A 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.
A 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.
A considerable sum of money had been laid up by Sir Nicholas for the purchase of an estate for his youngest son, the only 'one otherwise unprovided for.
A continued fraction may always be found whose n th convergent shall be equal to the sum to n terms of a given series or the product to n factors of a given continued product.
A custom also sprang up, and was common at the time of the Commutation Acts, for a tithe-owner to accept a fixed sum of money or fixed quantity of the goods tithable in place of the actual tithes, known as a modus decimandi, whether in respect of a whole parish or only of particular lands within it; and this could be sued for in the ecclesiastical courts.
A 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.
A 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.
A handsome sum was raised for Bell by subscription among the citizens of Glasgow; and he also received from the trustees of the river Clyde a pension of X100 a year.
A man of doubtful reputation, Alexander's confidant and favourite, he paid the pope a large sum for his elevation.
A 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.
A sinking fund commission was established in 1875, and the entire sum was extinguished by the 1st of August 1894.
A sum of 20 millions sterling was voted as compensation to the planters.
A 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.
A 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.
A Supplementary Act of the 3rd of March 1905 provides that writs of error and appeals may be taken from the Supreme Court of Hawaii to the Supreme Court of the United States " in all cases where the amount involved exclusive of costs or value exceeds the sum of five thousand dollars."
A 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.
A vast sum of money and the labour of thousands of men were employed to clear harbours for them, at and near Boulogne.
According to Herodotus, Anion being desirous of exhibiting his skill in foreign countries left Corinth, and travelled through Sicily and parts of Italy, where he gained great fame and amassed a large sum of money.
According to the statistics furnished in the Vierteljahreshefte zur Statistik des deutschen Reiches for 9o5, the receipts amounted to upwards of Io,000,000 for 1903, and the expenditure to somewhat less than this sum.
According 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.
After much deliberation the republic agreed to transport 4500 horse and 29,000 foot to Palestine with provisions for one year, for a sum of 85,000 marks; in addition 50 Venetian galleys would be provided free of charge, while Venice was to receive half the conquests made by the crusaders.
After the over throw of Samas - sum - yukin, Kandalanu, the Chineladanos of Ptolemy's canon, had been appointed viceroy.
Again it is necessary and sufficient for equilibrium that the sum of the projections of the forces on each of two perpendicular directions should vanish, and (moreover) that the sum of the moments about some one point should be zero.
Al-Alfi and his partisans were unable to pay the sum promised to the Porte; Salih Pasha received plenipotentiary powers from Consta,ntinople, in consequence of the letter from the ulema; and, on the condition of Mehemet Alls paying 4000 purses to the Porte, it was decided that he should continue in his post, and the reinstatement of the beys was abandoned.
All our knowledge is but the sum of our conscious experience, and is consequently material for imagination.
Almost half of this sum was required for snagging operations alone.
Along with this view has arisen the question whether the burden of taxation should not be progressive - the proportion of the sum taken by the state from the tax-payers increasing with the wealth of the individual; because ability to pay taxes is assumed to be not in proportion to, but to increase with the size of, the income.
Although 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.
Altogether 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.
An annual sum is voted by parliament out of which loans are granted to cottagers who desire to purchase small freehold plots.
Another 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.
Any quaternion may now be expressed in numerous simple forms. Thus we may regard it as the sum of a number and a line, a+a, or as the product, fly, or the quotient, be-', of two directed lines, &c., while, in many cases, we may represent it, so far as it is required, by a single letter such as q, r, &c.
Any 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.
Article 7 provided that the decision should be made within three months from the close of the argument, and gave power to the arbitrators to award a sum in gross in the event of Great Britain being adjudged to be in the wrong.
As a proof of their sincerity they were required at once to pay a fixed sum for the Imam.
As is shown by his verses and sometimes by his prose, his mind was highly imaginative; the poet Coleridge declared that if he "had not been the first chemist, he would have been the first poet 1 Davy's will directed that this service, after Lady Davy's death, should pass to his brother, Dr John Davy, on whose decease, if he had no heirs who could make use of it, it was to be melted and sold, the proceeds going to the Royal Society" to found a medal to be given annually for the most important discovery in chemistry anywhere made in Europe or Anglo-America."The silver produced £736, and the interest on that sum is expended on the Davy medal, which was awarded for the first time in 1877, to Bunsen and Kirchhoff for their discovery of spectrum analysis.
As 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.
As such, it was considered to represent the sum of human knowledge at the beginning of the 20th Century.
As the provincial revenues annually decreased, it became impossible to pay this sum, and Salih the son of Wasif, in spite of the remonstrances of the caliph, confiscated the property of state officials.
As 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.
At 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.
At 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.
At 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.
At the same time George Finlay, the historian, was urging his own grievances against the Greek government, and as both claims were repudiated Palmerston took them up. Eventually Pacifico received a substantial sum.
Banking.-The banks of issue number thirteen; their paid-up capital amounts to £13,918,000 and the capital and reserves to £19,319,000, but of this sum only about £9,000,000 is used in the state.
Bayezid 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.
Before that date there existec thirty-two banks with the privilege of issuing notes, and on the 31s1 of December 1872, 67,100,000 in all was in circulation, L25,Ioo,00c of that sum being uncovered.
Being bound to pay a stated sum to the public authorities these publicani naturally aimed at extracting the largest possible amount from the unfortunate provincials, and, as they belonged to the Roman capitalist class, they were able to influence the provincial governors.
Belgium undertook at her own charges and at an estimated cost of £2,000,000 to complete" the works of embellishment "begun in Belgium with funds derived from the Fondation and to create a debt of £2,000,000 chargeable on the funds of the colony, which sum was to be paid to the king in fifteen annual instalments - the money, however, to be expended on objects" connected with and beneficial to the Congo."The annuities to members of the royal family were to be continued, and other subsidies were promised.
Besides 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.
Bishop Kennion of Bath and Wells entered into an agreement to raise a sum of £31,000, the cost of the purchase; this was completed, and the site and buildings were formally transferred at a dedicatory service in 1909 to the Diocesan Trustees of Bath and Wells, who are to hold and manage the property according to a deed of trust.
Bit 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.
Both 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.
Both ideas, or both modes of expressing what is fundamentally the same idea, have this in common, that life is not a sum of the qualities of the chemical elements contained in protoplasm, but a function first of the peculiar architecture of the mixture, and then of the high complexity of the compounds contained in the mixture.
