This website uses cookies to ensure you get the best experience. Learn more

obtain

I should like much to see it, and to obtain a few copies if possible.

298176Obtain something from someone along with instructions on how to use it.

11285There is but one way to obtain it, yet few take that way.

10252If the reading for coincidence of the movable with the fixed webs is known, we then obtain from the single reading of S the difference from coincidence of the divisions of the two scales.

7361By the judicious selection of a type of yeast it is possible to improve the bouquet, and from an inferior must obtain a better wine or cider than would otherwise be produced.

6249Have I not for eighteen months been doing everything to obtain it?

4948The latter was a great magician, able, by operating upon waxen figures of the armies and ships of his enemies, to obtain complete power over their real actions.

3739With regard to the region north of the Rhine we first obtain information from the accounts of the campaigns of Nero, Claudius, Drusus and Tiberius.

3535To obtain an absolutely pure culture with certainty it is necessary, even when the gelatin method is employed, to start from a single cell.

3433It is hunted chiefly for the sake of the ivory of its immense tusks, of which it yields the principal source of supply to the European market, and the desire to obtain which is rapidly leading to the extermination of the species.

3036This expedition put an end to the hope, so long entertained, that it was possible to obtain a direct and practicable route for stock between Kimberley and Coolgardie gold-fields; and it also proved that, with the possible exception of small isolated patches, the desert traversed contained no auriferous country.

2953Shall we always study to obtain more of these things, and not sometimes to be content with less?

2833The cost derives from the application of huge amounts of energy, intelligence, and technology to obtain and process the raw materials: digging and smelting to create high-grade steel, harvesting and refining and molding to make rubber parts, and so on.

2432Dean explained Cynthia Byrne's request for as much detail as possible in his report to help her obtain a death certificate.

2330The nobles protested, and Egmont was deputed to go to Madrid and try to obtain from the king a mitigation of the edicts and redress of grievances.

2124About 1350 she went to Rome, partly to obtain from the pope the authorization of the new order, partly in pursuance of her self-imposed mission to elevate the moral tone of the age.

1929Finally, as for salt, that grossest of groceries, to obtain this might be a fit occasion for a visit to the seashore, or, if I did without it altogether, I should probably drink the less water.

17238d., while those possessed of lands of the yearly value of £ioo might obtain licences to play on their own private greens.

1729Thus a latent image of the " reseau-lines " will be formed on the sensitive plate, and, when the latter has been exposed to the sky in the telescope, we obtain, on development, a negative of the images both of the stars and of the reseau-lines.

1523He drew up a scheme for the construction of a pier at Madras, to avoid the dangers of landing through the surf, and instructed his brother-in-law in England to obtain estimates from the engineers Brindley and Smeaton.

1524Unfortunately Poland profited little or nothing by this great triumph, and now that she had broken the back of the enemy she was left to fight the common enemy in the Ukraine with whatever assistance she could obtain from the unwilling and unready Muscovites.

1526On the death of William Longsword, duke of Normandy, who had been assassinated by Arnulf, count of Flanders, in December 942, Louis endeavoured to obtain possession of the person of Richard, the young son and heir of the late duke.

1526(2) Such supplies will be bought from them at such prices as seller and buyer may agree on, and if a seller is unable to obtain a fair price he will be free to take his goods back to his village and no one may hinder him under any pretense.

1320It generally happens that to obtain the greatest possible amount of work from a given supply of energy, and to obtain it at the greatest rate, are conflicting interests.

1326The portion of the lachrymal duct communicating with the cavity of the nose has, on the other hand, been abnormally developed, apparently for the purpose of cleansing that chamber from particles of sand which may obtain an entrance while the animal is burrowing.

1224John (afterwards Sir John) Forrest was despatched by the Perth government with general instructions to obtain information regarding the immense tract of country out of which flow the rivers falling into the sea on the northern and western shores of Western Australia.

1224Petya was not at home, he had gone to visit a friend with whom he meant to obtain a transfer from the militia to the active army.

1224On her return she fell in love with the duc de la Rochefoucauld, the author of the Maxims, who made use of her love to obtain influence over her brother, and thus win honours for himself.

1116The queen set about to obtain a divorce, and used her influence for the return of Albany as a means of undoing her husband's power.

1120The first lasts four years, and at the end of this the pupil may obtain (after examination) the certificate of secondary studies.

1128Probably owing to the same cause, there is less cut stone in the walls, the Palenque builders using plaster to obtain smooth surfaces.

1016In their hurry to obtain wealth, this crowd of office-mongers from the provinces lent themselves to all kinds of bribery and corruption.

1018This element was introduced via Torres Strait, and spread down the Queensland coast to portions of the New South Wales littoral, and also round the Gulf of Carpentaria, but has never been able to obtain a hold in the more arid interior.

1018Ministers were naturally anxious to obtain the reversion to his vacant post, and Indian affairs formed at this time the hinge on which party politics turned.

1020The day after the review, Boris, in his best uniform and with his comrade Berg's best wishes for success, rode to Olmutz to see Bolkonski, wishing to profit by his friendliness and obtain for himself the best post he could--preferably that of adjutant to some important personage, a position in the army which seemed to him most attractive.

1022The desire to obtain the monopoly of the spice trade has been a potent force in the fashioning of Asiatic history.

915We have no information regarding Jerusalem during the period of the captivity, but fortunately Nehemiah, who was permitted to return and rebuild the defences about 445 B.C., has given a fairly clear description of the line of the wall which enables us to obtain a good idea of the extent of the city at this period.

916The publication of this work was, however, impeded for some time by differences with the admiralty, during which Forster proceeded to the continent to obtain an appointment for his father as professor at Cassel, and found to his surprise that it was conferred upon himself.

917Prince Andrew needed his father's consent to his marriage, and to obtain this he started for the country next day.

921New South Wales was the first country which endeavoured to settle its labour grievances through the ballot-box and to send a great party to parliament as the direct representation of Labour, pledged to obtain through legislation what it was unable to obtain by strikes and physical force.

814The prince, after vainly endeavouring to obtain the recall of the generals, restored the constitution with the concurrence of all the Bulgarian political parties (September 18, 1883).

819One of the results of these investigations was to extend the meaning of the word mechanism, and comprise under it all laws which obtain in the phenomenal world, not excepting the phenomena of life and mind.

718In delicate researches two divisions of the scale should always be read, not merely for increased accuracy but to obtain the corrections for " run " from the observations themselves.

718To obtain a larger heating surface than a pipe affords, radiators are connected with the pipes where desired, and the water passing through them warms the surrounding air.

718By this time much had thus been done to obtain an acquaintance with the eastern parts of the Australian continent, although the problem of what could become of the large rivers flowing north-west and south-west into the interior was still unsolved.

718If the purpose of marriage is the family, the person who wishes to have many wives or husbands may perhaps obtain much pleasure, but in that case will not have a family.

718Chicheley had been careful enough to obtain " Papal provisions " for himself, his pluralities, his bishopric and archbishopric.

719Up to 1889 wages held their ground, although work had become more difficult to obtain, and some industries were being carried on without any profit.

719The "man of great merit," despite his desire to obtain the post of director, could not refrain from reminding Prince Vasili of his former opinion.

722For this, the king granted Berford's Hall, formerly Charleston's Inn, which Chicheley's trustees had granted to him so as to obtain a royal grant and indefeasible title.

618In 1537 she was anxious to obtain a divorce from Methven, and her desire was on the point of being realized when it was defeated by the intervention of James.

516Boris, during the campaign, had made the acquaintance of many persons who might prove useful to him, and by a letter of recommendation he had brought from Pierre had become acquainted with Prince Andrew Bolkonski, through whom he hoped to obtain a post on the commander-in-chief's staff.

517The conspirators endeavoured to obtain the co-operation of the prince of Carignano, afterwards King Charles Albert, who was known to share their patriotic aspirations.

521And as it always happens in contests of cunning that a stupid person gets the better of cleverer ones, Helene--having realized that the main object of all these words and all this trouble was, after converting her to Catholicism, to obtain money from her for Jesuit institutions (as to which she received indications)-before parting with her money insisted that the various operations necessary to free her from her husband should be performed.

416If 127 parts of iodine, which is an almost black solid, and loo parts of mercury, which is a white liquid metal, be intimately mixed by rubbing them together in a mortar, the two substances wholly disappear, and we obtain instead a brilliant red powder quite unlike the iodine or the mercury; almost the only property that is unchanged is the weight.

419The National Telephone Company applied to the London County Council for permission to lay wires underground and continued efforts till 1899 to obtain this power, but without success.

22By this reasoning Helmholtz showed how to obtain an expression for the work done.

22For the Master hath sworn by His glory (` His Son,' below) touching His elect, that if there be more sinning after this day which He hath limited, they shall not obtain salvation.

22He was most respectfully received at the camp, but could obtain no definite pledges from the king, who was bent on first coming to Florence.

22We can then draw a continuous surface through the summits of all these ordinates, and so obtain a freezing-point surface, or liquidus; points above this surface will correspond to wholly liquid alloys.

