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successive

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successive

successive Sentence Examples

  • Successive types have arisen in ascendi-,.L-s., ~ r~-,A ..,,i, ..

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  • Nevertheless, on careful examination of these three successive stages, it will easily be seen that, in spite of the apparent difference between them, all have a common foundation, source and purpose.

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  • - Diagrams illustrating the successive stages in the development of the cyclosystems of the Stylasteridae.

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  • Successive nations perchance have drank at, admired, and fathomed it, and passed away, and still its water is green and pellucid as ever.

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  • The aspects which stand out most prominently in this history are: (a) The vacillation of successive governments due to the conflicting policies adopted from time to time to protect the telegraph revenues of the Post Office and to avoid the suppression of an enterprise which was becoming a public necessity and yielding substantial royalties to the PostmasterGeneral.

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  • phellogen is replaced by successive new phellogenic layers of de~per and deeper origin, each forming its own layer of cork.

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  • I have in my mind's eye the western, indented with deep bays, the bolder northern, and the beautifully scalloped southern shore, where successive capes overlap each other and suggest unexplored coves between.

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  • The older, which extends to 150 B.C., set forth, in bald, unattractive language, without any pretensions to style, but with a certain amount of trustworthiness, the most important events of each successive year.

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  • Analysts declared each successive generation might be "the first to have a lower standard of living than their parents."

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  • 9) by a rich and well-watered plain, from which it rises in successive terraces of fertile soil to a height of 400 or 500 ft.

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  • Thus for a dash the interval between the positive and the negative current is equal to the time the paper takes to travel over twice the space between two successive holes.

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  • If the coenosteum of Millepora be broken across, each pore-canal (perhaps better termed a polypcanal) is seen to be interrupted by a series of transverse partitions, representing successive periods of growth with separation from the underlying dead portions.

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  • The complex system of dead and dying tissues cut off by these successive periderms, together with the latter themselves in fact, everything outside the innermost phellogen, constitutes what is often known botanically as the bark of the tree.

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  • His great work appeared in successive parts - e.g.

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  • - At least four periods in the history of the dialect can be distinguished in the records we have left to us, by the help of the successive changes (a) in alphabet and (b) in language, which the Tables exhibit.

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  • His eldest son Alexander, who succeeded him in 1 454, was provost of Edinburgh in 1 455, 1 457 and 1469; he was knighted and held various important court offices under successive monarchs; at the time of his death in 1473 he was master of the household to James III.

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  • Thus, if x= horned and y = sheep, then the successive acts of election represented by x and y, if performed on unity, give the whole of the class horned sheep. Boole showed that elective symbols of this kind obey the same primary laws of combination as algebraical symbols, whence it followed that they could be added, subtracted, multiplied and even divided, almost exactly in the same manner as numbers.

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  • A and A' carry two light vertical rods S, M, the one as much in front of the other as there is space between two successive holes in the perforated ribbon.

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  • The suggestion of Bourseul and the experiments of Reis are founded on the idea that a succession of currents, corresponding in number to the successive undulations of the pressure on the membrane of the transmitting instrument, could reproduce at the receiving station sounds of the same character as those produced at the sending station.

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  • The great beauty and fertility of the country, as well as the charm of its climate, undoubtedly attracted, even in early ages, successive swarms of invaders from the north, who sometimes drove out the previous occupants of the most favored districts, at others reduced them to a state of serfdom, or settled down in the midst of them, until the two races gradually coalesced.

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  • With the surrounding district, known as the barony of Sorau, it became the seat of successive noble families; and in 1400 it was united with the barony of Triebel.

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  • During summer there may be eight or nine successive generations when conditions are favourable and food abundant.

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  • The progress of the archbishop's opinion towards that middle Protestantism, if it may be so called, which he did so much to impress on the formularies of the Church of England, was gradual, as a brief enumeration of the successive steps in that progress will show.

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  • The outer membranes are spread out between two or more successive bronchial semi-rings, a distance from the trachea which is, in typical cases, devoid of sounding membranes; some Cuculi, Caprimulgi, and some owls.

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  • Who would not be early to rise, and rise earlier and earlier every successive day of his life, till he became unspeakably healthy, wealthy, and wise?

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  • With this or a mixture of horse-dung, loam, old mushroom-bed dung, and half-decayed leaves, the beds are built up in successive layers of about 3 in.

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  • By kunde, by permission of Julius successive adjustments of this kind Springer, Berlin.

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  • With Descartes the use of exponents as now employed for denoting the powers of a quantity becomes systematic; and without some such step by which the homogeneity of successive powers is at once recognized, the binomial theorem could scarcely have been detected.

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  • There are also several Albanian settlements in European Turkey and Asia Minor, some founded by military colonists who received grants of land from successive sultans, others owing their origin to enforced migrations after insurrections in Albania.

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  • In 1882-1884 three successive annual exhibits of a National Mining and Industrial Exposition were held.

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  • During the next two or three years public attention was occupied with Captain King's maritime explorations of the north-west coast in three successive voyages, and by explorations of Western Australia in 1821.

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  • After the fall of Rome it suffered attacks and devastations from the successive masters of Italy, until it was finally taken by the Neapolitans in 1299.

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  • It is probable that Leibnitz's notion of time and space, which approaches Kant's theory, led him to attach but little importance to the successive order of the world.

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  • The latter are often swollen at the ends, so that the cross-wall separating two successive cells has a larger surface than if the cells were of uniform width along their entire length.

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  • There has been in effect a successive shifting of zones of vegetation southwards from the pole.

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  • The economic development of Uruguay was retarded by the corruption of successive governments, by revolutionary outbreaks, by the seizure of farm stock without adequate compensation for the support of military forces, by the consequences of reckless borrowing and over-trading in 1889 and 1890, and also by the transference of commercial undertakings from Montevideo to Buenos Aires between 1890 and 1897.

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  • Some of these words have successive steps of meaning, beginning with what is simple and leading on to what is abstract.

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  • Beyond the introduction of the spider line it is unnecessary to mention the various steps by which the Gascoigne micrometer assumed the modern forms now in use, or to describe in detail the suggestions of Hooke, 4 Wren, Smeaton, Cassini, Bradley, Maskelyne, Herschel, Arago, Pearson, Bessel, Struve, Dawes, &c., or the successive productions of the great artists Ramsden, Troughton, Fraunhofer, Ertel, Simms, Cooke, Grubb, Clarke and Repsold.

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  • As the stele is traced farther upwards it becomes bulkier, as do the successive leaf-bundles which leave it.

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  • Sometimes the activity of the successive cambiums simply results in the formation of concentric rings or arcs of secondary xylem and phloem.

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  • The Arctic-Alpine sub-region consists of races of plants belonging originally to the general flora, and recruited by subsequent additrons, which have been specialized in low stature and great capacity of endurance to survive long dormant periods, sometimes even unbroken in successive years by the transitory activity of the brief summer.

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  • While the tendency is for the living forms to come into harmony with their environment and to approach the state of equilibriumby successive adjustments if the environment should happen to change, it is to be observed that the action of organisms themselves often tends to change their organisms environment.

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  • A remnant of the chorda dorsalis and its sheath persists as the ligamentum suspensorium between the central portions of the successive vertebrae.

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  • From this point backwards the successive abdominal segments, as far as the seventh or eighth, can be readily made out.

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  • Sharp to indicate a stage in the life-history of an insect between two successive castings of the cuticle.

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  • This is followed by a resting (pseudo-pupal) stage, and thisby two successive larval stages like the grub of a chafer.

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  • The Russian plains have been, however, the scene of so many migrations of successive races, that at many places a series of deposits belonging to widely distant epochs are found one upon another.

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  • Collisions, on the other hand, are preventable, and derailments nearly so, and the records of deaths and injuries in this class in successive years are therefore justly taken as an index to the efficiency with which the railways are managed.

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  • In France the doctrine of successive reincarnations with intervals of spirit life promulgated by Allan Kardec (L.

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  • The successive explorations of B.

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  • In pursuance of his method of successive studies he began in 1823 the study of Italian literature, passing over German as demanding more labour than he could afford.

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  • For nine centuries Peking, under various names and under the dominion of successive dynasties, has, with some short intervals, remained an imperial city.

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  • Hampshire, Kent, Wiltshire and Dorsetshire formed the successive theatres of what he calls his " bloodless and inglorious campaigns."

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  • Bernoulli, this theory was advanced by the successive labours of John Herapath, J.

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  • Having filled the post of nuncio in England and Spain, he served successive popes as adviser in matters pertaining to heresy and reform.

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  • In spite of this, Aristobulus (56 B.C.) and Alexander (55 B.C.) found loyalists to follow them in their successive raids.

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  • The principal wealth of the island is derived from its olive groves; notwithstanding the destruction of many thousands of trees during each successive insurrection, the production is apparently undiminished, and will probably increase very considerably owing to the planting of young trees and the improved methods of cultivation which the Government is endeavouring to promote.

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  • The successive " Minoan " strata, which go well back into the fourth millennium B.C., reach down to a depth of about 17 ft.