Broadly speaking, it is the sum of an individual's bodily, mental and spiritual growth; having its roots, as it were, spread over many lives, past and future.
But f o 2dx=0 since the sum of the displacements = o.
But 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.
But in order to avoid the necessity of besieging Milan itself, he offered the Swiss a large sum to retire into their own country.
But 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.
But 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.
But 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.
But 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.
But when the surface-tension of A exceeds the sum of the tensions of the surfaces of contact of B with air and with A, it is impossible to construct the triangle of forces, so that equilibrium becomes impossible.
By 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.
By 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.
By continual economy he left in the former the immense sum of 70 million thalers; the latter, at the time of his death, numbered 200,000 men, disciplined with all the strictness to which he had throughout life accustomed his troops.
By 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.
By the death of the archduke Sigismund in 1665 he not only gained Tirol, but a considerable sum of money, which he used to buy back the Silesian principalities of Oppeln and Ratibor, pledged by Ferdinand III.
Calling 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.
Certain rents and taxes were set aside for the use of the redemption bureau, and a nominally large sum has been withdrawn from circulation through this channel.
Charles, 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.
Christopher Aubrey appeared at the bar of the House, and charged Bacon with having received from him a sum of money while his suit was going on, and with having afterwards decided against him.
Clearly 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 +...
Communal franchise is further restricted, however, to those electors who pay a certain sum to the communal rates.
Considerable works have also been made to connect the different lakes and lake-basins for inland navigation, a sum of £1,000,000 having been spent for that purpose.
Considering 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.
Creditor and debtor have also lost their Roman law signification; they have been narrowed to mean the parties where the obligation is the payment of a sum of money.
Denoting 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)].
Denoting 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.
Depositors 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.
Disregarding 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.
Down to 1910 the sum expended by Japan on Korean reforms was estimated to approach fifteen millions sterling.
During the calendar year 1906 a sum of £840,000 was expended on primary instruction.
During the journey Louis won over the seigneurs of Croy, the principal counsellors of the duke of Burgundy, and persuaded Philip to allow him to redeem the Somme towns for the sum stipulated in the treaty of Arras.
Each year a large sum would be paid to the states from the imperial treasury, and another sum as before paid back to meet the deficit in the form of state contributions.
Engagements, sometimes yearly, sometimes for a term of years, were entered into with the zamindars to pay a lump sum for the area over which they exercised control.
Every 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),...
Every year, not only the interest, but part of the capital is expended in paying these pensions, and the capital sum was thus reduced in 1903 to 15,100,000, and in 1904 to 13,200,000.
Fibonacci's series is a sequence of numbers such that any term is the sum of the two preceding terms; also known as Lame series.
Finally Mill took from him his definition of cause as sum of conditions,9 which played no small part in the applied logic of the 19th century.
Finally, it may be mentioned that a sum proportionately large is available from public funds and regular parliamentary grants for furthering science and arts by temporary subventions to students, authors, artists and others of insufficient means, in order to enable them to carry out particular works, to profit by foreign travel, &c. The principal scientific societies and institutions are detailed under Copenhagen.
Financial 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.
For an interpretation is assigned to the product of two directed lines in one plane, when each is expressed as the sum of a real and an imaginary part.
For by giving the body (in imagination) a displacement of translation we learn that the sum of the resolved parts of the forces in any assigned direction is zero, and by giving it a displacement of pure rotation we learn that the sum of the moments about any assigned axis is zero.
For 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.
For 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.
Fortified 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.
Four 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.
From 1871 to 1879 the contribution of the states had varied from 94 to 67 million marks; under the new system the surplus of the contributions made by the states over the grant by the imperial treasury was soon reduced to a very small sum, and in 1884-1885 the payments of the empire to the states exceeded the contributions of the states to the empire by 20 million marks, and this excess continued for many years; so that there was, as it were, an actual grant in relief of direct taxation.
From these tolls Gustavus derived, in 1629 alone, 500,000 rix-dollars, a sum equivalent to the whole of the extraordinary subsidies granted to him by the Riksdag.
Fully 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.
Further, 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.
Gaussian 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.
George 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.
Guicciardini reckoned the cost of the war to Leo at the prodigious sum of 800,000 ducats.
Having had the soundness of this method tested by Jean Darcet (1725-1801), the professor of chemistry at the College de France, the duke of Orleans in June 1791 agreed to furnish a sum of 200,000 francs for the purpose of exploiting it.
He concluded with the Greeks a treaty, by which he pledged himself to pay a large sum of money annually on condition that the emperor should give him hostages as a pledge for the maintenance of peace.
He 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.
He did not indeed hold it very long, but was permitted to sell it for a large sum, retaining the rank and privileges.
He 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.
He had fixed on that number because forty-three was the sum of his and Sonya's joint ages.
He left his books and manuscripts to the British Museum, and a sum of about f500 to increase the salaries of the three assistant librarians.
He 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.
He returned to Aberdeen to paint landscapes and portraits for any trifling sum which his work could command.
He 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.
He soon transferred his services to Tachos's cousin and rival Nectanabis, who, in return for his help, gave him a sum of over zoo talents.
He thus emphasizes in apperception the connexion with the self as resulting from the sum of antecedent experience.
He thus showed that at a curved part of the surface, a superficial particle would be urged towards the centre of curvature of the surface, and he gave reasons for concluding that this force is proportional to the sum of the curvatures of the surface in two normal planes at right angles to each other.
He took a keen interest in all the work of the college, presented to it the Marmor Homericum, and finally bequeathed the reversion of £6000 for the endowment of a chair of philosophy of mind and logic. The emoluments of this sum were, however, to be held over and added to the principal if at any time the holder of the chair should be "a minister of the Church of England or of any other religious persuasion."
He 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.
He was afterwards appointed advocate to the admiralty, and to the "waters and forests," but both these posts must have been of small value, as we find him parting with them in 1650 for the insignificant sum of 6000 livres.
He 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.
He 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.
He was held personally responsible for the loss of a large sum of money during his administration of the state department, and after years of litigation was judged by an arbitrator to be indebted to the government for more than $49,000, which he paid at great sacrifice to himself.
He 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.
He was originally a mere tax-collector, or farmer of the land revenue, who agreed to furnish a lump sum from the tract of country assigned to him.
Hence if a system of vertical forces be in equilibrium, so that the funicular polygon ii closed, the length which this polygon intercepts on the vertical through any point P gives the sum of the moments about P of all the forces on one side of this vertical.
