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Numerically the flocks of Australia represent one-sixth of the world's sheep, and in just over half a century (1851-1905) the exports of Australian wool alone reached the value of £650,000,000.

00The whole number of this race is 620,229, and nowhere do they form a majority of the whole population in a state; but they are strongest, numerically, in the northern states and in Udaipur.

00This last circuit has a natural frequency of its own which is numerically measured by I/27r-!(CL), where C is the capacity of the condenser and L is the inductance of the circuit.

00Numerically insufficient to reject such measures, and lacking the fibre and the cohesion necessary for the pursuance of a far-sighted policy, the Right thought prudent not to employ its strength in uncompromising opposition, but rather, by supporting the government, to endeavour to modify Radical legislation in a Conservative sense.

0030 be numerically the same as the ratio of the electromagnetic and electrostatic units.

00His general formula for getting at the number of units in any sensation is S = C log R, where s stands for the sensation, R for the stimulus numerically estimated, and c for a constant that must be separately determined by experiment in each particular order of sensibility.

00His name is numerically equivalent to that of the Lord (Zohar, iii.

00Thus the manoeuvre against Vitebsk again miscarried, and Napoleon found himself in a far worse position, numerically and materially, than at the outset of the campaign.

00Then he had stood with 420,000 men on a front of 160 m., now he had only 229,000 men on a front of 135; he had missed three great opportunities of destroying his enemy in detail, and in five weeks, during which time he had only traversed 200 m., he had seen his troops reduced numerically at least one-third, and, worse still, his army was now far from being the fighting machine it had been at the outset.

00They are dextrorotatory, and the specific rotation is numerically greater than that of albumin; hence the proteids are, in general, dextrorotatory.

00Since the poles of different magnets differ in strength, it is important to agree upon a definite unit or standard of reference in terms of which the strength of a pole may be numerically specified.

00Bismuth, the strongest of the diamagnetics, has a negative susceptibility which is numerically 20 times less than that of liquid oxygen.

00Hence if the induction per square centimetre at any point is denoted by B, then in empty space B is numerically equal to H; moreover in isotropic media both have the same direction, and for these reasons it is often said that in empty space (and practically in air and other nonmagnetic substances) B and H are identical.

00(26) Also A = B = H H4?rI _ I +41K, (27) and (28) 471 Since in empty space B has been assumed to be numerically equal to H, it follows that the permeability of a vacuum is equal to i.

00When P is the neutral point, H is equal and opposite to R; therefore M = Hd 3, or the moment is numerically equal to the cube of the distance from the neutral point to a pole, multiplied by the M.

00Then if a known change of induction SB a inside the standard coil is found to cause a throw of d scale-divisions, any change of induction SB through the experimental coil will be numerically equal to the corresponding throw D multiplied by snRBa/SNrd.

00The argument involves the theorem that, if 0 is a positive quantity less than I, 0 t can be made as small as we please by taking t large enough; this follows from the fact that tlog 0 can be made as large (numerically) as we please.

00+u r by Sr. Then (ï¿½ 56 (iii.)) (x+h)" lies between S r and Sr+i; and provided S r includes the numerically greatest term, I Sr+i-Sri constantly decreases as r increases, and can be made as small as we please by taking r large enough.

00is the greatest (numerically).

00(11), when g i numerically exceeds 2h 1; and, when g i lies between 2h,, I = 7r{2h,+ (2h, g, 2) cos p'}.

00Next, numerically, to the Basuto and Bechuana peoples are the tribes known collectively as Transvaal Kaffirs, of whom there were 159,860 enumerated at the 1904 census.

00to the east and thus made himself numerically equal to his enemy, but elsewhere left barely 45,000 men to oppose 150,000.

00As the army of the Elbe was numerically inferior to Clam-Gallas and the Saxons, the reserve corps was at once despatched to reinforce it, and the Guard was sent to the crown prince.

00Numerically, the contending armies would at this very critical juncture of the campaign be almost equal, the invaders rather the stronger; but the Turks were much dispersed, so that the result almost hinged upon the speed with which the attacking side should gain ground before the defenders had time to concentrate.