22Having failed, however, to obtain any share in politics, he returned to France in 1739, and subsequently sold Dawley.

22They established a factory there in 1521, but did not obtain peaceable possession of it till 1580, and were dispossessed by the Dutch in 1609.

222 They do not, however, obtain full recognition in Sanskrit literature until the Brahmana period (7th or 8th century B.C.).

22Heating by warmed air, one of the oldest methods in use, has been much improved by attention to the construction of the apparatus, and if properly installed will give as good effects as it is ossible to obtain.

11deep, which baffled every effort to reach the interior until in 1813, when a summer of severe drought had made it of vital importance to find new pastures, three of the colonists, Messrs Blaxland, Lawson and Wentworth, more fortunate than their predecessors in exploration, after crossing the Nepean river at Emu Plains and ascending the Dividing Range, were able to reach a position enabling them to obtain a view of the grassy valley of the Fish river, which lies on the farther side of the Dividing Range.

12As with other duplex systems it is possible to obtain several approximately correct adjustments with the bridge and its accessories, but only one gives a true balance, and careful experiment is required to make sure that this is obtained.

12Morse and Gale, who assisted him, found, however, that the distance of the plates up and down the canal must be at least three or four times the width of the canal to obtain successful results.

12adjust the frequency so that it has the value of the normal time period of the circuit formed of the condenser and transformer secondary circuit, and thus it is possible to obtain condenser oscillatory discharges free from any admixture with alternating current arc. In this manner the condenser discharge can be started or stopped at pleasure, and long and short discharges made in accordance with the signals of the Morse FIG.

12The corporation of Glasgow having persisted in its efforts to obtain a licence, the Treasury appointed Sheriff Andrew Jameson (afterwards Lord Ardwall) a special commissioner to hold a local inquiry in Glasgow to report whether the telephone service in that city was adequate and efficient and whether it was expedient to grant the corporation a licence.

12Telephone subscribers may also obtain the services of an express messenger by telephoning to the nearest post office connected with the exchange.

12The London County Council, according to the statement of its comptroller, was disturbed by the hope expressed by the manager of the company, that the holders of the company's ordinary shares would obtain the par value of their shares in 1911.

12Accurate statistics with regard to the area occupied in different forms of cultivation are difficult to obtain, both on account of their varied and piecemeal character and from the lack of a complete cadastral survey.

12The schools which do not obtain equality with government schools are either some of those conducted by religious orders, or else those in which a sufficient standard is not reached.

12Charles Albert, realizing ~ his own failure and thinking that his son might obtain better terms, abdicated and departed at once for Portugal, where he died in a monastery a few months later.

12He suggested an international congress on the question; inspired a pamphlet, Le Pape el le Con grs, which proposed a reduction of the papal territory, and wrote to the pope advising him to cede Romagna in order to obtain better guarantees for the rest of his dominions.

12This was the only immediate advantage Italy could hope to obtain by drawing nearer the central Powers.

12Italian action was hastened by news that, in December 1884, an exploring party under Signor Bianchi, royal commissioner for Assab, had been massacred in the Aussa (Danakil) country, an event which aroused in Italy a desire to punish the assassins and to obtain satisfaction for the still unpunished massacre of Signor Giulietti and his companions.

12Antoneili profited by the situation to obtain Mneleks signature to a treaty fixing the frontiers of the Italian colony and defining Italo-Abyssinian relations.

12to allow him to dissolve parliament, entrusted Signor Giolitti, a Piedmontese deputy, sometime treasury minister in the Crispi cabinet, with the formation of a ministry of the Left, which contrived to obtain six months supply on account, and dissolved the Chamber, The ensuing general election (November 1892), marked by unprecedented violence and abuse of official pressure upon B k the electorate, fitly ushered in what proved to be scandals, the most unfortunate period of Italian history since the completion of national unity.

12Baratieri, anxious probably to obtain some success before the arrival of Baldissera, and alarmed by the rapid diminution of his stores, which precluded further immobility, called a council of war (29th of February) and obtained the approval of the divisional commanders for a plan of attack.

12in height, greatly resembling the beech, except I See the description of the instrument and of other attempts to obtain the same result by Gottfried Weber, "Wichtige Verbesserung des Horns" in Allg.

12A masterly device, initiated by him, was to collect gases over mercury instead of water; this enabled him to obtain gases previously only known in solution, such as ammonia, hydrochloric acid, silicon fluoride and sulphur dioxide.

00In the same year as Klaproth detected uranium, he also isolated zirconia or zirconium oxide from the mineral variously known as zircon, hyacinth, jacynth and jargoon; but he failed to obtain the metal, this being first accomplished some years later by Berzelius, who decomposed the double potassium zirconium fluoride with potassium.

00Three such compounds are possible according to the number of valencies acting directly between the carbon atoms. Thus, if they are connected by one valency, and the remaining valencies saturated by hydrogen, we obtain the compound H 3 C CH 3, ethane.

00If the carbon atoms are connected by two valencies, we obtain a compound H2C:CH2, ethylene; if by three valencies, HC: CH, acetylene.

00By introducing a methyl group we may obtain CH 3.

00Substituting one hydroxyl group into each of these residues, we obtain radicals of the type - CH 2.

00Thus from the acid-amides, which we have seen to be closely related to the acids themselves, we obtain, by replacing the carbonyl oxygen by chlorine, the acidamido-chlorides, R CC1 2 NH 2, from which are derived the imido-chlorides, R CC1:NH, by loss of one molecule of hydrochloric acid.

00By replacing the chlorine in the imido-chloride by an oxyalkyl group we obtain the imido-ethers, R C(OR') :NH; and by an amino group, the amidines, R C(NH 2): NH.

00By fusing two nuclei we obtain the formula of naphthalene, C 1 oH 8; by fusing three, the hydrocarbons anthracene and phenanthrene, C14H10; by fusing four, chrysene, C18H12, and possibly pyrene, C16H1n; by fusing five, picene, C22 H 14.

00If, however, phosphoric acid is present in the original substance,we may here obtain a precipitate of the phosphates of the remaining metals, together with aluminium, chromium and ferric hydrates.

00The average value for primary alcohols is 44.67 cal., but many large differences from this value obtain in certain cases.

00Mendeleeff endeavoured to obtain a connexion between surface energy and constitution; more successful were the investigations of Schiff, who found that the " molecular surface tension," which he defined as the surface tension divided by the weight.

00Ferdinand appealed to Spain for help; but Spain was anxious to be on good terms with the pope to obtain a title over the newly discovered continent of America and could not afford to quarrel with him.

00Brisson, who had had a majority of votes on the first ballot, but had failed to obtain an absolute majority.

00Some years ago these rabbits were sold as "leporides" or hybrids, produced by the union of the hare and the rabbit; but the most careful experimenters have failed to obtain any such hybrid, and the naked immature condition in which young rabbits are born as compared with the clothed and highly developed young hare renders it unlikely that hybrids could be produced.

00in 1380, the king of Navarre did not interfere in the internal affairs of France, although he endeavoured vainly again to obtain aid from Richard II., and to regain Cherbourg.

00At the same time Musha Island, at the entrance to the Gulf of Tajura, was bought by the British " for ten bags of rice," Bab Island, in the same gulf, and Aubad Island, off Zaila, were also purchased, the object of the East India Company being to obtain a suitable place " for the harbour of their ships without any prohibition whatever."

00There can be no doubt that the government of the Restoration, in seeking to obtain possession of the island, had the intention of reestablishing slavery, and even of reopening the slave trade for the purpose of recruiting the diminished population.

00The conspirators, the chief of whom were Norman Leslie, master of Rothes, and William Kirkaldy of Grange, contrived to obtain admission at daybreak of the 29th of May 1546, and murdered the cardinal under circumstances of horrible mockery and atrocity.

00As the Ecclesiastical History was written in 731, we obtain the following dates for the principal events in Bede's uneventful life: - birth, 672-673 entrance into the monastery, 679-680; ordination as deacon, 691-692; as priest, 702-703.

00To obtain these heavenly mysteries, which alone make the Torah superior to profane codes, definite hermeneutical rules are employed, of which the following are the most important.

00Simon, its reputed author, and exalts him above Moses; (2) it mystically explains the Hebrew vowel points, which did not obtain till 570; (3) the compiler borrows two verses from the celebrated hymn called " The Royal Diadem," written by Ibn Gabirol, who was born about 1021; (4) it mentions the capture of Jerusalem by the crusaders and the re-taking of the Holy City by the Saracens; (5) it speaks of the comet which appeared at Rome, 15th July 1264, under the pontificate of Urban IV.; (6) by a slip the Zohar assigns a reason why its contents were not revealed before5060-5066A.M., i.e.1300-1306A.D., (7) the doctrine of the En Soph and the Sephiroth was not known before the 13th century; and (8) the very existence of the Zohar itself was not known prior 1 See, e.g., G.

00Solomon reminds kings and rulers that they will be held to strict account by God, and, urging them to learn wisdom from his words, proceeds to give his own experience: devoting himself from his youth to the pursuit of wisdom he had found her to be a treasure that never failed, the source and embodiment of all that is most excellent and beautiful in the world - through her he looks to obtain influence over men and immortality, and he concludes with a prayer that God would send her out of his holy heavens to be his companion and guide.

