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sum

In 1831, from a study of the specific heats of compounds, he formulated "Neumann's law," which expressed in modern language runs: "The molecular heat of a compound is equal to the sum of the atomic heats of its constituents."

30759The score against him reached the fateful sum of forty-three thousand.

26921Depositors in savings banks represent about twentynine in every hundred persons, and in 1906 the sum deposited amounted to £37,205,000 in the names of 1,152,000 persons.

6633Slater Fund, and the same sum from the General Education Board.

5839The books he read were chiefly historical, and on these he spent a certain sum every year.

3518This sum represents the interest payable on government loans placed outside Australia, mainly in England, and the income from British and other capital invested in the country; the former may be estimated at £7,300,000 and the latter £8,000,000 per annum.

3025AMICABLE NUMBERS, two numbers so related that the sum of the factors of the one is equal to the other, unity being considered as a factor.

269Let me sum up a few of the elements that made Helen Keller what she is.

249I'd lived so clement an existence that the sum total of my exposure to mayhem came from the soft cushioned sofa fronting a wide screen television.

2323Of the rest of the sum assigned to the ministry of finance (593/4 millions in all) 81/2 millions went in the expense of collection of revenue.

209The one hundred and twenty-five dollars annually subscribed for a Lyceum in the winter is better spent than any other equal sum raised in the town.

168The sum received by the Post Office as rental in respect of private wires was £183,000.

169In each of a number of experiments he found that the weight of the silver iodide did not differ by one twenty-thousandth of the whole from the sum of the weights of the silver and the iodine used.

1515To this sum the land and poll-tax and other direct taxes contributed £374,630.

126of Spain, and costing the enormous sum of £60,000.

127Letters insured for a fixed sum are not delivered under any circumstances.

127When they heard that Arion had a large sum of money with him they began to make plans to get it.

128Guicciardini reckoned the cost of the war to Leo at the prodigious sum of 800,000 ducats.

129The caliph was so well pleased with these jewels that he bought them and paid the merchant a large sum of money.

1213As such, it was considered to represent the sum of human knowledge at the beginning of the 20th Century.

116His widow left a sum of Ioo,000 francs to the Institut de France, to found in his memory scholarships in political economy or law.

1010Long before I learned to do a sum in arithmetic or describe the shape of the earth, Miss Sullivan had taught me to find beauty in the fragrant woods, in every blade of grass, and in the curves and dimples of my baby sister's hand.

1010She gets web hosting set up for the princely sum of $30 a month.

98After not a little hesitation, Hastings consented to allow the Company's troops to be used to further the ambitious designs of his Oudh ally, in consideration of a sum of money which relieved the ever-pressing wants of the Bengal treasury.

87But in cases where a debt or instalment is in arrear and it is proved to the satisfaction of the court that the person making default either has or has had since the date of the order or judgment the means to pay the sum in respect of which he has made default and has refused or neglected to pay, he may be committed to prison at the discretion of the judge for a period of not more than forty-two days.

810Fortified by this exhaustive preparation, Aquinas began his Summa Theologiae, which he intended to be the sum of all known learning, arranged according to the best method, and subordinate to the dictates of the church.

73To find component forces equal to the composite or resultant force, the sum of the components must equal the resultant.

76In the future, every single person will have at his or her disposal the sum total of the life experience of everyone alive.

78She can add and subtract with great rapidity up to the sum of one hundred; and she knows the multiplication tables as far as the FIVES.

78The plaintiff could swear to his loss by brigands, as to goods claimed, the price paid for a slave purchased abroad or the sum due to him.

710The Italian parishes had in 1901 a total gross revenue, including assignments from the public worship endowment fund, of 1,280,000 or an average of 63 per parish; 51% of this gross sum consists of revenue from glebe lands.

62If she had no children, he returned her the dowry and paid her a sum equivalent to the bride-price, or a mina of silver, if there had been none.

63Of this sum 260,000 was spent for religious purposes.

65They did, indeed, represent the aristocracy of wealth, for they had to pay a subscription of four louis, a large sum at that time, besides six livres for attendance.

66Twenty-one rubles, he said, pointing to the figure twenty-one by which the total exceeded the round sum of forty-three thousand; and taking up a pack he prepared to deal.

67But the tendency is towards a system of charging a moderate sum to cover the rent of the instrument and an additional fee per message.

610Of the sum spent by the provincial authorities, over half goes to lunatic asylums and over a quarter to the maintenance of foundling hospitals.

610As to judgment debts, it is sufficient to say that, when by the judgment of a court of competent jurisdiction an order is made that a sum of money be paid by one of two parties to another, such a debt is not only enforceable by process of court, but it can be sued upon as if it were an ordinary debt.

52Man himself cannot increase the sum of motion; he can only alter its direction.

54Of the sum spent by the communes, about 1/2 goes for the sanitary service (doctors, midwives, vaccination), 3/4 for the maintenance of foundlings, i11 for the support of the sick in hospitals, and I~1 for sheltering the aged and needy.

54It is estimated that Sardinia pays, in local and general, direct and indirect taxation of all kinds, 23,000,000 lire (920,000), a sum corresponding to 35.44 lire per head.

55It was then proposed to arrange a detector so that it was affected by the algebraic sum of the two oscillations, and by swivelling round the double receiving antennae to locate the direction of the sending station by finding out when the detector gave the best signal.

56Some years ago, the State met me in behalf of the Church, and commanded me to pay a certain sum toward the support of a clergyman whose preaching my father attended, but never I myself.

56The general position which He takes up, that "the Sabbath is made for man and not man for the Sabbath," 2 is only a special application of the wider principle that the law is not an end in itself but a help towards the realization in life of the great ideal of love to God and man, which is the sum of all true religion.

57He may, in fact, be called the father of modern pathology, for his view, that every animal is constituted by a sum of vital units, each of which manifests the characteristics of life, has almost uniformly dominated the theory of disease.since the middle of the 59th century, when it was enunciated.

43In the Summa Catholicae Fidei contra Gentiles he shows how a Christian theology is the sum and crown of all science.

43Both entered the country, but George William proved himself the stronger and occupied Ratzeburg; having paid a substantial sum of money to the elector, he was recognized by the inhabitants as their duke.

43Taking into account the variations in wages and in the price of wheat, it may be calculated that the number of hours of work requisite to earn a sum equal to the price of a cwt.

43In ordinary banks the deposits amounted to £106,625,000, so that the total deposits stood at £143,830,000, equivalent to the very large sum of £34, 18s.

44~x ndl- The sum paid in interest on debt amounted to 17,640,000

44That said, if I had to pick one function I think the Internet will turn out to "be," it is this: The Internet will become a repository and a set of applications for storing the sum total of all life experiences of all people on earth.

45Such a pair are 220 and 284; for the factors of 220 are 1,2,4,5,10,11,20,22,44,55 and 110, of which the sum is 284; and the factors of 284 are 1,2,4,71, and 142, of which the sum is 220.

32The liabilities of the fund (capitalized) amounted to 10,668,105, of which monastic pensions represented a rapidly diminishing sum of 2,564,930.

32"Well, they've sent you a tidy sum," said Berg, eying the heavy purse that sank into the sofa.

32The historian evidently decomposes Alexander's power into the components: Talleyrand, Chateaubriand, and the rest--but the sum of the components, that is, the interactions of Chateaubriand, Talleyrand, Madame de Stael, and the others, evidently does not equal the resultant, namely the phenomenon of millions of Frenchmen submitting to the Bourbons.

32Godfrey received a large sum of money, was confirmed in the possession of Friesland, and on being converted to Christianity in 882, received in marriage Gisela, daughter of Lothaire II.

33Nearly all the cable companies possess their own steamers, of sufficient dimensions and specially equipped for making ordinary repairs; but for exceptional cases, where a considerable quantity of new cable may have to be inserted, it may be necessary to charter the services of one of the larger vessels owned by a cable-manufacturing company, at a certain sum per day, which may well reach £200 to £300.

33Under the Pacific Cable Act 1901 the capital sum of £2,000,000 was provided in the following proportions: United Kingdom, 5/18ths with 3 representatives including the chairman.

33The value of the product has, however, proportionately increased, so that the sum realized was little less, while less than half the number of men was employed.

33Sometimes he staked a large sum, but Dolokhov refused to accept it and fixed the stake himself.

34debitum, a thing owed), a definite sum due by one person to another.

21A fourth of this sum was to be handed to the communes to be employed on works of beneficence or education as soon as a surplus was obtained from that part of the annuity assigned for the payment of monastic pensions; and in Sicily, 209 communes entered on their privileges as soon as the patrimony was liquidated.

21The superintendent of police, who had gone that morning by Count Rostopchin's orders to burn the barges and had in connection with that matter acquired a large sum of money which was at that moment in his pocket, on seeing a crowd bearing down upon him told his coachman to stop.

21After the close of the war with Mexico Green was sent to that country in 1849 by President Taylor to negotiate concerning the moneys which, by the treaty of Guadalupe Hidalgo, the United States had agreed to pay; and he saved his country a considerable sum by arranging for payment in exchange instead of in specie.

22This sum consists of 4,240,000 of naval expenditure proper, 220,000 for naval pensions and 380,000 for premiums upon mercantile shipbuilding.