00Large bodies of infantry with a fair proportion of guns still remained on shore on the 17th, but of these roughly half - about io,000 men and a number of guns in each area - were removed that night, so that on the 18th only a meagre force, composed almost wholly of infantry and disposed almost entirely in the trenches, was holding a long front face to face with a numerically far stronger enemy.

00Her artists and artisans alike aim at symmetry, not by an equal division of parts, as we do, but rather by a certain balance of corresponding parts, each different from the other, and not numerically even, with an effect of variety and freedom from formality.

00The solid angles subtended by all normal sections of a cone at the vertex are therefore equal, and since the attractions of these sections on a particle at the vertex are proportional to their distances from the vertex, they are numerically equal to one another and to the solid angle of the cone.

00capacity of the sphere in free space is Q/V = R, or is numerically the same as its radius reckoned in centimetres.

00The simplest method of determining it numerically is, therefore, that adopted by Faraday.4 Table Dielectric Constants (K) of Solids (K for Air = I).

00The Normans, like the Arabs, were not numerically strong; the rule of both, in Sicily as well as Malta, was based on a recognition of municipal institutions under local officials; the Normans, however, exterminated the Mahommedans.

00Blucher's force was numerically very superior.

00The causes of Napoleon's failure in the Waterloo campaign were as follows: - The French army was numerically too weak for the gigantic task it undertook.

00The statement that, if the adjacent sides of a rectangle are represented numerically by 3 and 4, the diagonal is represented by 5, is as much a matter of mensuration as the statement that the area is represented by 12.

00An equally important school, though numerically smaller, came into existence in eastern Massachusetts under the leadership of Charles Chauncy (1592-1672) and Jonathan Mayhew (1720-1766).

00In the interior are several towns, though none of any size numerically.

00Numerically, Christians may have formed perhaps a tenth of the population, i.e.

00In Bloemfontein the Constitutionalists had a strong following; elsewhere their supporters were numerically weak.

00Such were the defences that the Japanese attacked, with a force at the outset (30th of July) little more than superior numerically to the defenders, and an entirely inadequate siege train (18 6-in.

00This attempt also failed; for the Germans were numerically too weak, ' For Hungary, as the other constitutional half of the old AustroHungarian Monarchy, see the separate article under that heading; also Bosnia-Herzegovina, and the articles on the different " succession states " which were formed on the break-up of the monarchy in 1918.

00In South America the species of parrots, though numerically nearly as abundant, are far less diversified in form, and all of them seem capable of being referred to two, or, at most, three sections.

00These functions, T, S, D, 1, A, are shown numerically in the following extract from an abridged ballistic table, in which the velocity is taken as the argument and proceeds by an increment of 10 f/s; the column for p is the one determined by experiment, and the remaining columns follow by calculation in the manner explained above.

00Even so the Confederacy was numerically, as in every other respect, far weaker, and rarely, after the second year, opposed equal numbers to the troops of the Union.

00The only real success achieved by this numerically imposing force was the capture on the 8th and 9th of August of a large British convoy of ships bound for the East and West Indies carrying troops.

00Mawara'lnahr was taken from Timur and entrusted to a son of Toghluk; but he was defeated in battle by the bold warrior he had replaced at the head of a numerically far inferior force.

00With conscription a national army corresponds more or less numerically to the proportion of males in the national population.

00He regards this universal experience as the result entirely of intersubjective intercourse, and concludes that its subject is not numerically distinct from the subject of individual experience, but is one and continuous with it, and that its conceptions depend on the perceptions of individual experience.

00It showed itself in a desire to throw off the governance of the missionaries, in a criticism of Protestant creeds as not adapted to Japanese needs, and in a slackened growth numerically and intensively.

00The Karen Christian communities are strong numerically and have a good name for self-support.

00- Numerically, the most important inhabitants of the clear Carboniferous seas were the crinoids, corals, Foraminifera and brachiopods.

00Although in all probability numerically superior at this time to the Romanists, the Protestants were weakened by divisions, which were becoming daily more pronounced and more serious, and partly owing to this fact the emperor was able to resist the demands of each party and to moderate their excesses.