00But the desire to obtain general enunciations of theorems without exceptional cases has led mathematicians to employ entities of ever-ascending types of elaboration.

00Any one can obtain a gratuitous permit to clear and cultivate such lands; the laws governing ordinary agricultural lands then apply to them.

00To obtain a concession, formalities detailed in the law must be complied with, under a penalty of £T10o to £Tl000.

00On the 22nd of June the Russian army, under Prince Gorchakov, crossed the Pruth, not - as was explained in a circular to the powers - for the purpose of attacking Turkey, but solely to obtain the material guarantees for the enjoyment of the privileges conferred upon her by the existing treaties.

00The viceroy of Egypt, Ismail Pasha, followed his suzerain's example in this respect, and was lavish in his bribes to his imperial overlord to obtain the extension of his own privileges and the establishment in Egypt of succession from father to son; these concessions were granted to him by the firmans of the 27th of May 1866 and the 8th of June 1867, in the latter of which the viceroy is addressed for the first time as " khedive."

00To delay him and obtain escape, Medea dismembered her young brother Absyrtus, whom she had taken with her, and cast his limbs about in the sea for his father to pick up. Her plan succeeded, and while Aeetes was burying the remains of his son at Tomi, Jason and Medea escaped.

00All that remained was to obtain the abdication of Benedict XIII., the successor of the Avignon pope Clement VII., but the combined efforts of the council and the emperor were powerless to overcome the obstinacy of the Aragonese pope.

00There was, indeed, a danger lest the rivalries in the assembly might render it exceedingly difficult, not to say impossible, to obtain such unanimity.

00Bernadotte's corps in Hanover was almost in the position of a beleaguered garrison, and the marshal could only obtain his transport by giving out that he was ordered to withdraw to France.

00The Prussian headquarters, however, spent the 12th and 13th in idle discussion, whilst the troop commanders exerted themselves to obtain some alleviation for the suffering of their starving men.

00Meanwhile the mathematical mind, with its craving for accurate data on which to found its plans (the most difficult of all to obtain under the conditions of warfare), had been searching for expedients which might serve him to better purpose, and in 1805 he had recourse to the cavalry screen in the hope of such results.

00Typical animals are holozoic, that is, they obtain their food by eating the tissues of other animals and plants: they take their food substances in the organized forms of proteids, fats and carbohydrates.

00Typical plants are holophytic, that is, they obtain their food substances from purely mineral sources.

00He negotiated with Rufus to obtain the possession of their mother's inheritance, but only incurred thereby the suspicions of the duke, who threw him into prison.

00Craft gilds were already in existence, but these had no share in the government; for, though the Lubeck rule excluding craftsmen from the Rath did not obtain, they were excluded in practice.

00The elder journeyed into Pannonia to obtain support from Attila; the younger betook himself to the imperial court at Rome.

00In batteries which use acids as the electrolyte, a film of hydrogen tends to be deposited on the copper or platinum electrode; but, to obtain a constant electromotive force, several means were soon devised of preventing the formation of the film.

00In 1876 eye (and brain) trouble caused him to obtain sick leave, and finally, in 1879, to be pensioned.

00To obtain the latex, deep incisions are made near the base of the tree extending up the trunk.

00To obtain the rubber, the latex is usually treated in the following manner.

00Blochmann to obtain in the genital arteries.

00b., we obtain by comparison with the middle series the symbolical representation of all symmetric functions in brackets () appertaining to the quantities p i, P2, P3,ï¿½ï¿½ï¿½ To obtain particular theorems the quantities a l, a 2, a 3, ...a, n are auxiliaries which are at our entire disposal.

00Thus to obtain Stroh's theory of seminvariants put b1=0-1+a2+ï¿½ï¿½.+0-m

00From this formula we obtain by elementary algebra 1) !

00so that A breaks u p into a sum of determinants, and we also obtain a theorem for the addition of determinants which have rows in common.

00Similarly, by putting one or more of the deleted rows or columns equal to rows or columns which are not deleted, we obtain, with Laplace, a number of identities between products of determinants of complementary orders.

00We thus obtain for the product a determinant of order n.

00We may say that, in the resulting determinant, the element in the ith row and k th column is obtained by multiplying the elements in the kth row of the first determinant severally by the elements in the ith row of the second, and has the expression aklb11+ak2b12+ak3b13ï¿½ï¿½ï¿½ +aknbin, and we obtain other expressions by transforming either or both determinants so as to read by columns as they formerly did by rows.

00We can eliminate the quantities S l, E2, ï¿½ï¿½ï¿½ In and obtain n relations AbXi = (2B 11 - Ab)'ï¿½k1 +2B21x2+2B31x3+ï¿½ï¿½ï¿½, AbX2 = 2B12x1+ (2B22 - Ab) x2 +2B32x3+..., and from these another equivalent set Abx1 = (2B11 - X1 +2B12X2+2B13X3+ï¿½ï¿½ï¿½, Abx2 = 2B21X1+(2B22 - Ab)X2+2B23X3+ï¿½ï¿½ï¿½, and now writing 2Bii - Ab 2Bik - aii, Ob = aik, Ob we have a transformation which is orthogonal, because EX 2 = Ex2 and the elements aii, a ik are functions of the 2n(n- I) independent quantities b.

00We have to multiply a01; -alas+a2 by ao, -aif32+a2 and we obtain ao (3 - aoal(f31N2 +01133) +aoa2(SI+13) -i-a?31a2 - aIa2(31 + 02) + al, 131+02 = b, 131132 = b t'i +s2 = 2bob2, and clearing of fractions R 1,5 = (a o b 2 - a2 b o) 2 + (a i b o - aobi) (aib2 - a2b1).

00Assuming then 01 to have the coefficients B1, B2,...B,, and f l the coefficients A 1, A21...A,n, we may equate coefficients of like powers of x in the identity, and obtain m+n homogeneous linear equations satisfied by the m+n quantities B1, 2, ...B n, A 1, A 2, ...A m.

00Forming the resultant of these equations we evidently obtain the resultant of f and 4,.

00and by elimination we obtain the resultant ao 0 bo 0 0 al ao b1 bo 0 a 2 a i b 2 b 1 bo a numerical factor being disregarded.

00For if u, v, w be the polynomials of orders m, n, p respectively, the Jacobian is (u 1 v 2 w3), and by Euler's theorem of homogeneous functions xu i +yu 2 +zu 3 = mu xv1 +yv2 +zv3 = /IV xw 1+y w 2+ zw 3 = pw; denoting now the reciprocal determinant by (U 1 V2 W3) we obtain Jx =muUi+nvVi+pwWi; Jy=ï¿½.., Jz=..., and it appears that the vanishing of u, v, and w implies the vanishing of J.

00Further, if m '=' p, we obtain by differentiation 7+x =m (u;1-2xl.

00= 0, we find that, eliminating x, the resultant is a homogeneous function of y and z of degree mn; equating this to zero and solving for the ratio of y to z we obtain mn solutions; if values of y and z, given by any solution, be substituted in each of the two equations, they will possess a common factor which gives a value of x which, corn bined with the chosen values of y and z, yields a system of values which satisfies both equations.

00Hence in all there are mn such systems. If, therefore, we have a third equation, and we substitute each system of values in it successively and form the product of the mn expressions thus formed, we obtain a function which vanishes if any one system of values, common to the first two equations, also satisfies the third.

00If three equations, each of the second degree, in three variables be given, we have merely to eliminate the six products x, 2, z 2, yz, zx, xy from the six equations u = v = w = o = oy = = 0; if we apply the same process :to thesedz equations each of degree three, we obtain similarly a determinant of order 21, but thereafter the process fails.

00af Expression in Terms of Roots.-Since x+y y =mf, if we take cx any root x 3, y1, ofand substitute in mf we must obtain, y 1 C) zaZ1 ï¿½; hence the resultant of and f is, disregarding numerical factors, y,y2...y,,.

00be enclosed in a bracket we obtain a partition of the weight w which appertains to the separated partition.

00We can multiply out this expression so as to obtain a series of monomials of the form 9(sl is2 2 s3 3 ...).

00and take therein the coefficient of the function (mi t tm7t t m 31 t ...), we obtain the same result as if we formed the separation function in regard to the specification (mï¿½ It t'tm2 32tm"`l3t...), multiplied by Alt!!

00+aï¿½xn multiply each side by I +px, thus introducing a new quantity A; we obtain (1 +a1x) (1+a2x)...(1 -Fanx)(1+,ux) = 1+(a1 +1a)x + (a2+1aa1)x2+...

00If in the identity f =f l f 2 ...fm we introduce a new root A we change a 8 into a8+/la8_l, and we obtain (1 +AD1 2 D2+...

00For write (pq) =sï¿½ and take logarithms of both sides of the fundamental relation; we obtain slox +soot' = + (3ly) S20x 2 +2siixy+s02y 2 = E(aix+(3 ly) 2, &C., and siox+SOly - (S 20 x2 + 2s ii x y+ s ooy 2) +...