22In civil matters there is appeal from the giadice conciliatore to the pretore (who has jurisdiction up to a sum of 1500 lire =~6o), from the pretore to the civil tribunal, from the civil tribunal to the court of appeal, and from the court of appeal to the court of cassation.

23The demands for reimbursement at par represented a sum of only 187,588 and the market value of the stock was hardly affected; while the saving to the Treasury was to be 800,000 per annum for the first five years and about double the amount afterwards.

23He had fixed on that number because forty-three was the sum of his and Sonya's joint ages.

23Once when making such calculations he wrote down his own name in French, Comte Pierre Besouhoff, but the sum of the numbers did not come right.

23Only when we have admitted the conception of the infinitely small, and the resulting geometrical progression with a common ratio of one tenth, and have found the sum of this progression to infinity, do we reach a solution of the problem.

23You're better off visiting on a weekday, as it's one of the most popular dim sum places in town (for good reason), and tends to be packed on Saturdays and Sundays.

10Check out the restaurant's classic offerings such as dim sum and dumplings, or branch out a bit with some airy pepper-salted squid.

10Arganthonius, king of Tartessus in Spain, invited them to emigrate in a body to his dominions, and, on their declining, presented them with a large sum of money.

13The former total is more than double add the latter more than treble the sum in 1873, while there is an increase of 62% in the former and 26% in the latter over the totals for 1882.

00He deposed Galeazzo Visconti on his downward journey, and offered Milan for a sum of money to his son Azzo upon his return.

00The royal commissioner for finance, Giacomelli, had, as a precautionary measure, seized the pontifical treasury; but upon being informed by Cardinal Antonelli that among the funds deposited in the treasury were 1,000,000 crowns of Peters Pence offered by the faithful to the pope in person, the commissioner was authorized by the Italian council of state not only to restore this sum, but also to indemnify the Holy See for moneys expended for the service of the October coupon of the pontifical debt, that debt having been taken over by the Italian state.

00During the same period the assumption of the Venetian and Roman debts, losses on the issue of loans and the accumulation of annual deficits, had caused public indebtedness to rise from 92,000,000 to 328,000,000, no less than f 100,000,000 of the latter sum having been sacrificed in premiums and commissions to bankers and underwriters of loans.

00and Barillon, the French ambassador, by whom he was supplied with a large sum of money, arranged a plan for effecting Danby's ruin.

00Yet again, nature is broken up into co-operating parts; the whole is the sum of these parts; or, if you prefer to say so, there is no whole.

00Kant takes for granted that we cannot sum up these imperfect conceptions in a wider reconciling truth.

00He or she must not, as had been so often the case in the past, be forced to marry some royal favourite, or some one who had paid a sum of money for the privilege.

00The custom was for the king to get a fixed sum from the sheriff of each county, this being called the firma comitatus, and for the sheriff to collect this as best he could.

00To sum up, the entocodon is a precocious formation of the umbrella, closing over to protect the organs in the umbrellar cavity.

00that, by the employment of "magic boys" (magici pueri), he helped to find a sum of money that had been lost.

00Having extorted a large sum of money from the burghers of Nuremberg, he quarrelled with his supporter, the French king, and offered his services to the emperor.

00He conformed to the Church of England and spent a vast sum in restoring Arundel Castle.

00His engagement was for a salary of 75 lire (about X30) a month, a sum so large for that period as to mark conspicuously the high regard in which his art was held.

00Maskelyne and John Pond, to defray the expense of which a large sum of money was allotted by the Treasury.

00After completing these reductions, Airy made inquiries, before engaging in any theoretical investigation in connexion with them, whether any other mathematician was pursuing the subject, and learning that Hansen had taken it in hand under the patronage of the king of Denmark, but that, owing to the death of the king and the consequent lack of funds, there was danger of his being compelled to abandon it, he applied to the admiralty on Hansen's behalf for the necessary sum.

00The president of the senate, Juan Cuestas, in accordance with the constitution, assumed the duties of president of the republic. He arranged that hostilities should cease on the conditions that representation of the Blancos was allowed in Congress for certain districts where their votes were known to predominate; that a certain number of the jefes politicos should be nominated from the Blancos; that free pardon be extended to all who had taken part in the revolt; that a sufficient sum in money be advanced to allow the settlement of the expenses contracted by the insurgents; and that the electoral law be reformed on a basis allowing the people to take part freely in e1ctions.

00Disregarding all the accidental excrescences of the doctrine, Cynicism must be regarded as a most valuable development and as a real asset in the sum of ethical speculation.

00"Just as a steamengine," he says in Kraft and Stoff (7th ed., p. 130), "produces motion, so the intricate organic complex of force-bearing substance in an animal organism produces a total sum of certain effects, which, when bound together in a unity, are called by us mind, soul, thought."

00The sum of 700,000,000 roubles per annum is thus excepted from the control of the chambers.

00Other exceptions are the " Institutions of the Empress Marie," which absorb, inter alia, the duties on playing-cards and the taxes on places of public entertainment; the imperial civil list, so far as this does not exceed the sum fixed in 1906 (16,359,595 roubles!); the expenses of the two imperial chanceries, 10,000,000 roubles per annum, which constitute in effect a secret service fund.

00Her hatred of Germans showed itself likewise in her persistent struggle with Frederick the Great, which cost Russia 300,000 men and 30 millions of roubles - an enormous sum for those days - but in the choice of a successor she could not follow her natural inclinations, for among the few descendants of Michael Romanov there was no one, even in the female line, who could be called a genuine Russian.

00The amount of capital which parliament authorized railway companies to raise was about 42 millions on the average of the two years 1842-1843, 174 millions in 1844, 60 millions in 1845, and 132 millions in 1846, though this last sum was less than a quarter of the capital proposed in the schemes submitted to the Board of Trade; and the wild speculation which occurred in railway shares in 1845 contributed largely to the financial crisis of 1847.

00If there are several driving-axles in a train, the product Tw must be estimated for each separately; then the sum of the products will be equal to RV.

00The sum of all these components of resistance is at any instant equal to the resistance represented by R.

00To sum up, there are of intra-urban railways two distinct classes: the elevated and the underground.

00Trade is carried on almost entirely with the United Kingdom; the approximate annual value of exports is £120,000, and of imports a little more than half that sum.

00With a portion of this sum he obtained release from the last six months of his apprenticeship, and with the rest he purchased a glass-polishing machine.

00George proposed to allow the prince 50,000 a year; but this sum was regarded as insufficient by the latter, whose appeal to parliament was unsuccessful.

00Charles's ambition aimed at wider fields, and when Margaret, countess of Flanders, asked help of the French court against the German king William of Holland, by whom she had been defeated, he gladly accepted her offer of the county of; Hainaut in exchange for his assistance (1253); this arrangement was, however, rescinded by Louis of France, who returned from captivity in 1254, and Charles gave up Hainaut for an immense sum of money.

00The term is also applied specifically to an offer to do a specified piece of work or to supply certain goods for a certain sum or at a certain rate or to purchase goods at a certain rate.

00The volume was issued by subscription, and brought in the sum of four hundred guineas.

00This land was sold in 1833 for $277,332.52, but the entire sum was lost in the failure of the Planters' Bank in 1840.

00It was not separated from the world of ideas, of which it was represented as either the crown or the sum.

00After a brief seclusion, Herod the Tetrarch, his uncle, who had married Herodias, his sister, made him Agoranomos (Overseer of Markets) of Tiberias, and presented him with a large sum of money; but his uncle being unwilling to continue his support, Agrippa left Judea for Antioch and soon after returned to Rome, where he was welcomed by Tiberius and became the constant campanion of the emperor Gaius (Caligula), then a popular favourite.

00In 1790 he conducted the military operations on the Dniester and held his court at Jassy with more than Asiatic pomp. In 1791 he returned to St Petersburg where, along with his friend Bezborodko (q.v.), he made vain efforts to overthrow the new favourite, Zubov, and in four months spent 850,000 roubles in banquets and entertainments, a sum subsequently reimbursed to him from the treasury.

00They are sometimes in the position of landlords, but often they are the assignees of the land revenue, which they are entitled under special grants to collect for themselves instead of for government, paying merely a small sum to Government by way of quit-rent.

00To find three numbers such that the product of any two added to the sum of those two gives a square (III.

00Tannery); To find four numbers such that, if we take the square of their sum any one of them singly, all the resulting numbers are squares (III.

0022) To find two numbers such that their product their sum gives a cube (IV.

00Thus Diophantus knew that no number of the form 8n-1-7 can be the sum of three squares.

00no number of the form 4n+3, or 4n - I, can be the sum of two squares), and goes on to a d, practically, the condition stated by Fermat, "and the double of it [n] increased by one, when divided by the greatest square which measures it, must not be divisible by a prime number of the form 4n - 1," except for the omission of the words "when divided.

00He defeated the Chatti, annexed the district of the Taunus, and established the Limes as a line of defence; but he suffered defeats at the hands of the Quadi, Sarmatae and ' Marcomanni; in Dacia he received a severe check, and was obliged to purchase peace (90) from Decebalus by the payment of a large sum of money and by guaranteeing a yearly tribute - the first instance in Roman history.