00To conciliate the Catholic Centre party, numerically the strongest of all, various concessions were from time to time made to the Roman Catholic Church, e.g.

00The Methodists are, numerically, the strongest religious body, then come Presbyterians, Roman Catholics and Anglicans, in the order named.

00Dividing the whole number of arcs, 156, whose angular velocities were measured into three numerically equal groups, according to their altitude, the following were the results in minutes of arc per second of time (or degrees per minute of time): - Each group contained auroras which appeared stationary.

00The Turkish element is not numerically stronga few thousands onlybut holds a high social position.

00The Bulgarian Mahommedans, or Pomaks, who inhabit the valleys of Rhodope and certain districts in northern Bulgaria, are numerically insignificant; the Greek followers of Islam are almost confined to Crete.

00The other Christian confessions are numerically inconsiderable.

00The two are compared numerically in Table II.

00For an attempt to treat the whole problem of differential fertility and assortative mating numerically, see Pearson, The Grammar of Science, 2nd edition, London, 1900.

00This officer was supported only by the Qaisite troops, the Kalbites, who were numerically superior, maintaining Ibn Omar in his residence at Hira.

00But a thing which has healthy lungs and a thing which has diseased lungs are only similar individuals numerically different.

00The fauna of Borneo comprises a large variety of species, many of which are numerically of great importance.

00The most important numerically are the Dyaks, the Dusuns and Muruts of the interior, the Malays, among whom must be counted such Malayan tribes as the Bajaus, Ilanuns, &c., the Bugis, who were originally immigrants from Celebes, and the Chinese.

00- This, though still the most important numerically of all the Uniat Churches, is but a fragment of the Church which proclaimed its union with Rome at the synod of Brest in Lithuania in 1596, a union which, after long and bitter resistance, was completed by the submission of the dioceses of Lemberg and Luzk in 1700 and 1702.

00An immediate deduction from Maxwell's theory was that in transparent dielectrics, the dielectric constant or specific inductive capacity should be numerically equal to the square of the refractive index for very long electric waves.

00Numerically the Brahuis are the strongest race in Baluchistan.

00The Oecumenical Patriarch is, of course, officially the superior; but the Russian Church is numerically by far the greatest, and the tendency to regard Russia as the head, not only of the Slav races, but of all orthodox nations, inevitably reacts upon the church in the form of what has been called pan-Orthodoxy.

00Serious popular agitation followed this step, on the ground (inter alia) that the Bengali population, the centre of whose interests and prosperity was Calcutta, would now be divided under two governments, instead of being concentrated and numerically dominant under the one; while the bulk would be in the new division.

00by earthworks; and the Allies found themselves forced, with scanty preparations, to undertake a regular- siege against an enemy ~vhose force was numerically superior to their own.

00The peculiar mode of displacement of the teeth from behind forwards in some members of both groups may perhaps indicate a relationship, although in the case of the Sirenia the replacement takes place by means of a succession of similar molars, while in the Proboscidea the molars remain the same numerically, but increase greatly in size and number of transverse ridges."

00The Ural-Altaians are numerically the predominant element, and consist of Turkomans, Kirghiz, Uzbegs and Sarts.

00The number is significant, since it agrees with that found in Edriophthalmous Crustacea, and assigns the labium of the Hexapod to the same somite numerically as that which carries the labium-like maxillipedes of those Crustacea.

00The new constitution was the embodiment of Radical principles, and the numerically strongest party in the country was Radical.

00Numerically this 1 It is important to notice the value of the following letters and signs, which recur frequently: - c = is; c = ch (hard); c = ch (soft); j =y, or j in German; s = sh; z =zh, or j in French.

00(2) In like manner the Many must be numerically both finite and infinite - numerically finite, because there are as many things as there are, neither more nor less; numerically infinite, because, that any two things may be separate, the intervention of a third thing is necessary, and so on ad infinitum.

00In mercantile contracts in computing the period of a month the day from which the time is to begin to run is excluded, but in sentences of imprisonment the day on which the sentence begins is included, so that the numerically corresponding day in the month in which the sentence expires would be excluded.

00succeeded only too well, since Protestantism was reduced both numerically and intellectually.

