Variations sentence example

variations
  • Numerous variations and modifications of these forms exist.
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  • Variations include roasted red peppers, dill and oregano.
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  • Numerous attempts have been made to find periodic variations in thunderstorm frequency.
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  • We find the ultimate explanation of this in the facts that all organisms vary, and that their variations are inherited and, if useful, perpetuated.
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  • I don't know why I am the way I am.  I don't even know much of the Immortal Code, just the few key parts Andre used to lecture me about.  Loyalty to my brothers, my mate, the Immortals, humanity.  Respect for Death and her domain.  Other variations of those.
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  • Moreover, we have good reasons for inferring that different constellations of external causes may determine whether the internal physiological disturbances induced by a given agent shall lead to pathological and dangerous variations, or to changes which may be harmless or even advantageous to the plant concerned.
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  • External tympaniform membranes exist, with great variations, between the specialized one or two last tracheal and some of the first bronchial rings.
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  • Variations in the structure and forms of leaves and leafstalks are produced by the increased development of cellular tissue, by the abortion or degeneration of parts, by the multiplication or repetition of parts and by adhesion.
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  • The climate of Manitoba, being that of a region of wide extent and of similar conditions, is not subject to frequent variations.
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  • The introduction of inductance coils into such circuits renders them more susceptible to trouble from atmospheric electricity and more sensitive to leakage variations.
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  • Th internal anatomy of the Hydromedusae shows numerous variations.
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  • This sketch of an enormous subject shuws us that the pathology of plants is a special department of the study of variations which threaten injury to the plant, and passes imperceptibly into the study of variations in general.
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  • This so-called direct effect of external conditions upon the form and structure of the body differs from the indirect effect in that the resulting variations bear a relation, of the nature of adaptation, to those conditions; the effect of the conditions is not only to cause variation, but to cause variation in a particular direction.
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  • Thus it is that the variations are produced upon which natural selection has to work.
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  • Structural complexity is brought about by the superposition of new variations on preceding ones.
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  • He formed a comprehensive theory of the variations of climate with latitude and season, and was convinced of the necessity of a circulation of water between the sea and rivers, though, like Plato, he held that this took place by water rising from the sea through crevices in the rocks, losing it .s dissolved salts in the process.
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  • The Hyoid apparatus is, in its detail, subject to many variations in accord with the very diverse uses to which the tongue of birds is III.
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  • Individual, specific and generic variations are frequent.
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  • It is, however, fair to state that his system was not built entirely upon these muscular variations, but rather upon a more laborious combination of anatomical characters, which were so selected that they presumably could not stand in direct correlation with each other, notably the oil-gland, caeca, carotids, nasal bones and above all, the muscles of the thigh.
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  • Amongst the most important of his works not already mentioned may be named the following: - Mathematical Tracts (1826) on the Lunar Theory, Figure of the Earth, Precession and Nutation, and Calculus of Variations, to which, in the second edition of 1828, were added tracts on the Planetary Theory and the Undulatory Theory of Light; Experiments on Iron-built Ships, instituted for the purpose of discovering a correction for the deviation of the Compass produced by the Iron of the Ships (1839); On the Theoretical Explanation of an apparent new Polarity in Light (1840); Tides and Waves (1842).
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  • He thinks that the variations in the inscriptions of the fifth treatise, which is not found in the best manuscript, are so great that the name of Boetius could not have originally been in the title.
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  • This latter work included the differential and integral calculus, the calculus of variations, the theory of attractions, and analytical mechanics.
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  • At intermediate stations the roofs are often carried on brackets fixed to the walls of the station buildings, and project only to the edge of the platforms. At larger stations where both the platforms and the tracks are covered in, there are two broad types of construction, with many intermediate variations: the roof may either be comparatively low, of the " ridge and furrow " pattern, borne on a number of rows of pillars, or it may consist of a single lofty span extending clear across the area from the side walls.
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  • The cost of the Metropolitan and Metropolitan District railways of London varied greatly on account of the variations in construction.
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  • The history in Kings was not finally settled until a very late date, as is evident from the important variations in the Septuagint, and it is especially in the description of the time of Solomon and the disruption that there continued to be considerable fluctuations.'
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  • The variations of temperature are very great in Siberia, amounting near the coast to more than 100° Fahr., between the mean of the hottest and coldest months, and to still more between the extreme temperatures of those months.
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  • The flora of the whole of northern Asia is in essentials the same as that of northern Europe, the differences being due rather to variations of species than of genera.
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  • This history, as we now have it, is extracted from various sources of unequal value, which are fitted together in a way which offers considerable difficulties to the critic. In the history of David's early adventures, for example, the narrative is not seldom disordered, and sometimes seems to repeat itself with puzzling variations of detail, which have led critics to the unanimous conclusion that the First Book of Samuel is drawn from at least two sources.
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  • The roadstead is very shallow, and exposed to winds which cause great variations in the height of the water; it is, moreover, rapidly silting up. At the quay the depth of water is only 8 to 9 feet, and large ships have to lie 5 to 13 miles from the town.
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  • The rotations extending to five, six, seven or more years are, in most cases, only adaptations of the principle to variations of soil, altitude, aspect, climate, markets and other local conditions.
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  • (6) That the local variations of wages and prices were what we should call excessive, so that the standard of comfort in one district was very different from that of others.
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  • In other Pectinibranchia (and such variations are representative for all Mollusca, and not characteristic only of Pectinibranchia) we find that there is a very unequal division of the egg-cell at the commencement of embryonic development, as in Nassa.
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  • Some form their diblastula by emboly, others by epiboly; and in the later history of the further development of the enclosed cells (archenteron) very marked variations occur in closely-allied forms, due to the influence of a greater or less abundance of food-material mixed with the protoplasm of the egg.
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  • Its variations may be due equally to natural denudation of a stratum once of uniform depth, or to the artificial heaping up of a mound by later builders.
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  • Among all the species (188, he tells us, in number) of which he examined specimens, he found only four variations in the structure of that vessel, namely: I.
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  • The same variations are observable in the second or middle series, but its side-pieces are said to exist in all groups of birds without exception.
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  • These laws, as formulated by him, are that (1) there is a coincidence of form of the anterior palatal and of the cranium in birds of the same order; (2) there is a likeness between the anterior palatal bones in birds of the same order; (3) there are relations of likeness 1 The title of the English translation is Johannes Muller on Certain Variations in the Vocal Organs of the Passeres that have hitherto escaped notice.
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  • Sudden variations in the amount of water supplied are injurious: a sandy soil cannot retain water; on the other hand a clay soil often maintains too great a supply, and rank growth with excess of foliage ensues.
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  • The variations of the gaps between " spot " and " present month futures " are somewhat mysterious, a matter to which we shall recur.
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  • Some spinners cover their yarn contracts merely by buying " futures," but the cover thus provided is frequently most inadequate owing to variations in the " points on or off" for the particular cotton that they want.
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  • On the one hand, it is argued that speculators are affected only by the absolute variations in price, while on the other hand it is contended that a movement of one " point," say, is less influential when the price is about 8d.
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  • (3) Desirable variations in the raw material might conceivably eventuate from the introduction of cotton to spots in the globe where its growth was previously unknown or little regarded.
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  • It has been found that variations in barometric pressure affect the flash-point and accordingly corrections have to be made in obtaining strictly comparative results at different pressures.
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  • Almost without exception potash soaps, even if made from the solid fatty acids, are " soft," and soda soaps, although made with fluid olein, are " hard "; but there are considerable variations according to the prevailing fatty acid in the compound.
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  • Of course there were numerous variations and refinements.
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  • 2 Accordingly, the baals are not to be regarded necessarily as local variations of one and the same god, like the many Virgins or Madonnas of Catholic lands, but as distinct numina.
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  • The existence, therefore, of much variation in the practice of the festival in historic times is scarcely proved by the seeming variations of the enactments concerning it in the Pentateuch.
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  • This formula, notwithstanding many attempts at both disproving and modifying it, has well stood the test of time; the subject has been the basis of constant discussion, many variations have been proposed, but the original conception of Kekule remains quite as convenient as any of the newer forms, especially when considering the syntheses and decompositions of the benzene complex.
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  • 4 is a more recent form, of which special variations have been FIG.
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  • In general, polysymmetric and polymorphous modifications suffer transformation when submitted to variations in either temperature or pressure, or both.
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  • More useful is the property of isomorphous substances of forming mixed crystals, which are strictly isomorphous with their constituents, for all variations in composition.
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  • The days are usually hot and the nights cold, the variations in temperature being a fruitful cause of bronchial and pulmonary diseases.
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  • The variations which have been perpetuated and intensified by artificial selection are, with the exception of those of the dog, greater than have been induced in any other mammal.
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  • It is not improbable that all dogs sprang from one common source, but climate, food and cross-breeding caused variations of form which suggested particular uses, and these being either designedly or accidentally perpetuated, the various breeds of dogs arose, and became numerous in proportion to the progress of civilization.
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  • A couple of the many passages in which the variations in a and /3 are due to variations in H a and HR will now be given.
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  • To the above we have a good parallel in the Book of Daniel; for the variations of its two chief Greek Versions - that of the Septuagint and of Theodotion - go back to variations in the Semitic.
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  • - Sinker, Testamenta XII Patriarcharum (1869); [this work gives b in the text and a in the footnotes; subsequently (1879) Sinker issued an Appendix with variations from cg]; Charles, The Greek Versions of the Testaments of the XII.
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  • Revelations concerning the last things and the future lot, whether bliss or woe, of human souls, promises for true believers, threatenings for misbelievers, his firm confidence as to the future triumph of the good - such are the themes continually dwelt on with endless variations.