00For La Devineresse he and his coadjutor de Vise (1638-1710, founder of the Mercure galant, to which Thomas contributed) received above 6000 livres, the largest sum known to have been thus paid.

00The county councils also expend sums varying at their own discretion on instruction in dairy-work, poultry-keeping, farriery and veterinary science, horticulture, agricultural experiments, agricultural lectures at various centres, scholarships at, and grants to, agricultural colleges and schools; the whole amount in 1904-1905 reaching £87,472.1 The sum spent by individual counties varies considerably.

00Galway); while lectures are given at farmers' meetings by 1 This sum was furnished out of a total of £693,851, forming the residue grant allocated for the purposes of education to the various county councils of England and Wales under the Local Taxation (customs and Excise) Act 1890.

00The occupation of Rome in February 1798 enabled Berthier to send a considerable sum to Paris and to style himself "treasurer to the chest of the Army of England."

00The revenge of the autocrat was characteristic. Besides driving Stein from office, he compelled Prussia to sign a convention(8th of September) for the payment to France of a sum of 140,000,000 francs, and for the limitation of the Prussian army to 42,000 men.

00Metamorphosis is, from this point of view, the sum of the changes that take place under the cuticle of an insect between the ecdyses, which changes only become externally displayed when the cuticle is cast off.

00Bionomically, metamorphosis may be defined as the sum of adaptations that have gradually fitted the larva (caterpillar or maggot) for one kind of life, the fly for another.

00The place was purchased for £25,000, and vested in the corporation of London for the use of the public. Of this amount the Gurney family contributed £io,000 and the corporation the same sum, the remaining £5000 being collected from the inhabitants of West Ham.

00During the progress of the works, however, he acted as surveyor, and accumulated in that lucrative employment a sum of several thousand pounds, discovered after his death in an old iron chest, which had evidently lain unopened for above thirty years.

00The cost of the public schools for the five years from 1901-1902 to 1906-1907 was $27,883,937, of which $7,057,895.42 was for new buildings; the cost of the police department was $11,387,314.66 for the six years 1902-1907; and of the water department $4,941,343.37 for the six years 1902-1907; of charities and social work a much larger sum.

00A breach of the covenant to repair gives the landlord an action for damages which will be measured by the estimated injury to the reversion if the action be brought during the tenancy, and by the sum necessary to execute the repairs, if the action be brought later.

00But no writer has surpassed him in the clearness and brevity with which he could sum up the characteristics of an epoch in the history of the world, or present and define the great forces by which the world has been influenced.

00The manufacture of turpentine and rosin, material for which is obtained from the pine forests, had increased greatly in importance between 1890 and 1900, the product in 1890 being valued at only $191,859, that of 1900 at $6,469,605, and from the latter sum it increased in 1905 to $9,901,905, an increase of more than one-half.

00has put the olam into men's minds, yet so that they cannot understand His work ": the olam, the sum of phenomena, is God's work.

00The hospital, opened in 1914, represents an investment of $2,000,000, the sum left 50 years ago by Robert A.

00The choir-screen was sold to the South Kensington Museum in London for goo, this sum being devoted to the work of modern restoration.

00that the sum of the units of affinity of all the atoms in a compound is an even number.

00We know the amount present in the precipitate, and since the same amount is present in the quantity of substance experimented with, we have only to work out a sum in proportion.

00Recent researches have shown that the law originally proposed by Kopp - " That the specific volume of a liquid compound (molecular volume) at its boiling-point is equal to the sum of the specific volumes of its constituents (atomic volumes), and that every element has a definite atomic value in its compounds " - is by no means exact, for isomers have different specific volumes, and the volume for an increment of CH 2 in different homologous series is by no means constant; for example, the difference among the esters of the fatty acids is about 57, whereas for the aliphatic aldehydes it is 49.

00it is equal to the sum of the thermal effects of the aldehyde and carbonyl groups.

00A true work of art is incomparably greater than the sum of its ideas; apart from the fact that, if its ideas are innumerable and various, prose philosophers are apt to complain that it has none.

00Sum.

00The enormous sum of i 50o has been paid for a collie, and 000 guineas for a bulldog, both show dogs pure and simple; while L50o is no uncommon price for a fox terrier.

00They agreed to raise an annual sum of £200 for the expenses of their commonwealth; they assigned their governor a salary of £20; they prohibited the sale of ardent spirits to the Indians and imprisonment for debt.

00By an agreement dated the 13th of January 1905 the sultan of Zanzibar ceded his sovereign rights in the Benadir ports to Italy in return for the payment of a lump sum of £144,000.

00The celebrated " homo sum " is a translation from Alexis, and the spirit of it breathes in many passages of the Greek drama.

00The Roman colonus was originally a free person who took land on lease, contracting to pay to the proprietor either a fixed sum annually or (when a colonus partiarius) a certain proportion of the produce of the farm.

00A sum of 20 millions sterling was voted as compensation to the planters.

00A clause was inserted to the effect that a certain sum should be annually set aside from fines to aid each province in emancipating slaves by purchase.

00Indeed it may be said that his works, scientific, historical and theological, practically sum up all the learning of western Europe in his time, which he thus made available for his countrymen.

00In 1858 the representatives of Austria, Belgium, France, the Netherlands, Piedmont, Russia, the Holy See, Sweden, Tuscany and Turkey appropriated the sum of 400,000 francs in recognition of the use of his instruments in those countries.

00of Mississippi river levees, within the state, was built almost entirely after 1866, and represents an expenditure of about $43,000,000 for primary construction alone; of this sum, the national government contributed probably a third (the state expended about $24,000,000 on levees before the Civil War).

00The operations of addition and multiplication of two given cardinal numbers can be defined by taking two classes a and 13, satisfying the conditions (1) that their cardinal numbers are respectively the given numbers, and (2) that they contain no member in common, and then by defining by reference to a and (3 two other suitable classes whose cardinal numbers are defined to be respectively the required sum and product of the cardinal numbers in question.

00terms in common; (2) their relation-numbers are the two relationnumbers in question, and then by defining by reference to R and S two other suitable relations whose relation-numbers are defined to be respectively the sum and product of the relation-numbers in question.

00The sum of two complex numbers x i e l +x 2 e 2 + ...

00In cases not involving a sum greater than 300 florins (£25), no appeal will lie; and where only 50 florins (£4:3:4) are in question, the case is summarily decided at the Bagatelle Gericht, or court for trifling cases.

00The Budget was supposed to be drawn up according to an excellent set of regulations sanctioned by imperial decree, dated the 6th of July 1290 (1875), of which the first article absolutely prohibited the increase, by the smallest sum, of any of the expenses, or the abandonment of the least iota of the revenues fixed by the budget.

00The sultan receives an annual allocation for himself and household of £T240,000, the crown prince one of £T24,000, and a sum of T153,000 is assigned to the Imperial princes and the sultanas.

00This sum covered " immigration expenses," i.e.

00Considering the dilatory methods of Orientals, even when they are creditors, it is doubtful whether this sum adequately covers the whole of the claims outstanding, and it may be found difficult, even for a parliament, to refuse claims which should equitably be admitted and which may be preferred later.

00The public debt council consented with good grace, although the minister of finance, by omitting to consult that council during the progress of negotiations, lost sight of the fact that a sum of £T87,823 was due to the public debt administration on account of arrears of the Eastern Rumelian annuity up to December 1887, and that a further sum of £T430,741 was due by the Bulgarian to the Turkish government itself in compensation Tor the Rustchuk-Varna railway under the Treaty of Berlin.

00As pointed out by Sir Adam Block, the representative of the British and Dutch bondholders, in his report for 1908-1909, the above arrangement would have been prejudicial to the bondholders had the public debt not been " unified " (as described below) since, however, as a result of that unification, the ceded revenues now produced a sum more than sufficient for the service of the debt, it was only the surplus of revenue reverting to the government which was affected.

00The capital sum per section was fixed, in round figures, at 54,000,000 francs (£2,160,000), subject to adjustment when the section was completed and its actual length definitely measured up. A minimum net price of 812% was fixed for the realization of these securities on the market.

00The first series (54,000,000 francs or £2,160,000), was duly handed over to the concessionaires in 1903, and was floated in Berlin at 86.4% realizing the sum of £1,868,000.

00If the clearance is effected without the necessary permit, the land is nevertheless granted on application, and on the payment of the tapu or sum paid by the proprietor to the state for the value of the land.

00Bayezid consented; later on John Palaeologus offered an equivalent sum and, since he engaged to furnish an auxiliary force of 12,000 men into the bargain, Bayezid replaced him on the throne.

00On the 2nd of September Suleiman entered the city, and to the ambassadors of Ferdinand, who came to offer a yearly sum if the sultan would recognize his claim to Hungary, he replied that he had taken possession of it by the sword and would negotiate only after the surrender of Gran, Tata, Visegrad and Szekesfehervar.

00A vast sum of money and the labour of thousands of men were employed to clear harbours for them, at and near Boulogne.

00Fibonacci's series is a sequence of numbers such that any term is the sum of the two preceding terms; also known as Lame series.

00The trade of Greenland has on the whole much decreased in modern times, and trading and missions cost the Danish state a comparatively large sum (about £i i,000 every year), although this is partly covered by the income from the royalty of the cryolite mines at Ivigtut.