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  • This monumental work seems to date from the close of the Middle Minoan age, but has been re-used for interments at successive periods (Evans, Archaeologic, 1906, p. 136 sqq.).

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  • Up to 1835 he was elected annually by the two houses of the legislature, and no man could serve as governor for more than three years in any six successive years.

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  • Although the establishment of a lucrative trade between India and central Asia had been the dream of many successive Indian viceroys, and much had been done towards improving the approaches to Simla from the north, very little was in really known of the highlands of the Pamirs, or of the regions of the great central depression, before the mission of central Asia.

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  • There were probably two successive Aryan immigrations, and the tradition of a struggle between them may be preserved in the Mahabharata.

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  • It cannot be doubted that the three types of David, represented by the books of Samuel, of Chronicles, and the superscriptions of the Psalms, are irreconcilable, and that they represent successive developments of the original traditions.

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  • This is the typical arrangement, which is exhibited in the majority of the Polychaeta and Oligochaeta; in these the successive chambers of the coelom are separated by the intersegmental septa, sheets of muscle fibres extending from the body wall to the gut and thus forming partitions across the body.

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  • The successive cavities are not, however, completely closed from each other; there is some communication between adjoining segments, and the septa are sometimes deficient here and there.

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  • Bergh (for Lumbricus and Criodrilus), whose figures show a derivation of the entire nephridium from mesoblast, and an absence of any connexion between successive nephridia by any continuous band, epiblastic or mesoblastic. A midway position is taken up by Wilson, who asserts the mesoblastic formation of the funnel, but also asserts the presence of a continuous band of epiblast from which certainly the terminal vesicle of the nephridium, and doubtfully the glandular part of the tube is derived.

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  • This connexion of successive nephridia (in Lanice) has its counterpart in Allolobophora, Lybiodrilus, and apparently in the Lumbriculids Teleuscolex and Styloscolex, among the Oligochaeta.

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  • But by a process of successive and continued artificial cultures under different conditions, the virus of the organism is found to become attenuated; and when this weakened virus is administered, the animal is rendered immune against further attacks.

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  • This conjoint valley of the Rion-Kura was in remote antiquity the site of several Greek colonial settlements, later the seat of successive kingdoms of the Georgians, and for centuries it has formed a bulwark against hostile invasions from the south and east.

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  • The very laws which were made during successive reigns for protecting the tillers of the soil from spoil are the best proofs of the deplorable state of the husbandman."' In the r7th century those laws were made which paved the way for an improved system of agriculture in Scotland.

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  • A more rational system of cropping now began to take the place of the thriftless and barbarous practice of sowing successive crops of corn until the land was utterly exhausted, and then leaving it foul with weeds to recover its power by an indefinite period of rest.

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  • The figure denoting the general average yield per acre of any class of crop needs readjustment after every successive harvest.

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  • The cleaning process is carried on through the next summer by means of successive hoeings of the spring-sown root-crop. As turnips or swedes May occupy the ground till after Christmas little time is left for the preparation of a seed-bed for barley, but as the latter is a shallow-rooted crop only surface-stirring is required.

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  • The Gastropoda are mainly characterized by a loss of symmetry, produced by torsion of the visceral sac. This torsion may be resolved into two successive movements.

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  • The earthworks, of British origin, were modified in almost every successive age.

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  • Armed with this he returns through the successive hells, compelling the disclosure of every secret, depriving the rulers of their power, and barring the doors of the several regions.

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  • This by successive divisions forms a group of four to eight cells, which subsequently pass through the blastoderm, and dividing into two groups become symmetrically arranged and surrounded by the rudiments of the ovarian tubes.

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  • during post-embryonic development - no insect being hatched with the smallest external rudiments of those organs - and on the necessity for successive castings or " moults " (ecdyses) of the cuticle.

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  • The presence of the two successive larval forms in the life-history constitutes what is called hypermetamorphosis.

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  • Successive editions of this work were produced under its author's supervision in 1740, 1748, 1758 and 1766.

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  • The chief merit of the latter work lies in its forty plates, whereon the heads and feet of many birds are indifferently figured .2 But, while the successive editions of Linnaeus's great work were revolutionizing natural history, and his example of precision in language producing excellent effect on scientific writers, several other authors were advancing the study of ornithology in a very different way - a way that pleased the eye even more than his labours were pleasing the mind.

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  • 1 Indeed, the study of this memoir, limited though it be in scope, could not fail to convince any one that it proceeded from the mind of one who taught with the authority derived directly from original knowledge, and not from association with the scribes - a conviction that has become strengthened as, in a series of successive memoirs, the stores of more than twenty years' silent observation and unremitting research were unfolded, and, more than that, the hidden forces of the science of morphology were gradually brought to bear upon almost each subject that came under discussion.

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  • Abich (Sur la structure et la geologic du Daghestan, 1862), the successive folds of Jurassic limestones and slates, all nearly parallel to the Caucasus, which form lofty, narrow plateaus.

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  • We can trace the continuous growth of Venice through the successive styles of Byzantine, Gothic, early Renaissance and late Renaissance architecture.

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  • In spite of the clean culture, good crops of cotton have been grown on some soils in the south for more than forty successive years.

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  • After the seedlings appear, thinning is completed in usually three successive hoeings, the plants being watered after thinning, and subsequently at intervals of from twelve to fifteen days, until about the end of August when picking commences.

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  • had taken Ascalon, which for fifty years had mocked the efforts of successive kings, and by this stroke he might appear to have closed for Nureddin the route to Egypt, and to have opened a path for its conquest by the Franks.

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  • The muscular layers by which the body-wall is constituted have been very differently and to some extent confusingly described by the successive authors on Nemertean anatomy.

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  • In addition to the musculature of the proboscis and proboscidian sheath, longitudinal muscular fibres are found in the walls of the oesophagus, whilst transverse ones are numerous and united into vertical dissepiments between the successive intestinal caeca, thus bringing about a very regular internal metamerization.

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  • The problem of finding a radius vector satisfying this condition is one which can be solved only by successive approximations, or tentatively.

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  • Among the first of these benefactions was the great gymnasium of Ptolemy, built in the neighbourhood of the Agora about 250 B.C. Successive princes of the dynasty of Pergamum interested themselves in the adorn western entrance being the well-known Doric portico of Athena Archegetis with an inscription recording its erection from donations of Julius Caesar and Augustus.

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  • The principal interest of the following centuries lies in the researches of successive travellers, who may be said to have rediscovered the city, and in the fate of its ancient monuments, several of which were still in fair preservation at the beginning of this period.

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  • Eberhard, duke and margrave of Rhaetia and Friuli, arranged the contents of the edict with its successive additamenta into a Concordia de singulis causis (829-832).

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  • He appeared personally before successive legislative committees, and in 1846 published a pamphlet, "The Reorganization of the Judiciary," which had its influence in persuading the New York State Constitutional Convention of that year to report in favour of a codification of the laws.

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  • The higher criticism sees, in these successive enactments of the various codes included in the Pentateuch (q.v.), a development in the character of the festival.

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  • Moreover, while methylamine, dimethylamine, and trimethylamine increase in basicity corresponding to the introduction of successive methyl groups, phenylamine or aniline, diphenylamine, and triphenylamine are in decreasing order of basicity, the salts of diphenylamine being decomposed by water.

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  • Hexachlorethane is trimorphous, forming rhombic, triclinic and cubic crystals; the successive changes occur at about 44° and 71°, and are attended by a decrease in density.

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  • Banda, which forms one of the districts included under the general name of Bundelkhand, has formed an arena of contention for the successive races who have struggled for the sovereignty of India.

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  • Of his many mistresses the one for whom his passion lasted longest was a certain Vannozza (Giovanna) dei Cattani, born in 1442, and wife of three successive husbands.

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  • A matrix of wood or iron is covered with successive layers of papers, pasted together so as to form pasteboard.

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  • The Book of Discipline in its successive printed editions from 1783 to 1906 contains the working rules of the organization, and also a compilation of testimonies borne by the Society at different periods, to important points of Christian truth, and often called forth by the special circumstances of the time.

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  • They are remarkable for the fanaticism displayed in successive attacks upon the Hindus, and they have several times resisted British troops.

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  • in width, interspersed with small chambers, all excavated at successive levels, in the they reach seven storeys), and communicate with one another by stairs cut out of the living rock.

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  • These were successive stages in the geologic process which has created, and is still actively modifying, the state.

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  • Gayarre, coming down to the war, based on deep and scholarly research, and greatly altered in successive editions.

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  • The president of the Republic, who is elected for four years by an electoral college, and cannot hold office for more than two successive terms, has a cabinet whose members he may appoint and remove freely, their number being determined by law.

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  • The policy of successive captains-general was alternately uncompromisingly repressive and conciliatory.

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  • The pentose is then obtained from the acetylated compound by successive treatment with ammonia and dilute acids: CH 2 OH ([[Choh) 3 Choh Ch: Noh -)Ch20h (Choh)3 Choh Cn - Ch 2 Oh (Choh) 3 Cho]].

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  • The disk really consists of a series of successive arcs which increase in size until they burst.