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  • Finally, we have the family Rhinocerotidae, which includes the existing representatives of the group. In this family the dentition has undergone considerable reduction, and may be represented inclusive of all the variations, by the formula i a or a m a The first upper incisor, whenpresent, has an 430r2; PP antero-posteriorly elongated crown, but the second is small; when fully developed, the lower canine is a large forwardly directed tusk-like tooth with sharp cutting-edges, and biting against the first upper incisor.
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  • It is noteworthy, however, that although the manner in which the prey is stung (for example) is on the whole similar in the case of the members of any given species - that is to say, all the wasps of the species behave in very much the same manner - yet there are minor variations in detail.
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  • Do they originate through the natural selection of those variations which are the more adaptive; or do they originate through the inheritance of those acquired modifications which are impressed on the nervous system in the course of individual and intelligent use ?
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  • The variations are only trivial.
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  • For the subjects of this heading see the articles DIFFERENTIAL EQUATIONS; FOURIER'S SERIES; CONTINUED FRACTIONS; FUNCTION; FUNCTION OF REAL VARIABLES; FUNCTION COMPLEX; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; MAXIMA AND MINIMA; SERIES; SPHERICAL HARMONICS; TRIGONOMETRY; VARIATIONS, CALCULUS OF.
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  • Rigorous and rainy in the south-east, the climate elsewhere is milder though subject to sudden variations.
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  • All ocean currents vary from year to year in their strength of flow and the main interest of physical oceanography in recent years has been the tracing-out of these variations and the search for the causes.
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  • The variations themselves are detected by the method of seasonally repeated hydrographic soundings.
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  • The connexion that seemed to be first established was between variations in the quantity of water transported from the tropical to the sub-polar Atlantic and variations in the intensit y of solar radiation.
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  • It was difficult to be sure as to the variations in the actual number of fish caught, but it was easy to show that there was a real variability in the yield of cod-liver oil (an important product of the fishery).
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  • Helland-Hansen and Nansen showed later that it was improbable that variations in the northerly drift of Atlantic water could be traced directly to variations in the quantity of heat received by the sea from solar radiation.
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  • Given, then, that the variations in tide-generating force are big enough, the periods when the maxima occur will be critical with regard to oceanographical and meteorological phenomena.
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  • Many economic changes probably occurred in consequence of the variations in tide-generating force, as, for instance, the decline in the mediaeval Baltic herring fisheries controlled by the Hanseatic League.
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  • It must be remembered, however, that variations in conditions modify the electromotive force required for any given process.
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  • Various attempts have been made to explain the variations in composition of the micas.
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  • The shell is likewise most beautiful in its endless shapes and variations.
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  • The variations in the story of the defeat of Aliscans or the Archant, and the numerous inconsistencies of the narratives even when considered separately have occupied many critics.
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  • He invented magnets that could withstand the effects of percussion and ordinary temperature variations.
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  • 29 shows the variations of resistance in relation to temperature for fields of different constant values.
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  • At the age of nineteen he communicated to Leonhard Euler his idea of a general method of dealing with "isoperimetrical" problems, known later as the Calculus of Variations.
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  • He is thus justly regarded as the inventor of the "method of variations" - a name supplied by Euler in 1766.
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  • 2 From the fundamental principle of virtual velocities, which thus acquired a new significance, Lagrange deduced, with the aid of the calculus of variations, the whole system of mechanical truths, by processes so elegant, lucid and harmonious as to constitute, in Sir William Hamilton's words, "a kind of scientific poem."
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  • The calculus of variations lay undeveloped in Euler's mode of treating isoperimetrical problems. The fruitful method, again, of the variation of elements was introduced by Euler, but adopted and perfected by Lagrange, who first recognized its supreme importance to the analytical investigation of the planetary movements.
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  • He had not attempted to include in his calculations the orbital variations of the disturbing bodies; but Lagrange, by the happy artifice of transferring the origin of coordinates from the centre of the sun to the centre of gravity of the sun and planets, obtained a simplification of the formulae, by which the same analysis was rendered equally applicable to each of the planets severally.
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  • The calculus of variations is indissolubly associated with his name.
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  • He investigated also the variations of temperature in the atmosphere and ocean.
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  • His published works include: Etudes geologiques sur les Iles de Tenerife et de Fogo (1848); Voyage geologique aux Antilles et aux Iles de TeneAife et de Fogo (1848-1859); Recherches sur les principaux phenomz nes de meteorologie et de physique generale aux Antilles (1849); Sur les variations periodiques de la temperature (1866), and Coup d'cell historique sur la geologie (1878).
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  • The more northern rivers are subject to periodical variations in volume caused by wet and dry seasons, but the greater distance of the coast range and the more gradual breaking down of the plateau toward the sea, give them longer courses and a greater extent of navigable water.
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  • Extreme variations in temperature are often produced by cold south-west storms from the Argentine pampas, which sweep across southern Brazil as far north as Cape Frio, the fall in temperature sometimes being 22° to 27°.
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  • The style is simple or branched, and the stigma is linear, capitate or globose in form; these variations afford means for distinguishing the different genera.
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  • Bodin showed a more rational appreciation than many of his contemporaries of the causes of this revolution, and the relation of the variations in money to the market values of wares in general as well as to the wages of labour.
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  • The area of biological knowledge which Darwin was the first to subject to scientific method and to render, as it were, contributory to the great stream formed by the union of the various branches, is that which relates to the breeding of animals and plants, their congenital variations, and the transmission and perpetuation of those variations.
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  • As the breeder selects a congenital variation which suits his requirements, and by breeding from the animals (or plants) exhibiting that variation obtains a new breed specially characterized by that variation, so in nature is there a selection amongst all the congenital variations of each generation of a species.
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  • Such " correlated variations " may attain to great size and complexity without being of use.
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  • Thus in many cases the difficulty of supposing that selection has acted on minute and imperceptible initial variations, so small as to have no selective value, may be got rid of.
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  • All organisms are essentially and necessarily built up by such correlated variations.
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  • The adherence to type, the favourite conception of the transcendental morphologist, was seen to be nothing more than the expression of one of the laws of thremmatology, the persistence of hereditary transmission of ancestral characters, even when they have ceased to be significant or valuable in the struggle for existence, whilst the so-called evidences of design which was supposed to modify the limitations of types assigned to Himself by the Creator were seen to be adaptations due to the selection and intensification by selective breeding of fortuitous congenital variations, which happened to prove more useful than the many thousand other variations which did not survive in the struggle for existence.
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  • Cuvier's morphological doctikne received its fullest development in the principle of the " correlation of parts," which he applied to palaeontological investigation, namely, that every animal is a definite whole, and that no part can be varied without entailing correlated and law-abiding variations in other parts, so that from a fragment it should be possible, had we a full knowledge of the laws of animal structure or morphology, to reconstruct the whole.
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  • Contemporaneous with these were various schemes of classification which were based, not on a consideration of the entire structure of each animal, but on the variations of a single organ, or on the really non-significant fact of the structure of the egg.
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  • It has been maintained that this tendency to a severance of the hybrid stock into its components must favour the persistence of a new character of large volume suddenly appearing in a stock, and the observations of Mendel have been held to favour in this way the views of those who hold that the variations upon which natural selection has acted in the production of new species are not small variations but large and " discontinuous."
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  • It does not, however, appear that " large " variations would thus be favoured any more than small ones, nor that the eliminating action of natural selection upon an unfavourable variation' could be checked.
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  • By some writers the word " mutation " is applied only to large and suddenly appearing variations which are found to be capable of hereditary transmission, whilst the term " fluctuation " is applied to small variations whether capable of transmission or not.
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  • By others the word " fluctuation " is apparently applied only to those small " acquired " variations due to the direct action of changes in food, moisture and other features of the environment.
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  • It is no discovery that this latter kind of variation is not hereditable, and it is not the fact that the small variations, to which Darwin attached great but not exclusive importance as the material upon which natural selection operates, are of this latter kind.
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  • The most instructive classification of the " variations " exhibited by fully formed organisms consists in the separation in the first place of those which arise from antecedent congenital, innate, constitutional or germinal variations from those which arise merely from the operation of variation of the environment or the food-supply upon normally constituted individuals.
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  • The former are " innate " variations, the latter are " superimposed " variations (so-called " acquired variations ").
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  • Both innate and superimposed variations are capable of division into those which are more and those which are less obvious to the human eye.
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  • Scarcely perceptible variations of the innate class are regularly and invariably present in every new generation of every species of living thing.
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  • An absolutely imperceptible physiological difference arising as a variation may be of selective value, and it may carry with it correlated variations which appeal to the human eye but are of no selective value themselves.
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  • The analysis of the specific variations of organic form so as to determine what is really the nature and limitation of a single " character " or " individual variation," and whether two such true and strictly defined single variations of a single structural unit can actually " blend " when one is transmitted by the male parent and the other by the female parent, are matters which have yet to be determined.
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  • He pointed to the admitted fact of congenital variation, and he showed that congehital variations are arbitrary and, so to speak, non-significant.
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  • It is held 1 that the Darwinian doctrine of selection of fortuitous congenital variations is sufficient to account for all cases, that the Lamarckian hypothesis of transmission cf acquired characters is not supported by experimental evidence, and that the latter should therefore be dismissed.
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  • But this instance is really fully explained (as the present writer has shown) by the theory of natural selection acting on congenital fortuitous variations.
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  • 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.
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  • It may be worth while to examine further the other variations from correct ruling which correspond to the various terms expressing the deviation of the wave-surface from a perfect plane.
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  • - (A) The oldest version, the LXX., follows a text generally closely corresponding to the Massoretic Hebrew, the main variations being in the titles and in the addition (lacking in some MSS.) of an apocryphal psalm ascribed to David when he fought with Goliath.