00By the exponential and multinomial theorems we obtain the results) 1,r -1 (E7r) !

00From the above D p4 is an operator of order pq, but it is convenient for some purposes to obtain its expression in the form of a number of terms, each of which denotes pq successive linear operations: to accomplish this write d ars and note the general result exp (mlodlo+moldol +...

00By solving the equations of transformation we obtain rE1 = a22x1 - a12x1, r = - a21x1 + allx2, aua12 where r = I = anon-anon; a21 a22 r is termed the determinant of substitution or modulus of transformation; we assure x 1, x 2 to be independents, so that r must differ from zero.

00(II.) Similarly in (I.), writing for c l, c 2 the cogredicnt pair -y2, +y1, we obtain axb5-a5bx=(ab)(xy)..

00To obtain the corresponding theorem concerning the general form of even order we multiply throughout by (ab)2' 2c272 and obtain (ab)2m-1(ac)bxc2:^1=(ab)2mc2 Paying attention merely to the determinant factors there is no form with one factor since (ab) vanishes identically.

00If the invariants and covariants of this composite quantic be formed we obtain functions of X such that the coefficients of the various powers of X are simultaneous invariants of f and 4).

00In particular, when 4) is a covariant of f, we obtain in this manner covariants of f.

00Moreover, if we add the first to the fourth we obtain aj 2w ak = 7 1=6, j, =0j, where 0 is the degree of the invariant; this shows, as we have before observed, that for an invariant w= - n0.

00If we have a symbolic product, which contains the symbol a only in determinant factors such as (ab), we may write x 2, -x 1 for a 1, a 2, and thus obtain a product in which (ab) is replaced by b x, (ac) by c x and so on.

00In particular, when the product denotes an invariant we may transform each of the symbols a, b,...to x in succession, and take the sum of the resultant products; we thus obtain a covariant which is called the first evectant of the original invariant.

00From (ac) 2 (bd) 2 (ad)(bc) we obtain (bd) 2 (bc) cyd x +(ac) 2 (ad) c xdx - (bd) 2 (ad)axb x - (ac)2(bc)axbx =4(bd) 2 (bc)c 2.

00The existence of such forms seems to have been brought to Sylvester's notice by observation of the fact that the resultant of of and b must be a factor of the resultant of Xax+ 12 by and X'a +tA2 for a common factor of the first pair must be also a common factor so we obtain P: = of the second pair; so that the condition for the existence of such common factor must be the same in the two cases.

00Hence, from the identity ax (pq) = px (aq) -qx (ap), we obtain (pet' = (aq) 5px - 5 (ap) (aq) 4 pxg x - (ap) 5 gi, the required canonical form.

00To obtain the real form we multiply out, and, in the result, substitute for the products of symbols the real coefficients which they denote.

00If ai, bx, cx be different forms we obtain, after development of the squared determinant and conversion to the real form (employing single and double dashes to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the dashes we obtain 6 (abc+2fgh -af t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines.

00Hesse's canonical form shows at once that there cannot be more than two independent invariants; for if there were three we could, by elimination of the modulus of transformation, obtain two functions of the coefficients equal to functions of m, and thus, by elimination of m, obtain a relation between the coefficients, showing them not to be independent, which is contrary to the hypothesis.

00In order to obtain the seminvari ants we would write down the (w; 0, n) terms each associated with a literal coefficient; if we now operate with 52 we obtain a linear function of (w - I; 8, n) products, for the vanishing of which the literal coefficients must satisfy (w-I; 0, n) linear equations; hence (w; 8, n)-(w-I; 0, n) of these coefficients may be assumed arbitrarily, and the number of linearly independent solutions of 52=o, of the given degree and weight, is precisely (w; 8, n) - (w - I; 0, n).

00we obtain 1 - z - 2 1 -az".

00retains the same value, however the suffixes be permuted, we shall obtain a i 7 2 ar a2 a33?Q"l 7r2 rr3 w hich in r a l sum of terms, such as w!

00Solving the equation by the Ordinary Theory Of Linear Partial Differential Equations, We Obtain P Q 1 Independent Solutions, Of Which P Appertain To S2Au = 0, Q To 12 B U =0; The Remaining One Is Ab =Aobl A 1 Bo, The Leading Coefficient Of The Jacobian Of The Two Forms. This Constitutes An Algebraically Complete System, And, In Terms Of Its Members, All Seminvariants Can Be Rationally Expressed.

00Taking The First Generating Function, And Writing Az P, Bz4, 2 For A, B And Z Respectively, We Obtain The Coefficient Of Aobe'Zpo 0' 2W That Is Of A E B E 'Z ï¿½, In 1 Z 2 1 Azp. 1 Azp 2....1 A2 P 2.1 Az P .

00Orthogonal System.-In particular, if we consider the transformation from one pair of rectangular axes to another pair of rectangular axes we obtain an orthogonal system which we will now briefly inquire into.

00Charcoal is now added, and the heat urged on to obtain Pressblei, an inferior metal formed partly by the action of the charcoal on the oxide of lead.

00At the beginning of the Insurrection of 1831 he was sent to London to obtain the assistance, or at least the mediation, of England; but the only result of his mission was the publication of the pamphlet Menzoire presente a Lord Palmerston (Warsaw, 1831).

00It can be shown 3 that in a uniform field an elongated piece of any non-crystalline material is in stable equilibrium only when its length is parallel to the lines of force; for diamagnetic substances, however, the directing couple is exceedingly small, and it would hardly be possible to obtain a uniform field of sufficient strength to show the effect experimentally.

00When it is desired to obtain a simple curve of induction, such as that in fig.

00by all observers in magnetic observatories, who are every day making measurements of magnetic quantities, and who obtain results which would be inconsistent with each other if the law of force had been erroneously assumed.

00As the equites practically monopolized the farming of the taxes, they came to be regarded as identical with the publicani, not, as Pliny remarks, because any particular rank was necessary to obtain the farming of the taxes, but because such occupation was beyond the reach of all except those who were possessed of considerable means.

00To obtain the support of the capitalists, Gaius Gracchus conceived the plan of creating friction between them and the senate, which he carried out by handing over to them the control (a) of the jury-courts, and (b) of the revenues of Asia.

00One of the main purposes of the exploration was to obtain light on the question of the foundation of atolls.

00Robert was in a good position to obtain information, for the Mont St Michel was one of the four great centres of pilgrimage in Europe.

00In 1855 Gauss died and was succeeded by Dirichlet, who along with others made an effort to obtain Riemann's nomination as extraordinary professor.

00He founded museums, libraries and schools, and inaugurated scholarships and a fund from which deserving scholars desirous of studying in England and America could obtain their expenses.

00For his account of earlier events he was able to obtain information from his father, who was one of the most prominent 1 A shortened form of Chalcocondyles, from xaXicos, copper, and xovSvXos, knuckle.

00In order to obtain alum from alunite, it is calcined and then exposed to the action of air for a considerable time.

00The great majority of the people are unused to wheaten bread, using the coarse flour of the mandioca root instead, consequently the demand for wheat and flour is confined to the large cities, which can obtain them from Argentina more cheaply than they can be produced in the country.

00Duguay Trouin departed to Bahia to obtain fresh spoils; but having lost in a storm two of his best ships, with an important part of the money received, he renounced this plan and returned directly to France.

00Thereupon Alphonso, duke of Calabria, who was fighting in Tuscany on the side of his father Ferdinand, came to an agreement with Siena and, in the same way as his grandfather Alphonso, tried to obtain the lordship of the city and the recall of the exiled rebels in 1456.

0028) furnishes us with a list of church offices very different from those which obtain in any church at the present day.'

00250) decree that a confessor who has suffered torment for his adherence to the Christian faith should merit and obtain the rank of presbyter forthwith - " Immo confessio est ordinatio ejus."

00Kenner as special commissioner to the courts of England and France to obtain recognition of the Confederacy on condition of the abolition of slavery.

00Provision is made whereby a native can obtain relief from the operation of native law and be subject to the colonial law (Law No.

00But he made little way, and failed to obtain a vacant physicianship at St George's hospital; the result was that he abandoned medicine and took to original research.

00C. Oersted (1777-1851) had shown that a magnetic needle is deflected by an electric current, he attempted, in the laboratory of the Royal Institution in the presence of Humphry Davy, to convert that deflection into a continuous rotation, and also to obtain the reciprocal effect of a current rotating round a magnet.

00The possession of this property brought about frequent disputes with an adjoining landowner, Thomas de Grey, and, after many actions in the courts, his friends endeavoured to obtain, by a bill forced through the houses of parliament, the privileges which the law had not assigned to him (February 1774).

00io, 1664) to obtain terms which should only have been conceded to a conqueror.

00As he was almost five years under the canonical age, he was obliged to go to Rome to obtain a dispensation and was consecrated there in April 1607.

00It is true that we obtain this result by subtracting 3 from io by means of a subtractiontable (concrete or ideal); but this table merely gives the generalized results of a number of operations of addition or subtraction performed with concrete units.