Hence there is a certain point, fixed relatively to the assemblage, through which the resultant of gravitational action always passes; this resultant is moreover equal to the sum of the forces on the several particles.
Hence 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.
Hence, in whatever way one system of forces is by successive steps replaced by another, no change is made in the sum of the moments about any assigned axis.
Her 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.
Here the fraction converges to the sum to infinity of the series.
Hides and tallow were the sum and substance of Californian economy.
His anger against Fesch was such that he stopped the sum of 150,000 florins which had been accorded to him.
His 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.
His father died in January 1799; and the slender sum which Hegel received as his inheritance, 3154 gulden (about 260), enabled him to think once more of a studious life.
His income amounted at Nuremberg to 1500 gulden (130) and a house; at Heidelberg, as professor, he received about the same sum; at Berlin about 3000 thalers (L300).
His last official act was to carry out his intention by passing through parliament resolutions, which even his colleagues deprecated in the cabinet, for taxing several articles, such as glass, paper and tea, on their importation into America, which he estimated would produce the insignificant sum of L40,000 for the English treasury, and which shrewder observers prophesied would lead to the loss of the American colonies.
His rule, though popular, was characterized by great severity, as may be inferred from the story of the monk Justus, who was denied Christian burial because he had secreted a small sum of money.
His wife had made over her income to her mother, but he had saved a small sum upon which to begin housekeeping.
Iannina 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.
If AB, AC represent infinitesimal rotations about intersecting axes, the consequent displacement of any point 0 in the plane BAC will be at right angles to this plane, and will be represented by twice the sum of the areas OAB, OAC, taken with proper signs.
If by pre-heating the blast we add to the sum of the heat available; or if by drying it we subtract from the work to be done by that heat the quantity needed for decomposing the atmospheric moisture; or if by removing part of its nitrogen we lessen the mass over which the heat developed has to be spread - if by any of these means we raise the temperature developed by the combustion of the coke, it is clear that we increase the proportion of the total heat which is available for this critical work in exactly the way in which we should increase the proportion of the water of a stream, initially too in.
If F, Q, R, be any three forces acting along BC, CA, AB, respectively, the line of action of the resultant is determined by the consideration that the sum of the moments about any point on it must vanish.
If he was slain, a fixed sum (wergild), varying according to his station, had to be paid to his relatives, while a further but smaller sum (manbot) was due to his lord.
If his policy miscarried in several quarters it was eminently successful in others; and if we consider the sum of his efforts to achieve the.
If k be the radius of gyration about p we find k2 =2Xarea AHEDCBAXONap, where a$ is the line in the force-diagram which represents the sum of the masses, and ON is the distance of the pole 0 from this line.
If no one of these tensions is greater than the sum of the other two, the drop will assume the form of a lens, the angles which the upper and lower surfaces of the lens make with the free surface of A and with each other being equal to the external angles of the triangle of forces.
If 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.
If T denote the kinetic energy, we may say then that the sum T + V is in any interval of time increased by an amount equal to the work done by the extraneous forces.
If the Cistercians and lesser offshoots of the order be added, the sum total of choir-monks and lay brothers exceeds 11,000.
If 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.
If the effort varies by insensible gradations, the energy exerted is the integral or limit towards which that sum approaches continually as the divisions of the path are made smaller and more numerous, and is expressed by JPds.
If the order of stratification differ from that of densities, we can show that each step of approximation to this order lowers the sum of tensions.
If the tension of the surface between the solid and one of the fluids exceeds the sum of the other two tensions, the point of contact will not be in equilibrium, but will be dragged towards the side on which the tension is greatest.
If the three fluids can remain in contact with one another, the sum of any two of the 3 quantities must exceed the third, and T 31 I by Neumann's rule the directions of the interfaces at the common edge must be parallel to the sides of a triangle, taken proportional to T12, T23, T31.
If 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.
If 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.
If 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.
If this amount be negative the sum in question is diminished by a corresponding amount.
If 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.
If 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 .
If we take the sum of n terms of the series '±'H-'±..
In 1007 !Ethelred bought them off for a larger sum than ever (36,000), and for two years the land enjoyed peace.
In 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."
In 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.
In 1826 the wild lands of Maine were surveyed and divided between the two states; and in 1853 Maine acquired from equal moieties " the sum of $300,000 as compensation for the lands which they had claimed and which under the treaty they were called upon to surrender.
In 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.
In 1867, by a treaty signed on the 30th of March, the purchase was consummated for the sum of $7,200,000, and on the 18th of October 1867 the formal transfer of the territory was made at Sitka.
In 1870, in further consideration of the sum of $10,000, Bolivia granted to an Anglo-Chilean company the right of working certain nitrate deposits north of the 24th parallel.
In 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.
In 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.
In addition to the grants above mentioned, the county council is required to grant to the guardians of every poor-law union wholly or partly in their county an annual sum for the costs of the officers of the union and of district schools to which the union contributes.
In 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.
In applying tests of memory, it may be legitimate to allow a candidate to pass who answers correctly from 30 to 50% of the questions; such an allowance if applied to a test of capacity, such as the performance of a sum in addition, the solution of triangles by means of trigonometrical tables, or the translation of an easy passage from a foreign language, appears to be irrational.
In April 1893 the reserve fell below this sum.
In case of injury, involving incapacity for more than, thirteen weeks (for the earlier period the Krankenkassen provide), the weekly sum payable during complete or permanent incapacity is fixed at the ratio of two-thirds of the earnings during the year preceding the accident, and in case of partial disablement, at such a proportion of the earnings as corresponds to the loss through disablement.
In despair !Ethelred again offered them money, which they again accepted, the sum paid on this occasion being £24,000.
In 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.
In 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."
In Like Manner The Epacts Of All The Following Years Of The Cycle Are Obtained By Successively Adding Eleven To The Epact Of The Former Year, And Rejecting Thirty As Often As The Sum Exceeds That Number.
In like manner, any school that raises $20 for a library will receive the same amount from the state, which will also contribute $10 each year thereafter for maintenance, if the school raises a similar sum.
In 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.
In 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.
In other words, the sum of the negative products is equal to the sum of the positive products.
In 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.
In price it varies from 6 or 12 dollars to the enormous sum of 300 or 400 dollars an ounce.
In Prussia, by the Lex Huene, from 1885 to 1895, all that sum paid to Prussia, so far as it exceeded 15 million marks, was handed over to the local authorities in relief of rates.