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  • It is without a heading, and by its abrupt transitions, and honestly preserved variations of style, invites us to such a theory as we are now indicating.
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  • In reality there were numerous minor variations in the cut and colour of ancient dress even as there are in the present day in or around Palestine.
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  • The Hittite warriors upon north Syrian sculptures (Zenjirli, perhaps ' all to 9th centuries) have a short-sleeved tunic which ends above the knees, and this type of garment recurs over a large area with numerous small variations (with or without girdle, slits at the neck, or bordering).
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  • The constitution of guncotton is a difficult matter to investigate, primarily on account of the very insoluble nature of cellulose itself, and also from the fact that comparatively slight variations in the concentration and temperature of the acids used produce considerable differences in the products.
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  • The healthy bone marrow reacts with remarkable rapidity to the demand for more blood cells which may be required by the organism; its reactions and variations in disease are very striking.
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  • In the treatment of disease, the Hippocratic school attached great importance to diet, the variations necessary in different diseases being minutely defined.
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  • Now the cellular pathology of the blood, investigated by the aid of modern staining methods, is as important as that of the solid organs; no clinical investigator - indeed, apart from research, no practitioner at this day - can dispense with examination of the blood for purposes of diagnosis; its coagulability and the kinds and the variations of the cells it contains being evidence of many def i nitely morbid states of the body.
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  • In heart disease the chief work of the latter half of the 19th century was, in the first quarter, such clinical work as that of William Stokes and Peter Mere Latham (1789-1875); and in the second quarter the fuller comprehension of the vascular system, central and peripheral, with its cycles and variations of blood pressure, venous and arterial.
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  • Notwithstanding the inherent difficulties of construction caused by the great variations in the level of the stream, amounting sometimes to 20 ft.
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  • Even when the outcrop is oxidized, and Surface the mineral character and richness of the deposit is Explora- altered thereby, it is possible to determine variations tion.
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  • If the deposit shows great variations in thickness in its outcrop along the surface it is probable that a drift or a slope would show the same thing in depth.
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  • The variations in engine load are thus reduced, and incidentally hoisting time is saved.
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  • The variations in the degree to which these appear in different passages are in the main to be accounted for by his having before him in many cases documents or oral reports, which he repro duces with only slight alterations in the language, while at other times he is writing freely.
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  • This is probably never completely attained, variations in the sixth significant figure of the refractive index being observed in different parts of single large blocks of the most perfect glass.
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  • While such minute and gradual variations are harmless for most optical purposes, sudden variations which generally take the form of striae or veins are fatal defects in all optical glass.
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  • It has been proved that these variations depend to a great extent on the chemical nature of the glass of which the thermometer is made.
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  • The better course seems to be to explain here the nature of these variations.
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  • The relative inferiority of the wines made at the Cape of Good Hope and in Australia is partly due to variations of climate, the vine not yet having adapted itself to the new conditions, - and partly to the deficient skill of the manufacturers.
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  • To make this apparatus more perfectly automatic, an arrangement for continually adding to and mixing with the juice the proper proportion of milk of lime has been adapted to it; and although it may be objected that once the proportion has been determined no allowance is made for the variation in the quality of the juice coming from the mill owing to the variations that may occur in the canes fed into the mills, it is obviously as easy to vary the proportion with the automatic arrangement from time to time as it is to vary in each separate direction, if the man in charge will take the trouble to do so, which he very seldom does with the ordinary defecators, satisfying himself with testing the juice once or twice in a watch.
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  • In the earliest of them, sacrilege in the narrower sense is not a separate class of crime, but the wider usage goes with variations through the different collections.
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  • Whilst, however, the plant adapts itself to a great variety of climatic conditions and will grow on almost all kinds of soil, the flavour and quality of the produce are profoundly affected by variations in these two factors.
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  • The variations are classified as: (1) Variation in type due to crossing, change of soil and climate, especially, for example, when seed from the tropics is introduced to temperate regions.
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  • (2) Variations within the type, due to natural tendency to vary, local conditions and maturity of seed.
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  • It included the original text and the variations of it dating from the 12th, 13th and 14th centuries.
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  • At that period there was at Rome a demand for copies of, or variations on, noted works of Greek sculpture: the demand was met by the workshops of Pasiteles and his pupils Stephanus and Menelaus and others, several of whose statues are extant.
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  • In the northern desert the temperature is subject to extreme variations.
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  • The whole work seems to have taken its present form (with local variations) about the 13th century.
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  • It can be grown in parks and gardens, and thrives well; but the young plants are unable to bear great variations of temperature.
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  • In the course of his inquiries he also noticed that different bodies in equal masses require different amounts of heat to raise them to the same temperature, and so founded the doctrine of specific heats; he also showed that equal additions or abstractions of heat produced equal variations of bulk in the liquid of his thermometers.
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  • The first volume, Vegetable Staticks (1727), contains an account of numerous experiments in plant-physiology - the loss of water in plants by evaporation, the rate of growth of shoots and leaves, variations in root-force at different times of the day, &c. Considering it very probable that plants draw "through their leaves some part of their nourishment from the air," he undertook experiments to show in "how great a proportion air is wrought into the composition of animal, vegetable and mineral substances"; though this "analysis of the air" did not lead him to any very clear ideas about the composition of the atmosphere, in the course of his inquiries he collected gases over water in vessels separate from those in which they were generated, and thus used what was to all intents and purposes a "pneumatic trough."
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  • On the slopes called Kiyomizu-zaka and Goj-zaka lived a number of ceramists, all following virtually the same models with variations due to individual genius.
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  • He, the satirist of the true-born Englishman, was himself a model, with some notable variations and improvements, of the Englishman of his period.
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  • In his last work he used, with doubtful success, the variations of the penes and the lungs as additional characters, chiefly for the grouping of the great mass of the Colubroid snakes.
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  • If now we wish to represent the variations in some property, such as fusibility, we determine the freezing-points of a number of alloys distributed fairly uniformly over the area of the triangle, and, at each point corresponding to an alloy, we erect an ordinate at right angles to the plane of the paper and proportional in length to the freezing temperature of that alloy.
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  • There are very considerable differences between the values assigned by different observers, sometimes no doubt due to differences in method, but in most cases unquestionably depending on variations in the quality of the specimens examined.
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  • Built on open undulating ground, the town is, however, subject to frequent dust storms and to considerable variations in the temperature.
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  • This is mathematically expressed by the statement that dE is an exact differential of a function of the co-ordinates defining the state of the body, which can be integrated between limits without reference to the relation representing the path along which the variations are taken.
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  • He remarks that ” the law according to which the motive power of heat varies at different points of the thermometric scale is intimately connected with that of the variations of the specific heats of gases at different temperatures - a law which experiment has not yet made known to us with sufficient exactness."
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  • The energy E and the total heat F are functions of the temperature only, by equations (9) and (I I), and their variations take the form dE = sdO, d F = Sd0.
    0
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  • Putting d0/dp=A/0 2 in equation (15), and integrating on the assumption that the small variations of S could be neglected over the range of the experiment, they found a solution of the type, v/0 =f(p) - SA /30 3, in which f(p) is an arbitrary function of p. Assuming that the gas should approximate indefinitely to the ideal state pv = R0 at high temperatures, they put f(p)=Rip, which gives a characteristic equation of the form v= Re/p - SA /30 2 .
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  • Many variations of the electrolytic process as above outlined have been suggested.
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  • In the 6th century we find creed forms in use in Gaul which include them, but include also other variations distinguishing them from the form which we seek.
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  • His ethical system was reproduced, though in a more precise and philosophical form, by Hutcheson, and from him descended, with certain variations, to Hume and Adam Smith.
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  • Besides these variations in the number of ridges or plates of which each tooth is composed, the thickness of the enamel varies so much as to have given rise to a distinction between a " thick-plated " and a " thin-plated " variety - the latter being most prevalent among specimens from the Arctic regions.
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  • The slight variations in specific gravity are due to the presence of small amounts of arsenic, sulphur or tellurium, or to enclosed impurities.
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  • Many variations of this apparatus are in use; in one of the commonest there are two cylindrical chambers, joined at the bottom, and each provided at the top with fine tubes bent at right angles; sometimes the inlet and outlet tubes are provided with caps.
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  • The differences of the readings of the screw, when converted into arc, afford the means of measuring the variations of the sun's apparent diameter.
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  • As Marcet had foreshadowed from the analysis of 14 samples in 1819, the larger series of exact analyses proved that the variations in the proportion of individual salts to the total salts are very small, and all analyses since Dittmar's have confirmed this result.
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  • The colour of ocean water far from land is an almost pure blue, and all the variations of tint towards green are the result of local disturbances, the usual cause being turbidity of some kind, and this in the high seas is almost always due to swarms of plankton.
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  • Great irregular variations in radiation and convection sometimes produce a remarkably abrupt change of temperature at a certain depth in calm water.
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  • Benjamin Franklin in 1775 and Charles Blagden in 1781, by means of numerous observations of temperature made on board the packets plying on the Atlantic passage, determined the boundaries of these two currents and their seasonal variations with considerable precision.
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  • The general lines of the currents of the oceans are fairly well understood, and along the most frequented ocean routes the larger seasonal variations have also been ascertained.
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  • Dickson and others leave no doubt, for example, that the variations in the intensity of the Gulf Stream, whether these be measured by the change in the strength of the current or in the heat stored in the water, produce great variations in the character of the weather of northern Europe.
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  • The connexion between variations of current strength and the conditions of existence and distribution of plankton are no less important, especially as they act directly or indirectly on the life-conditions of food fishes.
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  • These variations in composition are attended with corresponding differences in qualities, which are distinguished by special names.
