and with the frequency of the applied electromotive force, and also owing to electric glow discharge from the edges of the tin foil coatings, the capacity of an ordinary Leyden jar is not an absolutely fixed quantity, but its

**numerical**value varies somewhat with the method by which it is measured, and with the other circumstances above mentioned.But the

**numerical**factor appears to be yz'+zy', while it is the quantity yz' - zy' which really vanishes.Hamilton seems never to have been quite satisfied with the apparent heterogeneity of a quaternion, depending as it does on a

**numerical**and a directed part.And we now see that the square of V is the negative of Laplace's operator; while V itself, when applied to any

**numerical**quantity conceived as having a definite value at each point of space, gives the direction and the rate of most rapid change of that quantity.It is evident that this is a very delicate method of determining the wetness z, but, since with dry saturated steam at low pressures this formula always gives negative values of the wetness, it is clear that Regnault's

**numerical**coefficients must be wrong.By assuming suitable forms of the characteristic equation to represent the variations of the specific volume within certain limits of pressure and temperature, we may therefore with propriety deduce equations to represent the saturation-pressure, which will certainly be thermodynamically consistent, and will probably give correct

**numerical**results within the assigned limits.Taking for ice and water the following

**numerical**data, L = 674.7, 6 74.7, L 1 =595.2, L r = 79.5, R = o 11 03 cal./deg., po = 4.61 mm., s-S = 519 cal./deg., and assuming the specific heat of ice to be equal to that of steam at constant pressure (which is sufficiently approximate, since the term involving the difference of the specific heats is very small), we obtain the following**numerical**formulae, by substitution in (23), Ice..They give the following

**numerical**values The error of the formula for water is less than t mm.As the mortality amongst boys, especially during the first year, is considerably above that of the other sex,

**numerical**equilibrium between the two is established in early youth, and in most cases girls outnumber boys, except for a few years between twelve and sixteen.Thus, though the generally higher proportion of females in the community may seldom be enough to depress more than slightly the death-rate as a whole, it has a substantial effect upon it at the ages where women are in more marked

**numerical**predominance, as in later life, and in places where the number of domestic servants is unusually great.A study of his works reveals an unusual combination of skill and originality in the mathematical treatment of many of the most difficult problems of astronomy, an unfailing patience and sagacity in dealing with immense masses of

**numerical**results, and a talent for observation of the highest order.It represents the Koppa of the earliest Greek alphabets surviving in that form of the Ionic alphabet, which ultimately superseded all others, merely as the

**numerical**symbol for 90.In the Phoenician alphabet a sibilant Zade (Tzaddi) stands between q and p. Hence Q is the nineteenth letter in the Phoenician alphabet, the eighteenth in the Greek

**numerical**alphabet, which alone contains it, the sixteenth (owing to the omission of 8 and E) in the Latin, and (from the addition of J) the seventeenth in the English alphabet.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.Lastly, statistical research has shown that the children of the married British clergy have been distinguished far beyond their mere

**numerical**proportion.8/n==Authorities== - Henry Charles Lea, History of Sacerdotal Celibacy (3rd ed., 1907, 2 vols), is by far the fullest and best work on this subject, though a good deal of important matter omitted by Dr Lea may be found in Die Einfiihrung der erzwungenen Ehelosigkeit by the brothers Johann Anton and Augustin Theiner, which was put on the Roman Index, though Augustin afterwards became archivist at the Vatican (Altenburg, 1828, 2 vols.).The remarkable

**numerical**progress of Baptists in South Carolina from 1787 to 1812 (from 1620 members to 11,325) was due to the "Separate" Baptist movement under Stearns and Marshall far more than to the activity of the churches of the Charleston Association.By 1812 there were in the United States 173,972 Baptist church members, the denominational

**numerical**strength having considerably more than doubled since the beginning of the 19th century.Lagrange used simple continued fractions to approximate to the solutions of

**numerical**equations; thus, if an equation has a root between two integers a and a+1, put x=a+I/y and form the equation in y; if the equation in y has a root between b and b+i, put y = b + I /z, and so on.He used them to represent square roots, but only for particular