In return for a sum of money these princes renounced their rights under their father's will, and the new elector thus secured the whole of Frederick William's territories.
In 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.
In sum, then, we may say that "philosophy" has come to be understood at least in modern times as a general term covering the various disciplines just enumerated.
In 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.
In the contest for the marshalate of the Diet the leaders of the two parties were again pitted against each other, when the verdict of the last Riksdag was exactly reversed, Fersen defeating Rudbeck by 234, though Russia spent no less a sum than £11,50o to secure the election of the latter.
In 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.
In the event of the decision being favourable to Peru a sum of io,000,000 dollars was to be paid by Peru to Chile.
In 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.
In the seventeen years ending1896-1897the capital expenditure on such works was Rx.10,954,948, including a sum of Rx.1, 742, 246 paid to the Madras Irrigation Company as the price of the Kurnool-Cuddapah canal, a work which can never be financially productive, but which nevertheless did good service in the famine of1896-1897by irrigating 87,226 acres.
In 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.
In this case the sum to n terms of the series is equal to the nth convergent of the fraction.
In this sense the individual is in himself his own universe, his whole existence being, in other words, the sum total of his psychic relations, and nothing else being for him in existence at all.
In 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.
In 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.
Indeed 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.
It appears then that this sum is a measure of the total capacity for doing work against extraneous resistances which the particle possesses in virtue of its motion and its position; this is in fact the origin of the term energy.
It does not, however, lie within the scope of the present article to examine the various sources underlying the narrative with any minuteness, but rather to sum up those results of modern criticism which have been generally accepted by Old Testament scholars.
It has been shown by Gordan that every symbolic product is expressible as a sum of transvectants.
It is also worthy of note that Panama refused to assume any part of this debt without a formal recognition of her independence by Colombia, and even then only a sum proportionate to her population.
It is clear, therefore, that from this point of view the sum of practical morals might be given in Butler's own words - "that mankind is a community, that we all stand in a relation to each other, that there is a public end and interest of society, which each particular is obliged to promote."
It 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.
It is now evident that in the process of reduction of a coplanar system no change is made at any stage either in the sum of the projections of the forces on any line or in the sum of their moments about any point.
It is said that he guaranteed Walid a large sum of money, which he hoped to extort from Khalid.
It 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.
It is sufficient then to show that the excess of pressure at any point is the sum of the excesses due to either train separately.
It 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.
It may be held that every action is causally connected not only externally with the sum of the agent's environment, but also internally with his motives and impulses.
It need not, therefore, surprise us that the man who formulated the sum of virtue in justice and benevolence was unable to be just to his own kinsfolk and reserved his compassion largely for the brutes, and that the delineator of asceticism was more than moderately sensible of the comforts and enjoyments of life.
It provided that, on any bishop desiring to retire on account of age or incapacity, the sovereign should be empowered to declare the see void by an order in council, the retiring bishop of archbishop to be secured the use of the episcopal residence for life and a pension of one-third of the revenues of the see, or £2000, whichever sum should prove the larger.
It 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.
It 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.
It was in this speech, which lasted five hours, that Palmerston made the wellknown declaration that a British subject - " Civis Romanus sum " - ought everywhere to be protected by the strong arm of the British government against injustice and wrong.
It 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.
Its length is, therefore, the product of the lengths of the factors, and its inclination to the real unit is the sum of those of the factors.
Its n th convergent is not equal to the sum to n terms of the series.
Iunius 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.
Khalid already had so many friends that the sum was brought together with the exception of 30,000 dirhems. At that moment tidings came about a rising in the province of Mosul, and a friend of Khalid said to the caliph that Khalid was the only man capable of putting it down.
King Liutprand (712744) bought the relics of St Augustine for a large sum to be placed in his church at Pavia.
Langham's tomb is the oldest monument to an ecclesiastic in Westminster Abbey; he left the residue of his estate - a large sum of money - to the abbey, and has been called its second founder.
Let 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.
Let me sum up a few of the elements that made Helen Keller what she is.
Letters insured for a fixed sum are not delivered under any circumstances.
Life 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."
Living at the commencement of an epoch of unparalleled scientific activity, Spencer could not possibly sum up and estimate its total production.
London 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.
Metamorphosis 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.
Military and civilian teachers were obtained from Europe, and the state granted a large sum of money for the support of the establishment.
Mill 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.
Mill persuaded Grote, Molesworth, and Raikes Currie to advance the sum of £240.
More 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.
More than half of this sum was exhausted while he made vain efforts to find employment.
Moreover, the order for payment of any sum must be made in pursuance of an order of the council signed by three members of the finance committee present at the meeting of the council, and countersigned by the clerk.
Motions' are either simple or compound, the latter being the sum of a number of the former.
Multiply, 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.
Nature 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.
Nearly one-third of the total value of the output represents winespirit, 23% tanneries, 18% tallow-melting and a considerable sum cigarette-making.
Nearly 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.
No 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.
Now from the laws of statics it is known that, in order that a system of forces applied to a system of connected points may be in equilibrium, it is necessary that the sum formed by putting together the products of the forces by the respective distances through which their points of application are capable of moving simultaneously, each along the direction of the force applied to it, shall be zero, products being considered positive or negative according as, the direction of the forces and the possible motions of their points of application are the same or opposite.
Of his professional earnings, the small sum for which, as we have seen, he gave up his offices, and the expression of Fontenelle that he practised "sans gout et sans succes," are sufficient proof.
Of 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.
On his way he came to the town of Yezdikhast, where he demanded a sum of money from the inhabitants, claiming it as part of secreted revenue; the demand was refused, and eighteen of the head men were thrown down the precipice beneath his window; a saiyid, or holy man, was the next victim, and his wife and daughter were to be given over to the soldiery, when a suddenly-formed conspiracy took effect, and Zakis own life was taken in retribution for his guilt (1779).
On the 17th of August 1805 the dam of the canal of Cairo was to be cut, and some chiefs of Mehemet Alis party wrote, informing them that he would go forth early on that morning with most of his troops to witness the ceremony, inviting them to enter and seize the city, and, to deceive them, stipulating for a certain sum of money as a reward.
On the 1st of December the king, "for a large sum of money paid down," gave Wykeham, not only the custody of the temporalities of the see, but all the profits from the day of Edingdon's death.
On the 24th of November 1394 Wykeham lent the king the sum of £t000 (some £30,000 of our money), which same sum or another £1000 he promised on the 21st of February 1395 XXVIII.