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  • Apparatus is added to some dynamometers by means of which a curve showing the variations of P on a distance base is drawn automatically, the area of the diagram representing the work done; with others, integrating apparatus is combined, from which the work done during a given interval may be read off directly.
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  • The heating at the surfaces, the variations in their smoothness, and the variations of the lubrication make continuously variable, and necessitate frequent adjustment of W or of the nuts.
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  • Occupying 135 degrees of latitude, living on the shores of frozen or of tropical waters; at altitudes varying from sea-level to several thousands of feet; in forests, grassy prairies or deserts; here starved, there in plenty; with a night here of six months' duration, there twelve hours long; here among health-giving winds, and there cursed with malaria - this brown man became, in different culture provinces, brunette or black, tall or short, long-headed or short-headed, and developed on his own hemisphere variations from an average type.
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  • The student will find differences among anthropologists in the interpretation of these marks - some averring that comparative anatomy is worthless as a means of subdividing the American subspecies, others that biological variations point to different Old World origins, a third class believing these structural variations to be of the soil.
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  • The yard scales were on detachable strips, so that fresh strips could be inserted for variations in velocity.
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  • Minute variations, however, do occur.
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  • About the 10th century the name was altered into Agenardus, and then to Eginhardus, or Eginhartus, but, although these variations were largely used in the English and French languages, the form Einhardus, or Einhartus, is unquestionably the right one.
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  • Remedies are intended to cover accidental variations from the exact standard and are now generally used only in this way.
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  • This account of the hero's principal labours, exploits and crimes is derived from the mythologists Apollodorus and Diodorus, who probably followed the Heracleia by Peisander of Rhodes as to the twelve labours or that of Panyasis of Halicarnassus, but sundry variations of order and incident are found in classical literature.
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  • However, the climate is so dry in eastern Washington that the " sensible " variations are much less than those recorded by the thermometer.
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  • From subsidiary experiments (for which the original memoir must be consulted) the pressure variations within the resonator could be calculated from the movements of the plate.
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  • There are variations, therefore, at the open end, and these are such that the loop may be regarded as situated a short distance outside the end of the pipe.
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  • The minor variations of Chronicles from the books of Samuel and Kings are analogous in principle to the larger additions and omissions, so that the whole work has a consistent and well-marked character, presenting the history in quite a different perspective from that of the old narrative.
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  • Many parts of the book offer a very hard task to the expositor, especially the genealogies, where to other troubles are added the extreme corruption and many variations of the proper names in the versions; on these see the articles in the Ency.
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  • The determination of the shortest distance between two small circles on a sphere is given in the article Variations, Calculus Of.
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  • Pufendorf, with some variations, states the same theory.
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  • In fact, small differences of composition or variations in thermal treatment during manufacture involve relatively large differences of quality.
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  • Under these ministries came the Statthalter, whose administrative area had ordinarily the proportions of a Crown territory (Kronland); but the immense variations in area of the Crown territories made a uniform and consistent intermediate administrative organization practically impossible.
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  • Owing to the northern latitude, comparatively high altitudes, and the great distance from the ocean, there are great annual variations of temperature and a very small amount of rainfall.
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  • Impressive as is their witness to the persistence of the Apostolic teaching in its essential features, amidst all personal and local variations, perhaps the most striking thing about these writings is the degree in which they fail to appreciate certain elements of the Apostolic teaching as embodied in the New Testament, and those its higher and more distinctively Christian elements.'
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  • The first investigates mathematical facts relating to the earth as a whole, its figure, dimensions, motions, their measurement, &c. The second part considers the earth as affected by the sun and stars, climates, seasons, the difference of apparent time at different places, variations in the length of the day, &c. The third part treats briefly of the actual divisions of_the surface of the earth, their relative positions, globe and map-construction, longitude, navigation, &c. Varenius, with the materials at his command, dealt with the subject in a truly philosophic spirit; and his work long held its position as the best treatise in existence on scientific and comparative geography.
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  • Cramer's celebrated "Variations."
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  • The work was characterized by the great pains taken to ascertain the true authorship of hymns which were either anonymous or attributed to those who had not composed them, and by a like effort to exclude all variations grafted on the ' In 1867 he founded an association for the improvement of legal education, in the hope of bringing about the establishment or the restoration of "a general school of law in London on a scale worthy of the importance of the law and of the resources of the Inns of Court."
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  • In the first place, we find in this group two distinct types of person or individual, the polyp and the medusa (qq.v.), each capable of a wide range of variations; and when both polyp and medusa occur in the life-cycle of the same species, as is frequently the case, the result is an alternation of generations of a type peculiarly characteristic of the class.
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  • Great apparent differences may also be brought about by variations in the period at which the embryo is set free as a larva, and since two free-swimming stages, planula and actinula, are unnecessary, one or other of them is always suppressed.
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  • After all care has been taken in laying and pointing, in accordance with the rules of theory and practice, absolute certainty of hitting the same spot every time is unattainable, as causes of error exist which cannot be eliminated, such as variations in the air and in the muzzle-velocity, and also in the steadiness of the shot in flight.
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  • The term Eudaemonia has been taken in a large number of senses, with consequent variations in the meaning of Eudaemonism.
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  • Many even of these readings merely relate to variations of spelling, pronunciation or grammatical forms; others substitute a more decent expression for the coarser phrase of the text, but in some instances the suggested reading really affects the sense of the passage.
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  • Externally also the ancient versions, especially the Septuagint, frequently exhibit variations from the Hebrew which are not only intrinsically more probable, but often explain the difficulties presented by the Massoretic text.
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  • Origen, in his Hexapla, placed side by side the Hebrew text, the Septuagint, and certain later Greek versions, and drew attention to the variations: he thus brought together for comparison, an indispensable preliminary to criticism, the chief existing evidence to the text of the Old Testament.
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  • Capellus drew conclusions from such important facts as the occurrence of variations in the two Hebrew texts of passages found twice in the Old Testament itself, and the variations brought to light by a comparison of the Jewish and Samaritan texts of the Pentateuch, the Hebrew text and the Septuagint, the Hebrew text and New Testament quotations from the Old Testament.
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  • The variations are analogous to those under (1), except that here the birth-years of the patriarchs in both Sam.
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  • To remedy the confusion produced by the variations of the Latin text Pope Damasus asked Jerome to undertake a revision, and the latter published a new text of the New Testament in A.D.
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  • The editions of Mill (1707) and of Wetstein (1751) proved once for all that variations in the text, many of them serious, had existed from the earliest times.
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  • The surface currents of the Pacific have not been studied in the same detail as those of the Atlantic, and their seasonal variations Circulation are little known except in the monsoon regions.
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  • In all essentials they agree with the African type: such variations as there are, for example, the more developed eyebrow ridges, narrower, often prominent nose, and somewhat higher narrower skull, obviously owing their existence to crossing with the Malay or the Polynesian races.
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  • Another defect in the evidence of coins is that, when one variety of the unit of weight was once fixed on for the coinage, there was (barring the depreciation) no departure from it, because of the need of a fixed value, and hence coins do not show the range and character of the real variations of units as do buildings, or vases, or the actual commercial weights.
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  • The variations of hon and uten, however, cover one another completely.
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  • -- For these we have far more complete data than for volumes or even lengths, and can ascertain in many cases the nature of the variations, and their type in each place.
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  • Perfectly black leopards, which in certain lights show the characteristic markings on the fur, are not uncommon, and are examples of melanism, occurring as individual variations, sometimes in one cub out of a litter of which the rest are normally coloured, and therefore not indicating a distinct race, much less a species.
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  • Gregory (Climatic Variations, their Extent and Causes, International Geological Congress, Mexico, 1906), who holds that the extent of climatic changes in past times has been greatly exaggerated.
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  • The mutations of Waagen may possibly, in fact, prove to be identical with the " definite variations " or " rectigradations " observed by Osborn in the teeth of mammals.
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  • Thus both invertebrate and vertebrate palaeontologists have reached independently the conclusion that the evolution of groups is not continuously at a uniform rate, but that there are, especially in the beginnings of new phyla or at the time of acquisition of new organs, sudden variations in the rate of evolution which have been termed variously " rhythmic," "pulsating," " efflorescent," "intermittent " and even " explosive " (Deperet).
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  • The oral arms are the starting-point of a further series of variations; they may be simple flaps, crinkled and folded in various ways, or they may be subdivided, and then the branches may simulate tentacles in appearance.
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  • From the stomach, canals arise termed the radial canals (r.c.); typically four in number, they run in a radial direction to the edge 2 For other variations of the medusa, often of importance for systematic classification, see Hydromedusae and Scyphomedusae.
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  • (For other anatomical variations see Hydromedusae and Scyphomedusae.) In development the medusa can be derived easily by a process of differential growth, combined with concrescence of cell-layers, from the actinula-larva.
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  • Among variations from this type may be mentioned higher stature in some districts, and lighter complexion in Tehuantepec and elsewhere.
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  • Thus the Pentateuch and the New Testament were reprinted from Tyndale's translations of 1530 and 1535 respectively, with very slight variations; See Dr Ginsburg's information to Mr Tedder, D.N.B.
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  • The winters are usually long and severe, and the summers cool and salubrious, but the diversity of surface together with unequal distances from the sea cause marked variations for the different regions.
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  • On this and other local variations a number of nominal species have been founded; but it is preferable to regard them in the light of geographical phases or races, such as the above-mentioned C. latrans estor of Nevada and Utah, C. 1.
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  • A series of municipal laws gives us a detailed knowledge of the constitution imposed, with slight variations, on all the municipia; and a host of private inscriptions gives particulars of their social life.
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  • Notwithstanding the facility and frequency of amendments, the variations between one constitution and another are less conspicuous than might have been expected.