**numerical**examples, and appears to have had no theory on the subject.Hence the

**numerical**value of the intensity of the surface-tension is equal to the**numerical**value of the surface-energy per unit of surface.In all these cases the internal pressure exceeds the external by 2T/a where a is the semi-transverse axis of the conic. The resultant of the internal pressure and the surface-tension is equivalent to a tension along the axis, and the

**numerical**value of this tension is equal to the force due to the action of this pressure on a circle whose diameter is equal to the conjugate axis of the ellipse.Army was still cramped and out of touch with its neighbours went far to neutralize the

**numerical**disadvantage.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.This, however, leads to a troublesome

**numerical**solution.The division into abstract and concrete, for instance, is logical, if the former is taken as relating to number and the latter to

**numerical**quantity (§ I I).If the term number is confined to number in the abstract, then number in the concrete may be described as

**numerical**quantity.The £I is termed the unit, A

**numerical**quantity, therefore, represents a certain unit, taken a certain number of times.Thus arithmetical processes deal with

**numerical**quantities by dealing with numbers, provided the unit is the same throughout.This question of direction is of importance in reference to the development of useful number-forms (§ 23); and the existence of the two methods mentioned under (iii) and (iv) above produces confusion in comparing

**numerical**tabulation with graphical representation.Over a large part of the civilized world the introduction of the metric system (§ 118) has caused the notation of all

**numerical**quantities to be in the denary scale.**Numerical**quantities, to be added or subtracted, must be in the same denomination; we cannot, for instance, add S5 shillings and loo pence, any more than we can add 3 yards and 2 metres.The application of the above principles, and of similar principles with regard to multiplication and division, to

**numerical**quantities expressed in any of the diverse British denominations, presents no theoretical difficulty if the successive denominations are regarded as constituting a varying scale of notation (§17).Multiplication occurs when a certain number or

**numerical**quantity is treated as a unit (§ II), and is taken a certain number of times.The pair of compartments on either side may, as here, contain

**numerical**quantities, or may contain numbers.The positive quantity or number obtained from a negative quantity or number by omitting the " - " is called its

**numerical**value.It should be observed that the

**numerical**value of the error is to be subtracted from or added to the stated value according as the error is positive or negative.In §§ 33 4 2 We Have Dealt With The Parallelism Of The Original Number Series With A Series Consisting Of The Corresponding Multiples Of Some Unit, Whether A Number Or A

**Numerical**Quantity; And The Relations Arising Out Of Multiplication, Division, &C., Have Been Exhibited By Diagrams Comprising Pairs Of Corresponding Terms Of The Two Series.Correspondence of

**Numerical**Quantities.-Again, in § 89, we have considered cases of multiple-tables of**numerical**quantities, where each quantity in one series is equivalent to the corresponding quantity in the other series.A B C of

**numerical**quantities, merely correspond with each other, the correspondence being the result of some relation.It is desirable, wherever possible, to perform operations on numbers or

**numerical**quantities from the left, rather than from the right.There is no difference in principle between addition (or subtraction) of numbers and addition (or subtraction) of

**numerical**quantities.We need therefore consider

**numerical**quantities only, our results being applicable to numbers by regarding the digits as representing multiples of units in different denominations.In calculating an average it should be observed that the addition of any

**numerical**quantity (positive or negative) to each of the measurements produces the addition of the same quantity to the average, so that the calculation may often be simplified by taking some particular measurement as a new zero from which to measure.In 1829 he discovered the theorem, regarding the determination of the number of real roots of a

**numerical**equation included between given limits, which bears his name (see Equation, V.), and in the following year he was appointed professor of mathematics at the College Rollin.This contains a reprint of the First Notions, an elaborate development of his doctrine of the syllogism, and of the

**numerical**definite syllogism, together with chapters of great interest on probability, induction, old logical terms and fallacies.**Numerical**computation of this kind might almost be described as his pastime.This is Spinoza's theory of the infinitely infinite," the limiting notion of infinity being of a