On 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.
On 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.'
On 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.
On the assumption, then, that time and space are not objects, but systems, of sensations, he concludes that a body in time and space is " a relatively constant sum of touch-and-light-sensations, joined to the same time-and-space-sensations," that each man's own body is included in his sensations, and that to explain sensations by motions would only be to explain one set of sensations from another.
Once 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.
One 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.
Only 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.
Other 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.
Prefectural roads are maintained by a joint contribution from the government and from the particular prefecture, each paying one-half of the sum needed.
Proceeding 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 +..
Ramsay (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.
Recent 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.
Right is not the sum of the conditions of external liberty but of absolute liberty, and embraces all the existence of nature, reason and humanity.
Roman 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.
Schmalkalden, 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."
She died at Weston-super-Mare, Somerset, on the 15th of April 1892, bequeathing her valuable collection of Egyptian antiquities to University College, London, together with a sum to found a chair of Egyptology.
She gets web hosting set up for the princely sum of $30 a month.
She 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.
She was punished for her obstinacy by being deprived of Norway, which she was compelled to surrender to Sweden by the terms of the treaty of Kiel (1814), on the 14th of January, receiving by way of compensation a sum of money and Swedish Pomerania, with Riigen, which were subsequently transferred to Prussia in exchange for the duchy of Lauenburg and 2,000,000 rix-dollars.
Similarly, 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.
Since - the side OA is common, we have o to prove that the sum of the - - perpendiculars from B and C on - -.
Since the projection of a vector- sum is the sum of the projections of the several vectors, the equation (2) gives if x be the projection of 0G.
Since 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).
Since two concurrent forces and their resultant obviously project into two concurrent forces and their resultant, we see that the sum of the moments of two concurrent forces about any axis HK is equal to the moment of their resultant.
So sense, memory and experience, the sum of sense and memory, though requiring conception, are the causes of the experiential judgment that there exist and have existed many similar, sensible things, and these sensory, memorial and experiential judgments about the existence of past and present sensible things beyond conceived ideas become the particular premises of primary inference.
Some further details are to be found in documents preserved by the archaeologist Maqrizi, from which it appears that the sum for which each district was responsible was distributed over the unit in such a way that artisans and tradesmen paid at a rate similar to that which was enforced on those employed in agriculture.
Some 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.
Sometimes he staked a large sum, but Dolokhov refused to accept it and fixed the stake himself.
Soon 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.
Sorensen 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.
Such 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.
Sylvester showed that the quintic might, in general, be expressed as the sum of three fifth powers, viz.
Taking 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.
Taking 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.
Taking this sum as the nth term, we obtain the series 1+3+6+10+..
Tannery); 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.
That 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.
That the thing made a great flame, a great noise, and struck terror into the beholder is about the sum of it all.
The 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.
The 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.
The amount of papers on Korea scattered through English, German, French and Russian magazines, and the proceedings of geographical societies, is very great, and for the last three centuries Japanese writers have contributed largely to the sum of general knowledge of the peninsula.
The amount recovered as mesne profits need not be limited to the rental value of the land, but may include a sum to cover such items as deterioration or reasonable costs of getting possession, &c.
The annual expenditure was over 26,000,000, of which sum 7,500,000 was provided by state subvention.
The assembly of all householders in villages of less than 30 households, and of 30 elected men in villages having from 30 to 300 households (dne from each io households in the more populous ones), constitutes the village assembly, similar to the mir, but having wider attributes, which assesses the taxes, divides the land, takes measures for the opening and support of schools, village grain-stores, communal cultivation, and so on, and elects its ataman (elder) and its judges, who settle all disputes up to fio (or above that sum with the consent of both sides).
The axiom of Cartesianism is, therefore, the Cogito ergo sum.
The 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.
The books he read were chiefly historical, and on these he spent a certain sum every year.
The capital expended on the state lines open for traffic was £43, 626, 000, of which sum £7,400,000 was expended on rolling stock and equipment and £36,226,000 on construction of roads, stations and permanent ways.
The 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.
The celebrated " homo sum " is a translation from Alexis, and the spirit of it breathes in many passages of the Greek drama.
The chief item of expenditure is on education; thus in 1913-4, out of a total expenditure by the provincial council of £1,142,000, the sum of £853,000 was spent on education.
The chief sources of revenue were customs duties, taxes on land and industries, duties on tobacco and breadstuffs, the Lisbon octroi, receipts from national property, registration and stamps, &c. The heaviest expenditure (nearly £ 5,000,000) was incurred for the service of the consolidated debt; payments for the civil list, cortes, pensions, &c., amounted to more than £2,000,000, and the cost of public works to nearly as large a sum.
The choir-screen was sold to the South Kensington Museum in London for goo, this sum being devoted to the work of modern restoration.
The collects of the Breviary are largely drawn from the Gelasian and other Sacramentaries, and they are used to sum up the dominant idea of the festival in connexion with which they happen to be used.
The commissioners of Inland Revenue also pay into the same account a sum equal to i 2% on the net value of personal property in respect of which estate duty is paid.
The Commons presented an address to the king praying that the deceased statesman might be buried with the honours of a public funeral, and voted a sum for a public monument which was erected over his grave in Westminster Abbey.
The company claimed io,000,000 rupees as compensation for losses; for the British, the Armenian and the Indian inhabitants of Calcutta there were demanded the sums of 5,000,000, 2,000,000 and 1,000,000 rupees; for the squadron 2,500,000 rupees, and an equal sum for the army.
The component vibrations at P due to the successive zones are thus nearly equal in amplitude and opposite in phase (the phase of each corresponding to that of the infinitesimal circle midway between the boundaries), and the series which we have to sum is one in which the terms are alternately opposite in sign and, while at first nearly constant in numerical magnitude, gradually diminish to zero.
The 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.
The construction of a harbour of refuge at Portland had been recommended in 1845; in 1847 an act was passed to facilitate the purchase of land there, and a sum of money was taken in the estimates for the erection of a prison which was begun next year.
The council-general of the department had granted him a sum of 600 francs, and the town council promised an annual pension of 400, but in spite of friendly help and introductions Millet went through great difficulties.
The 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.
The degree of the separation is the sum of the degrees of the component separates.
The distinction between these two classes is not sharp; though when the properties of the resultant are sensibly the sum of those of the pure components, as is nearly the case for a complex gas such as air, it is usual to class it as a mixture.