00The reunited current was then led through another cell C, in which the strength of the current must be the sum of those in the arms A and B.

00Faraday found that the mass of substance liberated at the electrodes in the cell C was equal to the sum of the masses liberated in the cells A and B.

00We may sum up the chief results of Faraday's work in the statements known as Faraday's laws: The mass of substance liberated from an electrolyte by the passage of a current is proportional (I) to the total quantity of electricity which passes through the electrolyte, and (2) to the chemical equivalent weight of the substance liberated.

00The velocity with which the ions move past each other is equal to the sum of their individual velocities, which can therefore be calculated.

00change is allowed by the mechanism of the system, and deal with the sum of all the alterations in energy.

00By both these methods the single potential-differences found at the surfaces of the zinc and copper have opposite signs, and the effective electromotive force of a Daniell's cell is the sum of the two effects.

00Nearly one-third of the total value of the output represents winespirit, 23% tanneries, 18% tallow-melting and a considerable sum cigarette-making.

00The second part of the act provides that if any person or persons, bodies politic and corporate, for any sum of money, reward, gift, profit or benefit, directly or indirectly, or for or by reason of any promise, agreement, grant, bond, covenant or other assurances.

00The declaration is to the effect that the clergyman has not received the presentation in consideration of any sum of money, reward, gift, profit or benefit directly or indirectly given or promised by him or any one for him to any one; that he has not made any promise of resignation other than that allowed by the Clerical Resignation Bonds Act 1828; that he has not for any money or benefit procured the avoidance of the benefice; and that he has not been party to any agreement invalidated by sec. 3 sub-sec. 3 of the act which invalidates any agreement for the exercise of a right of patronage in favour or on the nomination of any particular person, and any agreement on the transfer of a right of patronage (a) for the retransfer of the right, or (b) for postponing payment of any part of the consideration for the transfer until a vacancy or for more than three months, or (c) for payment of interest until a vacancy or for more than three months, or (d) for any payment in respect of the date at which a vacancy occurs, or (e) for the resignation of a benefice in favour of any person.

00He fixed the sum to be paid by each group of inhabitants, who then had to see that it was assessed, collected, and paid to the lord, electing commissaries (preud hommes) from among themselves for this purpose.

00each head of a family, paid the same sum, arrived at by dividing the local contingent of the taille by the number of fires.

00It was also a distributory tax (impot de repartition); every year the king in his council fixed the total sum which the taille was to produce in the following year; he drew up and signed the brevet de la taille (warrant), and the contribution of the individual taxpayer was arrived at in the last analysis by a series of subdivisions.

00The conseil du roi first divided the total sum among the various generalites (the higher financial divisions), again dividing the amount due from each generalite among the elections of which it was composed.

00The towns in general were not subject to it, at least directly; some had been exempt from time immemorial, others (redimees) had purchased exemption for a sum of money, yet others (abonnees) had compounded for the tax, i.e.

00instead of paying the taille they paid into the royal treasury a sum fixed by contract, which they generally raised by octrois, or entrance dues.

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.

00From the theorem given above for the expansion of a determinant as a sum of products of pairs of corresponding determinants it will be plain that the product of A= (a ll, a22, ï¿½ï¿½ï¿½ ann) and D = (b21, b 22, b nn) may be written as a determinant of order 2n, viz.

00the sum of the suffixes in each term of the resultant is equal to mn.

00The degree of the separation is the sum of the degrees of the component separates.

00the sum of the n th powers of the quantities, is expressible in terms of functions which are symbolized by separations of any partition (n"1n'2n'3...) 1 !

00ation of (l Al l h2 1 A3 ...) of specification (m"lmH2m"...), and the sum is for all such separations.

00'?^ the sum being for all separations of 1 A1112 ` / a3 3 ...) which have the specification (m41 m2 2 m3 3 ...).

00The weight of the function is the sum of the numbers in the bracket, and the degree the highest of those numbers.

00The sum of the monomial functions of a given weight is called the homogeneous-product-sum or complete symmetric function of that weight; it is denoted by h.; it is connected with the elementary functions by the formula 1 7r1l7r2!7r3!

00Every symbolic product, involving several sets of cogredient variables, can be exhibited as a sum of terms, each of which is a polar multiplied by a product of powers of the determinant factors (xy), (xz), (yz),...

00It has been shown by Gordan that every symbolic product is expressible as a sum of transvectants.

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.

00The Hessian 0 =A 2 is such that (f, 2 and if f is expressible in the form X(p x) 3 +,i(g x) 3, that is as the sum of two perfect cubes,.

00Sylvester showed that the quintic might, in general, be expressed as the sum of three fifth powers, viz.

00Thus the ternary quartic is not, in general, expressible as a sum of five 4th powers as the counting of constants might have led one to expect, a theorem due to Sylvester.

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!

00Now the symbolic expression of the seminvariant can be expanded by the binomial theorem so as to be exhibited as a sum of products of seminvariants, of lower degrees if alai 0-2a2 +...+crea0 can be broken up into any two portions (alai -1-0-2a2-1-ï¿½ï¿½ï¿½ +asas) +(as+1as +1 +o-8+2as+2+ï¿½ï¿½ï¿½ +ooae), such that Q1 +a2+...

00for a sum of £25; for a liquor measure or glass containing less than a half-pint; and in America for a literal translation of a foreign or classical author, a "crib."

00The great names at this period were those of Isaac Barrow (1630-1677); Robert South (1634-1716), celebrated for his wit in the pulpit; John Tillotson (1630-1694), the copyright of whose sermons fetched the enormous sum of 2500 guineas after his death, and of whom it was said that he was "not only the best preacher of the age, but seemed to have brought preaching to perfection"; and Edward Stillingfleet (1635-1699), styled, for his appearance in the pulpit, "the beauty of holiness."

00residence in the college, meeting his expenses by a small sum amassed by school-keeping and by help from a poor students' fund, and graduating in 1836.

00The sum of the corresponding numbers multiplied by 332600 gives Log.

00terminate outside the magnet or inside, have a resultant, equal to the sum of the forces and parallel to their direction, acting at a certain point N.

00The experiment may be made in two different ways: (I) the magnetizing current is increased by a series of sudden steps, each of which produces a ballistic throw, the value of B after any one throw being proportional to the sum of that and all the previous throws; the magnetizing FIG.

00When the magnetizing current is twice reversed, so as to complete a cycle, the sum of the two deflections, multiplied by a factor depending upon the sectional area of the specimen and upon the constants of the apparatus, gives the hysteresis for a complete cycle in ergs per cubic centimetre.

00A sum of money (aes equestre) was given to each eques for the purchase of two horses (one for himself and one for his groom), and a further sum for their keep (aes hordearium); hence the name equites equo publico.

00(b) The taxes of Asia had formerly been paid by the inhabitants themselves in the shape of a fixed sum.

00The sum fixed was subsequently thought too large, and in 1832 the arrears, amounting to a considerable sum, were remitted, and all future payments on this account relinquished.

00In October 1902, the court decided both questions in the affirmative, awarding the payment by Mexico of the annual sum claimed, not in gold, but en monnaie ayant cours legal au Mexique.

00Financial embarrassments increased to an alarming extent; the emperor was compelled by the British government to make peace with Buenos Aires and to renounce the Banda Oriental; and to fill the sum of disasters Dom Miguel had treacherously usurped the crown of Portugal.

00A sum of Lioo,000 was bequeathed by Mr Andrew Usher (1826-1898) for a hall to be called the Usher Hall and to supplement I The original Tolbooth was completed in 1501, but a new one took its place in 1563-1564, and was subsequently altered.

00Thereupon Charles came to terms with the government, granted it an imperial patent, and left the city, consoled for his humiliation by the gift of a large sum of money.

00Roman theologians generally reckon only seven orders, although, if we count the episcopate an order distinct from the presbyterate, the sum is not seven, but eight.

00No sooner was the idea of such a tribute started than liberal contributions came from all quarters, which enabled his friends to present him with a sum of 80,000.

00It may be added that he first examined the conditions of stability of the system formed by Saturn's rings, pointed out the necessity for their rotation, and fixed for it a period (Io h 33 m) virtually identical with that established by the observations of Herschel; that he detected the existence in the solar system of an invariable plane such that the sum of the products of the planetary masses by the projections upon it of the areas described by their radii vectores in a given time is a maximum; and made notable advances in the theory of astronomical refraction (Mec. cel.

00The statement, for instance, that 32 - x = 25, is really a statement that 32 is the sum of x and 25.

00The problem of finding the sum of r terms is aided by graphic representation, which shows that the terms may be taken in pairs, working from the outside to the middle; the two cases of an odd number of terms and an even number of terms may be treated separately at first, and then combined by the ordinary method, viz.

00a 7; and from this we easily pass to the general formula for the sum of a geometrical progression having a given number of terms.

00Proceeding in this way, we may be able to express P= Q as the sum of a finite number of terms k+m/r+n/r 2 +..

00(a) Let S r denote the sum u o+ u 1+.

00+u,, this sum being taken so as to include the greatest term (or terms); and let u r+1 /u r = 0, so that 0

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 .