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  • The English Cistercian houses, of which there are such extensive and beautiful remains at Fountains, Rievaulx, Kirkstall, Tintern, Netley, &c., were mainly arranged of ter the same plan, with slight local variations.
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  • - There are three main types of movable weirs, namely frame weirs, shutter weirs and drum weirs, which, however, present several variations in their arrangements.
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  • There are many variations in the treatment of the legend, for which, as also for a discussion of the modern plays on the subject by Voltaire and Alfieri, see Jebb's Introduction to his edition of the Electra of Sophocles.
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  • 42° to the Arctic regions and touching three oceans, there must be great variations of climate.
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  • A text so transmitted must in the lapse of time be profoundly though insensibly modified, its forms and expressions modernized, and, if widely disseminated, local variations introduced into it.
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  • This he accomplished, first in 1859, a number of times, always with different theatric variations: blindfold, in a sack, trundling a wheelbarrow, on stilts, carrying a man on his back, sitting down midway while he made and ate an omelette.
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  • The cycle of the sun brings back the days of the month to the same day of the week; the lunar cycle restores the new moons to the same day of the month; therefore 28 X 19 = 53 2 years, includes all the variations in respect of the new moons and the dominical letters, and is consequently a period after which the new moons again occur on the same day of the month and the same day of the week.
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  • Since about 1880 the silk production of the world (including only exports from the East) has more than doubled, the variations owing to partial failures from some countries being more than compensated by increase from others.
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  • In order to form a relative idea of the importance of the various countries engaged in silk manufacture, a tabulation of the number of looms employed in each country would prove an inadequate guide, owing to the variations from time to time of the fabrics woven, as also to the difficulty in obtaining trustworthy statistics of the number in active operation.
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  • In 1680 Jean Picard, in his Voyage d'Uranibourg, stated, as a result of ten years' observations, that Polaris, or the Pole Star, exhibited variations in its position amounting to 40" annually; some astronomers endeavoured to explain this by parallax, but these attempts were futile, for the motion was at variance with that which parallax would occasion.
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  • The question as to whether the motion was due to an irregular distribution of the earth's atmosphere, thus involving abnormal variations in the refractive index, was also investigated; here, again, negative results were obtained.
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  • Experimentally we should be confined to a strict investigation of absorption spectra, because in the electric discharge temperature has no definite meaning, and variations of pressure and density are not easily measured.
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  • These variations are largely borrowed from and closely follow the language of various Lutheran litanies, especially that given in the consultation of Archbishop Hermann of Cologne issued in 1543.
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  • The Municipal Elections (Corrupt and Illegal Practices) Act 1884 applied to school board elections subject to certain variations, and has been extended by the Local Government Act 1888 to county council elections, and by the Local Government Act 1894 to elections by parochial electors.
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  • There are then, at least within the limits of moderate sensations, concomitant variations between stimuli and sensations, not only in " quality," as in the intervals of sounds, which were understood long ago, but also in " intensity "; and the discovery of the latter is the importance of Weber's and Fechner's law.
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  • By the rules of induction from concomitant variations, we are logically bound to infer the realistic conclusion that outer physical stimuli cause inner sensations of sensible effects.
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  • We know, from the concomitant variations between its vibrations and our perceptions, that its vibrations are not mere conditions but real causes of our perceptions; and that those vibrations are not our perceptions, because we cannot perceive them, but are real attributes of the bell.
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  • The badge of the order is, with variations for the different classes, a white enamelled Danish cross with red and gold borders, bearing in the centre the letter W (V) and on the fourarms the inscription Gud og Kongen (For God and King).
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  • The perithecium is very constant in form and since the gonidia take no part variations are of value in classification some more details may be added.
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  • These, however, may with propriety be regarded as but different names for the same pigmentary substance, the variations in the character of which are attributable to the different modes in which the pigments are manufactured.
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  • Here we may conveniently mention certain variations from the normal condition in the size, form or disposition of buds or shoots on a given plant.
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  • Supposing seedlings to have been developed, it is found that a large number of them present considerable variations, some being especially robust, others peculiar in size or form.
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  • Some species had an almost world-wide range with only minor variations; such are Productus semireticulatus, P. cora, P. pustulosus; Orthotetes (Streptorh_ynchus) crenistria, Dielasma hastata, and many others.
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  • As waterways all the rivers labour under the drawbacks of rapids, mud-banks at their mouths, banks overgrown with forest, sparse population, and currents liable to serious variations due to irregularity of supply from the mountains and sudden rainfalls.
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  • As throughout the whole of the Malayan Archipelago, so in Sumatra, which lies about equally balanced on both sides of the equator, the temperature stands at a high level subject to but slight variations.
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  • As regards its composition, the cell-wall of fungi exhibits variations of the same kind as those met with in higher plants.
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  • Like these, also, they respire oxygen, and are independent of light; and their various powers of growth, secretion, and general metabolism, irritability, and response to external factors show similar specific variations in both cases.
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  • These variations in the properties of iron are brought about in part by corresponding variations in mechanical and thermal treatment, by which it is influenced profoundly, and in part by variations in the proportions of certain foreign elements which it contains; for, unlike most of the other metals, it is never used in the pure state.
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  • Further, the point at which the process should be arrested is recognized by the appearance of the flame which issues from the converter's mouth, and variations in the silicon-content of the cast iron treated alter this appearance, so that the indications of the flame become confusing, and control over the process is lost.
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  • In the basic Bessemer process, also, unforeseen variations in the siliconcontent are harmful, because the quantity of lime added should be just that needed to neutralize the resultant silica and the phosphoric acid and no more.
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  • In the acid Bessemer process the reason why the sulphur-content must be small is that the process removes no sulphur; and the reason why the silicon-content should be constant is that, because silicon is here the chief source of heat, variations in its content cause corresponding variations in the temperature, a most harmful thing because it is essential to the good quality of the steel that it shall be finished and cast at the proper temperature.
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  • It is true that the use of the " mixer " (§ 77) lessens these variations, and that there are convenient ways of mitigating their effects.
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  • But if the conversion is only begun in the converter and finished on the open-hearth, then there is no need of regulating the temperature in the converter closely, and variations in the silicon-content of the pig iron thus become almost harmless in this respect.
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  • These numbers must be varied with the variations in other conditions, such as casting temperature, rapidity of solidification, &c.
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  • Sumerian presents a significant list of internal phonetic variations which would not have been possible in an arbitrarily invented language.
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  • The prices quoted are subject to constant fluctuation and represent purely trade prices for bulk, and it should be explained that the very great variations are due to different sizes, qualities and colours, and moreover are only first cost, before skins are dressed and prepared.
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  • He goes on to show that the variations of prices are due solely to money and commodities in circulation.
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  • Another manuscript that tells the same story, with only verbal variations, is found in No.
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  • The variations in external characters which lions present, especially in the colour and the amount of mane, as well as in the general colour of the fur, indicate local races, to which After a Drawing by Woll in Elliot's Monograph of the Felidae.
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  • A different type of problem is presented in those cases in which the temperature at each point varies with the time, as is the case near the surface of the soil with variations in the external conditions between day and night or summer and winter.
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  • The, chief uncertainty in applying this method appears to have arisen from variations of temperature at different parts of the surface, due to inequalities in the heating or cooling effect of the stream of water flowing over the surfaces.
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  • One of the best methods of studying the flow of heat in this case is to draw a series of curves showing the variations of temperature with depth in the soil for a series of consecutive days.
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  • Excluding these exceptional cases, however, the variations of the diffusivity appeared to follow the variations of the seasons with considerable regularity in successive years.
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  • 4, showing the propagation of temperature waves due to diurnal variations in the temperature of the surface.
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  • A similar method has frequently been applied to the study of variations of soil-temperatures by harmonic analysis of the annual waves.
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  • Rambaut's results were obtained with similar instruments similarly located, but he did not investigate the seasonal variations of diffusivity, or the effect of percolation.
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  • He deduced the variations of the mean temperature of a section of a bar from the sum S of the E.M.F.'s of a number of couples, inserted at suitable equal intervals 1 and connected in series.
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  • The conductivity of liquids has been investigated by similar methods, generally variations of the thin plate or guard-ring method.
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  • 00136 at 19.5° C. The variations of these results illustrate the experimental difficulties.
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  • The methods described hereafter are those generally followed in India and Ceylon in the manner of the most modern application, but variations must take place according to district and elevation.
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  • - Diagram showing the alterations in the relative proportions of different growths of tea consumed during the 21 years ended the 31st of December 1907; the variations in the London average prices for Indian teas, and the changes in the English rate of duty.
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  • The mass of the working-class population in the Protestant parts of Germany belonged to the Social Democracy, an inclusive term covering variations of opinion from the doctrinaire system of Marx to a degree of Radicalism which in England would not be considered a bar to a peerage.
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  • In Manetho's list of kings, the six above named (with many variations in detail) form the XVth dynasty, and are called "six foreign Phoenician kings."
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  • He was the inventor also of the photophone, an instrument for transmitting sound by variations in a beam of light, and of phonographic apparatus.
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  • 0393 44 9 74 5 95.9 These figures are not wholly free from uncertainties, arising from true diurnal and annual variations in the frequency, but they give a good general idea of the influence of twilight.
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  • It can still be pretty clearly shown in detail that these four codices deviated from one another in points of orthography, in the insertion or omission of a wa (" and ") and such-like minutiae; but these variations nowhere affect the sense.
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  • The general scheme of Egyptian tombs remained the same throughout the whole of the dynastic period, thoughthere were Tombs, many variations of detail.