The edge of the drop is drawn out by the surface-tension of A with a force greater than the sum of the tensions of the two surfaces of the drop. The drop, therefore, spreads itself out, with great velocity, over the surface of A till it covers an enormous area, and is reduced to such extreme tenuity that it is not probable that it retains the same properties of surface-tension which it has in a large mass.
The 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.
The estimated revenue for the year1908-1909amounted to about 0650,000, and the expenditure to a like sum.
The expenditure in1907-1908was £131,582, which sum included £11,987 for bands.
The Federal war debt eventually reached the sum of $2,700,000,000.
The financial treaties in which the Egyptian government were bound up prevented their ever paying so large a sum as this within five years; but a company was formed in London to advance periodically the sum due to the contractors, on receipt from the government of Egypt of promissory notes to pay sixty half-yearly instalments of £78,613, beginning on the 1st of July 1903.
The 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.
The 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.
The force R is the geometric sum of the given forces, and the moment (G) of the couple is equal to the sum of the moments of the given forces about 0.
The full boo is treated as the amount to be made good, but the owner of the goods is made to contribute towards that upon the sum of X100 thus saved to him.
The 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.
The government has aided immigrant farmers and farm labourers having a certain sum of money, also female domestics, by paying part of their passage money.
The 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."
The handsome Roman Catholic cathedral for the diocese of Raphoe occupies a commanding site, and cost a large sum, as it contains carving from Rome, glass from Munich and a pulpit of Irish and Carrara marble.
The heir offered to fix the amount at 500 florins, but Spinoza accepted only 300, a sum which was regularly paid till his death.
The Imperial Bank of Persia, which had already advanced a large sum of money, and thereby greatly facilitated the shahs early departure from Tabriz and enabled the grand vizier at Teheran to carry on the government, started buying up the copper coinage at all its branches and agencies.
The income of the postal and telegraph department in 1905 was £1,065,618 and the expenditure £933,121, but there were some items of expenditure not included in the sum named, such as interest charges, &c., and cost of new buildings.
The 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.
The 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.
The king proposed that the actual noble holders of crown property should either pay an annual sum of 200,000 rix-dollars, to be allowed for out of any further crown lands subsequently falling in to them, or should surrender a fourth of the expectant property itself to the estimated amount of 600,000 rix-dollars.
The largest addition to the sum of Ciceronian writings was made by Poggio (Gian Francesco Poggio Bracciolini) in the course of his celebrated mission to the Council of Constance (1414-1417).
The largest aerodrome, intended to carry passengers and to be available for war purposes, was built to the order and at the expense of the American government, which granted a sum of fifty thousand dollars for its construction.
The length of the vector must be proportional to the moment of the couple, and its sense must be such that the sum of the moments of the two forces of the couple about it is positive.
The lengths of several reigns in the XIIth, XVIIIth and XIXth Dynasties are known, and the sum total for the XIIth Dynasty is preserved better than any other in the Turin Papyrus, which was written under the XIXth Dynasty.
The 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.
The 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.
The 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.
The 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.
The milk given each day by each cow is entered in a book, and then made into butter and cheese, the cow-herds and cheese-makers having the right to a certain proportion of milk, butter and cheese for their own sustenance, and receiving a small sum per head of cattle for looking after them.
The mines, which were the property of the state, were usually farmed out for a certain fixed sum and a percentage on the working; slave labour was exclusively employed.
The mixture consequently distils at the temperature at which the sum of the partial pressures equals that of the atmosphere.
The money they cost her was a small sum in comparison to the f 12,000,000 she lavished on her long series of lovers, who began with Soltykov and Stanislaus Poniatowski before she came to the throne, and ended with the youthful Platon Zubov, who was tenant of the post at her death.
The municipal revenues aggregated 2,317,670 bolivianos in 1902, and the expenditures 61,510 bolivianos in excess of that sum.
The net opium revenue represents the difference between the sum realized at these sales and the cost of production.
The numerous and complicated details which we sum up under the convenient, but often misleading, single name of caste, are solely dependent for their sanction on public opinion.
The 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.
The only modification required in the formulae is, that in equation (26) the difference of the angular velocities should be substituted for their sum.
The original inhabitants had been left on the conquered lands as agriculturists, on condition of paying a fixed sum yearly for each district.
The other and probably the correct view is that any considerable sum of money paid to a child at that child's request is an advancement; thus payment of a son's debts of honour has been held to be an advancement.
The payers of income tax, unfortunately, are not one class but many, and although the rate of duty is the same, the definition of income seems imperfect, so that many pay on a much larger assessment of income than seems fair in comparison with other incomes of nominally the same amount, but really of much greater value when all deductions from the gross sum are fairly reckoned.
The pension began at the age of seventy, the amount varying by very complicated rules, but the state paid a fixed sum of two pounds ten shillings annually in addition to the pension.
The philosopher Thomas Harriot (1560-1621), one of his colleagues, laboured for the conversion of the natives, amongst whom the first baptism is recorded to have taken place on the 13th of August 1587.9 Raleigh himself presented as a parting gift to the Virginian Company the sum of loo " for the propagation of the Christian religion " in that settlement.
The poet however cleared by his benefit nights, and by the sale of the copyright of his tragedy, about three hundred pounds, then a great sum in his estimation.
The problem is to make the sum of the interfacial tensions a minimum, each tension being proportional to the square of the difference of densities of the two contiguous liquids in question.
The 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.
The 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.
The 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.
The qualities of water are no sum of the qualities of oxygen and hydrogen, and still less can we expect to explain the qualities of life without regard to the immense complexity of the living substance.
The reason is that the sum of the solar and lunar inequalities, which are compensated in the whole period, may amount in certain cases to io, and thereby cause the new moon to arrive on the second day before or after its mean time.
The relief was a sum paid by the heir for the lord's recognition of his succession.
The resistance offered by the liquid, and therefore the force F, required to drive one grammemolecule through the liquid with unit velocity is the sum of the corresponding quantities for the individual ions.
The result was that the sum to be contributed by the individual states constantly increased, and the amount to be raised by direct taxation, including local rates, threatened to become greater than could conveniently be borne.
The 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.
The 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.
The 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.
The 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.
The sacred law (Torah) was the earthly reproduction of a heavenly Torah which had no origin in time, and constituted the sum of ideal wisdom into which God looked when he would create the world.'
The same hospodar was often reappointed again and again as he succeeded in raising the sum necessary to buy back his title.