00By successive stages we obtain (ï¿½ 18) s5 = 2, X = 12; or we may write at once x = of io= 5 of 10 = 12.

00(iii.) By writing (A+a) 2 = A 2 + 2Aa+a 2 in the form (A+a)2= A 2 +(2A+a)a, we obtain the rule for extracting the square root in arithmetic.

00We then obtain a set of equations, and by means of these equations we establish the required result by a process known as mathematical induction.

00we obtain I, 4, 9, ï¿½ ï¿½ ï¿½ This suggests that, if u n is the sum of the first n odd numbers, then u n = n 2 .

00do not contain n; and thence we can obtain the sum of the numbers found by putting n= 1, 2, 3,.

00Thus, to divide i by i +x algebraically, we may write it in the form I+o.x+o.x 2 +o.x 3 +o.x 4, and we then obtain I I +0.x+0.x2+0.x3 '+0.x4 = I' x+x2 - x 3 + x4 I+x I+x' where the successive terms of the quotient are obtained by a process which is purely formal.

00If P and M are rational integral functions of x, arranged in descending powers of x, the division of P by M is complete when we obtain a remainder R whose degree (ï¿½ 45) is less than that of M.

00(I dx) n we obtain (22) of ï¿½ 44 (ii.).

00We therefore take a third step, and obtain theoretical continuity by considering that every point on the line, if it does not represent a rational number, represents something which may be called an irrational number.

00Applying the distributive law, we obtain, when r+s>n, ArB 8 = EaErE i 3E 8 = E(a(3)ErEs, where the regressive products E r E B are to be reduced to units of species (r+s-n) by the foregoing rule.

00After his return to France the cardinal was anxious to regain the favour of the queen in order to obtain the position of prime minister.

00He begged the countess to obtain a secret interview for him with the queen, and a meeting took place in August 1784 in a grove in the garden at Versailles between him and a lady whom the cardinal believed to be the queen herself.

00The entry of Italy into the war was a serious set-back to the Yugoslav cause, for under the Treaty of London (April 27 1915) she was to obtain, in the event of an Entente victory, wide districts in Gorizia, Carniola, Istria and Dalmatia, peopled by not less than 700,000 Yugosla y s.

00The record of Brown-Sequard's original experiment is not satisfactory, and the subsequent attempts to obtain similar results have not been attended with success.

00In order to obtain the effect of the primary wave, as, retarded by traversing the distance r, viz.

00In the absence of a heliostat it is more convenient to obtain a point of light with the aid of a lens of short focus.

00The integrations may also be effected by means of polar coordinates, taking first the integration with respect to 4) so as to obtain the result for an infinitely thin annular aperture.

00But, to obtain an equally good result in the m th spectrum, the error must be less than I/m of the above amount.'

00If the subject of examination be a luminous line parallel to n, we shall obtain what we require by integrating (4) with respect to 77 from - oo to + oo.

00If, instead of supposing the motion at dS to be that of the primary wave, and to be zero elsewhere, we suppose the force operative over the element dS of the lamina to be that corresponding to the primary wave, and to vanish elsewhere, we obtain a secondary wave following quite a different law.

00(b2V2 + n2) (a2 - b 2) = - z It will now be convenient to introduce the quantities a l, a 2', 7731 which express the rotations of the elements of the medium round axes parallel to those of co-ordinates, in accordance with the equations Ty - 1 = dz ' 3= - dy 2 = dx - In terms of these we obtain from (7), by differentiation and subtraction, (b 2 v 2 + n 2) 7,3 = 0 (b 2 0 2 +n 2) .r i = dZ/dy (b 2 v 2 +n 2)', , 2 = - dZ/dx The first of equations (9) gives 3 = 0 (10) For al we have ?1= 47rb2, f dy e Y tkr dx dy dz

00It did not, however, obtain ecclesiastical currency - the old versions holding their ground, just as English churchmen still read the Psalms in the version of the " Great Bible " printed in their Prayer Book.

00A determination to keep clear of the British and to obtain access to the outer world through an independent channel led Potgieter and a considerable number of the Potchefstroom and Winburg burghers in 1845 to migrate towards Delagoa Bay.

00It was also in accord with the desire of the Transvaal Boers to obtain a seaport, a desire which had led them as early as 1860 to treat with the Zulus for the possession of St Lucia Bay.

00By 1892 the Uitlanders began to feel that if they were to obtain any redress for their grievances combined constitutional action was called for, and the first reform move ment began.

00Following this incident came a further alteration in the franchise law, making the franchise practically impossible to obtain.

00Jameson did not obtain more than 50o men.

00It no sooner opened than it was evident that Kruger had come to obtain, not to grant, concessions.

00Milner, anxious above everything else to obtain sufficient revenue to carry on his work of reconstruction, gave his consent to the experiment.

00By applying the method of the differential calculus, we obtain cos i= { (µ 2 - 1)/(n24-2n)} as the required value; it may be readily shown either geometrically or analytically that this is a minimum.

00Living things which present this visible structure are said to be organized; and so widely does organization obtain among living beings, that organized and living are not unfrequently used as if they were terms of co-extensive applicability.

00It adds many new features to the shorter form of the story as given by Eusebius, among which is the noteworthy promise of Christ about the impregnability of the city - " Thy city shall be blessed and no enemy shall ever henceforth obtain dominion over it.

00The council of Trent, while reproving all superstitious practices in the invocation of the saints, the veneration of relics and the use of images, expresses as follows the doctrine of the Roman Church: "That the saints who reign with Christ offer to God their prayers for men; that it is good and useful to invoke them by supplication and to have recourse to their aid and assistance in order to obtain from God His benefits through His Son our Saviour Jesus Christ, who alone is our Saviour and Redeemer" (Sess.

00It is often difficult to obtain quite accurate or even adequate reproductions of scenes and subjects, and, when this is done, it is obviously necessary to refrain from treating the work of the old artists and sculptors as equivalent to photographic representations.

00On the 23rd of August 1268 he encountered the troops of Charles at Tagliacozzo, but the eagerness of his soldiers to obtain plunder gave the victory to the French.

00After bringing out these plays Terence sailed from Greek parts, either to escape from the suspicion of publishing the works of others as his own, or from the desire to obtain a more intimate knowledge of that Greek life which had hitherto been known to him only in literature and which it was his professed aim to reproduce in his comedies.

00Finding that diplomacy was of no avail to obtain the reparation from Castro that was demanded by their subjects, the three powers unwillingly had recourse to coercion.

00and other princes, but as no settlement was reached the master continued his efforts to obtain help in view of a renewal of the war.

00They did not, however, occupy Euryelus, at the western extremity of the high ground of Epipolae, and this omission allowed the Athenians to obtain possession of the whole plateau, and to begin the investment of the city.

00Indeed, in such early stages, and in patients who are enabled to command the means of an expensive method of cure, phthisis is no longer regarded as desperate; while steps are being taken to provide for those who of their own means are unable to obtain these advantages, by the erection of special sanatoriums on a more or less charitable basis.

00As early as 1794 the government had information that placed Lord Edward under suspicion; but it was not till 1796 that he joined the United Irishmen, whose aim after the recall of Lord Fitzwilliam in 1795 was avowedly the establishment of an independent Irish republic. In May 1796 Theobald Wolfe Tone was in Paris endeavouring to obtain French assist ance for an insurrection in Ireland.

00It fell to his lot as war minister to obtain the duke of Cambridge's resignation of the' office of commander-in-chief; but his intended appointment of a chief of the staff in substitution for that office was frustrated by the resignation of the ministry.

00A proclamation issued (December 6, 1553) directed the churchwardens to obtain the proper ornaments for the churches; and the bishops (at any rate Bishop Bonner, see Visitation Articles 1 554, Cardwell's Doc. Ann.

00Metropolitan borough councils have to obtain the sanction of the Local Government Board to loans for baths, washhouses, public libraries, sanitary conveniences and certain other purposes under the Public Health Acts; for cemeteries the sanction of the Treasury is required, and for all other purposes that of the London County Council; poor law authorities, the metropolitan asylums board, the metropolitan water board and the central (unemployed) body require the sanction of the Local Government Board the receiver for the metropolitan police district that of the Home Office, and the London County Council that of parliament and the Treasury.

00If we take from the Itinerary the last station before Londinium in all the routes we shall be able to obtain some idea of the position of the gate entered from each route by drawing a line on the map of London to the nearest point.

00C. Coote in his Romans of Britain elaborated a description of the survival of Roman influence in English institutions, but his views did not obtain much support from London historians.

00When Stephen seized the crown on the death of Henry I., he tried successfully to obtain the support of the people of London.

00The citizens, however, did not obtain their rights without paying for them, and in 1139 they paid Stephen one hundred marks of silver to enable them to choose their own sheriffs.

00By the help of these maps we are able to obtain a clear notion of the extent and chief characteristics of Tudor London.

00Bedford House in Bloomsbury Square had its full view of Hampstead and Highgate from the back, and Queen's Square was built open to the north in order that the inhabitants might obtain the same prospect.

00He estimates the population to have been 180,000 persons, which Dr Creighton affirms to be nearly three times the number that we obtain by a moderate calculation from the bills of mortality in 1532 and 1 535.