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  • Bosnia was regarded by successive sultans as the Turkish gateway into Hungary; hatred of the Hungarians and their religion was hereditary among the Bogomils.

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  • Promotion was regular, but was obtainable only by entering at an early age one of the medresses or colleges; the student, after passing through the successive degrees of danishmend, mulazim and muderris, became first a molla, then a judge, rising to the higher ranks as fortune and opportunity offered.

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  • q Y imam of Sana, necessitated the despatch of large and costly expeditions to Arabia, in which thousands of Turkish .troops have fallen in guerrilla warfare or through the inhospitable climate; in Albania disturbance became almost endemic, owing to the resistance offered by the intractable population to successive attempts of the central authorities to subject the country to regular taxation and the operation of the laws.

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  • Briefly summarized, the battle came to this - in four successive efforts the Prussians failed because they were locally outnumbered.

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  • Scarcely leaving his troops time to restore their worn-out footgear, or for the cavalry to replace their jaded horses from captured Prussian resources, he set Davout in motion towards Warsaw on the 2nd of November, and the remainder of the army followed in successive echelons as rapidly as they could be despatched.

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  • He himself retreated towards Etoges endeavouring to rally his scattered detachments, but Napoleon was too quick for him and in three successive days he defeated Sacken at Montmirail,York at Champ Aubert and Blucher and his main body at Etoges, pursuing the latter towards Vertus.

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  • All the operations connected with the successive invasion schemes are recorded, with exhaustive quotations of documentary evidence, in Projets et tentatives de debarquement aux Iles Britanniques, by Captain Desbriere (Paris, 1901).

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  • This view claims to determine the respective ages and relative chronological position of the various passages in which the Passover is referred to in the Pentateuch, and assumes that each successive stratum represents the practice in ancient Israel at the time of composition, laying great stress upon omissions as implying non-existence.

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  • And Clement conceived that this development took place not merely in this life, but in the future through successive grades.

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  • Each successive occupant of the Spanish throne has done something, however slight, to the restoration or adornment of Philip's convent-palace, and Ferdinand VII.

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  • For both legislative and administrative purposes the Convention used committees, with powers more or less widely extended and regulated by successive laws.

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  • 17) in which Sir Arthur Wellesley attacked and drove him from two successive positions.

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  • For these reasons he marched by land; and as the roads north of the Tagus were deemed impassable for guns, while transport and supplies for a large force were also difficult to procure, he sent Sir John Hope, with the artillery, cavalry and reserve ammunition column, south of the river, through Badajoz to Almaraz, to move thence through Talavera, Madrid and the Escurial Pass, involving a considerable detour; while he himself with the infantry, marching by successive divisions, took the shorter roads north of the Tagus through Coimbra and Almeida, and also by Alcantara and Coria to Ciudad Rodrigo and Salamanca.

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  • The yield of latex is at first small, but increases with successive tappings, which appear to stimulate the local production of latex, and finally reaches a maximum.

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  • These trenches have for successive geological periods been the drainage valleys of immense lakes (probably also of glaciers) which formerly extended over the plateau or fiords of the seas which surrounded it.

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  • Further, if DA 1 DA 2 denote successive operations of DA 1 and DA2, DX1DA2(x1X2X2...) 2 1 + b l(1) + b (12) + b 2(2) +bi (13) + b 1b2(21) + b 3(3) +...

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  • If the successive weights of the separates w 1, w 2, w 3, ...

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  • 1 1 where laan and di denotes, not s successive operations of d1, but the operator of order s obtained by raising d l to the s th power symbolically as in Taylor's theorem in the Differential Calculus.

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  • di denotes, in fact, an operator of order s, but we may transform the right-hand side so that we are only concerned with the successive performance of linear operations.

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  • 1890, p. 490) that exp(mldl +m2d2+m3d3+...) = exp (Midi +M2d2+M3d3+...), where now the multiplications on the dexter denote successive operations, provided that pp t exp(MiE+M2 2+M3E3+...) +mlH+m2V+m3S3+..., being an undetermined algebraic quantity.

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  • in terms of dl, d 2, d 3, ..., products denoting successive operations, by the same law which expresses the ele mentary function a s in terms of the sums of powers s l, s 2, s3,...

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

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  • d d the last written relation having, in regard to each term on th right-hand side, to do with 17r successive linear operations.

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  • If the worldpowers were hard as flint in their dealings with Israel, the people of God were steeled to such moral endurance that each clash of their successive onsets kindled some new flame of devotion.

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  • It seems probable that the Archant was situated in Spain near Vivien's headquarters at Tortosa, and that Guillaume started from Barcelona, not from Orange, to his nephew's help. The account of the disaster was modified by successive trouveres, and the uncertainty of their methods may be judged by the fact that in the ChanQun de Willame two consecutive accounts (I I.

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  • ' The most remarkable feature of the discussion since 1862 is that the successive examinations of the subject have led to a continually diminishing value, so that at the present time it seems possible that the actual parallax of the sun is almost as near to the old value of Encke as to that which first replaced it.

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  • The older operation of magnetizing a steel bar by drawing a magnetic pole along it merely consists in exposing successive portions of the bar to the action of the strong field near the pole.

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  • The results of an example which they quote in detail may be briefly summarized as follows: - It is remarked by the experimenters that the value of the index e is by no means constant, but changes in correspondence with the successive well-marked stages in the process of magnetization.

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  • Honda subjected tubes of iron, steel and nickel to the simultaneous action of circular and longitudinal fields, and observed the changes of length when one of the fields was varied while the other remained constant at different successive values from zero upwards.

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  • Throughout the 12th and 13th centuries the castle was strengthened and enlarged under successive earls palatine of Pembroke, who made this fortress their chief seat.

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  • A comes was generally raised from childhood in the king's palace, and rose to be a count through successive stages.

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  • It was named Sao Paulo, and has been at once the source whence knowledge and civilization have been diffused through Brazil, and the nucleus of a colony of its manliest and hardiest citizens, which sent out successive swarms of hardy adventurers to people the interior.

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  • The northern provinces had fallen into the power of Holland; the southern, peopled in a great measure by the hardy descendants of the successive colonists who had issued on all sides from the central establishment of Sao Paulo, had learned from their habits of unaided and successful enterprise to court independence.

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  • The area of the city has been enlarged by successive extensions of its municipal boundaries, especially towards the west and south.

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  • Munich, Erlangen, Coire and Leipzig became for brief successive intervals his home.

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  • Laplace published in 1779 the method of generating functions, the foundation of his theory of probabilities, and the first part of his Theorie analytique is devoted to the exposition of its principles, which in their simplest form consist in treating the successive values of any function as the coefficients in the expansion of another function with reference to a different variable.

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  • We must count with something; and the successive somethings obtained by the addition of successive units are in fact numerical quantities, not numbers.

    0
    0
  • By successive stages we obtain (� 18) s5 = 2, X = 12; or we may write at once x = of io= 5 of 10 = 12.

    0
    0
  • (i.) To divide P by Q, we cut off from P successive portions each equal to Q, till we have a piece R left which is less than Q.

    0
    0
  • we cut off from Q successive portions each equal to R.

    0
    0
  • Hence the successive remainders are successively smaller multiples of L, but still integral multiples, so that the series of quotients k, s, t,.

    0
    0
  • Continuing to develop the successive powers of A+a into multinomials, we find that (A+a)3=A3+3A2a+3Aa2+a3, &c.; each power containing one more term than the preceding power, and the coefficients, when the terms are arranged in descending powers of A, being given by the following table I I ' 'I 2 I 1 3 3 I 4 6 4 I 5 IO to 5 I I x 6 15 20 15 6 &c., where the first line stands for (A+a)°=1.

    0
    0
  • A°a°, and the successive numbers in the (n+i)th line are the coefficients of A n a O An-lal ..

    0
    0
  • In practice the successive factorials I !, 2 !, 3!.

    0
    0
  • where x=a/A; thus the successive terms are obtained by successive multiplication.

    0
    0
  • (iii.) The table might be regarded as constructed by successive applications of (9) and (4); the initial data being (r6) and (Io).

    0
    0
  • Constructed in this way, the successive diagonal rows, commencing with the first, give the figurate numbers of the first, second, third,.

    0
    0
  • each number in the table) by a, and for the second series we multiply it by b, and the terms and their successive sums are given for the first series by the first and the second columns, and for the second series by the second and the third columns.

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

    0
    0
  • by successive multiplications by Ada.

    0
    0
  • a series whose successive terms correspond to the numbers I, 2, 3, ...

    0
    0
  • It will be noticed that, although the differences between successive terms of the sequence will ultimately become indefinitely small, there will always be intermediate numbers that do not occur in the sequence.

    0
    0
  • The successive terms of the sequence in that case were formed by successive additions of terms of a series; the series is then also said to converge to the limit which is the limit of the sequence.

    0
    0
  • Another example of a sequence is afforded by the successive convergents to a continued fraction of the form ao+ I I, al+ a2+� where ao,a 1, a 2, ...

    0
    0
  • �; the successive terms of this series, after the first, are alternately positive and negative, and consist of fractions with numerators I and denominators continually increasing.