The score against him reached the fateful sum of forty-three thousand.
The second minus the first, or the increase in the sum of tensions, is thus 2 (U n - o' n+l) (o n+ 1 - Q n +2) Hence, if an+1 be intermediate in magnitude between a,, and a71+2, the sum of tensions is increased by the abolition of the stratum; but, if a-n+1 be not intermediate, the sum is decreased.
The 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.
The shah offered him a sum of money to return to Kandahar, but the Afghan answered by advancing to a place called Gulnabad, within 9 m.
The small-livings fund aims at bringing up to £200 a year all stipends which fall short of that sum, of which there are nearly 400.
The special occasion for which the House had been sum moned was the discovery of one of the numerous popish plots that distracted Elizabeth's reign.
The state will duplicate any yearly sum between $250 and $5000 which a school district may raise to maintain a school or courses of manual training.
The statement, for instance, that 32 - x = 25, is really a statement that 32 is the sum of x and 25.
The sum agreed on by way of penalty might be either specific or unliquidated, e.g.
The 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.
The 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.
The sum of $463,454 was finally awarded as compensation to the Canadian sealers who had been unlawfully seized and punished.
The sum of 700,000,000 roubles per annum is thus excepted from the control of the chambers.
The sum of his conclusion is that the perfect orator must also be a perfect man.
The 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.
The sum of the corresponding numbers multiplied by 332600 gives Log.
The 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.
The sum of the moments of the two forces of a couple is the same about any point in the plane.
The sum of the moments of two forces about any point 0 is equal to the moment of their resultant (P. Varignon, 1687).
The 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!
The 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.
The sum of the two upward vertical reactions must clearly be equal to the sum of the loads.
The sum received by the Post Office as rental in respect of private wires was £183,000.
The sum total amounts to 419 objects, besides hundreds of fragments, cores, spalls and rejects, retained for study and comparison.
The sum total expended upon the buildings amounted to half a million of money, and the yearly charges of the establishment were a heavy burden on the exchequer.
The sum total of all these contributions to electrical knowledge had the effect of establishing Maxwell's principles on a firm basis, but they also led to technical inventions of the very greatest utility.
The sum voted by the British government to slave-owners in Cape Colony, out of a total compensation paid of £20,oOo,000, was 1,250,000 (the official estimate of their value being £3,000,000).
The sum which they agreed to pay him was only fifteen hundred guineas; and out of this sum he had to pay several poor men of letters who assisted him in the humbler parts of his task.
The Sum Will Be The Year Of The Christian Era, And The Day Of The Year Will Be Found By Multiplying The Decimal Figures By 365.
The sums borrowed must not exceed, with the outstanding loans, the amount of the assessable value for two years of the district for which the money is borrowed; and if the sum borrowed would, with the outstanding loans, exceed the assessable value for one year, the sanction of the Local Government Board may not be given except after local inquiry.
The taxation on flocks and herds exists either as a supplementary method of land taxation, or as a contribution of a certain sum per animal, and the tax on shopkeepers, artisans and trades sometimes takes the form of a poll-tax, sometimes that of an impost on the profits of the trades.
The taxes are collected directly, and must meet the needs of the province, before any sum is remitted to the Imperial Treasury.
The tctal absence of easy means of communication, the high rates of transport, and the scarcity of fuel and water in the mineral districts made profitable operations impossible, and the corporation liquidated in f 894, after having expended a large sum of money.
The 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.
The total aberration of two or more very thin lenses in contact, being the sum of the individual aberrations, can be zero.
The total imports for that year reached the sum of £5,397,918, and the exports £3,367,805.
The 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.
The total moment of friction of a pair of rotating rubbing surfaces is the sum or integral of the moments of friction of their several portions.
The total sum paid out in eight and a quarter years had been a million and three quarters.
The total value of farm products in 1899 was $33,048,576; of this sum 97% was almost equally divided between crop products and animal products, the forests contributing the remainder.
The 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.
The 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.
The twelve companies contributed in equal portions the sum of £60,000 for the new scheme, by which it was intended to settle a Protestant colony in the lands forfeited by the Irish rebels.
The two forces at B will cancel, and we are left with a couple of moment P.AC in the plane AC. If we draw three vectors to represent these three couples, they will be perpendicular and proportional to the respective sides of the triangle ABC; hence the third vector is the geometric sum of the other two.
The Union gave a considerable impetus to the manufacture, as did also the establishment of the Board of Manufactures in 1727, which applied an annual sum of £2650 to its encouragement, and in 1729 established a colony of French Protestants in Edinburgh, on the site of the present Picardy Place, to teach the spinning and weaving of cambric. From the 1st of November 1727 to the 1st of November 1728 the amount of linen cloth stamped was 2,183,978 yds., valued at £103,312, but for the year ending the 1st of November 1822, when the regulations as to the inspection and stamping of linen ceased, it had increased to 36,268,530 yds., valued at £1,396,296.
The 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.
The velocity with which the ions move past each other is equal to the sum of their individual velocities, which can therefore be calculated.
The wazir promised to assist them in return for a sum of money; but when the Mahrattas were driven off the Rohilla chiefs refused to pay.
The wazir then decided to annex their country, and appealed to Hastings for assistance, which was given in return for a sum of forty lakhs of rupees.
The weight of the function is the sum of the numbers in the bracket, and the degree the highest of those numbers.
The whole of the extraordinary expenditure of the Sudan campaigns of 1896-1898, with the exception of 800,000 granted by the British government, was paid out of this funda sum amounting in round figures to 1,500,000.
The workmen contribute at the rate of two-thirds and the employers at the rate of one-third; the sum payable in respect of each worker varying from 11/2-3% of the earnings in the communal sick fund to at most 11/2-4% in the others.
Then in 1697, by the Treaty of Ryswick, Louis abandoned his claim in return for a sum of money.
Then 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.
Then the figure is (usually) the sum of two trapezoids F on base AE, and its area can be calculated as in § 24.
There is a further appeal in all cases where the sum in dispute exceeds a thousand pounds, to a superior council at Brussels, composed of a number of jurisconsults who sit as a tour de cassation.
There 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.
There 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.
Thereupon 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.
These bonds had then reached a sum exceeding 20,000,000 and were held chiefly by French firms. The unification scheme was elaborated in a khedivial decree of the 7th of May 1876, but was rendered abortive by the opposition of the British bondholders.