00The remarkable instance of this after the Conquest was the election of Stephen, but William the Conqueror did not feel secure until he had the sanction of the Londoners to his kingship, and his attitude towards London when he hovered about the neighbourhood of the city for a time shows that he was anxious to obtain this sanction freely rather than by compulsion.

00Coming over the Drakensberg in considerable numbers during 1837, the Boers found the land stretching south from the mountains almost deserted, and Retief went to Arrival Dingaan to obtain a formal cession of the country of the west of the Tugela, which river the Zulu recognized as the boundary of Zululand proper.

00In 1860 a Boer commission was appointed to beacon the boundary, and to obtain, if possible, from the Zulu a road to the sea at St Lucia Bay.

00At that time the Transvaal government - which had been the first to reap the benefit of Great Britain's defeat of the Zulu by acquiring the " New Republic " - was endeavouring to obtain the territories of Zambaan and Umtegiza, hoping also to secure a route through Tongaland to Kosi Bay.

00But the court was eager to obtain command of a seaport, and Zumalacarregui was ordered to besiege Bilbao.

00By sinking additional pits or by extending the costeaning trenches and uncovering the outcrop of the deposit more fully it is sometimes possible to obtain all the information required for the most extensive and important mining operations.

00A large number of holes must be bored to obtain, even approximately, the average thickness and value of the ore and the shape and size of the ore bodies.

00In many cases the state or the ruler has sought to obtain a share in the profits of mining, or even to work mines for the individual profit of the ruler or of the state.

00The land tax is supplemented by a poll tax on the male population from 18 to 60 years of age, with the exception of immigrants during the first five years of their residence, religious teachers, schoolmasters, government servants and those unable to obtain their own livelihood.

00To obtain the effect it was necessary to reproduce as far as possible the conditions under which the early craftsmen worked, and to create scientifically glass which is impure in colour, irregular in section, and non-homogeneous in texture.

00In 675 Benedict Biscop, abbot of Wearmouth, was obliged to obtain glass-workers from France, and in 758 Cuthbert, abbot of Jarrow, appealed to the bishop of Mainz to send him artisans to manufacture " windows and vessels of glass, because the English were ignorant and helpless."

00The roadstead is tolerably safe, and passing vessels take advantage of it in order to obtain water and fresh provisions, of which Annobon contains an abundant supply.

00(to) Integrating over the base, to obtain one-third of the kinetic energy T, 3T = 2 pf '3 4R2(3x4-h4)dx/h 3 = pR2h4 / 1 35 V 3 (II) so that the effective k 2 of the liquid filling the trianglc is given by k 2 = T/Z p R 2 A = 2h2/45 = (radius of the inscribed circle) 2, (12) or two-fifths of the k 2 for the solid triangle.

00and putting a=b, Maclaurin's solution is obtained of If 1 - =o or 8 3 =1" in addition, we obtain the solution of Jacobi's the rotating spheroid.

00the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

00of the Kings' List, and we obtain for the rise of the Dynasty of Ur a date not much earlier than 2300 B.C.

00Fortunately, in the case of a large number of names occurring on business documents as the interested parties or as scribes or as witnesses - and it is through these documents that we obtain the majority of the Babylonian-Assyrian proper names - we have variant readings, the same name being written phonetically in whole or part in one instance and ideographically in another.

00But this connexion was not found to obtain as a rule in life, and the difficulties arising from this conflict between promise and experience centred round the lot of the righteous as a community and the lot of the righteous man as an individual.

00The apocalyptic writer could obtain no hearing from his contemporaries, who held that, though God spoke in the past, "there was no more any prophet."

00He assisted Biren to obtain the regency in the last days of the empress Anne, but when his patron fell three weeks later, his own position became extremely precarious.

00His friends tried in vain to obtain his appointment as minister of the marine; and he failed to obtain even a post as officer.

00The pans are provided with steam worms to keep the mass hot as required, and with mechanical stirrers to keep it in movement and thoroughly mixed with the water and sweet water which are added to the sugar to obtain a solution of the specific gravity desired.

00The manufacturers who have adopted this system assert that, as compared with other methods, not only do they obtain an increased yield of sugar of better quality, but that they do so at a less cost for running their machines and with a reduced expenditure in sugar and " clairce."

00In the chamber he still sought to obtain liberty for the press - a theme upon which he published a volume of his speeches (Paris, 1817).

00After in vain attempting to obtain an apology for " the unparalleled outrage against a friendly power " he issued on the 10th of December a solemn hatti sheriff summoning the faithful to a holy war.

00The inorganic materials within it supply some of the chief substances utilized by plants for their development and growth, and from plants animals obtain much of their sustenance.

00Leguminous crops take some of the nitrogen which they require from the air, but most plants obtain it from the nitrates present in the soil.

00In the semi-arid regions of the United States, Argentina and other countries where the average annual rainfall lies between ioa to 20 in., irrigation is necessary to obtain full crops every year.

00For the carrying on of their functions they all need to be supplied with carbohydrates or other carbon compounds which they obtain ordinarily from humus and plant residues in the soil, or possibly in some instances from carbohydrates manufactured by minute green algae with which they live in close union.

00There is little doubt, however, that in the near future means will be devised to obtain the most efficient work from these minute organisms, either by special artificial cultivation and subsequent application to the soil, or by improved methods of encouraging their healthy growth and activity in the land where they already exist.

00The fermentation is very carefully controlled, and to obtain the desired light colour the temperature is kept comparatively low.

00In more recent years tobacco has been grown in Ireland, but up to 1910 it had been found impracticable to obtain from the government sufficient relaxation from fiscal restrictions to encourage the home cultivation, though in 1907 the prospect of licences being issued was held out.

00In some parts of England the trees are thrashed with rods or poles to obtain the nuts, but this is not a commendable mode of collecting them.

00To obtain a product free of Cl or S04, there must be an excess of alkali and the zinc salt must be poured into the hot solution of the carbonate.

00The protection which normally it is the business of government to furnish he could no longer obtain.

00As in the last days of the Roman empire the poor landowner had found his only refuge from the exactions of the government in the protection of the senator, who could in some way obtain exemptions, so the poor Frank could escape the ruinous demands of military service only by submitting himself and his lands to the count, who did not hesitate on his side to force such submission.

00Sadlier hesitated about going farther, but he was unable to obtain a safe conduct to Basra, or to return by the way he had come, and was compelled reluctantly to accompany the army to Medina.

00of Turkey to obtain possession of its important harbour.

00It became, indeed, increasingly difficult to obtain the support of the inland towns for a policy of seapower in the Baltic. Cologne sent no representatives to the regular Hanseatic assemblies until 1383, and during the 15th century its independence was frequently manifested.

00Even the clergy were by no means altogether on Innocent's side; the council of Lyons was attended by but 150 bishops, mainly French and Spanish, and the deputation from England, headed by Robert Grossetete of Lincoln and Roger Bigod, came mainly in order to obtain the canonization of Edmund of Canterbury and to protest against papal exactions.

00During the second rising in Baden in the spring of 1849 he again made efforts to obtain a footing in his own state, but without success.

00The aim of the French Canadian opposition at this time was to obtain financial and also constitutional reforms. Matters came to a head when the legislative assembly of Lower Canada refused supplies and Papineau arranged for concerted action with William Lyon Mackenzie, the leader of the reform party in Upper Canada.

00It was his chief duty to hire foreign sailors and obtain everything necessary for the construction and complete equipment of a fleet.

00In 1880 and 1888 he aspired actively to the Republican nomination for the presidency, but failed to obtain the requisite support in the Convention.

00A large increase in imports, caused by fictitious prosperity and inability to obtain drafts against guano shipments, led to the exportation of coin to meet commercial obligations, and this soon reduced the currency circulation to a paper basis.

00In 1875 the banks were granted a moratorium, to enable them to obtain coin, but without result.

00He entered the service of Pardaillan, and in 1587 was sent on a mission to many of the princes of northern Europe, after which he visited England to obtain help from Queen Elizabeth for Henry of Navarre.

00The only vote which he had ever cast for a presidential candidate was in 1856 for James .Buchanan; and leading Democrats, so late as by Grant, but a treaty negotiated with this end in view failed to obtain the requisite two-thirds vote in the Senate.

00The gonfalonier, Francesco Valori, used his strongest influence to obtain their condemnation, and all five were put to death.

00But menacing briefs poured in from Rome; the pope had read one of Savonarola's recent sermons on Exodus; the city itself was threatened with interdict, and the Florentine ambassador could barely obtain a short delay.

00All objects, therefore, which lie beyond a certain point (the conjugate focus of the dioptric system of the eye, the far point) are indistinctly seen; rays from them have not the necessary divergence to be focused in the retina, but may obtain it by the interposition of suitable concave lenses.

00So Comte remained in Paris, living as he best could on something less than 80 a year, and hoping, when he took the trouble to break his meditations upon greater things by hopes about himself, that he might by and by obtain an appointment as mathematical master in a school.