    0
    0
  • Another kind of sequence is that which is formed by introducing the successive factors of a continued product; e.g.

    0
    0
  • the successive factors on the right-hand side of Wallis's theorem it 2.2 4.4 6.6 2 = 1.3.

    0
    0
  • Clemenceau and Lloyd George found themselves between two irreconcilable standpoints - between Sonnino, who claimed the liberal fulfilment of their treaty pledges, with the addition of the port of Fiume, and President Wilson, 'who refused all cognizance of the secret treaties and regarded them as expressly abrogated by the Allies when they accepted his successive notes as the basis of the Armistice.

    0
    0
  • The most ready means of noting the progress of zoology during the 16th, 17th and 18th centuries is to compare the Aristotle's classificatory conceptions of successive naturalists classifi- with those which are to be found in the works of cation.

    0
    0
  • The assumption made was that (with the rare exception of parasites) all the change of structure through which the successive generations of animals have passed has been one of progressive elaboration.

    0
    0
  • Thus the occurrence of blind animals in caves and in the deep sea was a fact which Darwin himself regarded as best explained by the atrophy of the organ of vision in successive generations through the absence of light and 1 Weismann, Vererbung, &c. (1886).

    0
    0
  • consequent disuse, and the transmission (as Lamarck would have supposed) of a more and more weakened and structurally impaired eye to the offspring in successive generations, until the eye finally disappeared.

    0
    0
  • If a character of much longer standing (certain properties of height, length, breadth, colour, &c.) had not become fixed and congenital after many thousands of successive generations of individuals had developed it in response to environment, but gave place to a new character when new moulding conditions operated on an individual (Lamarck's first law), why should we suppose that the new character is likely to become fixed and transmitted by mere heredity after a much shorter time of existence in response to environmental stimulus ?

    0
    0
  • At first sight it appears difficult to understand how g PP the complicated series of actions which are definitely exhibited as so-called " instincts " by a variety of animals can have been due to the selection of congenital variations, or can be otherwise explained than by the transmission of habits acquired by the parent as the result of experience, and continuously elaborated and added to in successive generations.

    0
    0
  • This factor is the Record of the Past, which grows and develops by laws other than those affecting the perishable bodies of successive generations of mankind, and exerts an incomparable influence upon the educable brain, so that man, by the interaction of the Record and his educability, is removed to a large extent from the status of the organic world and placed in a new and unique position, subject to new laws and new methods of development unlike those by which the rest of the living world is governed.

    0
    0
  • All that it is necessary to assume is that the effects of the successive zones gradually diminish, whether from the increasing obliquity of the secondary ray or because (on account of the limitation of the region of integration) the zones become at last more and more incomplete.

    0
    0
  • 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.

    0
    0
  • Substituting this, we find cot y = U-y, whence 5 7 y U(1+/-1-2:-+2...) - y3 -15-315' This equation is to be solved by successive approximation.

    0
    0
  • Since the maxima occur when u = (m +1)7r it nearly, the successive values are not very different from 4 4 4 &c The application of these results to (3) shows that the field is brightest at the centre =o, =0, viz.

    0
    0
  • For the osculating circle at any point includes the whole of the y curve which lies beyond; and the successive convolutions envelop one another without intersection.

    0
    0
  • Such objects might be imitated in other materials and by successive copying lose their identity, or their first meaning might be otherwise forgotten, and they would ultimately exercise a purely decorative function.

    0
    0
  • Successive civil wars prevented their recovery, and these great plains which ought to be one of the chief sources of meat supply for the world are comparatively destitute of stock, and the only source of revenue from this industry is the small number of animals shipped to the West Indies.

    0
    0
  • He evaded the clause in the constitution prohibiting the election of a president for successive terms of office by invariably arranging for the nomination of some adherent of his own as chief of the executive, and then pulling the strings behind this figurehead.

    0
    0
  • There was to be no taking up of successive positions in accordance with the normal practice of rearguard actions.

    0
    0
  • Then the troops along the front were quietly withdrawn in successive groups, the fine weather continuing to the end and work at the beaches proceeding without a hitch.

    0
    0
  • The work of removing stores, war material, animals and personnel was to be carried out on successive nights, the fighting force ashore was to be gradually reduced, the front line of trenches was to be held up till the very last - the final night being fixed provisionally for the 8th-9th - and the detachments vacating it were to hurry straight off to the beaches.

    0
    0
  • Successive flexures or ridges are ranged in more or less parallel lines, and from between the bands of hard, unyielding rock of older formation the soft beds of recent shale have been washed out, to he carried through the enclosing ridges by rifts which break across their axes.

    0
    0
  • Commodore Sir Home Popham persuaded Sir David to lend him troops for an expedition against Buenos Aires; the successive failures of operations against this place involved the recall of Baird, though on his return home he was quickly re-employed as a divisional general in the Copenhagen expedition of 1807.

    0
    0
  • The word is applied to any group of one hundred, and more particularly to a period of a hundred years, and to the successive periods of a hundred years, dating before or after the birth of Christ.

    0
    0
  • The Assyrian forces became a standing army, which, by successive improvements and careful discipline, was moulded into an irresistible fighting machine, and Assyrian policy was directed towards the definite object of reducing the whole civilized world into a single empire and thereby throwing its trade and wealth into Assyrian hands.

    0
    0
  • Successive improvements were introduced into it by the kings of the second Assyrian empire; chariots were superseded by cavalry; Tiglath-pileser III.

    0
    0
  • Beginning in the bosom of prophecy, and steadily differentiating itself from it in its successive developments, it never came to stand in absolute contrast to it.

    0
    0
  • - xc.) interprets the 70 years of Jeremiah as the 70 successive reigns of the 70 angelic patrons of the nations, which are to come to a close in his own generation.

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    0
  • Other charters were granted to it by successive lords of Glamorgan in 1290, 1340, 1 359, 1 397, 1421 and 1423.

    0
    0
  • Its successive occupants, from the emperor Charles V.

    0
    0
  • In the south of Spain, in some favoured spots where sugar-canes can be grown, they are submitted even to four successive crushings.

    0
    0
  • The earliest writers upon cholera emphasized its remarkable preference for particular places; and the history of each successive epidemic implies, besides an importation of the contagion, certain local conditions which may be either general sanitary defects or peculiarities of climate and soil.

    0
    0
  • A fresh charge is then put in at once, the muffles being cleared only after three successive distillations.

    0
    0
  • Borchers, trace it to the presence of oxide, produced, for example, either by the use of a solution containing a trace of basic salt of zinc (to prevent which the bath should be kept just - almost imperceptibly - acid), or by the presence of a more electro-negative metal, which, being co-deposited, sets up local action at the expense of the zinc. Many processes have been patented, the ore being acted upon by acid, and the resulting solution treated, by either chemical or electrolytic means, for the successive removal of the other heavy metals.

    0
    0
  • He unsuccessfully contested York in 1859, but was elected for Southwark in 1860, and from 1861 to 1866 was under-secretary for foreign affairs in the successive administrations of Lord Palmerston and Lord John Russell.

    0
    0
  • The periods are externally indicated by the successive names by which the chosen people were called - Hebrews, Israelites, Jews.

    0
    0
  • On the decline of the Roman empire Vindobona became the prey of successive barbarian invaders.

    0
    0
  • The combined effect of these successive blows, aggravated by the long period of decentralizing policy from Taaffe to Badeni, is still felt in the Kaiserstadt.

    0
    0
  • As the meteors have been numerously visible in five or six successive years it follows they must be pretty densely distributed along a considerable arc of their orbit.

    0
    0
  • The contest was long and doubtful, but the Russians gradually drove back Legrand and a part of Davout's corps; numerous attacks both of infantry and cavalry were made, and by the successive arrival of reinforcements each side in turn received fresh impetus.

    0
    0
  • The number of cercariae produced by the pullulating rediae in a single water-snail is immense, and as they are emitted at a given period or a few successive periods, the snail at these times appears enclosed in a cloud of whitish flocculent matter.

    0
    0
  • The height of the mountain varies from time to time within limits of several hundred feet, according to the effects of successive eruptions, but averages about 4000 ft.

    0
    0
  • The facts of history must be explained, not by providential interventions, but by referring them to conditions inherent in the successive stages of social existence.

    0
    0
  • The poet subsequently told Mr Edmund Gosse that his father would not let him leave Somersby till, on successive days, he had recited from memory the whole of the odes of Horace.

    0
    0
  • Though he took a part in the work of the reconquest, this king is chiefly remembered by the difficulties into which his successive marriages led him with the pope.

    0
    0
  • A wonderfully accurate register, or successive superposition of each block, is got mainly by the skill of the printer, who is assisted only by a mark defining one corner and another mark showing the opposite side limit.

    0
    0
  • The next few years saw the introduction, under successive ministries, of Liberal reforms in the constitution, in criminal and civil law, and in education.

    0
    0
  • Before the fall this influx was free and unhindered, and the conjunction of man with God and the creation complete, but from that time the connexion was interrupted and God had to interpose by successive dispensations.

    0
    0
  • Amyot's book, therefore, obtained an immense popularity, and exercised great influence over successive generations of French writers.