00In this table any number is equal to the sum of the numbers which lie horizontally above it in the preceding Column, And The Difference Of Any Two Numbers In A Column Is Equal To The Sum Of The Numbers Horizontally Between Them In The Preceding Column.

00., the sum of the indices in each product being r.

00Comparing this with the table in ï¿½43 (iv.), and with formula (21), we see that the series expressing the sum may be regarded as consisting of two, viz.

00(ii.) In the same way, if we multiply the table by c, the sum of the first n numbers in any column is equal to the nth number in the next following column.

00Thus we get a formula for the sum of n terms of a series such as 2.4.6+4.6.8+..., or 6.8.10.12+8.10.12.14+...

00The sum of n terms is therefore (ï¿½ 43 (iv.)) 18nr 31 -6n [21 -2nr 11 =3n3+6n2+n.

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

00(v.) A particular case is that of the sum I'd2r +3 r + ...

00If we divide the sum of x 2 and a 2 by the sum of x and a, we get a quotient x - a and remainder 2a 2, or a quotient a - x and remainder 2x 2, according to the order in which we work.

00These laws can be established either by tracing the individual terms in a sum or a product or by means of the general theorem in ï¿½ 52 (vi.).

00in ï¿½ 46 (iii.) is 18(n3)[2]; formula (20) of ï¿½ 43 (iv.) holds for the extended coefficients, and therefore the sum of n terms of this series is 18.(n-3) [3] -18.

00In this way we get the general rule that, to find the sum of n terms of a series, the rth term of which is (a+rb) (a+r+ i ï¿½ b) ...

00The sum of two weighted points aA, (3B is, by definition, the point (a+13) G, where G divides AB so that AG: GB =0: a.

00The sum and product of two quaternions are defined by the formulae mi ase + F+lases = (a s + 133) es 2arer X ZO,es = Fiarfseres, where the products e,e, are further reduced according to the following multiplication table, in which, for example, the eo e1 e2 e3 second line is to be read eieo = e1, e 1 2 = - eo, e i e 2 = es, eie3 = - e2.

00The sum and product of two quantities are defined in the first instance by the formulae zae -IE(3e = E (a +0) e, Za,ei X E ai e j = (a iai) eie9, so that the laws A, C, D of ï¿½ 3 are satisfied.

00In the preface to this work, which is dedicated to one Dionysius, Diophantus explains his notation, naming the square, cube and fourth powers, dynamis, cubus, dynamodinimus, and so on, according to the sum in the indices.

00He solved quadratic equations both geometrically and algebraically, and also equations of the form x 2 "+ax n +b=o; he also proved certain relations between the sum of the first n natural numbers, and the sums of their squares and cubes.

00The component vibrations at P due to the successive zones are thus nearly equal in amplitude and opposite in phase (the phase of each corresponding to that of the infinitesimal circle midway between the boundaries), and the series which we have to sum is one in which the terms are alternately opposite in sign and, while at first nearly constant in numerical magnitude, gradually diminish to zero.

00In such a series each term may be regarded as very nearly indeed destroyed by the halves of its immediate neighbours, and thus the sum of the whole series is represented by half the first term, which stands over uncompensated.

00The sum of such a series is very approximately zero, each term being neutralized by the halves of its immediate neighbours, which are of the opposite sign.

00If we put for shortness 7 for the quantity under the last circular function in (I), the expressions (i), (2) may be put under the forms u sin T, v sin (T - a) respectively; and, if I be the intensity, I will be measured by the sum of the squares of the coefficients of sin T and cos T in the expression u sin T +v sin (T - a), so that I =u 2 +v 2 +2uv cos a, which becomes on putting for u, v, and a their values, and putting f =Q .

00In despair !Ethelred again offered them money, which they again accepted, the sum paid on this occasion being £24,000.

00In 1007 !Ethelred bought them off for a larger sum than ever (36,000), and for two years the land enjoyed peace.

00On the 4th of December 1891 an attempt was made to assassinate him in his office by one Henry Norcross, who demanded a large sum of money, and upon being refused exploded a dynamite bomb, and was himself killed.'

00To sum up the history of Scythia, the oldest inhabitants of whom we hear in Scythia were the Cimmerii; the nature of the country makes it probable that some of them were nomads, while others no doubt tilled some land in the river valleys and in the Crimea, where they left their name to ferries, earthworks and the Cimmerian Bosporus.

00In 1905 when a full supply of labour was again available the output was 4,760,000 oz., in which year the sum distributed in dividends to shareholders in the Rand mines was over £4,800,000.

00Fully two-thirds of the revenue and ' Besides this £5,000,000 an additional sum of £9,500,000 was spent by the imperial government in relieving the necessities of those who had suffered during the war, but of this £9,500,000 the sum of £2,500,000 was in payment for goods received.

00He was empowered by the volksraad to raise £300,000, but with great difficulty he obtained in Holland the sum of £90,000 only, and that at a high rate of interest.

00With this inadequate sum some railway plant was obtained, and subsequently lay for ten years at Delagoa Bay, the scheme having to be abandoned for want of funds.

00Then in 1697, by the Treaty of Ryswick, Louis abandoned his claim in return for a sum of money.

00The following table summarizes the local budget of Annam for the years 1899 and 1904: - In 1904 the sum allocated to the expenses of the court, the royal family and the native administration, the members of which are paid by the crown, was £85,000, the chief remaining heads of expenditure being the government house and residencies (£39,7 0 9), the native guard (£32,609) and public works (£24,898).

00In the year named a special commission was appointed for the regulation of the Moldau and Elbe between Prague and Aussig, at a cost estimated at about I, 000,000, of which sum two-thirds were to be borne by the Austrian empire and one-third by the kingdom of Bohemia.

00A parliamentary commission, appointed to inquire into the charges against him, discovered only that Crispi, on assuming office in 1893, had found the secret service coffers empty, and had borrowed from a state bank the sum of £12,00o for secret service, repaying it with the monthly instalments granted in regular course by the treasury.

00The use of the term " pathological physiology " may at first appear strange, for if we define physiology as the sum of the normal functions of the body or organism, it may be hard to see how there can be a physiology which is pathological.

00When Virchow wrote, in 1850, " every animal presents itself as a sum of vital unities, every one of which manifests all the characteristics of life," he expressed a doctrine whose sway since then has practically been uninterrupted.

00Nearly the same thing is true even of the Aphorisms, in which, following the example of Hippocrates, he endeavoured to sum up the results of his long experience.

00Altogether a sum approaching 2,500,000 was spent in Holland within the latter part of the 19th century on the improvement of the Rhine and its principal arteries.

00He did not indeed hold it very long, but was permitted to sell it for a large sum, retaining the rank and privileges.

00The roadbridges mentioned (except the City bridges) are maintained by the London County Council, who expended for this purpose a sum of £9149 in 1907-1908.

00The expenditure in1907-1908was £131,582, which sum included £11,987 for bands.

00There was thus raised in the year1906-1907a sum of £ 1 5,393,95 6 (in1898-1899the amount was £10,401,441); of this £11,012,424 was for central rates, which was subdivided into £7,930,275 for county services and £3,082,149 for local services, leaving a balance of £4,381,532, strictly local rates.

00London had to pay heavily towards his ransom; and, when the king made his triumphal entry into London after his release from imprisonment, a German nobleman is said to have remarked that had the emperor known of the wealth of England he would have insisted on a larger sum.

00This definition, however, is highly artificial and objectionable on principle, because when we speak of metals we think, not of their chemical relations, but of a certain sum of mechanical and physical properties which unites them all into one natural family.

00The time rate of increase of momentum of the fluid inside S is )dxdydz; (5) and (5) is the sum of (I), (2), (3), (4), so that /if (dpu+dpu2+dpuv +dpuw_ +d p j d xdyd z = o, (b)` dt dx dy dz dx / leading to the differential equation of motion dpu dpu 2 dpuv dpuv _ X_ (7) dt + dx + dy + dz with two similar equations.

00Calling the sum of the pressure and potential head the statical head, surfaces of constant statical and dynamical head intersect in lines on H, and the three surfaces touch where the velocity is stationary.

00After the over throw of Samas - sum - yukin, Kandalanu, the Chineladanos of Ptolemy's canon, had been appointed viceroy.

00When the king began to hint at the recall of Piero de' Medici, whose envoys had gained his ear, the signory ordered the citizens to be ready to fly to arms. The proposal was dropped, but Charles demanded an immense sum of money before he would leave the city; long discussions followed, and when at last he presented an insolent ultimatum the syndics refused to accept it.

00One day there appeared upon the scene a piper clad in a fantastic suit, who offered for a certain sum of money to charm all the vermin into the Weser.

00Apart from increased yield in sugar of good quality, we may sum up the advantages procurable from the use of Hatton defecators as follows: cold liming; heating gently to the temperature required to coagulate the albumen and not beyond it, whereby disturbance would ensue; the continuous separation of the scums; the gradual drying of the scums so as to make them ready for the fields, without carrying away juice or requiring treatment in filter presses; and the continuous supply of hot defecated juice to the evaporators, without the use of subsiding tanks or eliminators; and, finally, the saving in expenditure on plant, such as filter presses, &c., and wages.