00of France had arisen when the French king sought to obtain authority over Lorraine and aided the German rebels in 939; but after the German king had undertaken an expedition into France, peace was made in 942.

00Indeed the necessity for obtaining complete control over the church was one reason which induced him to obtain the imperial crown.

00The Duke was anxious to obtain a capable candidate to aid him in regaining his ascendancy over the rebellious borough.

00In 900, after the death of the emperor Arnulf, he went to Italy to obtain the imperial crown.

00The pope was, however, compelled to modify his measures by the threat that if the people could not obtain the services of religion they would not support the clergy, and that heresy would spread.

00Its proprietor, Maruyama Ryuhei, spared no expense to obtain news from all qerarters of tli world, and for the first time the Japanese public learned what stores of information may be found in the columns of a really enterprising journal.

00but highly artistic device is that of gradually rounding off the surfaces where necessary, in order to obtain in printing a soft and graduated mass of color which does not terminate too abruptly.

00Foreign demand has shown so little discrimination that experts, finding it impossible to obtain adequate remuneration for first-class work, have been obliged to abandon the field altogether, or to lower their standard to the level of general appreciation, or by forgery to cater for the perverted taste which attaches unreasoning value to age.

00At Hirado the ceramists affected a lighter and more delicatetone than that of the Chinese, and, in order to obtain it, subjected the choice pigment of the Middle Kingdom to refining processes of great severity.

00He was brought to Canterbury, possibly by Becket, together with a supply of books upon the civil law, to act as counsel (causidicus) to Archbishop Theobald in his struggle, which ended successfully in 1146, to obtain the transfer of the legateship from the bishop of Winchester to himself.

00In 1680 he travelled in England and Holland in order to obtain literary assistance, and the first number appeared in 1682, under the title of Acta eruditorum lipsiensium, and, like its successors, was written in Latin.

00"In the beginning of my mathematical studies, when I was perusing the works of the celebrated Dr Wallis, and considering the series by the interpolation of which he exhibits the area of the circle and hyperbola (for instance, in this series of curves whose common base 0 or axis is x, and the ordinates respectively (I -xx)l, (i (I &c), I perceived that if the areas of the alternate curves, which are x, x 3x 3, x &c., could be interpolated, we should obtain the areas of the intermediate ones, the first of which (I -xx) 1 is the area of the circle.

00Plausible excuses were made for the alliance, but to the country at large this union, formed with a man whom he had denounced for years, had the appearance of an unscrupulous conspiracy to obtain office on any terms. In the House of Commons the coalition was strong enough to drive Shelburne from office on the 24th of February.

00Disappointed at his failure to obtain a post in the gymnasium of his native town, he left Germany for good.

00Sigismund, anxious to obtain another vote in the electoral college, appointed Frederick to exercise the Brandenburg vote on his behalf, and it was largely through his efforts that Sigismund was chosen German king.

00If we melt copper and add to it about 30% of zinc, or 20 of tin, we obtain uniform liquids which when solidified are the well-known substances brass and bell-metal.

00We can sometimes obtain definite compounds in a pure state by the action of appropriate solvents which dissolve the rest of the alloy and do not attack the crystals of the compound.

00The Finance Act of 1902 allows a manufacturer to obtain a license which permits the use of duty-free alcohol, if he can show that such alcohol is absolutely essential for the success of his business, and that methylated spirit is unsuitable.

00Notwithstanding this permission there have been many agitations on the part of chemical manufacturers to obtain a less restricted use of absolute alcohol, and in 1905 an Industrial Alcohol Committee was appointed to receive evidence and report as to whether any modification of the present law was advisable.

00We can, however, obtain another equation called the " surface characteristic equation " as follows: - Suppose a very small area dS described on a conductor having a surface density of electrification a.

00Dividing by (0' - e"), and writing dp/do and dL/do for the limiting values of !the ratios (p' - p")/(o' - o") and (L' - L")/(o' - o"), we obtain the important relations s' - s"+dL/do= (v" - v')dp/do=L/o,..

00Substituting for H its value from (3), and employing the notation of the calculus, we obtain the relation S - s =0 (dp /do) (dv/do),.

00If we write K for the adiabatic elasticity, and k for the isothermal elasticity, we obtain S/s = ECÃ†F = K/k.

00We thus obtain the expressions dH = sdo +0 (dp I dO) dv = Sd0 - o (dv/do) dp..

00If we put dH=o in equations (8), we obtain the relations between dv and do, or dp and do, under the condition of no heat-supply, i.e.

00Since the two expressions (9) are the partial differential-coefficients of a single function E of the independent variables v and 0, we shall obtain the same result, namely d 2 E/d0dv, if we differentiate the first with respect to v and the second with respect to 0.

00We thus obtain the relation ds/dv(o const) =od 2 p/d0 2 (v const),.

00Observing that F is a function of the co-ordinates expressing the state of the substance, we obtain for the variation of S with pressure at constant temperature, dS/dp (0 const) '=' 2 F/dedp =-0d 2 v/d0 2 (p const) (12) If the heat supplied to a substance which is expanding reversibly and doing external work, pdv, is equal to the external work done, the intrinsic energy, E, remains constant.

00Denoting by So, so, these constant limiting values at p=o, we may obtain the values at any pressure by integrating the expressions (27) and (28) from co to v and from o to p respectively.

00We thus obtain S=So±n(n+I)pc/O.

00We thus obtain E - g o= s 0 (B-o)) - n(pc - poco) (31) We have similarly for the total heat F = E + pv, F - Fo=So(O - oo) - (n+1)(cp - copo)+b(p - p.).

00In the case of an ideal gas, dp/d9 at constant volume =R/v, and dvld6 at constant pressure =R/p; thus we obtain the expressions for the change of entropy 0-4)0 from the state poeovo to the state pev, log e e/eo+R logev/vo =S log e 9/00-R (32) In the case of an imperfect gas or vapour, the above expressions are frequently employed, but a more accurate result may be obtained by employing equation (17) with the value of the specific heat, S, from (29), which gives the expression 4-¢o = Sologe0/00 - R logep/po-n(cp/B-copo/Bo)

00Putting dJ /dm =o at constant volume, we obtain as the condition of equilibrium of the two states J' + p'v' = J" -}- p "v".

00Writing formulae (3r) and (33) for the energy and entropy with indeterminate constants A and B, instead of taking them between limits, we obtain the following expressions for the thermodynamic functions in the case of the vapour: " =Solog e 0 - R log e p - ncp/D+A".

00Rearranging the terms, and dividing throughout by 0, we obtain an equation of the form R log ep= A - B/D - (s' - So)loge0+(c - b)p/D+(dh/D - d4)) (44) in which B=B" - B', and A = A'+s' - So.

00He was the son of a Unitarian minister, and entered Trinity College, Cambridge, in 1823, though it was then impossible for any but members of the Established Church to obtain a degree.

00During his visits to England he was at the disposal of Cardinal Wiseman, who through him, at the time of the Crimean War, was enabled to obtain from the government the concession that for the future Roman Catholic army chaplains should not be regarded as part of the staff of the Protestant chaplain-general.

00Their creed became the passport by which Christians in strange cities could obtain admission to assemblies for worship and to common meals.

00Bonaparte had arranged to obtain Malta by treachery, and he took possession without resistance in June 1798; after a stay of six days he proceeded with the bulk of his forces to Egypt, leaving General Vaubois with 6000 troops to hold Valletta.

00Canon Caruana and other leaders of the Maltese aspired to obtain for Malta the freedom of the Roman Catholic religion guaranteed by England in Canada and other dependencies, and promoted a petition in order that Malta should come under the strong power of England rather than revert to the kingdom of the two Sicilies.

00He was liberal, kindly, good-tempered and easy of access, and his yielding to his subjects' wishes in order to obtain supplies for carrying on the French war contributed to the consolidation of the constitution.

00the prince therefore had to consider how long it would take to obtain a decision.

00The turning of them outdoors to ripen their growth is the surest way to obtain flowers, but they do not take on a free blooming habit until they have attained some age.

00In order to obtain observation and jumping-off ground for the attack on the main Hindenburg system it was necessary to clear the enemy from the positions still held by him forward of this line.

00Moreover, any slight movement of the head will cause the image to appear to move relatively to the paper, and will render it difficult to obtain an accurate drawing.

00of France on the 3rd of March and the 26th of April 1585, to obtain Vieta's restoration to his former office, but without result.

00Artaxerxes himself had done very little to obtain this result.

00To obtain privacy for the maintenance of his personal religion, he established the monastery of Marmoutier-les-Tours (Martini monasterium) on the banks of the Loire.

00The English were ill supplied, and were compelled to anchor at Southwold Bay on the coast of Suffolk in order to obtain water and provisions.

00They obtain their supply of air from the surface.

00It is probable therefore that Charles either considered the coronation premature, as he was hoping to obtain the assent of the eastern empire to this step, or that, from fear of evils which he foresaw from the claim of the pope to crown the emperor, he wished to crown himself.

00and Dec. of the object to be observed, the scale divisions to be pointed upon, and thus, in measures of distance, with the aid of the chronograph and printing micrometer, enable the observer to adjust the instrument for observation and obtain a record of his observations without the aid of a hand-lamp or the necessity to make any records in his notebook.