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    0
  • Among the contributors in successive years were Canning, Scott (who reviewed himself), Robert Southey, 1 Archibald Bower (1686-1766) was educated at Douai, and became a Jesuit.

    0
    0
  • On the whole, the Hebrew statement of the successive stages of creation corresponds so nearly to that in the Babylonian epic that we are bound to assume that one has been influenced by the other.

    0
    0
  • The idealizing poetry of passion, which found a genuine voice in Catullus and the elegiac poets, could not prolong itself through the exhausting licence of successive generations.

    0
    0
  • Salvius Julianus was entrusted by Hadrian with the task of reducing into shape the immense mass of law which had grown up in the edicts of successive praetors - thus taking the first step towards a code.

    0
    0
  • The enthusiasm of the allies (numbering about seventy) waned rapidly before the financial exigencies of successive campaigns, and it is abundantly clear that Thebes had no interest save the extension of her power in Boeotia.

    0
    0
  • Such legends often arise to connect towns bearing identical or similar names (such as are common in Greece) and to justify political events or ambitions by legendary precedents; and this certainly happened during the successive political rivalries of Dorian Sparta with non-Dorian Athens and Thebes.

    0
    0
  • The site of the temple itself carries the remains of successive structures.

    0
    0
  • Let us then suppose that a conductor originally at zero potential has its potential raised by administering to it small successive doses of electricity dq.

    0
    0
  • Here we have a series of celebrations representing the occupations of the successive seasons, addressed sometimes to numina who developed later on into the great gods of the state, such as Jupiter, Mars or Ceres, sometimes to vaguer divinities who remained always indefinite and rustic in character, such as Pales and Consus.

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    0
  • The consequence was the introduction of certain new deities, the di novensides, from external sources, and the birth of new conceptions of the gods and their worship. We may distinguish three main influences, to a certain extent historically successive.

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    0
  • The intermediate rice plains, known as the Mogholbandi, from their having been regularly settled by the Mahommedans, have yielded to the successive dynasties and conquerors of Orissa almost the whole of the revenues derived from the province.

    0
    0
  • Meanwhile Baldwin repelled in successive years the attacks of the Egyptians (1102, 1103, 1105), and in the latter years of his reign (1115-1118) he even pushed southward at the expense of Egypt, penetrating as far as the Red Sea, and planting an outpost at Monreal.

    0
    0
  • For most of the period in question Thucydides is the only source; and despite the inherent merits of a great writer, it can hardly be doubted that the tribute of almost unqualified praise that successive generations of scholars have paid to Thucydides must have been in some measure qualified if, for example, a Spartan account of the Peloponnesian War had been preserved to us.

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    0
  • of the canal the Germans had as successive defensive positions the Marquion trench line, running from Oisy by Marquion to the main Hindenburg line near Graincourt; the Marcoing line, covering Cambrai at a distance of some two miles from its outskirts; and the Scheldt canal, from the Sensee at Estrun by the western suburbs of the city to Marcoing, Creveceeur and the south.

    0
    0
  • Up to this line four successive objectives were assigned; from there onwards the second phase of the advance was to carry the assailants to the line of the Scheldt canal and the Sensee.

    0
    0
  • The image is formed by 674° s°° successive total reflection at the surfaces b c and a b.

    0
    0
  • By successive trials two beads, of known density, say di, d 2, are obtained, one of which floats above, and the other below, the test crystal; the distances separating the beads from the crystal are determined by means of a scale placed behind the tube.

    0
    0
  • which successive generations are produced Highly magnified.

    0
    0
  • It is the first example in Italian literature of a national biography, the first attempt in any literature to trace the vicissitudes of a people's life in their logical sequence, deducing each successive phase from passions or necessities inherent in preceding circumstances, reasoning upon them from general principles, and inferring corollaries for the conduct of the future.

    0
    0
  • 54 shows the record of several successive paintings on the same scale as that given by the micrometer.

    0
    0
  • Others, like the Ascension of Isaiah, betray the handiwork of successive editors, and are accordingly to be explained on the "redaction hypothesis."

    0
    0
  • The work underwent three later redactions at the hands of successive editors in the reigns of Trajan and Hadrian.

    0
    0
  • This theory holds that no progress is designed in the successive visions of the seven seals, the seven trumpets and the seven bowls; for that in the vision of the seals we have already an account of the last judgment (vi.

    0
    0
  • The yellow solution is made up of i part of neutral potassium chromate in 199 parts of water, and to give the various degrees of the scale, 1, 2, 3, 4, &c.,% of the yellow solution is mixed with 99, 9 8, 97, 96, &c.,% of the blue in successive tubes.

    0
    0
  • prevail right northwards across the equator into the Bay of Biscay, showing a steady rise of bottom temperature as successive submarine elevations restrict communication with 'the Antarctic. On the other hand, in the more open Argentine Basin, which carries deep water far to the south, the bottom temperature in 40° S.

    0
    0
  • His own experiences in the Reichstag, and the close contact with the political parties which his advocacy of successive naval bills had involved, made him a master of political intrigue.

    0
    0
  • The mycelium produced from the spores dropped by the fungus or from the "spawn" in the soil, radiates outwards, and each year's successive crop of fungi rises from the new growth round the circle.

    0
    0
  • Chaeroneia is also notable as the birthplace of Plutarch, who returned to his native town in old age, and was held in honour by its citizens for many successive generations.

    0
    0
  • The Protectorate, as declared in 1884, with its seat of government at Port Moresby, was subsidized by the three Australian colonies of Queensland, New South Wales and Victoria, and lasted, under the administration of two successive special commissioners (Major-General Sir Peter Scratchley and the Hon.

    0
    0
  • The district subsequently suffered under the successive invasions of Huns, Varangians (who captured the chief town Barda in the 10th century) and Mongols.

    0
    0
  • This post he occupied for three successive sessions, during which he continued writing for the Westminster, and also in 1842 helped Mill with the revision of the MS. of his System of Logic. In 1843 he contributed the first review of the book to the London and Westminster.

    0
    0
  • Further privileges were granted by successive kings, and a charter was finally given by Charles I.

    0
    0
  • Population.-The population of the state in 1910 was 3,366,416, the increases in successive decades after 1790 being respectively 11 6, 11 6, 10.9, 16.6, 20.9, 34.8, 23.8, 18.4, 22.4, 2 5.6, 25.3 and 20%.

    0
    0
  • Harris has said that " The history of education since the time of Horace Mann is very largely an account of the successive modifications introduced into elementary schools through the direct or indirect influence of the normal school."

    0
    0
  • He made three investigations of the case in the three successive months, and brought it to trial in the fourth month.

    0
    0
  • During many successive years he saw a great deal of hard service, and so constantly had he to contend, on his various expeditions, with adverse gales and dangerous storms, that he was nicknamed by the sailors, "Foul-weather Jack."

    0
    0
  • Between 1586 and 1603 Sir Walter made successive efforts to settle a colony in the wide territory called Virginia, in honour of Queen Elizabeth, a name of much wider significance then than in later days.

    0
    0
  • At court, though no trifler or flatterer, he was a favourite counsellor in three successive reigns, but he never meddled much in civil or temporal affairs.

    0
    0
  • beautiful old age in his Concord home, the Orchard House,where every comfort was provided by his daughter Louisa, Alcott was gratified at being able to become the nominal, and at times the actual, head of a Concord "Summer School of Philosophy and Literature," which had its first session in 1879, and in which - in a rudely fashioned building next his house - thoughtful listeners were addressed during a part of several successive summer seasons on many themes in philosophy, religion and letters.

    0
    0
  • Outwardly they are Mussulmans of the Shiah branch, but most of them show little veneration for either Prophet or Koran, and the religion of some of them seems to be a mixture of Ali-Illahism involving a belief in successive incarnations combined with mysterious, ancient, heathen rites.

    0
    0
  • Pushing on through the night, they drove the French out of seven successive bivouacs and at length drove them over the Sambre.

    0
    0
  • On this occasion he delivered two speeches on successive days, one in favour of justice, the other against it.

    0
    0
  • The standard set up by eminent statisticians, therefore, may be taken to represent an ideal, not likely to be attained anywhere under present conditions, but towards which each successive census may be expected to advance.

    0
    0
  • The rate of increase during the decade ending in 1900 was even less than that for the preceding decade; and it is impossible that a falling off so marked could in two successive enumerations be the result of sheer inaccuracy.

    0
    0
  • The distance between two points can, at any rate in theory, be measured directly, by successive applications of the unit of measurement.

    0
    0
  • But an area or a volume cannot generally be measured by successive applications of the unit of area or volume; intermediate processes are necessary, the result of which is expressed by a formula.

    0
    0
  • made up of a number of successive elements, so that the analytical treatment involves the ideas and the methods of the infinitesimal calculus.

    0
    0
  • denote the values for x = xim ' of the successive differential coefficients of u with regard to x; the series continuing until the differential coefficients vanish.

    0
    0
  • Writing m = 2p, and grouping the coefficients of the successive differences, we shall find area = 2ph up+ 2 652up + 3 p4365p2 84up 3p,6 - 21p4 28p2 15120 If u is of degree 2f or 2f + i in x, we require to go up to b 2f u p, so that m must be not less than 2f.