**numerical**, quantitative series, each term of which is a qualitative determination itself quantitatively little, e.g.It was conceived by Huxley, among others, that the same number of cephalic somites would be found to be characteristic of all the diverse classes of Arthropoda, and that the somites, not only of the head but of the various regions of the body, could be closely compared in their

**numerical**sequence in classes so distinct as the Hexapods, Crustaceans and Arachnids.The range of modification of which the rami or limb-branches of the limbs of Arthropoda are capable is very large, and in allied orders or even families or genera we often find d z what is certainly the palp of the same appendage (as determined by

**numerical**position of the segments) - in one case antenniform, in another chelate, in another pediform, and in another reduced to a mere stump or absent altogether.To the days Fabre d'Eglantine gave names which retained the idea of their

**numerical**order, calling them Primedi, Duodi, &c., the last day of the ten, the day of rest, being named Decadi.The

**numerical**quantities by which the distance and direction, and therefore the position, are defined, are termed co-ordinates of the point.This

**numerical**proportion, as being a necessary consequence of the law of gravitation, must prevail in every system under its sway.It consisted, first, in the identification, by strict

**numerical**comparisons, of terrestrial gravity with the mutual attraction of the heavenly bodies; secondly, in the following out of its mechanical consequences throughout the solar system.The third method seeks to avoid the difficulty by using the

**numerical**values of the elements instead of their algebraic symbols.This method has the advantage of leading to a more rapid and certain determination of the

**numerical**quantities required.During the twenty years following he devoted a large part of his energies to the

**numerical**computation of the lunar inequalities, the redetermination of the elements of motion, and the preparation of new tables for computing the moon's position.It was therefore necessary that the

**numerical**inequalities should be again determined by an entirely different method.The

**numerical**computations were worked out by Hill only for the first approximation.The principal feature of his work was that the quantity m, which is regarded as constant, appears only in a

**numerical**form, so that the uncertainties arising from development in a series accruing to its powers is done away.Subsequent investigations naturally modified the

**numerical**values upon which this nomenclature was based, but without altering the order of the periods.But as this surface is obtained by assuming that the interfering streams follow the same route in the crystal, and by neglecting the refraction out of the crystal, it does not lend itself to accurate

**numerical**calculations.The function n sin u = A, for the microscope, has been called by Abbe the

**numerical**aperture.On the other hand, in immersion-systems the

**numerical**aperture can almost amount to the refractive index, for A=n sin uFrom the Fraunhofer formula I =X/n sin a one can immediately deduce the limit to the diffraction constant I, so that the banding by an objective of fixed

**numerical**aperture can be perceived.The value n sin u equals the

**numerical**aperture A, where n is the refractive index of the immersion-liquid, and u is the semi-aperture on the object-side.If microscopic preparations are observed by diffused daylight or by the more or less white light of the usual artificial sources, then an objective of fixed

**numerical**aperture will only represent details of a definite fineness.With the best immersion-system, having a

**numerical**aperture of 1.6, details of the size o.Then the denominator of the fraction, the

**numerical**aperture, must be correspondingly increased, in order to ascertain the real resolving power.In this way a monochromat for glycerin of a

**numerical**aperture 1.25 gives a relative**numerical**aperture of 2.50.From the section Regulation of the Rays (above) it is seen that the resolving power is opposed to the depth of definition, which is measured by the reciprocal of the

**numerical**aperture, I/A.The resolving power of an objective depends on its

**numerical**aperture.The

**numerical**aperture can be determined in two ways.The sine of this angle is the

**numerical**aperture for dry lenses.The angular or

**numerical**aperture can then be read off.If the

**numerical**aperture be known the resolving power is easily found.It is noteworthy that the difference between Albrecht's

**numerical**results and Chandler's formulae is generally less than o 05".Symmetry, then, in botanical language, has reference to a certain definite

**numerical**relation of parts.At the beginning of 1632, in order to bring about the general peace he so earnestly desired, he proposed to take the field with an overwhelming