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  • But these variations are practically limited to the explanatory comments attached to the 2nd, 4th, 5th and 10th commandments; and the majority of critics are now agreed that these comments were added at a later date, and that all the commandments, like the 1st and the 6th to the 9th, were originally expressed in the form of a single short sentence.
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  • They can scarcely, however, have been transferred from Deuteronomy to Exodus (or vice versa), owing to the variations between the two versions: we must rather regard them as the work of a Deuteronomic redactor.
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  • This remarkable double fertilization as it has been called, although only recently discovered, has been proved to take place in widely-separated families, and both in Monocotyledons and Dicotyledons, and there is every probability that, perhaps with variations, it is the normal process in Angiosperms. After impregnation the fertilized oosphere immediately surrounds itself with a cell-wall and becomes the oospore which by a process of growth forms the embryo of the new plant.
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  • His story is told in one of the oldest songs of the Edda, the V OlundarkiOda and, with considerable variations, in the prose P13rekssaga (Thidrek's sage), while the Anglo-Saxon Beowulf and Deor's Lament contain allusions to it.
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  • To the eye, however, members of this group present a greater variety of colour than those of any other - yellow, brown, olive, red, purple, violet and variations of all these being known.
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  • Although the phenomena attending isogamous and oogamous reproduction respectively are essentially the same in all cases, slight variations in both instances appear in different families, attributable doubtless to the independent origin of the process in different groups.
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  • (De Toni's Sylloge Algarum, 5897.) After this survey of the four groups comprised under Algae it is easier to indicate the variations in the limits of the class as defined by different authorities.
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  • The composition of Portland cement varies within comparatively narrow limits, and for given raw materials the variations are tending = to become smaller as regularity and skill in manufacture Compost increase.
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  • The following analysis may be taken as typical of cements made from chalk and clay on the Thames and 100.0 There may be variations from this composition according to the nature of the raw materials employed.
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  • All such variations are permissible provided that the quantity of silica and alumina is sufficient to saturate the whole of the lime and to leave none of it in a "free" condition, likely to cause the cement to expand after setting.
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  • The name of the people has many variations.
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  • Living organisms vary, that is to say, no two individuals are exactly alike; the death-rate and the multiplication-rate are to a certain extent selective, that is to say, on the average, in the long run, they favour certain variations and oppress other variations.
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  • He appeared to believe, however, that the successive variations and modifications had arisen in response to mechanical laws of the organisms themselves rather than to the influence of their surroundings.
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  • Although the pre-Darwinian writers amongst them invoked nearly every principle that Darwin or his successors have suggested, they failed to carry conviction with regard to evolution, and they neither propounded a coherent philosophy of variation nor suggested a mechanism by which variations that appeared might give rise to new species.
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  • He laid much stress on the unity of the organism in every stage of its existence, with the resulting correlation of variations, so that the favouring of one particular variation entailed modifications of correlated structures.
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  • He recognized the existence of the large variations, but he believed these to be of little value in evolution, and he attached preponderating importance to relatively minute indeterminate variations.
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  • On the other hand, he was far from advocating the view that has been pithily expressed as the "selection of the fit from the fortuitous"; he recognized that variations, although perhaps suggested or excited by the environment, were determined by internal causes.
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  • He pointed to the changes wrought on domesticated organisms by the artificial selection of similar variations, and drew the inference that there must be parallel occurrences under wild nature.
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  • Wallace, whilst insisting that the range of observed and measured variation was much larger in proportion to the size of the organisms or parts of organism affected than was generally believed, leaned to the Darwinian view in excluding from the normal factors in the origin of species variations of the extremer ranges of magnitude.
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  • De Vries gave the name "mutations" to such considerable variations (it is to be noted that a further concept, that of the mode of origin, has been added to the word mutation, and that the conception of relative size is being removed from it), and Bateson, de Vries and other writers have added many striking cases to those recorded by Darwin.
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  • It is doubtful, however, if there is any philosophical basis for distinguishing between variations merely by their magnitude.
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  • Differences which at their first appearance are very minute may result in the kind of variations which certainly would be classed as discontinuous.
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  • Even amongst the extreme advocates of the theory of mutations, the importance of magnitude is being discounted by their suggestion that some of the minute variations which have hitherto been regarded by them as insignificant "fluctuating variations" may be significant mutations.
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  • This in effect is to say that not magnitude but something else has to be sought for if we are to pick out amongst observed variations those which may be the material for the differentiation of species.
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  • So far as magnitude is concerned, the attack on the Darwinian position has failed, and it is agreed that species may be discontinuous and none the less have been produced from minute variations.
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  • The variations which de Vries has called mutations, and which were at first associated by Bateson with what he called discontinuous variations as the exclusive source of new species, are now supposed by de Vries to be distinguished from fluctuating variations by their mode of origin.
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  • In the first place the variations in question are "acquired characters."
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  • Successful organisms, or well-adapted organisms, are those that have responded to the environment, whether by large or small variations, in suitable fashion.
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  • The conceptions of Weismann afford no ground for rejecting fluctuating variations from the materials for the production of species.
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  • Breeders, he says, who try to build up qualities by the selection of the fluctuating variations that occur soon find that they reach a maximum beyond which their efforts fail, unless they turn to the more rarely occurring but heritable mutations.
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  • As yet no solid reason has been alleged for excluding fluctuating variations, on account of their limitation, from the materials for specific change.
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  • And finally, there are a series of variations, amongst which no doubt are the mutations of de Vries and the disintegrations and recombinations of the unit factors with which Mendel and his followers have worked, in which the external or environmental factor is most remote from the actual result.
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  • One aspect of organic individuality is the correlation of variations, the fact that when one part varies, other parts vary more or less simultaneously.
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  • So long as we confine our attention to one or two individuals, we fail to detect any order in the occurrence of variations; but when we examine large numbers we find that it is possible to arrange them in an orderly series, which can be easily and simply described.
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  • How is it possible, it was said, that fortuitous variations can furnish the material for the precise and balanced adaptations that all nature reveals?
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  • No doubt a large amount of variation is truly indefinite, so that many meaningless or useless variations arise, and in one sense it is a mere coincidence if a particular variation turn out to be useful.
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  • Obviously variations depend on the constitution of the varying organism; a modification, whether it be large or small, is a modification of an already definite and limited structure.
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  • Darwin himself showed that different species in a genus, or varieties in a species, tended to show parallel variations, whilst comparative anatomy has made known a multitude of cases where allied series of animals or plants show successive stages of parallel but independent variations of important organs and functions.
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  • Variations >>
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  • In the inter-andine region the variations in temperature are frequent and the averages comparatively low.
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  • In the higher altitudes there are wide variations in the snow-fall and intensity of the cold even on the same mountain.
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  • The climate shows great variations in temperature.
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  • The title of the section and the contents recall, though with some important variations, the earlier half of his first work; only that here the historical background on which the stages in the development of the ego were represented has disappeared.
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  • The variations in the details of the polity of the Lutheran churches were very numerous, but they all preserved the same distinctive principles.
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  • But it is remarkable that, although within the Old Testament itself there are certain different backgrounds, important variations and developments of law, these are relatively insignificant when we consider the profound changes from the 15th-13th centuries (apparent by the period of the conquest) to the close of Old Testament history.
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  • Many of the patent bronzes are by slight variations in the proportions of the constituents made suitable for casting, for forging, and for rolling into sheets.
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  • In the other provinces variations of the zamindari and ryotwari systems are found.
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  • (12) Greater elasticity in the revenue collection, facilitating its adjustment to the variations of the seasons, and the circumstances of the people.
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  • In accordance with the monthly variations in temperature at Manila the year is divided into three seasons: temperate (November, December, January and February), hot (April, May and June) and intermediate (March, July, September and October).
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  • As already indicated, the local cults in the important centres of the south and north maintained themselves despite the tendency towards centralization, and while the cults themselves varied according to the character of the gods worshipped in each centre, the general principles were the same and the rites differed in minor details rather than in essential variations.
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  • If such variations of density exist, they may introduce some uncertainty in the absolute values of results obtained with the ice calorimeter, and may account for some of the discrepancies above enumerated.
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  • This Variation May Have Been Due To The State Of The Lagging, Which Moorby Distrusted In Spite Of The Great Reduction Of The Heat Loss, Or It May Have Been Partly Due To The Difficulty Of Regulating The Speed Of The Engine And The Watersupply To The Brake In Such A Manner As To Maintain A Constant Temperature In The Outflow, And Avoid Variations In The Heat Capacity Of The Brake.
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  • These Variations, So Far As They Were Of A Purely Accidental Nature, Would Be Approximately Eliminated On The Mean Of A Large Number Of Trials, So That The Accuracy Of The Final Result Would Be Of A Higher Order Than Might Be Inferred From A Comparison Of Separate Pairs Of Trials.
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  • But For The Determination Of Relative Values Of Specific Heats In Terms Of A Standard Liquid, Or Of The Variations Of Specific Heat Of A Liquid, The Method Depends Only On The Constancy Of The Standards, Which Can Be Readily And Accurately Tested.
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  • Considering The Wide Variations In The Physical Condition And Melting Points, The Comparatively Close Agreement Of The Atomic Heats Of The Metals At Ordinary Temperatures, Known As Dulong And Petit'S Law, Is Very Remarkable.
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  • No Doubt There Must Be Approximate Relations Between The Atomic And Molecular Heats Of Similar Elements And Compounds, But Considering The Great Variations Of Specific Heat With Temperature And Physical State, In Alloys, Mixtures Or Solutions, And In Allotropic Or Other Modifications, It Would Be Idle To Expect That The Specific Heat Of A Compound Could Be Accurately Deduced By Any Simple Additive Process From That Of Its Constituents.