    0
    0
  • The volume of the briquette for which u is a function of x and y is found by the operation of double integration, consisting of two successive operations, one being with regard to x, and the other with regard to y; and these operations may (in the cases with which we are concerned) be performed in either order.

    0
    0
  • The first, which is the best known but is of limited application, consists in replacing each successive portion of the figure by another figure whose ordinate is an algebraical function of x or of x and y, and expressing the area or volume of this latter figure (exactly or approximately) in terms of the given ordinates.

    0
    0
  • The justification of the above methods lies in certain properties of the series of successive differences of u.

    0
    0
  • (iii) Different formulae have to be adopted for different values of m; the method is therefore unsuitable for the construction of a table giving successive values of the area up to successive ordinates.

    0
    0
  • (iv) In order to find what formula may be applied, it is necessary to take the successive differences of u; and it is then just as easy, in most cases, to use a formula which directly involves these differences and therefore shows the degree of accuracy of the approximation.

    0
    0
  • In cases other than those described in § 82, the pth moment with regard to the axis of u is given by Pp = XPrA where A is the total area of the original trapezette, and S 2 _ 1 is the area of a trapezette whose ordinates at successive distances h, beginning and ending with the bounding ordinates, are o, x1P -1A, x2 P-1 (AI+AI),.

    0
    0
  • The calculation of the expressions in brackets may be simplified by taking the pairs in terms from the outside; by finding the successive differences of uo + um, ill + um_l, ..., or of uI u i +umi, ..

    0
    0
  • i g h oo hsuvii where T is the area of a trapezette whose ordinates at successive distances h are o, Ali' (x i), (Al +A4), g 5' (x2), (Az +A 2 + ...

    0
    0
  • Thus, to construct a table of values of f x udx by intervals of h in x, we first form a table of values of hu for the intermediate values of x, from this obtain a table of values of 62 - -) hu for these values of x, and then construct the table of f x udx by successive additions.

    0
    0
  • The blanks are placed in the slide J and the lowest one is carried forward to the die in two successive movements of the " layer-on " K, a rod working backwards and forwards on a horizontal plate and actuating the finger L, fig.

    0
    0
  • Tompkins served as governor by successive re-elections until 1817, his term covering the trying period of the second war with Great Britain.

    0
    0
  • Polynesian canoe-men had reached its northern shores in successive voyages.

    0
    0
  • The desire of New Zealanders to strike a blow for the mother-country took the practical shape of despatching to South Africa ten successive contingents.

    0
    0
  • The two great political issues of the time were the secularization of the clergy reserves in Ontario, and the abolition of seigniorial tenure in Quebec. Both of these reforms Macdonald long opposed, but when successive elections had proved that they were sup ported by public opinion, he brought about a coalition of Conservatives and moderate reformers for the purpose of carrying them.

    0
    0
  • the upper part, moving faster, gains on the lower, and the front tends to swing round as shown by the successive positions in.

    0
    0
  • Consequently a wave front such as b 1 tends to turn upwards, as shown in the successive positions b 2, 3 and 4.

    0
    0
  • Since the velocity increases as we go upwards the front tends to swing round and travel downwards, as shown in the successive positions a I, 2, 3 and 4, in fig.

    0
    0
  • Then the front tends to swing round and travel upwards as shown in the successive positions b I, 2, 3, and 4, in fig.

    0
    0
  • In the scale of C the intervals from the key-note, the frequency ratios with the key-note, the successive frequency ratios and the successive intervals are as follows: - If we pass through two intervals in succession, as, for instance, if we ascend through a fourth from C to F and then through a third from F to A, the frequency ratio of A to C is a, which is the product of the ratios for a fourth 4, and a third I That is, if we add intervals we must multiply frequency ratios to obtain the frequency ratio for the interval which is the sum of the two.

    0
    0
  • Taking the successive key-notes D, A, E, B, it is found that besides small and negligible differences, each introduces a new sharp, and so we get the five sharps, C, D, F, G, A, represented nearly by the black keys.

    0
    0
  • The successive terms of (21) are called the harmonics of the first term.

    0
    0
  • According to Helmholtz, the ear probably contains within it a series of resonators, with small intervals between the periods of the successive members, while the series extends over the whole range of audible pitch.

    0
    0
  • The ordinate of the curve changes sign as we pass through a node, so that successive sections are moving always in opposite directions and have opposite displacements.

    0
    0
  • The tangent to the displacement curve is always parallel to the axis, that is, for a small distance the successive particles are always equally displaced, and therefore always occupy the same volume.

    0
    0
  • We may illustrate the successive modes of vibration by using as pipe a tall cylindrical jar, and as exciter a vibrating tuning-fork held over the mouth.

    0
    0
  • If L is the distance between successive dust-heaps, i.e.

    0
    0
  • Thus, an interval of one-third of a second elapses between two successive maxima or beats, and there are produced three beats per second.

    0
    0
  • The harshness of deep notes on instruments rich in overtones may be explained as arising from beats between successive overtones.

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  • Thus, if a note of frequency 64 is sounded, and if all the successive overtones are present, the difference of frequency will be 64, and this is an unpleasant interval when we get to the middle of the scale, say to overtones 256 and 320 or to 512 and 576.

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  • But inasmuch as the successive orders are proportional to A X 2 A 3, or µµ 2 µ 3, and X and µ are small, they are of rapidly decreasing importance, and it is not certain that any beyond those in equation (35) correspond to our actual sensations.

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  • He was thus frequently straitened, and, as his necessities pressed, he sold successive interests in his newspaper.

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  • It rose in a time of great political excitement to a total circulation of a quarter of a million, and it sometimes had for successive years 140,000 to 150,000.

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  • Under Britishrule Colombo has shared in the prosperity brought to the island by the successive industri e s of coffee and teaplanting.

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  • The general distribution of the Russian forces was now as follows: The main army under Kuropatkin was forming, by successive brigades, in two groups - I.

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  • In his successive offices Mr Roosevelt not merely exerted a strong influence upon the immediate community, whose official representative he was at the time being, but by reason both of his forceful personality and of the often unconventional, although always effective, methods of work which he employed he achieved a national prominence out of ordinary proportion to the importance of his official position.

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  • The island was in the possession of successive religious bodies from the Conquest (when it was given to the Benedictines of Jumieges, near Rouen), until the Dissolution.

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  • Produced by long-continued subaerial decay and erosion, in later Cretaceous times this lowland extended from the Atlantic Ocean well toward the interior of North America; since then the whole continent has been generally elevated, and by successive steps the Appalachian belt has been raised to form a wide but relatively low arch.

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  • In the autumn of 1898 he became the leader of the obstructionists or "Independence Party," against the successive Szell, Khuen-Hadervary, Szapary and Stephen Tisza administrations (1898-1904), exercising great influence not only in parliament but upon the public at large through his articles in the Egyetertes.

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  • JOHN CHARLES HERRIES (1778-1855), English politician, son of a London merchant, began his career as a junior clerk in the treasury, and became known for his financial abilities as private secretary to successive ministers.

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  • The twelvefold division of the zodiac was evidently suggested by the occurrence of twelve full moons in successive parts of it in the course of each year.

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  • The successive entries of the moon and planets into the nakshatras (the ascertainment of which was of great astrological importance) were fixed by means of their conjunctions with the yogataras.

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  • Though his sentences themselves are not wordy, he is extremely diffuse in treatment, habitually repeating an idea in successive sentences of much the same import.

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  • Here is supposed to have been the northern frontier of the ancient Chola kingdom, the successive capitals of which were Uriyur on the Cauvery, Combaconum and Tanjore.

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  • But as each successive range, proceeding south, represents a higher step in the terraced ascent from the desert of Gobi to the plateau of Tibet, the ranges when viewed from the north frequently appear like veritable upstanding mountain ranges, and this appearance is accentuated by the general steepness of the ascent; whereas, when viewed on the other hand from the south, these several ranges, owing to their long and gentle slope in that direction, have the appearance of comparatively gentle swellings of the earth's service rather than of well-defined mountain ranges.

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  • Jean Baptiste's brother, Jacques-Marie, Vicomte Cavaignac (1773-1855), French general, served with distinction in the army under the republic and successive governments.

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  • This Land Act was to be carried out in a series of successive periods, during the first of which only estates over 5,000 hectares (12,350 ac.) would be affected.

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  • His last years were devoted to researches into the history of science, resulting in the successive publication of: Histoire de l'astronomie ancienne (2 vols., 1817); Histoire de l'astronomie au moyen age (1819); Histoire de l'astronomie moderne (2 vols., 1821); and Histoire de l'astronomie au XVIII' sieele, issued in 5827 under the care of C. L.

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  • Successive governments in France made endeavours to break with the prohibitive system, but naturally met with strong opposition from the manufacturing interests, not prepared to meet the competition of Great Britain, whose industries had made, and were continually making, rapid strides.

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  • The third and fourth books, like the larger part of the second, treat of ethics; the third, of virtues and vices, in pairs; the fourth, of more general ethical and political subjects, frequently citing extracts to illustrate the pros and cons of a question in two successive chapters.