These three salient facts are practically the sum of our knowledge of early Danish history previous to the Viking period.
They 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.
They 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.
They released themselves by paying the enormous sum of 240,000 dinars and 16,000,000 dirhems, which constituted nearly their whole fortune, and were then sent to Bagdad, where father and son died three years later.
They took the form of a piece of paper about an inch broad and five to eight inches long, on which was written the sum, the date of payment and the name of the payer and payee, with their seals; the paper was then torn down its length, and one half given to each party.
This 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.
This business is frequently performed by a gamekeeper, a sum being paid him for any litter of cubs or fox found on his beat.
This definition correctly indicates that the mass of any portion of matter is equal to the sum of the masses of its parts, and that the masses of bodies alike in other respects are equal, but gives no test for comparison of the masses of bodies of different substances; this test is supplied only by a comparison of motions.
This 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.
This drop will not spread out like the first drop, but will take the form of a flat lens with a distinct circular edge, showing that the surface-tension of what is still apparently pure water is now less than the sum of the tensions of the surfaces separating oil from air and water.
This number is called the Golden Number, either because will therefore be given by the formula (x 1 53) r, that is to say, add 3 totlzedate,divide the sum by 15, and the remainder is the year of the indiction.
This 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.
This shameful "subsidy policy" dates from 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.
This sum covered " immigration expenses," i.e.
This sum is called the moment of the couple; it must of course have the proper sign attributed to it.
This 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.
This sum was collected with difficulty.
This sum was ostensibly paid by the transference to the treasury of the royal yacht " Amelia " and certain palaces; but the cost and upkeep of the " Amelia " had been paid with public money, while the palaces had long been maintained as state property.
This sum was paid by the United States - in 1898.
This sum, or integral, is called the " line integral of electric force" or the electromotive force (E.M.F.) along this line.
This wily chief professed his willingness to obey the commands of the Porte, but stated that his troops, to whom he owed a vast sum of money, opposed his departure.
Three-dimensional Statics.A system of, parallel forces can be combined two and two until they are replaced by a single resultant equal to their sum, acting in a certain line.
Through 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.
Thus Diophantus knew that no number of the form 8n-1-7 can be the sum of three squares.
Thus 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.
Thus in the figure the sum of the moments about 0 is P. OAP. OB or P. AB, which is independent of the position of o 0.
Thus 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.
Thus 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+...
To Argyll he promised the payment of £40,000 at his restoration, doubtless the sum owing as arrears of the Scottish army unpaid when Charles I.
To escape the necessity of working to the end of his days at the orders of the State in order to pay this sum, Courbet went to Switzerland in 1873, and died at La Tour du Peilz, on the 31st of December 1877, of a disease of the liver aggravated by intemperance.
To sum up briefly the history of the development of the heliometer.
To 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.
To sum up the incidents of this eventful period of his life, it was during it that he lost his mother, always loved and dutifully honoured, by death; his sister had been estranged from him some years before by an imprudent marriage, which, though making her a liberal allowance, he never forgave.
To 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."
To sum up, the are excursions into the great unknown made with a full acknowledgment of the greatness of that unknown.
To the former belong the theorems (t), (2), and (3), and to the latter especially the theorem (4), and also, probably, his solution of the two practical problems. We infer, then, [t] that Thales must have known the theorem that the sum of the three angles of a triangle are equal to two right angles.
To 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.
To this sum the land and poll-tax and other direct taxes contributed £374,630.
Towards 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.
Trade 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.
Twenty-eight boats engaged in haddock-fishing at Eyemouth used between October 1882 and May 1883 920 tons of mussels (about 47,000,000 individuals), costing nearly £1800 to the fishermen, about one-half of which sum was expended on the carriage of the mussels.
Two positions on which he repeatedly insisted have taken a firm hold - first, that it is of the essence of a church to be comprehensive of various views and tendencies, and that a national church especially should seek to represent all the elements of the life of the nation; secondly, that subscription to a creed can bind no one to all its details, but only to the sum and substance, or the spirit, of the symbol.
Two years later they were joined by Hugh, dean of St Peter's, York, who brought with him a large sum of money and a valuable collection of books.
Until he made a large sum by the publication of Political Justice, he lived on an average of £120 a year.
Walid wished to have his son Abdalaziz chosen as his successor, and had offered Suleiman a large sum of money to induce him to surrender his rights.
We 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.
We 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.
We know, however, that in addition to the sum paid to the bride's guardian, it was customary for the bridegroom to make a present (morgengifu) to the bride herself, which, in the case of queens, often consisted of a residence and considerable estates.
We 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.
We see, then, that the removal of a stratum from between neighbours where it is out of order and its introduction between neighbours where it will be in order is doubly favourable to the reduction of the sum of tensions; and since by a succession of such steps we may arrive at the order of magnitude throughout, we conclude that this is the disposition of minimum tensions and energy.
We shall show that if we sum these up for a whole wave the potential energy is equal to the kinetic energy.
When a contribution is required from county rate, the county council assess the amount payable by each parish according to the basis previously made, and send their precept to the guardians of the unions comprising the several parishes in the county, the guardians in their turn requiring the overseers of each parish to provide the necessary quota of that parish out of the poor rate, and the sum thus raised goes into the county fund.
When 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.
When 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.
When the expenditure during the same period was examined the extraordinary fact was disclosed that the sum raised by revenue was only three millions less than that spent on administration, tribute and public works, including a sum of 10,500,000, described as expenses of questionable utility or policy.
When 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.
When 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.
When they heard that Arion had a large sum of money with him they began to make plans to get it.
When 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.
While the war with Scotland dragged on through the early years of the reign of Edward II., the fortification of Berwick was a matter of importance, and in 1317 the mayor and bailiffs undertook to defend it for the yearly sum of 6000 marks; but in the following year, "owing to their default," the Scots entered and occupied it in spite of a truce between the two kingdoms. After Edward III.
With 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.
With regard to the first., in ultimate result it depends upon the theory of forms; for whenever the compound body can be regarded as the sum of certain simple natures, then our knowledge of the forms of these natures gives us the power of superinducing a new nature on the concrete body.
With the vast sum raised front guano and nitrate deposits President Balta commenced the execution of public works, principally railroads on a gigantic scale.
With 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.
Yet this explanation is open to question owing to the very early date at which the regulation appears, and to the fact that in the case of widows the sum specified had to be paid to relatives of the widow herself on the female side, and by preference to those of a younger generation.