**numerical**majority.Verbal reasoning,

**numerical**reasoning and abstract reasoning are timed tests, each lasting 20 minutes.The test is very similar to those used by major employers and covers verbal,

**numerical**and diagrammatic reasoning.By being presented as Grid services,

**numerical**optimization algorithms can be consumed with a number of message interactions.Archimedes the

**numerical**analyst Here we summarize the main points in the paper by Phillips with the above title.Further

**numerical**analysis to deal with the effects of sea ice data assimilation.Furthermore, they can replace heavy 3D

**numerical**calculations (for example finite element calculations) with high accuracy.You are advised to bring a simple,

**numerical**, non-programmable, pocket calculator.They all require a certain amount of

**numerical**computation.He is a

**numerical**analyst who specializes in the development and analysis of algorithms in matrix computations.**Numerical**Geometry Ltd. Games Writing games is a good way of exploring strongly interactive computer graphics.A very commonly used dry condenser has a

**numerical**aperture (NA) of 0.9.Priority values define a

**numerical**rank or ordering of the threads that a thread scheduler can use to resolve simultaneous contention for processing resources.The function installs a forward type converter to convert string values to

**numerical**representation type values.A robust measure of

**numerical**model parameter sensitivity was employed, namely the rank order correlation coefficient.The professional user can adjust any operation via

**numerical**input and can precisely monitor the results using an online densitometer.However, returning to the problem in hand which is to compute the accurate

**numerical**derivative of a given external function.The UM uses a full compressible equation set, no turbulence closure (

**numerical**diffusion only) and a hybrid terrain following co-ordinate system.It has

**numerical**gain 8.4 with respect to a practical half-wave dipole.The magnitude of the

**numerical**uncertainity of the results is controlled through the input parameter epsilon.One involves experimental and

**numerical**research into the behavior of liquid gallium under the combined action of a temperature gradient and a magnetic field.This report is intended primarily for

**numerical**modelers in civil engineering hydraulics.Will be followed by an

**numerical**indiction of how far the progress has gone.**Numerical**Model Simulates the impact of alternative operating policies or changed water and sediment inputs on future sedimentation.For Hamiltonian systems, one can exactly preserve the symplectic structure of the system using

**numerical**methods the have become known as symplectic integrators.The

**numerical**method used is multisection for eigenvalues [16] and repeated inverse iteration and orthogonalization for eigenvectors [17] .All controllers are easily programmed via the

**numerical**keypad to create custom setups in minutes.In

**numerical**linear algebra he developed backward error analysis methods.The approach will be to apply 3-D

**numerical**modeling methods to existing ship-board magnetometer survey data.And so I think there is a whole range of variation in the

**numerical**field as there is in the purely mathematical relativity area.The candidate should ideally have experience in statistical data analysis and/or

**numerical**modeling and in mountain meteorology.E.g. br / attribute values must be quoted even when purely

**numerical**.The work of Barbara Thiering, tho not

**numerical**, depends upon word codes and time codes, and seems just as incredible.The problem was not simply

**numerical**but also political.They are in alphabetical and then

**numerical**order but the actual process of cataloging them all will be a massive task.You ask the questions in a variety of formats, including true or false, multiple choice or even

**numerical**.Your site should combine information in text, graphical and possibly

**numerical**format.The project has been funded to investigate the causes of cardio vascular problems and cancer using

**numerical**modeling.You will also conduct comparisons between the

**numerical**models and satellite observations of flows around sunspots and coronal activity above active regions.The

**numerical**method then must be able to handle discontinuities without introducing non-physical, spurious oscillations.We will integrate aspects of these standards and extend them for

**numerical**computing on massively parallel systems.The method is illustrated by two

**numerical**examples, namely a single pendulum on a cart and a parametrically driven inverted double pendulum.Wyn Williams uses powerful computer facilities for intensive

**numerical**modeling of the underlying physics of magnetism in mineral grains.**Numerical**values can be integer, real, or double precision.Efforts are underway to compare the