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  • A, B, C, three successive stages.

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  • he owed his cardinal's hat; but the steady favour which he enjoyed under successive popes was due to his own cleverness and capacity for affairs.

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  • The Schoolmen devoted most of their attention to Aristotle, and we may here briefly note the successive stages in their gradually increasing knowledge of his works.

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  • The method gives all the partitions of a number, but we may consider different classes of partitions: the partitions into a given number of parts, or into not more than a given number of parts; or the partitions into given parts, either with repetitions or without repetitions, &c. It is possible, for any particular class of partitions, to obtain methods more or less easy for the formation of the partitions either of a given number or of the successive numbers 1, 2, 3, &c. And of course in any case, having obtained the partitions, we can count them and so obtain the number of partitions.

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  • As against the civilian enemy the navy strangled commerce; its military preponderance nipped in the bud every successive attempt of the Confederates to create a fleet (for each new vessel as it emerged from the estuary or harbour in which it had been built, was destroyed or driven back), while at any given point a secure base was available for the far-ranging operations of the Union armies.

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  • A war of manoeuvre followed, each side being reduced in turn by successive detachments sent to aid Rosecrans and Bragg in the struggle for Tennessee.

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  • records, which set before us the successive stages in the history of revelation.

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  • It represents three successive stages in the history of the collection.

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  • When the need began to be felt events were probably at first dated by the regnal years of kings; the reigns of successive kings were then arranged in order, and grouped, if necessary, in dynasties, and thus a fixed standard was gradually constructed.

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  • In the following parts of this article the chronological character of each successive period of the Old Testament history will be considered and explained as far as the limits of space at the writer's disposal permit.

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  • the corresponding dates in the contemporary reigns in the other kingdom were derived, it is practically certain, by computation from the lengths of the successive reigns.

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

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  • And there is no need at all to suppose that all the incidents which the historian masses under his account of Felix were successive: events in Emesa, Chalcis, Caesarea and Jerusalem may easily have been synchronous.

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  • In the ensuing account a constant repetition of the names of the main archipelagoes will be found; it may of course be assumed that each successive voyager added something to the knowledge of them, but on the other hand, as has been said, islands were often rediscovered and renamed in cases where later voyagers took no account of the work of their predecessors, or where the earlier voyagers were unable clearly to define the positions of their discoveries.

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  • 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.

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  • Kentucky is governed under a constitution adopted in 1891.3 A convention to revise the constitution or to draft a new one meets on the call of two successive legislatures, ratified by a majority of the popular vote, provided that majority be at least one-fourth of the total number of votes cast at the preceding general election.

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  • Lieutenant-governor Beckham, elected in 1900 to fill out the unexpired term of Governor Goebel (assassinated in 1900), was re-elected in 1903, the leading lawyers of the state holding that the constitutional inhibition on successive terms did not apply in such a case.

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  • The resolutions further declare that " this Commonwealth is determined, as it doubts not its co-states are, tamely to submit to undelegated and therefore unlimited powers in no man or body of men on earth," and that " these and successive acts of the same character, unless arrested on the threshold, may tend to drive these states into revolution and blood."

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  • "By a prophet Yahweh brought Israel out of Egypt, and by a prophet" in each successive age Israel had been watched over and preserved.

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  • His possessions had been enlarged by four successive marriages, particularly by that which he contracted in 1221 with Margaret, the sister of Alexander II.

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  • It is indeed an image and reflection of the first Being; but the further the line of successive projections is prolonged the smaller is its share in the true existence.

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  • Even those who do not fall into the error of making Smith the creator of the science, often separate him too broadly from Quesnay and his followers, and represent the history of modern economics as consisting of the successive rise and reign of three doctrines - the mercantile, the physiocratic and the Smithian.

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  • The longest and most elaborate of these occupies the third book; it is an account of the course followed by the nations of modern Europe in the successive development of the several forms of industry.

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  • The work went through several editions during the 18th century, and was at length superseded in 1785 by Hutton's tables, which continued in successive editions to maintain their position for a century.

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  • Successive observers in Italy, notably Fracastoro (1483-1553), Fabio Colonna (1567-1640 or 1650) and Nicolaus Steno (1638 - c. 1687), a Danish anatomist, professor in Padua, advanced the still embryonic science and set forth the principle of comparison of fossil with living forms. Near the end of the 17th century Martin Lister (1638-1712), examining the Mesozoic shell types of England, recognized the great similarity as well as the differences between these and modern species, and insisted on the need of close comparison of fossil and living shells, yet he clung to the old view that fossils were sports of nature.

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  • Abraham Gottlob Werner (1750-1817), the famous exponent of the aqueous theory of earth formation, observed in successive geological formations the gradual approach to the forms of existing species.

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  • In Cuvier's defence Charles Deperet maintains that the extreme theory of successive extinctions followed by a succession of creations is attributable to Cuvier's followers rather than to the master himself.

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  • It was Alcide Dessalines d'Orbigny (1802-1857) who pushed to an extreme Cuvier's ideas of the fixity of species and of successive extinctions, and finally developed the wild hypothesis of twenty-seven distinct creations.

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  • Successive discoveries gradually revealed the world of extinct Reptilia; in 1821 Charles Konig (1784-1851), the first keeper of the mineralogical collection in the British Museum, described Ichthyosaurus from the Jurassic; in the same year William Daniel Conybeare (1787-1857) described Plesiosaurus; and a year later (1822) Mosasaurus; in 1824 William Buckland described the great carnivorous dinosaur Megalosaurus; while Gideon Algernon Mantell (1790--1852) in 1848 announced the discovery of Iguanodon.

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  • The greatest generalization of this second period, however, was that partly prepared for by d'Orbigny, as will be more fully explained later in this article, and clearly expressed by Agassiz - namely, the law of repetition of ancestral stages of life in the course of the successive stages of individual development.

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  • Hyatt went further and demonstrated that ancestral characters are passed through by successive descendants at a more and more accelerated rate in each generation, thus giving time for the appearance of new characters in the adult.

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  • He discovered the actual transmutations in direct genetic series of species on the successive deposition levels of the old lake basin.

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  • Hyatt, in a re-examination of the Steinheim deposits, proved that successive modifications occur at the same level as well as in vertical succession.

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  • He proposed the term " mutations " for the minute progressive changes of single characters in definite directions as observed in successive stratigraphic levels.

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  • More recent analysis has shown, however, that certain modifications observed within the same stratigraphic level are really grades of mutations which show divergences comparable to those found in successive levels.

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  • Melchior Neumayr, the great Austrian palaeontologist, especially extended the philosophic foundations of modern invertebrate palaeontology, and traced a number of continuous genetic series (formenreihe) in successive horizons.

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  • - It is obvious that the Linnaean binomial terminology and its subsequent trinomial refinement for species, sub-species, and varieties was adapted to express the differences between animals as they exist to-day, distributed contemporaneously over the surface of the earth, and that it is wholly inadapted to express either the minute gradations of successive generic series or the branchings of a genetically connected chain of life.

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  • In tracing the phylogeny, or ancestral history of organs, palaeontology affords the only absolute criterion on the successive evolution of organs in time as well as of (progressive) evolution in form.

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  • Successive discoveries have revealed certain grand centres, such as (1) the marsupial radiation of Australia, (2) the littleknown Cretaceous radiation of placental mammals in the northern hemisphere, which was probably connected in part with the peopling of South America, (3) the Tertiary placental radiation in the northern hemisphere, partly connected with Africa, (4) the main Tertiary radiation in South America.

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  • The Mongolian peoples not only count their lunar months by these signs, but they reckon the successive days by them, rat-day, bull-day, tiger-day, &c., and also, by combining the twelve signs in rotation with the elements, they obtain a means of marking each year in the sixty-year cycle, as the woodrat year, the fire-tiger year, &c. This method is highly artificial, and the reappearance of its principle in the Mexican and Central American calendar is suggestive of importation from Asia.

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  • They were pyramids on a square or oblong base, rising in successive terraces to a small summit-platform.

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  • It was in all probability the original from which all the above-mentioned Old English glosses were derived, though in several instances changes and modifications were introduced by successive scribes.

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  • The order of the successive colours in all colourless transparent media is red, orange, yellow, green, blue, indigo and violet.

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  • P. Leroux discovered that iodine vapour refracted the red rays more than the violet, the intermediate colours not being transmitted; and in 1870 Christiansen found that an alcoholic solution of fuchsine refracted the violet less than the red, the order of the successive colours being violet, red, orange, yellow; the green being absorbed and a dark interval occurring between the violet and red.

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  • His philosophical writings are the successive ma-iifestations of a restless highly endowed spirit, striving unsuccessfully after a solution of its own problems. Such unity as they possess is a unity of tendency and endeavour; in some respects the final form they assumed is the least satisfactory.

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  • The theoretical side of inner nature in its successive grades from sensation to the highest form of spirit, the abstracting reason which emphasizes the difference of subjective and objective, leaves an unsolved problem which receives satisfaction only in the practical, the individualizing activity.