00The Moors decimated the native population; when they in turn were expelled, the country lost not only a numerically large section of its inhabitants, but the section best able to develop its natural wealth.

00Be aware that floating point arithmetic is not exact; matrices that are theoretically equal are not always numerically equal.

00This will have the effect of placing a numerically greater limit on the high resolution cutoff.

00Similarly, there may be some groups of people within society which, tho numerically small, are suffering some common disadvantage.

00The key one is the second: humanity in Socrates and humanity in Plato are numerically distinct, and essentially so.

00This will sort in ascending order, either numerically or alphabetically depending on the data format.

00How can a group so numerically inferior wield so large an influence upon the majority of the world?

00Outside the Protestant community and numerically insignificant, The Roman Catholic community had one great claim on Charles ' good offices.

00Based on these three analytic inverses, three formulae were developed for computing the inverse numerically.

00overtopping of a wall on which water waves impact violently, both numerically and theoretically.

00The full conditional densities are evaluated and inverted numerically to obtain random draws of the joint posterior.

00Solution method: The program solves the Cauchy principal value integrals numerically using adaptive Gaussian quadrature.

00However when dealing with patients who have decompression illness or migraine, large pulmonary shunts are numerically more important.

00The aim of the project is to investigate current developments in the literature and numerically simulate the behavior of a population.

00This can even be done rigorously using a variational procedure, which will be implemented numerically on a high-performance workstation.

00The presumption is either that d 2 V/dh 2 near the ground is much larger numerically than Gerdien supposes, or else that the ordinary instruments for measuring ionization fail to catch some species of Ion Whose Charge Is Preponderatingly Negative.

00+u r by Sr. Then (Ã¯¿½ 56 (iii.)) (x+h)" lies between S r and Sr+i; and provided S r includes the numerically greatest term, I Sr+i-Sri constantly decreases as r increases, and can be made as small as we please by taking r large enough.

00(See Thermometry.) Fusibility and Volatility.-The fusibility in different metals is very different, as shown by the following table, which, besides including all the fusing points (in degrees C.) of metals which have been determined numerically, indicates those of a selection of other metals by the positions assigned to them in the table.

00Thus if x= log x =1 - where the path of integration in the plane of the complex variable t is any curve which does not pass through the origin; but now log x is not a uniform function, that is to say, if x describes a closed curve it does not follow that log x also describes a closed curve: in fact we have log (E +in) = log,/ Q 2 +7)2) t i (a + 2 n 7r), where a is the numerically least angle whose cosine and sine are (2 +n 2) and 71/,i (t 2 +n 2), and n denotes any integer.

00(See Artiodactyla and Swine.) The teeth of the peccaries differ from those of the typical Old World pigs (Sus), numerically, in wanting the upper outer incisor and the anterior premolar on each side of each jaw, the dental formula being: i.

00Internal difficulties, low transport capabilities, and the necessity of garrisoning almost all parts of Albania and Macedonia to prevent local risings, added to the customary slackness in administration and training and the customary dishonesty in supply and equipment matters, resulted in the putting into the field of two armies which were numerically inferior, unequally trained, and poorly equipped - possessing indeed few assets beyond the solid fighting-worth of the individual Mahommedan Turk .2 With all this, however, the prestige of a great Power facing a group of small states, whose mutual hatred and rivalries had only just been composed, stood high, especially in Germany where the positive effects of the Turkish army reforms initiated by von der Goltz and others were overrated.

00How was it that the Russian army, which when numerically weaker than the French had given battle at Borodino, did not achieve its purpose when it had surrounded the French on three sides and when its aim was to capture them?

00Why was the Russian army--which with inferior forces had withstood the enemy in full strength at Borodino--defeated at Krasnoe and the Berezina by the disorganized crowds of the French when it was numerically superior?

00The program is also indicated by name, numerically and by a three-color LED, for superb visibility even on a dimly lit stage.

00Here we use the approach to study numerically the viscoelastic response of a suspension of hard spheres.

00Digital: Watches where the time is displayed numerically like a calculator.

00(i) The formula itself may not be numerically exact.

01

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