**numerical**predictions of the response of gravity key walls with those obtained for flexible key walls.A

**numerical**prefix says how many places to rotate the text.The project will combine analytical studies and

**numerical**modeling tools for simulating wave propagation in fractured porous rock.The default

**numerical**method used by NEURON produces values which have an error proportional to dt.There is qualitative sameness, and then there is

**numerical**sameness.So there can be qualitative sameness without

**numerical**sameness.**Numerical**studies like this can help to understand wave propagation phenomena observed on field recordings in volcano seismology.Series A number of items arranged in

**numerical**or alphabetical sequence.The project aim is to develop a new process-based

**numerical**model to predict rates and styles of periglacial solifluction.Dynamo models of our Galaxy as a flattened spheroid have been investigated, using asymptotic analytic methods and high resolution

**numerical**techniques.The

**numerical**substructure may be either linear or non-linear, the latter using a new, fast non-linear analysis algorithm which we have developed.Each reduction rule contributes to the final summation formula by a

**numerical**factor or by an additional summation variable.The attacker is likely to have

**numerical**superiority to offset the defender being hidden.In particular the paper links to the use of

**numerical**taxonomy within the natural sciences where similar techniques have met with considerable success.For the extension of a squid tentacle, our

**numerical**results are in excellent agreement with existing experimental results.For the future it would be beneficial to have fortnightly tutorials to go over

**numerical**examples.**Numerical**Equations These are based on the diffusion equation in one dimension, where is the eddy viscosity.It is a fundamental result in dynamics that, if a body be projected vertically upwards in vacuo, with a velocity of v centimetres per second, it will rise to a height of v 2 /2g centimetres, where g represents the

**numerical**value of the acceleration produced by gravity in centimetre-second units.If the two circuits are in tune so that the

**numerical**product of capacity and inductance of each circuit is the same or C L, = C L +CL and if k is the coefficient of coupling then the natural frequency of each circuit is n = I /2w / (CL), and when coupled two oscillations are set up in the secondary circuit having frequencies n and n2 such that n = n0/ (i - k) and n = nh,/ (I +k).The height or length of the arm of a human being, for instance, is the result of many factors, some inherent, some due to environment, and until these have been sifted out,

**numerical**laws of inheritance or of correlation can have no more than an empirical value.It is among the Invertebrata that epidemics of destruction are referred to, though we should bear in mind that it is only the difference in

**numerical**proportion that prevents our speaking of an epidemic of elephants or of rabbits, though we use the term when speaking of blight insects; there is little consistency in the matter, as it is usual to speak of an invasion or scourge of locusts, caterpillars, &c. Insect injuries are very varied in degree and in kind.It consisted essentially in the adoption of Delauny's final

**numerical**expressions for longitude, latitude and parallax, with a symbolic term attached to each number, the value of which was to be determined by substitution in the equations of motion.When a homogeneous polynomial is transformed by general linear substitutions as hereafter explained, and is then expressed in the original form with new coefficients affecting the new variables, certain functions of the new coefficients and variables are

**numerical**multiples of the same functions of the original coefficients and variables.**Numerical**relativity makes use of methods which are conceptually very different.Anatomical age is the

**numerical**assessment of a child's physical growth in relation to the statistical average based on the child's chronological age.Manchester in 1906, when the Labour party were returned for the first time in

**numerical**force - over 50 in all.The old B retained the

**numerical**value of the Greek i as 2, and no**numerical**value was given to the new symbol.In Greek, where I is the twentieth letter of the alphabet, or, if the merely

**numerical**and p are excluded, the eighteenth, another form 1 or S according to the direction of the writing is also widespread.Largesse was especially given on the field of victory, and was, moreover, liberally distributed to stifle sedition and mutiny among the troops, the

**numerical**strength of which was continually increased as the empire enlarged its borders.When, therefore, the latter, on the 22nd, marched southward to reopen his communications by the defeat of the enemy's army, always the surest means of solving this difficulty, he actually reached the neighbourhood of Eckmuhl with a sufficient

**numerical**superiority had he only been prompt enough to seize his opportunity.Other " Galois " groups were defined whose substitution coefficients have fixed