00There is, therefore, no absolute knowledge, for every man has different perceptions, and, further, arranges and groups his data in methods peculiar to himself; so that the sum total is a quantity with a purely subjective validity.

00A man of doubtful reputation, Alexander's confidant and favourite, he paid the pope a large sum for his elevation.

00The relief was a sum paid by the heir for the lord's recognition of his succession.

00c. 32) his majesty is enabled to remit wholly or in part any sum of money imposed upon conviction, and, if the offender has been imprisoned in default of payment, to extend to him the royal mercy.

00Ramsay (Lancaster and York) estimates that in the four years from 1399 to 1403 they had received from the king the sum of X41,750, which represented a very large capital in the 14th century, and they had also received considerable grants of land.

00of private lines, the estimated cost to be about £37,500,000-a sum far beyond the resources of the republic. The two transandean lines were the famous Oroya railway, running from Callao to Oroya (1893), which crosses the Western Cordillera at an elevation of 15,645 ft., and later on to Cerro de Pasco (1904), the Goillarisquisga coal mines (1904) and Hauri (1906); and the southern line from Mollendo to Lake Titicaca, which reached Arequipa in 1869, Puno in 1871 and Checcacupe (Cuzco branch) in 1906.

00Then followed the ambitious schemes of President Balta, which with the loans of 5870 and 1872 raised the total foreign debt to £49,000,000, on which the annual interest charge was about £ 2, 5 ©0, 000, a sum wholly beyond the resources of the treasury.

00inhabitants were bound to pay tribute and give personal service to the grantee, were to pass to the Crown on the death of the actual holder; a fixed sum was to be assessed as tribute; and forced personal service was forbidden.

00With the vast sum raised front guano and nitrate deposits President Balta commenced the execution of public works, principally railroads on a gigantic scale.

00A further condition was enacted that an indemnity of 10,000,000 soles was to be paid by the country finally remaining in possession - a sum equal to about L1,000,000 to-day.

00" I was sent, quoth he, to show thee again all that thou sawest before, to wit the sum of the things profitable for thee.

00The mixture consequently distils at the temperature at which the sum of the partial pressures equals that of the atmosphere.

00He put up for auction the highest offices and honours; even remitting to William the Lion of Scotland, for a sum of 15,000 marks, the humiliating obligations which Henry II.

00Mill persuaded Grote, Molesworth, and Raikes Currie to advance the sum of £240.

00Mill applied to them again, but with the exception of Grote, who sent a small sum, they gave Comte to understand that they expected him to earn his own living.

00A sinking fund commission was established in 1875, and the entire sum was extinguished by the 1st of August 1894.

00The intervening ground upon which the railway lines and buildings stood was sold for building sites, the sum obtained being more than sufficient to cover the cost of the majestic central terminus (the third largest in the world), which, in addition to spacious and handsome halls for passenger accommodation, has three glass-covered spans of 180 ft.

00The sum of the matter is that the modern Japanese ceramist, after many efforts to cater for the taste of the Occident, evidently concludes that his best hope consists in devoting all his technical and artistic resources to reproducing the celebrated wares of China.

00Prefectural roads are maintained by a joint contribution from the government and from the particular prefecture, each paying one-half of the sum needed.

00The actual purchase price of the 17 lines was calculated at 43 millions sterling (about double their cost price), on the following basis: (a) An amount equal to 20 times the sum obtained by multiplying the cost of construction at the date of purchase by the average ratio of the profit to the cost of construction during the six business terms of the company from the second half-year of 1902 to the first half-year of 1905.

00Taking both together the receipts into the exchequer on behalf of Coburg were estimated for 1909-1910 at about £ioo,000 and those for Gotha at about £200,000, while the common state expenditure amounted to about the same sum.

00Besides the civil list the duke of Saxe-Coburg-Gotha enjoys a very large private fortune, amassed chiefly by Ernest I., who sold the principality of Lichtenberg, which the congress of Vienna had bestowed upon him in recognition of his services in 1813, to Prussia for a large sum of money.

00Living at the commencement of an epoch of unparalleled scientific activity, Spencer could not possibly sum up and estimate its total production.

00bi-, bis, twice, and nomen, a name or term), in mathematics, a word first introduced by Robert Recorde (1557) to denote a quantity composed of the sum or difference to two terms; as a+b, a-b.

00The magnitude of the sum, and his acquiescence in the grant of pensions by the Shelburne ministry, convinced the country that his zeal for economy was hypocritical.

00Through the intervention of the pope in 1702, the French, on payment of a large sum, agreed to vacate the town, and in 1715 its fortifications were rebuilt.

00Towards the end of this same year The Complete English Tradesman, which may be supposed to sum up the experience of his business life, appeared, and its second volume followed two years afterwards.

00Iunius Iuvenalis or Juvenal (c. 47-130), sum up for posterity the moral experience of the Roman world from the accession of Tiberius to the death of Domitian.

00The taxes are collected directly, and must meet the needs of the province, before any sum is remitted to the Imperial Treasury.

00In 1654, after many fruitless negotiations, Cromwell compelled the United Provinces to give the sum of 30o,000, together with a small island, as compensation to the descendants of those who suffered in the "Amboyna massacre."

00We can take the sum of all the products of the length of each element by the resolved part of the electric force in its direction.

00This sum, or integral, is called the " line integral of electric force" or the electromotive force (E.M.F.) along this line.

00Hence we see that if the whole surface of the sphere is divided into pairs of elements by cones described through any interior point, the resultant force at that point must consist of the sum of pairs of equal and opposite forces, and is therefore zero.

00Since then they are all charged with the same quantity of electricity, and the total over all potential difference V is the sum of each of the individual potential differences V1, V2, V3, &c., we have Q=C I V I =C 2 V 2 =C 3 V 3 =&c., and V=V1-FV2+V3+&c. The resultant capacity is C = Q/V, and C= I/(I/C1 +I /C2+1/C3+&c) = I/Z(I /C) (15).

00The mathematical importance of this function called the potential is that it is a scalar quantity, and the potential at any point due to any number of point charges ql, q2, q3, &c., distributed in any manner, is the sum of them separately, or qi/xl+q2/x2+q3/x3+&c. =F (q/x) =V (17), where xi, x2, x 3, &c., are the distances of the respective point charges from the point in question at which the total potential is required.

00In any case, therefore, in which we can sum up the elementary potentials at any point we can calculate the resultant electric force at the same point.

00The resultant force due to these two pointcharges must then be in the direction CP, and its value E is the vector sum of the two forces along AP and BP due to the two point-charges.

00In virtue of relations (2), the change of entropy of a substance between any two states depends only on the initial and final states, and may be reckoned along any reversible path, not necessarily isothermal, by dividing each small increment of heat, dH, by the temperature, 0, at which it is acquired, and taking the sum or integral of the quotients, dH/o, so obtained.

00In 1845 a Britton Club was formed, and a sum of £1000 was subscribed and given to Britton, who was subsequently granted a civil list pension by Disraeli, then chancellor of the exchequer.

00He was only in part successful, and there was great difficulty in raising the chartermoney among those who had actually assembled (in 1202) at Venice, the sum collected falling far short of the stipulated amount.

00It is said, for instance, that an adult slave used to be valued at from $800 to $1000, so that every adult immigrant may be looked upon as worth that sum to the country.

00Schmalkalden, drawn up by Luther in 1536, Luther's catechisms, and the Formula of Concord which was an attempt to settle doctrinal divisions promulgated in 1580, sum up what is called " the confessional theology of Lutheranism."

00By his will he left a large sum for the building and the perpetual repair of public baths, and the interest of a still larger sum for the benefit of one hundred freedmen of the testator and, ultimately, for an annual banquet.

00But his negotiations yielded no definite result; and every other means of obtaining redress and security proving unsuccessful, the Assam Dwars were wrested from the Bhutias, and the British government consented to pay to Bhutan a sum of £l000 per annum as compensation for the resumption of their tenure, during the good behaviour of the Bhutias.

00In 1897 the sum o was subscribed by citizens to found a hospital (1903) to commemorate the Diamond Jubilee of Queen Victoria, and named after her.

00When the event in question happened between the 1st of January and the 1st of the following July, the sum of the Olympic year and of the year before Christ is always equal to 776.

00When the event took place between the summer solstice and the 1st of January following, the sum of the Olympic year and of theyear before Christ is equal to 777.

00In fact, the period of Calippus containing 2 7,759 days, and the octacteris 2922 days, the sum, which is 30,681, is exactly the number of days in eighty-four Julian years.

00Multiply, therefore, the number of Armenian years elapsed by 365; add the number of days from the commencement of the current year to the given date; subtract 176 from the sum, and the remainder will be the number of days from the 1st of January 553 to the given date.

00This number of days being reduced to Julian years, add the result to 552, and the sum gives the day in the Julian year, or old style.

00To the year of the Persian era, therefore, add 631, and the sum will be the year of our era in which the Persian year begins.

00That principle had been made use of by the Greek authors of the classic age; but of later mathematicians only Hero, Diophantus, &c., ventured to regard lines and surfaces as mere numbers that could be joined to give a new number, their sum.