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  • But such scepticism is unjustifiable in view of the perfect unanimity with which, in spite of variations of detail, all Portuguese writers from the beginning of the 16th century onwards reiterated the assertion that there was a powerful rule known far and wide by that title.
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  • Other investigators had shown that Cicero's clausulae are generally variations of some three or four forms in which the rhythm is trochaic. Dr Thaddaeus Zielinski of St Petersburg, after examining all the clausulae in Cicero's speeches, finds that they are governed by a law.
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  • On the other hand, the variations in the light of the sun must be very small compared with the enormous fluctuations in the light of variable stars.
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  • Also the variations recur with perfect regularity.
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  • The ministration to memory, aided by registering and arranging the data, of observation and experiment in tables of instances of agreement, difference and concomitant variations.
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  • The more logical method of procedure is to determine the specific heat independently of the total heat, and then to deduce the variations of total heat by equation (52).
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  • By assuming suitable forms of the characteristic equation to represent the variations of the specific volume within certain limits of pressure and temperature, we may therefore with propriety deduce equations to represent the saturation-pressure, which will certainly be thermodynamically consistent, and will probably give correct numerical results within the assigned limits.
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  • Local government is of the ordinary southern county type, without noteworthy variations.
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  • Tulare lake, which with Buena Vista lake and Kern lake receives the drainage of the southern Sierra, shows extreme local variations of shore-line, and is generally believed to have shrunk extremely since 1850, though of this no adequate proof yet exists.
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  • Amid great variations of local weather there are some peculiar features that obtain all over the state.
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  • The following figures give some idea of the climatic variations.
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  • The light reflected from the fixed mirror traces a straight line on the paper, serving as a base line from which the variations in declination are measured.
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  • To record the variations of the vertical component use is made of a magnet mounted on knife edges so that it can turn freely about a horizontal axis at right angles to its 1 Report British Association, Bristol, 18 9 8, P. 741.
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  • Considerable variations occur in the thickness of Cambrian deposits, which may generally be explained by the greater rapidity of deposition in some areas than in others.
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  • It is clear, from the extreme variations in the severity of the illness, that the resisting power of individuals varies greatly.
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  • The seasonal variations have been well marked and extremely regular in Bombay.
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  • Baldwin Latham made an elaborate examination of the meteorological conditions, and more particularly of the vapour tension, from which he draws the conclusion that the seasonal variations are due to exhalation from the ground.
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  • Thus in the case of fig 36 it may be required to connect, the infinitesimal rotations f, i1, l about OA, OB, OC with the variations of the angular co-ordinates 0, ~, ~.
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  • Stability of Position, and Stability of Frictio-n.The resistances at the several joints having been determined by the principles set forth in 6, 7, 8, 9 and 10, not only under the ordinary load of the structure, but under all the variations to which the load is subject as to amount and distribution, the joints are now to be placed and shaped so that the pieces shall not suffer relative displacement under any of those loads.
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  • Condition of Stability of Position.If the materials of a structure were infinitely stiff and strong, stability of position at any joint would be insured simply by making the centre of resistance fall within the joint under all possible variations of load.
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  • The amount and effect of the variations of pressure and temperature undergone by the air depend on the principles of the mechanical action of heat, or THERMODYNAMIcS, and are foreign to the subject of pure mechaifisni.
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  • Flywheels.A flywheel is a rotating piece in a machine, generally shaped like a wheel (that is to say, consisting of a rim with spokes), and suited to store and restore energy by the periodical variations in its angular velocity.
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  • The principles according to which variations of angular velocity store and restore energy are the same as those of 117, only substituting moment of inertia for mass, and angular for linear velocity.
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  • The periodical excess e may arise either from variations in the effort exerted by the prime mover, or from Variations in the resistance of the work, or from both these causes combined.
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  • For example, in a machine-work, the steam-engine, which is the prime mover of the various tools, has a flywheel on the crank-shaft to store and restore the periodical excess of energy arising from the variations in the effort exerted by the connecting-rod upon the crank; and each of the slotting machines, punching machines, riveting machines, and other tools has a flywheel of its own to store and restore energy, so as to enable the very different resistances opposed to those tools at different times to be overcome without too great unsteadiness of motion.
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  • It has been shown by means of spectroscopic observations that the green colour of the elytra, &c., is due to the presence of chlorophyll; and that the variations of the spectral bands are sufficient, after the lapse of many years, to indicate with some certainty the kind of leaves on which the insects were feeding shortly before they were killed.
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  • The internal variations of the rate in a single community, however, can be fairly indicated in this way, as is done in Table VI., which, it is to be noted, refers to those born alive only and excludes the still-born, statistics regarding whom are incomplete.
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  • The variations from period to period in the same country are more instructive.
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  • To waverers it held up an absolutely sure and uniform Rule of Faith, contrasting impressively with the already multitudinous variations of the Protestant Churches.
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  • The soil varies very considerably in its character, and it is due to these variations that so many different types of wine are produced in this district.
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  • The tables below will give a fair idea of the variations which occur in the same wine as a result of different vintages, and the variations due to differences of growth " in the same vintage.
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  • Wines Of Germany Although the quantity of wine produced in Germany is comparatively small and subject to great variations, the quality of the finer wines is, in successful years, of a very high order.
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  • The very great variations which are shown by the same growths of different vintages makes it impracticable in the case of the German white wines to give representative analyses of them.
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  • The Palaeographia graeca (1708), illustrating the whole history of Greek writing and the variations of the characters, has not yet been superseded; in its own field it is as original as the De re diplomatica of Mabillon.
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  • It can be said, however, that the south-east is the warmest portion of the state, lying as it does without the mountains; that the north-central region is usually coldest; that the normal yearly rainfall for the entire state is about 15.5 in., with great local variations (rarely above 27 in.).
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  • This is a general description of the principles on which these machines are built, but, as in other classes, there are many variations in details.
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  • It appals the reader with its irregularity of treatment, its variations of style, and its abrupt transitions from the spiritual to the crude and trivial, and from superstition to the purest insight.
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  • A mass of evidence exists showing that variations of every conceivable kind occur among the offspring of all plants and animals, and that, in particular, constitutional variations are by no means uncommon.
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  • It is also impossible to determine how far the effects described are produced by spontaneous favourable variations or by the direct action of local conditions; but it is probable that in every case both causes are concerned, although in constantly varying proportions.
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  • There is no positive evidence that the influence of new climatal conditions on the parents has any tendency to produce variations in the offspring better adapted to such conditions.
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  • Neither does it appear that this class of variations are very frequent.
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  • It is, however, certain that whenever any animal or plant is largely propagated constitutional variations will arise, and some of these will be better adapted than others to the climatal and other conditions of the locality.
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  • Favourable variations of constitution will soon show themselves, and these should be carefully selected to breed from, the tender and unhealthy individuals being rigidly eliminated.
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  • A number of foreign animals have been introduced, and more or less domesticated, and some useful exotics have been cultivated for the purpose of testing their applicability to French agriculture or horticulture; but neither in the case of animals nor of plants has there been any systematic effort to modify the constitution of the species, by breeding largely and selecting the favourable variations that appeared.
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  • But he entirely ignored the effect of � favourable variations, as well as the direct influence of climate acting on the organization from infancy.
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  • The common carp (Cyprinus carpio), originally a Chinese fish, has for centuries been acclimatized in Europe, where indeed it is in places a true domestic creature, with definite variations.
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  • Although examples of both species present considerable variations in size, it is ascertained that the length of the largest-sized Bengal tiger may exceed that of any lion.
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  • Whatever be the derivation of the name, however, it is now universally used to describe a set of verses formed on this model, with the variations in rhyme noted above: "There was an old man who said ' Hush!
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  • There are considerable variations as to their names.
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  • As a result of the wide latitudinal extent of the country there are also marked local variations to be contrasted.
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  • But the local variations thus indicated are brought out more fully by a consideration of seasonal, and especially winter, temperatures.
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  • Natural beds of oysters occur on stony and shelly bottoms at depths varying from 3 to 20 fathoms. In nature the beds are liable to variations, and, although Huxley was somewhat sceptical on this point, it seems that they are easily brought into an unproductive condition by over-dredging.
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  • Arago is also fairly entitled to be regarded as having proved the long-suspected connexion between the aurora borealis and the variations of the magnetic elements.
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  • So great were his variations even in his latter years, that he could speak to his friend Allsop in a highly latitudinarian sense, declaring that in Christianity "the miracles are supererogatory," and that "the law of God and the great principles of the Christian religion would have been the same had Christ never assumed humanity."
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  • A thawing night is said to promote the flow, and it ceases during a south-west wind and at the approach of a storm; and so sensitive are the trees to aspect and climatic variations that the flow of sap on the south and east side has been noticed to be earlier than on the north and west side of the same tree.
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  • Out of twenty so-called species he considers six to be really distinct, while the others are merely synonymous or trifling variations.
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  • These variations have arisen chiefly through cross-breeding, though not entirely so, there being a few cases upon record of the production of "sports" from tubers that have become the parents of new varieties, but authentic cases of the sporting of tubers are few and far between.
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  • If, on the other hand, the true seeds of any of our cultivated varieties are sown, the seedlings show very wide variations from one another and from the parents.
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  • Various experimenters, especially Fenn, have asserted that by engrafting an eye of one variety into the tuber of another, not only will adhesion take place but the new tubers will present great variety of character; this seems to be the case, but it can hardly be considered as established that the variations in question were the result of any commingling of the essences of the two varieties.
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  • The heights of peaks determined by exact processes of trigonometrical observation are bound to be more or less in error for three reasons: (1) the extraordinary geoidal deformation of the level surface at the observing stations in submontane regions; (2) ignorance of the laws of refraction when rays traverse rarefied air in snow-covered regions; (3) ignorance of the variations in the actual height of peaks due to the increase, or decrease, of snow.