**numerical**values, and are particularly associated with the theory of equations.Remark.-The invariant C is a

**numerical**multiple of the resultant of the covariants i and j, and if C = o, p is the common factor of i and j.The magnetic susceptibility expresses the

**numerical**relation of the magnetization to the magnetizing force.Curves of magnetization (which express the relation of I to H) have a close resemblance to those of induction; and, indeed, since B = H+47r1, and 47rI (except in extreme fields) greatly exceeds H in

**numerical**value, we may generally, without serious error, put I = B /47r, and transform curves of induction into curves of magnetization by merely altering the scale to which the ordinates are referred.It seems that confusion and trouble will be best avoided by abstaining from the introduction of the non-evident somites, the ocular and the praegenital, into the

**numerical**nomenclature of the component somites of the three great body regions.The chamber has the right of initiative in the organization of the annual budget laws and those relative to the

**numerical**strength of the army and navy.And, their own predominance being assured by their

**numerical**strength and influence, they accorded equal shares of power to the other monti.The commission also called attention to the

**numerical**insufficiency of magistrates and native commissioners in certain parts of Natal.According to this reading, William sought to rectify his position by asserting, not the

**numerical**identity of the universal in each individual, but rather its sameness in the sense of indistinguishable similarity.In the case of division we get two kinds of arithmetical formula, which, however, may be regarded as requiring a single kind of

**numerical**process in order to determine the final result.We must count with something; and the successive somethings obtained by the addition of successive units are in fact

**numerical**quantities, not numbers.While mensuration is concerned with the representation of geometrical magnitudes by numbers, graphics is concerned with the representation of

**numerical**quantities by geometrical figures, and particularly by lengths.There are also cases in which graphics and mensuration are used jointly; a variable

**numerical**quantity is represented by a graph, and the principles of mensuration are then applied to determine related**numerical**quantities.Graphic representation thus rests on the principle that equal

**numerical**quantities may be represented by equal lengths, and that a quantity mA may be represented by a length mL, where A and L are the respective units; and the science of graphics rests on the converse property that the quantity represented by pL is pA, i.e.His

**numerical**table, therefore, differs from all others made before or since, prophetically assigning the place of honour to the one ancient scale now recognized as the foundation of the modern tonal system.Hippocrates, influenced as is thought by the Pythagorean doctrines of number, taught that they were to be expected on days fixed by certain

**numerical**rules, in some cases on odd, in others on even numbers - the celebrated doctrine of "critical days."The quartic will have two pairs of equal roots, that is, will be a perfect square, if it and its Hessian merely differ by a

**numerical**factor.Equations (33) and (34) show that when, as is generally the case with ferromagnetic substances, the value of is considerable, the resultant magnetic force is only a small fraction of the external force, while the

**numerical**value of the induction is approximately three times that of the external force, and nearly independent of the permeability.This is rendered possible by the fact that we can use a single letter to represent a single number or

**numerical**quantity, however many digits are contained in the number.In this mode of treating the question the order of the terms is

**numerical**, and though the amount of labour is such as might well have deterred a younger man, yet the details were easy, and a great part of it might be entrusted to a mere computer.The overwhelming

**numerical**superiority of the Sla y s, and the very great differences in ethnical type, belief and mythology between the IndoEuropean and the Ural-Altaic races, may have contributed to the same end.The Church of England claims as adherents 39% of the population, and the Roman Catholic Church 22%; next in

**numerical**strength are the Wesleyans and other Methodists, numbering 12% i the various branches of the Presbyterians 11%, Congregationalists 2%, and Baptists 2%.Next in

**numerical**importance to the Mongolians are the races which have been called by Professor Huxley Melanochroic and Xanthochroic. The former includes the dark-haired people of southern Europe, and extends over North Africa, Asia Minor, Syria to south-western Asia, and through Arabia and Persia to India.Carpenter (1899, 1902-1904) has lately endeavoured to show an exact

**numerical**correspondence in segmentation between the Hexapoda, the Crustacea, the Arachnida, and the most primitive of the Diplopoda.