00He had already called attention to the inadequacy of his salary and been granted a sum of 6000 (9th of April 1642); and he was now appointed master of the rolls (22nd of November 1643), and one of the commissioners of the great seal (Oct.

00In his will he desired to be buried without any state and without a monument, "but at the utmost a plain stone with this superscription only, Vermis sum, acknowledging myself to be unworthy of the least outward regard in this world and unworthy of any remembrance that hath been so great a sinner."

00To sum up briefly the history of the development of the heliometer.

0030.1), the commentary of Ticonius, and the uncial C, can be explained from the Latin form of the name Nero, which by its omission of the final n makes the sum total 616 instead of 666.

00Sorensen and Martin Knudsen after a careful investigation decided to abandon the old definition of salinity as the sum of all the dissolved solids in sea-water and to substitute for it the weight of the dissolved solids in 1000 parts by weight of sea-water on the assumption that all the bromine is replaced by its equivalent of chlorine, all the carbonate converted into oxide and the organic matter burnt.

00The sum total amounts to 419 objects, besides hundreds of fragments, cores, spalls and rejects, retained for study and comparison.

00At the close of 1857, £8,000,000, of which the breakwater cost over £2,500,000, had been expended on the works; in 1889 a further sum of £680,000 was voted by the Chamber of Deputies for the improvement of the port.

00and therefore T, are measured by the algebraical sum of their individual moments with respect to the axis.

00If we take the sum of n terms of the series '±'H-'±..

00., the sum of n terms of which is n .n-1-1.

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

00., which has for the sum of n terms n (n+i) (n+2)/3!

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) ...

00It is to be noticed that each number is the sum of the numbers immediately 35 above and to the left of it; and 35 that the numbers along a line, termed a base, which cuts off an equal number of units along the top row and column are the co efficients in the binomial expansion of (I+x) r - 1, where r represents the number of units cut off.

00In terms of the molecular theory this indicates that the total energy of the gas is the sum of the separate energies of its different molecules: the potential energy arising from intermolecular forces between pairs of molecules may be treated as negligible when the matter is in the gaseous state.

00The aggregate amount of these pressures is clearly the sum of the momenta, normal to the boundary, of all molecules which have left dS within a time dt, and this will be given by expression (pp), integrated with respect to u from o to and with respect to v and w from - oo to +oo, and then summed for all kinds of molecules in the gas.

00Clearly the integral is the sum of the values of mu g for all the molecules of the first kind in unit volume, thus p=v mu l +v'm'u 2 +...

00- The pressure as given by formula (12) can be written as the sum of a number of separate terms, one for each gas in the mixture.

00sures which would be exerted separately by the several The pressure of a mixture of gases is the sum of the pres- Avogadro's Law.

00Wetzel, are: that money as coin may have more than its bullion value; that natural interest is determined by the rent of land valued at the sum of money loaned - an anticipation of Turgot; that high wages are not inconsistent with a large foreign trade; that the value of an article is determined by the amount of labour necessary to produce the food consumed in making the article; that manufactures are advantageous but agriculture only is truly productive; and that when practicable (as he did not think it practicable at the end of the War of Independence) state revenue should be raised by direct tax.

00Soon afterwards, his uncle, the wine merchant at Lisbon, having left David a sum of £t000, he and his brother entered into partnership as wine merchants in London and Lichfield, David taking up the London business.

00It was begun in 1607 - a year when the city was completely flooded - but was not completed until 1789, and then it was found that the city was still subject to partial inundations, although an enormous sum of money and 70,000 lives of Indian labourers had been expended upon it.

00If the Cistercians and lesser offshoots of the order be added, the sum total of choir-monks and lay brothers exceeds 11,000.

00In April 1893 the reserve fell below this sum.

00the area is half the sum of the products obtained by, multiplying each ordinate by the distance between the two adjacent ordinates.

00The quadrilateral, for instance, consists of two triangles, and its area is the product of half the length of one diagonal by the sum of the perpendiculars drawn to this diagonal from the other two angular points.

00Then the figure is (usually) the sum of two trapezoids F on base AE, and its area can be calculated as in § 24.

00- For every material body there is a point, fixed with regard to the body, such that the moment of the body with regard to any plane is the same as if the whole mass were collected at that point; the moment being the sum of the products of each element of mass of the body by its distance from the plane.

00In the case of a plane area or a plane continuous line the moment with regard to a straight line in the plane is the same as the moment with regard to a perpendicular plane through this line; it is the sum of the products of each element of area or length by its distance from the straight line.

000, where M is the sum of the quantities h.

00Then it may be shown that DE is parallel to AB, and that the area of the figure between chord DE and arc DE is half the sum of the areas DHA and EJB.

00The multiplication is shown in the adjoining diagram; the factors s ands are kept outside, so that the sum uo,o+3uo,1+ ...

00u m _ 4, we can form a series of trapezia by drawing the tangents at the extremities of these ordinates; the sum of the areas of these trapezia will be h(u 4 .+u 2 +...

00Let a be the radius of a circle, and 0 (circular measure) the unknown angle subtended by an arc. Then, if we divide 0 into m equal parts, and L 1 denotes the sum of the corresponding chords, so that L i =2ma sin (0/2m), the true length of the arc is L1 +a9 3 - 5 + ..., where cp. =B/2m.

00Similarly, if L2 repre sents the sum of the chords when m (assumed even) is replaced by 2m, we have an expression involving L2 and 20.

00apparently the sum of all its male adult members, is the primary body, and, it would seem, even the primary authority."

00At a meeting held in January 1766, in protest against the Stamp Act, it was declared, that "Whereas it appears from ancient Records and other Memorials of Incontestible Validity that our Ancestors with a great Sum Purchased said township, with great Peril possessed and Defended the Same, we are Born free (having never been in bondage to any), an inheritance of Inestimable Value," and a penalty of 20S.

00This act appropriated £ 20,000 annually for five years for the establishment and maintenance of elementary schools, required each city and town to raise by taxation a sum for the same purpose equal to onehalf of its share from the proceeds of the state fund, and provided for the election of school commissioners in each town and of trustees of each school.

00Although the interest on the state fund had risen to $70,000 in 1819, this together with an equal sum raised by the cities and towns was insufficient, and to meet the deficiency the patrons in each district were required by a " rate bill " to contribute in proportion to the attendance of their children.

00The government has aided immigrant farmers and farm labourers having a certain sum of money, also female domestics, by paying part of their passage money.

00The total sum paid out in eight and a quarter years had been a million and three quarters.

00His best-known papers, however, deal with prime numbers; in one of these (" Sur les nombres premiers," 1850) he established the existence of limits within which must be comprised the sum of the logarithms of the primes inferior to a given number.

00the square of the hypotenuse equals the sum of the squares on the sides), may have suggested the strictly analogous problem of doubling a cube.

00We shall show that if we sum these up for a whole wave the potential energy is equal to the kinetic energy.

00But f o 2dx=0 since the sum of the displacements = o.

00If the train of waves is reflected, the value of p at AB will be the sum of the values for the two trains, and will, on the average, be doubled.

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 for the interval which is the sum of the two.

00(25) The sum of the disturbance is obtained by adding (24) and (25) y = y l +y 2 = 2a cos Ut s i n 57 x, (26) At any given instant t this is a sine curve of amplitude 2a cos (27r/A)Ut, and of wave-length A, and with nodes at x = o, a A, A, ..., that is, there is no displacement at these nodes whatever the value of t, and between them the displacement is always a sine curve, but of amplitude varying between +2a and - 2a.

00For this it is necessary that the total force on an element due to the sum of the displacements should be equal to the sum of the forces due to the two displacements considered separately.

00It is sufficient then to show that the excess of pressure at any point is the sum of the excesses due to either train separately.

00We must show then that the force called out by the sum of the disturbances is equal to the sum of the forces called out by each train separately.

00We shall then obviously be led to the following results: If the two waves are of equal length X, and are in the same phase (that is, each producing at any given moment the same state of motion in the air particles), their combined effect is equivalent to that of a wave of the same length X, but by 2 which the excursions of the particles are increased, being the sum of those due to the two component waves respectively, as in fig.

00More than half of this sum was exhausted while he made vain efforts to find employment.

00But the verdict was looked upon with suspicion, and it was known for a fact that one of the jurymen had received a large sum of money for distribution amongst his colleagues.

007, which refers to the time of David, a sum of money is reckoned by darics, which certainly implies that the author wrote after this Persian coin had been long current in Judaea.

00The sum agreed on by way of penalty might be either specific or unliquidated, e.g.

00An arbitrator or umpire ought not, however, to state his award in such a way as to deprive the parties of their right to challenge the amount charged by him for his services; and accordingly where an umpire fixed for his award a lump sum as costs, including therein his own and the arbitrators' fees, the award was remitted back to him to state how much he allotted to himself and how much to the arbitrators (in Re Gilbert v.

00Further, the range of stress to which they are subjected is the sum of the stresses due to the load advancing from the left or the right.

00The total moment at WI, due to three loads, is the sum mC-Fmn--Emo of the intercepts which the triangle sides cut off from the vertical under W 1.

00If these are first drawn it is easy, for any position of the loads, to draw the lines B'C, B'D, B'E, and to find the sum of the intercepts which is the total bending moment under a load.