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  • of two successive rajas of Lahore, the conqueror assumed the right of nominating the governors of the Punjab as a dependency of Ghazni, a right which continued to be exercised by seven of his successors.

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  • (2) During the second period the successive interventions of France, Spain and Holland extended the naval war till it ranged from the West Indies to the Bay of Bengal.

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  • He recovered from small-pox in his fourth year with crippled hands and eyesight permanently impaired; and a constitution enfeebled by premature birth had to withstand successive shocks of severe illness.

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  • The two chief sites to be cleared were the temples of Apollo and of Aphrodite, in both of which successive buildings of various date were found.

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  • The complexity of the glacial period and its subdivision into several glacial epochs, separated by interglacial epochs of considerable length (certainly longer than the postglacial epoch) has a structural consequence in the superposition of successive till sheets, alternating with non-glacial deposits, and also a physiographic consequence in the very different amount of normal postglacial erosion suffered by the different parts of the glacial deposits.

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  • Successive channels are found at lower and lower levels on the plateau slope, thus indicating the successive courses taken by the lake outlet as the ice melted farther and farther back.

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  • The absolute excess of males rn the aggregate population has been progressively greater at every successive census since 1820, save that of 1870Which followed the Civil War, and closed a decade of lessened immigration.

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  • This latter became of increasing moment in the successive periods of European colonial wars of the 18th century.

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  • At the conclusion of peace the debt had risen to 63 millions, near which point it remained until about 1852, from which time successive reductions brought it down to 28 millions in 1857.

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  • The latter, as we know, calculated the perimeters of successive polygons, passing from one polygon to another of double the number of sides; in a similar manner Gregory calculated the areas.

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  • The river systems are therefore in many cases complex and tortuous, and very often the successive connecting links between the lakes receive different names.

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  • The rocks underlying it have been subjected to successive foldings and crumplings by forces acting chiefly from the direction of the Atlantic Ocean, with alternating prolonged periods of waste and denudation.

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  • G.) employed in the interests of successive fur-trading g colony.

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  • above the timber-bearing soil along the banks, and all along the lower river the country is liable to overflow; and as the land backward from the stream slopes downward from the banks heaped up by successive flood-deposits, each overflow creates along the river a fringe of swamps.

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  • The kaleidophone, intended to present visibly the movements of a sonorous body, consisted of a vibrating wire or rod carrying a silvered bead reflecting a point of light, the motions of which, by persistence of the successive images on the retina, were thus represented in curves of light.

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  • The four orders now retained exhibit successive stages in the modification of the ctenidia by reflection and concrescence of the filament, but other organs, such as the heart, adductors, renal organs, may not show corresponding stages.

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  • This deterioration increases with the number of successive copyings.

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  • The Third 3 3, Gives Eight Intercalations In Thirty Three Years Or, Seven Successive Intercalations At The End Of Four Years Respectively, And The Eighth At The End Of Five Years.

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  • As The Number Of Days In The Week And The Number In The Year Are Prime To One Another, Two Successive Years Cannot Begin With The Same Day; For If A Common Year Begins, For Example, With Sunday, The Following Year Will Begin With Monday, And If A Leap Year Begins With Sunday, The Year Following Will Begin With Tuesday.

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  • To Compute The Times Of The New Moons Which Determine The Commencement Of Successive Years, It Must Be Observed That In Passing From An Ordinary Year The New Moon Of The Following Year Is Deduced By Subtracting The Interval That Twelve Lunations Fall Short Of The Corresponding Gregorian Year Of 365 Or 366 Days; And That, In Passing From An Embolismic Year, It Is To Be Found By Adding The Excess Of Thirteen Lunations Over The Gregorian Year.

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  • Hence, Knowing Which Of The Years Are Embolismic, From Their Ordinal Position In The Cycle, According To The Rule Before Stated, The Times Of The Commencement Of Successive Years May Be Thus Carried On Indefinitely Without Any Difficulty.

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  • After The Dates Of Commencement Of The Successive Hebrew Years Are Finally Adjusted, Conformably With The Foregoing Directions, An Estimation Of The Consecutive Intervals, By Taking The Differences, Will Show The Duration And Character Of The Years That Respectively Intervene.

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  • The Moslem Calendar May Evidently Be Carried On Indefinitely By Successive Addition, Observing Only To Allow For The Additional Day That Occurs In The Bissextile And Intercalary Years; But For Any Remote Date The Computation According To The Preceding Rules Will Be Most Efficient, And Such Computation May Be Usefully Employed As A Check On The Accuracy Of Any Considerable Extension Of The Calendar By Induction Alone.

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  • He served throughout the war, distinguished himself particularly at South Mountain, Winchester, Fisher's Hill and Cedar Creek, and by successive promotions became a brigadier-general of volunteers and, by brevet, a major-general of volunteers.

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  • are usually deep and narrow, but in the Coastal Plain they are broad and in most cases rise in three successive terraces above the stream.

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  • Three successive subsequent editions had the benefit of extensive revision by the author; a fifth edition in to vols.

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  • Suppose the successive divisions of the scale to be numbered o, I, 2 ...

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  • Also W = (V +IA)w i; or w1=W/(V+/A), w p =W/(V+plA), and wn =W/(Vd-nIA), or the densities of the several liquids vary inversely as the respective volumes of the instrument immersed in them; and, since the divisions of the scale correspond to equal increments of volume immersed, it follows that the densities of the several liquids in which the instrument sinks to the successive divisions form a harmonic series.

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  • If we wish the successive divisions of the scale to correspond to equal increments in the density of the corresponding liquids, then the volumes of the instrument, measured up to the successive divisions of the scale, must form a series in harmonical progression, the lengths of the divisions increasing as we go up the stem.

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  • The weights were adjusted for successive intervals of 5° F., but for degrees intermediate between these no additional correction was applied.

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  • In the centesimal hydrometer of Francceur the volume of the stem between successive divisions of the scale is always, oath of the whole volume immersed when the instrument floats in water at 4° C. In order to graduate the stem the instrument is first weighed, then immersed in distilled water at 4° C., and the line of flotation 7.1 F marked zero.

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  • The addition to the top of the stem of successive weights, each th of the weight of the instrument itself, serves to determine the successive degrees.

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  • In the above table for Sikes's hydrometer two densities are given corresponding to each of the degrees 20, 30, 40, 50, 60, 70, 80 and 90, indicating that the successive weights belonging to the particular instrument for which the table has been calculated do not quite agree.

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  • All petitions for divorce must be approved by two successive juries, and a woman holds in her own name all property acquired before and after marriage.

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  • The Know-Nothing party was nearly destroyed by its crushing defeat in 1856 and in the next year the Democrats by a large majority elected for governor Joseph Emerson Brown (1821-1894), who by three successive re-elections was continued in that office until the close of the Civil War.

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  • From the Julian Alps, which traverse the province in the north, the country descends in successive terraces towards the sea, and may roughly be divided into the upper highlands, the lower highlands, the hilly district and the lowlands.

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  • As thus purified by successive advances of embryological research, the Mollusca were reduced to the Cuvierian classes of Cephalopoda, Pteropoda, Gastropoda and Acephala.

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  • The zone of the external surface of the mantle within the edge secretes a layer formed of prisms of calcite; the rest of the epithelium from this zone to the apex secretes the inner layer of the shell, composed of successive laminae; this is the nacreous layer, and in certain species has a commercial value as nacre or mother-of-pearl.

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  • When the segmentation is unequal one of the megameres gives rise by successive divisions to two primary mesoderm cells called mesomeres; these divide to form two masses of cells called mesoblastic bands.

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  • This intermediary they called " the perfect Shi`ite," and his prototype is to be found in the four successive Babs or " gates " through whom alone the twelfth Imam, during the period of his " minor occultation " (Ghaybat-i-sughra, A.D.

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  • Owing to the timely submission of the monks to the Turks after the capture of Salonica (1430), their privileges were respected by successive sultans: a tribute is paid to the Turkish government, which is represented by a resident kaimakam, and the community is allowed to maintain a small police force.

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  • was carried off from Rome in 1809, Cappellari withdrew to Murano, near Venice, and in 1814, with some other members of his order, he removed to Padua; but soon after the restoration of the pope he was recalled to Rome, where he received successive appointments as vicar-general of the Camaldoli, councillor of the Inquisition, prefect of the Propaganda, and Pxaminer of bishops.

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  • Thus he came to the conclusion that the malady had been inherent in many successive generations of the silkworm, and that the epidemic condition was only an exaggeration of a normal state brought about by the method of cultivation and production of graine pursued.

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  • The course of his opinions and his practice is fully explained in successive letters in Fors.

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  • Let somehow or other retardations be introduced so that the optical length of the successive parts increases by the same quantity nX, n being some number and X the wave-length.

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  • Deslandres,s who found that the successive differences in the frequencies formed an arithmetical progression.

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  • The careful measurements of Kayser and Runge of the carbon bands show that the successive differences in the frequencies do (1900), I, p. 399.

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  • It was found that during the successive electrical oscillations the metallic lines can be observed to stretch farther and farther away from the poles, thus giving a measure of the gradual diffusion of the metal.

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