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  • The tale is told much more fully and with many variations in the tragedians.
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  • Experiments with labelled plaice, carried out in 1904 by the Marine Biological Association, showed that small plaice transplanted to the Dogger Bank in spring grew three times as rapidly as those on the inshore grounds, and the same result, with insignificant variations, has been obtained by similar experiments in each succeeding year.
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  • Here, too, the occurrence of repetitions and divergencies, the variations of standpoint and practice, and, at times, the linguistic peculiarities point no less clearly to diversity of origin.
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  • - Bolivia lies wholly within the torrid zone, and variations in temperature are therefore due to elevation, mountain barriers and prevailing winds.
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  • The valle zone includes the deep valleys from 5000 to 9500 ft., has a warm climate with moderate variations in temperature and no cold weather, is sub-tropical in character and productions, and is sometimes described as a region of perpetual summer.
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  • The early writers on capillary action supposed that the diminution of capillary action was due simply to the change of density corresponding to the rise of temperature, and, therefore, assuming the surface-tension to vary as the square of the (37)?(f) =eP f (38) density, they deduced its variations from the observed dilatation of the liquid by heat.
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  • Lippmann, who has made a careful investigation of the subject, finds that exceedingly small variations of the electromotive force produce sensible changes in the surfacetension.
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  • Beyerinck and Jegunow have shown that some partially anaerobic sulphur bacteria can only exist in strata at a certain depth below the level of quiet waters where SH 2 is being set free below by the bacterial decompositions of vegetable mud and rises to meet the atmospheric oxygen coming down from above, and that this zone of physiological activity rises and falls with the variations of partial pressure of the gases due to the rate of evolution of the SH 2.
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  • Variations in chemiotaxis towards different organisms probably depend in natural conditions, as well as in active immunity, upon the opsonic content of the serum.
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  • Observations made on this property with respect to the anthrax bacillus at first gave the hope that it might explain variations in natural immunity.
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  • Indeed the great age of the seneschal of Champagne, and his intimate first-hand acquaintance with his subject, made such variations extremely improbable.
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  • If the hypothesis already outlined is set aside, it is open to the critic to regard large portions of the canonical Romans as having originally occupied a separate setting,5 or to ascribe the textual variations to the exigencies of church reading after the formation of the canon (which might explain the absence of Ev `Pt)t7j in i.
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  • Those who in the same way identify Rabelais with Panurge can never explain the education scheme, the solemn apparition of Gargantua among the farcical and fantastic variations on Panurge's wedding, and many other passages; while, on the other hand, those who insist on a definite propaganda of any kind must justify themselves by their own power of seeing things invisible to plain men.
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  • A further application is that in bell-ringing, of the variations in order in which a peal of bells may be rung.
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  • Similar forms are also found in early Aramaic, but another form 1 or L, which is found in the Phoenician of Cyprus in the 9th or 10th century B.C. has had more effect upon the later development of the Semitic forms. The length of the two back strokes and the manner in which they join the upright are the only variations in Greek.
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  • The cause of the climatic variations which brought about this complex history of the Salt Lake region is not known; but it is worthy of note that the periods of highest water levels were coincident with a great expansion of local valley glaciers, some of which terminated in the waters of lake Bonneville.
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  • We find moreover as emi-scientific conception of the basis of divination; the whole of nature is linked together; just as the variations in the height of a column of mercury serve to foretell the weather, so the flight of birds or behaviour of cattle may help to prognosticate its changes; for the uncultured it is merely a step to the assumption that animals know things which are hidden from man.
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  • The variations in length of the general slope of the land towards successive natural divisions of the coast may be illustrated by a comparative table of the mileage and drainage areas of the principal English rivers.
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  • The amount of the rainfall shows great variations in different years, the records at Banana showing a total fall of 16 in.
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  • Other outgrowths of similar character, but less conspicuous, occur lower down the tube, and their variations afford useful means of discriminating between the species.
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  • Meteorological optical phenomena, due to variations in the refractive index of the atmosphere, may be divided into groups: (I) those due to the permanent or normal variation experienced as one ascends in the atmosphere, and (2) those due to sporadic variations occasioned by irregular heating.
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  • But the whole class, apart from minor variations, was characterized by the idea that the peasants in question were serfs of the soil (servi terrae) on which they were settled, though protected by the laws in their personal and even in their praedial status.
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  • In the economic development of states taxes have come to be grouped in different ways, according to variations in the method of levying them or the means of enforcing compulsion or other differences.
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  • Here there are the greatest variations.
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  • Although there were variations in the ceremony itself and in its date, the central idea was the death and resurrection of Adonis.
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  • Slight differences in the method of budding produce great variations in the form of the colonies, which may be distinguished in a general way as spreading, massive or arborescent.
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  • Whilst the general characteristics of the climate are as here outlined, in a country of so large an area as Cape Colony there are many variations in different districts.
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  • Apart altogether from the variations of actual rainfall produced by irregular surface levels, the very small area of a single rain-gauge is subject to much greater variations in short periods than can possibly occur over larger areas.
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  • It is merely a geometrical determination of the conditions necessarily consequent in England, Scotland and Wales, upon a given mean rainfall over many years, upon evaporation and absorption in particular years (both of which he must judge or determine for himself), and upon certain limiting variations of the rainfall, already stated to be the result of numerous records maintained in Great Britain for more than 50 years.
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  • Applied to most parts of Ireland and some parts of Great Britain, the diagram will give results rather unduly on the safe side, as the extreme annual variations of rainfall are less than in most parts of Great Britain.
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  • Throughout Europe the annual variations follow nearly the same law as in Great Britain, but in some parts the distribution of rainfall in a single year is often more trying.
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  • It is obvious that experiments of the kind referred to cannot take into account all the conditions of the problem met with in actual practice, such as the effect of the rock at the sides of the valley and variations of temperature, &c., but deviations in practice from the conditions which mathematical analyses or experiments assume are nearly always present.
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  • There are many and obvious variations of the system.
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  • Variations in matters of detail (having respect chiefly to the depth and distance apart of the parallel drains) have indeed been introduced; but the distinctive features of his system are recognized and acted upon.
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  • The very important part played by the Victoria Nyanza in the Nile system has led to careful study of its drainage basin and rainfall and the perplexing variations in the level of the lake.
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  • These variations are attributed by Sir William Garstin to deficiency or excess of rainfall.
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  • Perhaps no state in the union has such great local variations in its climate as has Oregon.
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  • This simple method is subject to variations in manufacture, and the addition of a small quantity of Jamaica rum, in particular, is said to much improve the flavour.
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  • The variations of external characters seen in the different breeds are very great.
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  • The British systems have various origins, and are still subject to variations caused by local usage or by the usage of particular businesses.
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  • In spite of these variations, however, the products in their main characteristics will remain the same.
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  • The fundamental objections to oil gas for the enrichment of coal gas are, first, that its manufacture is a slow process, requiring as much plant and space for retorting as coal gas; and, secondly, that although on a small scale it can be made to mix perfectly with coal gas and water gas, great difficulties are found in doing this on the large scale, because in spite of the fact that theoretically gases of such widely different specific gravities ought to form a perfect mixture by diffusion, layering of the gas is very apt to take place in the holder, and thus there is an increased liability to wide variations in the illuminating value of the gas sent out.
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  • It will perch on the topmost bough of a tree, if a tree be near, to watch his proceedings, and the cock exhibits all the astounding gesticulations in which the males of so many other Limicolae indulge during the breeding-season - with certain variations, however, that are peculiarly its own.
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  • It is natural that the " variations " with which Bossuet reproached the Protestants should demand more space.
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  • Owing to the absence of rivers, the paucity of springs, and the almost complete deforestation, Antigua is subject to frequent droughts, and although the average rainfall is 45.6 in., the variations from year to year are great.
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  • Hence we only allude to some of the principal variations and to those characteristics which are found to be unstable.
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  • (2) The variations in root-development have not been much attended to, although it would be well to study them in order to ascertain the degree of adaptability to various depths and conditions of soil.
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  • It was to be foreseen that a similar assertion of independence would make itself heard in ethics also; and, indeed, amid the clash of dogmatic convictions, and the variations of private judgment, it was natural to seek for an ethical method that might claim universal acceptance from all sects.
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  • Even in the case of the planets, the variations in the form and position of the orbits are so slow that long periods of observation are required for their correct determination.
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  • This is called the osculating orbit: The essential principle of Lagrange's elegant method consists in determining the variations of this osculating ellipse, the co-ordinates and velocities of the planet being ignored in the determination.
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  • The reason for taking the elements as the variables is that they vary very slowly, a property which facilitates their determination, since the variations may be treated as small quantities, of which the squares and products may be neglected in a first solution.
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  • This pull determines the variations of the ideal elements.
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  • Knowing these variations it becomes possible to represent by integration the value of the elements as algebraic expressions containing the time, and the elements with which we started.
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  • But the variations thus determined will not be rigorously exact, because the pull from which they arise has been determined on the supposition that the planets are moving in unvarying orbits, whereas the actual pull depends on the actual position of the planets.
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  • Another approximation is, therefore, to be made, when necessary, by correcting the expression of the pull through taking account of the variations of the elements already determined, which will give a yet nearer approximation to the truth.
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  • When, following the preceding method, the variations of the elements are expressed in terms of the time, they are found to be of two classes, periodic and secular.
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  • The periodic variations can be represented algebraically as the resultant of a series of harmonic motions in the following way: Let L be an angle which is increasing uniformly with the time, and let n be its rate of increase.
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  • Not only the grosser facts concerning radial velocity, but variations in it so small as a mile, or less, per second, have been recorded and interpreted in terms of deep meaning.
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