00The sum of the two upward vertical reactions must clearly be equal to the sum of the loads.

0070, at a distance x from the vertex, the horizontal component of the resultant (tangent to the curve) will be unaltered; the vertical component V will be simply the sum of the loads between 0 and F, or wx.

00per lb respectively; and in 1307 I lb for the king's wardrobe cost 9s., a sum representing about 3, 12S.

00His anger against Fesch was such that he stopped the sum of 150,000 florins which had been accorded to him.

00(C) In attempting a final estimate of the value of the Apostolic Fathers for the historian to-day, we may sum up under these heads: ecclesiastical, theological, religious.

00On the 4th of July she laid the foundation stone of the Imperial Institute, the building at Kensington to which, at the instance of the prince of Wales, it had been determined to devote the large sum of money collected as a Jubilee offering, and which was opened by the queen in 1893.

00In the end the Geneva tribunal made an award requiring the payment by Great Britain to the United States of a sum of about £3,000,000.

00A further sum of £4,000,000 was borrowed in 1909 from the government of the Federated (British) Malay States at par and bearing interest at 4%, also for railway construction.

00But now, under the idea that an alliance between Charles and Orange would be more hostile to English liberty than would the progress of the French arms, he acted with Barillon in influencing members of parliament in this sense, and is twice mentioned as receiving the sum of Soo guineas from the ambassador.

00According to this the Catholic Church is not a visibly organized body, but the sum of all " faithful people " throughout the world, who group themselves in churches modelled according to their convictions or needs.

00In north German politics he interfered vigorously to protect his brotherin-law the Margrave Louis of Brandenburg against the lords of Mecklenburg and the dukes of Pomerania, with such success that the emperor, Charles IV., at the conference of Bautzen, was reconciled to the Brandenburger and allowed Valdemar an annual charge of 16,000 silver marks on the city of Lubeck (1349) Some years later Valdemar seriously thought of reviving the ancient claims of Denmark upon England, and entered into negotiations with the French king, John, who in his distress looked to this descendant of the ancient Vikings for help. A matrimonial alliance between the two crowns was even discussed, and Valdemar offered, for the huge sum of 600,000 gulden, to transport 12,000 men to England.

00Another enactment assures to miners a 10% share of the net profits, this sum to be employed for educative, philanthropic, or other purposes of utility for the benefit of the miners.

00At least 40,000 men were necessary for the purpose, and these could have been obtained for 200,000 ducats; but a congress of magnates, whose collective fortunes amounted to hundreds of millions, having decided that it was impossible to raise this sum, there was nothing for it but to fight a few skirmishes and then take refuge abroad.

00Iannina had previously been one of the chief centres of the Thessalian grain trade; it now exports little except cheese, hides, bitumen and sheepskins to the annual value of about £120,000; the imports, which supply only the local demand for provisions, textile goods, hardware, &c., are worth about double that sum.

00She received from parliament a grant of 30,000 a year in compensation for the loss of her dower-lands, and the king added a similar sum as a pension from himself.

00He took a prominent part in opposing the Socialist movement, and in April 1870, having subscribed a large sum to the funds of a committee formed to combat the Napoleonic plebiscite, had to leave the country.

00Denoting the value of T at any velocity v by T (v), then (8) T(v) = sum of all the preceding values of AT plus an arbitrary constant, expressed by the notation (9) T(v) =Z(Av)/gp+ a constant, or fdv/gp+ a constant, in which p is supposed known as a function of v.

00Denoting by S(v) the sum of all the values of AS up to any assigned velocity v, (is) S(v) =E(OS)+ a constant, by which S(v) is calculated from AS, and then between two assigned velocities V and v, V AT, = vAv or rvvdv vgp gp' and if s feet is the advance of a shot whose ballistic coefficient is C, (17) s=C[S(V) - S(v)].

00The lumber industry, nevertheless, has steadily increased in importance, the value of the product in 1860 amounting to only $605,864, that in 1890 to $1,600,472, and that in 1900 to $2,650,082, of which sum $2,495,169 was the value of products under the factory system; in 1905 the value of the factory product was $2,750,339.

00The beginning of this shameful "subsidy policy" was the treaty of Fontainebleau, 1661, by a secret paragraph of which Sweden, in exchange for a considerable sum of money, undertook to support the French candidate on the first vacancy of the Polish throne.

0026 agrees very nearly with the sum of the years (namely, 319) given in the preceding chapters for the successive periods of oppression and independence.

00To sum up: the various dates and intervals, to the approximate determination of which this article has been devoted, do not claim separately more than a tentative and probable value.

00To sum up: an attempt has been made, it is hoped with some success, to provide a framework of history equipped with dates from the time of St Peter's arrest by Herod Agrippa I.

00But their representatives, assisted by the senators and deputies of the Basque Provinces in the Cortes, negotiated successive pacts, each lasting several years, securing for the three Provinces their municipal and provincial self-government, and the assessment, distribution and collection of their principal taxes and octroi duties, on the understanding that an agreed sum should be paid annually to the state, subject to an increase whenever the national taxation of other provinces was augmented.

00To sum up, it may be said that the Wealth of Nations certainly operated powerfully through the harmony of its critical side with the tendencies of the half-century which followed its publication to the assertion of personal freedom and "natural rights."

00Gaussian logarithms are intended to facilitate the finding of the logarithms of the sum and difference of two numbers whose logarithms are known, the numbers themselves being unknown; and on this account they are frequently called addition and subtraction logarithms. The object of the table is in fact to give log (a =b) by only one entry when log a and log b are given.

0019 a nuances, or grades of difference, which are the more gradual the more finely we dissect the geologic column, while the terms species, sub-species and variety are generally based upon a sum of changes in several characters.

00Bit by bit mutations are added to each other in different single characters until a sum or degree of mutations is reached which no zoologist would hesitate to place in a separate species or in a separate genus.

00The sum of the primitive characters approximately restores the primitive form; and the gaps in palaeontological evidence are supplied by analysis of the available zoological, embryological and anatomical evidence.

00Thus Huxley, with true prophetic instinct, found that the sum of primitive characters of all the higher placental mammals points to a stem form of a generalized insectivore type, a prophecy which has been fully confirmed by the latest research.

002 Barlow, Sum and Substance of the Conference..

00Any town upon application, and by contracting to appropriate annually a certain fixed sum for its maintenance, may receive state aid for establishing a library, and in 1904 libraries had been established by this means in 146 towns.

00The fundamental features of knowledge, whether as activity or as sum of apprehended fact, and of conduct had been deduced as elements necessary in the attainment of self-consciousness.

00Nature as the sum of that which is objective, intelligence as the complex of all the activities making up self-consciousness, appear thus as equally real, as alike exhibiting ideal structure, as parallel with one another.

00He was appeased by Khalaf's speedy submission, together with the gift of a large sum of money, and further, it is said, by his subdued opponent addressing him as sultan, a title new at that time, and by which Mahmud continued to be called,, though he did not formally adopt it, or stamp it on his coins.

00Life is not "a series of detached acts, in each of which a man can calculate the sum of happiness or misery attainable by different courses."

00agreed to give him a sum of 4000 merks in four yearly payments.

00Mill) equivalent to Intension, which is used to describe the sum of the qualities regarded as belonging to any given thing and involved in the name by which it is known; thus the term "elephant" connotes the having a trunk, a certain shape of body, texture of skin, and so on.

00Four statesNew York, Pennsylvania, Illinois and Massachusetts each manufactured in 1900 products valued at over $1,000,000,000; New York exceeding and Pennsylvania attaining almost twice that sum.

00More than $250,000,000 has been spent by the national government for the improvement of waterways, yet no general system exists, and a large part of this enormous sum has been wasted on unimportant or impossible projects, especially in recent decades, since the river navigation has been a declining interest.

00all states, members of the 1egislature receive a salary, which is the same for both houses, some states fixing an annual sum, but most preferring a per diem rate, while the maximum is generally determined by a limitation on the length of the session.

00the area of a lune or meniscus is expressible as the difference or sum of two segments, and the circumference as the sum of two arcs.

00right angled at C, semicircles are described on the three sides, thus forming two lunes Afcda and Cgbec. The sum of the areas of these lunes equals the area of the triangle ABC.] As for Euclid, it is sufficient to recall the facts that the original author of prop. 8 of book iv.

00The Fishery Commission, on the other hand, which sat in Halifax, awarded Canada $5,500,000 as the excess value of its fisheries for twelve years, and after much hesitation this sum was paid by the United States into the Canadian treasury.

00The sum of $463,454 was finally awarded as compensation to the Canadian sealers who had been unlawfully seized and punished.

00This sum was paid by the United States - in 1898.

00Almost half of this sum was required for snagging operations alone.

00Charles, however, won over many of Gunther's adherents, defeated him at Eltville, and Gunther, who was now seriously ill, renounced his claims for the sum of 20,000 marks of silver.

00In price it varies from 6 or 12 dollars to the enormous sum of 300 or 400 dollars an ounce.

00To Find The Year Of The Cycle, We Have Therefore The Following Rule: Add Nine To The Date, Divide The Sum By Twenty Eight; The Quotient Is The Number Of Cycles Elapsed, And The Remainder Is The Year Of The Cycle.

00Hence, to