00The Austrians had long tried to obtain influence in the town, especially when its support of the Protestant cause attracted the sympathy of the Swiss.

00For by transliterating Ka7vap Nepc'ev into Hebrew 1113 10,P and adding together the sums denoted by the Hebrew letters we obtain the number 666.

00Oceanic Deposits.-It has long been known that the deposits which carpet the floor of the ocean differ in different places, and coasting sailors have been accustomed from time immemorial to use the lead not only to ascertain the depth of the water but also to obtain samples of the bottom, the appearance of which is often characteristic of the locality.

00This has made it possible to obtain many samples from moderate depths along a long line in a very short space of time.

00as a result of which he resigned his professorship. Several universities were eager to obtain his services, and he had accepted a post offered him by the elector palatine at Heidelberg, when he died suddenly on the 12th of September, 1672.

00About onehalf of the total coal (or less) is obtained in the first working; the roof is then allowed to fall, and when the gob is sufficiently consolidated, fresh roads are driven through it to obtain the ribs and pillars left behind by a second or even, in some cases, a third, _!?/i _ ?

00This great height is necessary to obtain head-room for the cages, the landing platforms being usually placed at some considerable height above the natural surface.

00In 1464 he married Zedena, or Sidonia, daughter of George Podï¿½ad, king of Bohemia, but failed to obtain the Bohemian crown on the death of George in 1471.

00He was successful in restoring the authority of Maximilian in Holland, Flanders and Brabant, but failed to obtain any repayment of the large sums of money which he had spent in these campaigns.

0099, p. 167), using Froude's turbine to obtain the highly resisting spiral vortices, and arranging passages in the casing for the entry of water at the hub of the wheel and its exit at the circumference.

00n, as the nth term of a new series, we obtain the series 1+2+3+..

00Taking this sum as the nth term, we obtain the series 1+3+6+10+..

00This sum is taken as the nth term of the next series, and proceeding in this way we obtain series having the following nth terms: I, n, n(n+1) /21, n(n+i) (n+2) /3 !,...n(n+1) ...

00T =273, we obtain R =1.35 X Io -16 and this enables us to determine the mean velocities produced by heat motion in molecules of any given mass.

00If p is the density corresponding to pressure p, we find that,}, formula (Ii) assumes the form P = 3PC2, where C is a velocity such that the gas would have its actual translational energy if each molecule moved with the same velocity C. By substituting experimentally determined pairs of values of p and p we can calculate C for different gases, and so obtain a knowledge of the magnitudes of the molecular velocities.

00If we divide throughout by T, we obtain d 2 (n+3)RN T +RNd v, showing that dQ/T is a perfect differential.

00We obtain Cv = z (n +3) R /J m.

00On giving different values to n in formula (21), we obtain the values for y: n = o, 1, 2, 3, 4, 5, y = 1.66, 1.5, 1.4, 1.33, 1.28, 1.25, &c.

00Lugard's first object was to obtain a treaty which would give him a right to intervene in the internal affairs of the country.

00Williams then led a successful expedition against the Sese islanders and went on to the south of the lake to obtain one of the young princes - heirs to the throne - who were at the French mission there.

00This monopoly had been abolished in 1787, and the trade had been declared free to all Danish subjects, but practically the old arrangement was continued under disguised forms. Jon Sigurbsson began a hard struggle against the Danish government to obtain a reform.

00The latter now sought to escape from France, where events were becoming intolerable; and after some unsuccessful attempts to obtain a passport to leave Paris,.

00In order, however, to obtain his recognition as count, Fulk IV.

00The existing ecclesiastical system was the practical evolution of dogma, and the overthrow of dogma was the only way to obtain permanent relief from the intolerable abuses of that system " (Cambridge Modern History, i.

00The schism extended down to the bishoprics, and even to the monasteries and parishes, where partisans of the rival popes struggled to obtain possession of sees and benefices.

00Albert, who was a Minnesinger, was loyal to the declining fortunes of the Hohenstaufen, and afterwards supported his brother-in-law, Rudolph of Habsburg, in his efforts to obtain the German throne.

00In order to obtain an intelligent grasp of the religion of tribes in their several culture provinces, it must be understood: (i) That the form of belief called animism by Tylor (more correctly speaking, personeity), was universal; everything was somebody, alive, sentient, thoughtful, wilful.

00To obtain it perfectly pure the crude alcohol is combined with oxalic, benzoic or acetic acid, and the resulting ester separated, purified, and finally decomposed with potash.

00Proceeding from bad to worse, he sacrificed the honour of his daughter in order to obtain the money to complete his pyramid; and the princess built herself besides a small pyramid of the stones given to her by her lovers.

00Having in his mind the scheme of his great work, he gave ample time to the elaboration of all its parts, and took care to obtain by personal observation a full knowledge of the various countries.

00Men were not men according to Greek notions unless they were citizens; and Herodotus, aware of this, probably sharing in the feeling, was anxious, having lost his political status at Halicarnassus, to obtain such status elsewhere.

00The necessary three days' warning of the French concentration they felt certain they would obtain, for Napoleon's troops were at this juncture distributed over an area (Lille-Metz-Paris) of 175 m.

00Hence his ability to concentrate hung on the mere good luck of obtaining timely information of Napoleon's plans, which in fact he failed to obtain.

00In this way only could the allies hope to obtain a decisive success against Napoleon.

00In 806 Charlemagne sent him to Rome to obtain the signature of Pope Leo III.

00How hard it must have been to obtain a footing there while he was a mere student and observer!

00In 1539 Las Casas was sent to Spain to obtain Dominican recruits, and through Loaysa, general of the order, and confessor of Charles V., he was successful in obtaining royal orders and letters favouring his enterprise.

00On the other hand, the scope of the subject, as described in § 3, is limited by the nature of the methods employed to obtain formulae which can be applied to actual cases.

00The length of the arc of a circle, for instance, is known if the length of the chord and its distance from the middle point of the arc are known; but it may be more convenient in such a case to use a formula such as Huygens's rule than to obtain a more accurate result by means of trigonometrical tables.

00The general formulae of § 54 (p being replaced (i) by 2m) may in the same way be applied to obtain formulae giving the area of the trapezette in terms of the mid-ordinates of the strips, the series being taken up to b 2f ul m or /th 2J ug m at least, where u is of degree 2f or 2f + I in x.

00The result of performipg both operations, in order to obtain the volume, is the result of the operation denoted by the product of these two expressions; and in this product the powers of E and of E' may be dealt with according to algebraical laws.

00If m is a multiple of 6, we can obtain an expression for A by applying the rule to each group of six strips.

00Combining this with the first equation, we obtain the values of P, Q, R, ..

00on the assumption that the volume of each minor briquette is concentrated along its mid-ordinate (§ 44), and we then obtain the formulae of correction by multiplying the formulae of § 82 in pairs.

00Thus, to construct a table of values of f x udx by intervals of h in x, we first form a table of values of hu for the intermediate values of x, from this obtain a table of values of 62 - -) hu for these values of x, and then construct the table of f x udx by successive additions.

00After Waterloo he tried to obtain the recognition of Napoleon II.

00The compulsory education law as amended in 1907 and 1909 requires the full attendance at a public school, or at a school which is an approximate equivalent, of all children who are between seven and fourteen years of age, are in the proper physical and mental condition, and reside in a city or school district having a population of 5000 or more and employing a superintendent of schools; in such a city or district children between fourteen and sixteen years must attend school unless they obtain an employment certificate and are regularly engaged in some useful employment or service; and outside of such a city or district all children between the ages of eight and fourteen years and those between fourteen and sixteen years who are not regularly employed must attend school on all school days from October to June.

00of Anjou, who wished to obtain the succession of Naples at Joanna's death, a course which met with the approval of the pope.

00Late in 405 Theramenes went as plenipotentiary to Lysander to obtain peace terms; after long negotiations he proceeded to Sparta and arranged a settlement which the Athenians ratified (April 404).

00We may obtain an excellent representation of the motion of the layers of air in a train of sound waves by means of a device due to Crova and known as " Crova's disk."

00If this is done for every point we obtain a continuous curve Apbqcrd, which represents the displacement at every point at the given instant, though by a length at right angles to the actual displacement and on an arbitrary scale.

00(8) If we take y =1.4 we obtain approximately for the velocity in dry air at 0° C.

00Substituting in the momentum equation, we obtain Pv 1 7V + y 2 I V / +PoU 2 I - v) V) = PoU2, whence U 2 = Po (I }-y21 U J .

00If we divide this by 2 3 or 8, we obtain 440 as the number of vibrations answering to the note A.

00In the scale of C the intervals from the key-note, the frequency ratios with the key-note, the successive frequency ratios and the successive intervals are as follows: - If we pass through two intervals in succession, as, for instance, if we ascend through a fourth from C to F and then through a third from F to A, the frequency ratio of A to C is a, which is the product of the ratios for a fourth 4, and a third I That is, if we add intervals we must multiply frequency ratios to obtain the frequency ratio fo