Surfaces sentence example

surfaces
  • Medical surfaces that detect pathogens.

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  • Similar to the bedroom, there was nothing on any of the flat surfaces, not even dust.

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  • In the late seventies and early eighties scaling these challenging surfaces really caught on.

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  • Even if the slide itself is mechanically perfect, the irregularity in the thickness of the lubricating oil between the bearing surfaces of the slide is apt to produce a variable error.

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  • The plates are compressed from before backwards, the anterior and posterior surfaces (as seen in the worn grinding face of the tooth) being nearly parallel.

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  • If the shape of the equipotential surfaces near it is influenced by trees, shrubs or grass, their influence will vary throughout the year.

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  • The presence, however, of apparatus or observers upsets the conditions, while above uneven ground or near a tree or a building the equipotential surfaces cease to be horizontal.

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  • In an ordinary climate a building seems to be practically at the earth's potential; near its walls the equipotential surfaces are highly inclined, and near the ridges they may lie very close together.

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  • Bearing this in mind, one can readily imagine how close together the equipotential surfaces must lie near the summit of a high sharp mountain peak.

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  • Air is drawn by an aspirator between the surfaces, and the ions having the opposite sign to the inner cylinder are deposited on it.

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  • The plane surfaces and XX are composed of a bronze of very close texture, which appears capable of receiving a finish having almost the truth and polish of an optical surface.

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  • Now, if CD is pressed by its weight or by a spring on the surface AB, the effect of wear will be to produce a symmetrical grinding away of both surfaces, which may be represented thus, fig.

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  • He notably enriched our knowledge of curves and surfaces.

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  • This method is frequently adopted in combined schemes of heating and ventilating; the fresh air is warmed by being passed over their surfaces previously to being admitted through the gratings into the room.

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

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  • Paint and coloured washes were liberally used to cover plastered surfaces and for ornamentation, and paints seem to have been used to bind plastered surfaces.

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  • In the South Atlantic the narrow land surfaces of Africa and South America produce comparatively little effect in disturbing the normal planetary circulation.

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  • By ca-sing two conical surfaces of cast-iron immersed in mercury and contained in an iron vessel to rub against one another when pressed together by a lever, Joule obtained 776.045 foot-pounds for the mechanical equivalent of heat when the heavy weights were used, and 774.93 foot-pounds with the small driving weights.

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  • The close agreement between the results at least indicates that "the amount of heat produced by friction is proportional to the work done and independent of the nature of the rubbing surfaces."

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  • In all cases there is a general tendency for other forms of energy to be transformed into heat on account of the friction of rough surfaces, the resistance of conductors, or similar causes, and thus to lose availability.

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  • Hence, when the coil at one fixed station was in action it generated high frequency alternating currents, which were propagated across the air gap between the ordinary telegraph wires and the metallic surfaces attached to one secondary terminal of the induction coil, and conveyed along the ordinary telegraph wires between station and moving train.

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  • When this is the case the amplitude of the potential difference of the surfaces of the tubular condenser becomes a maximum, and this is indicated by connecting a vacuum tube filled with neon to the surfaces of the condenser.

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  • The amount of watery vapour in the air passing through a stoma has no effect upon it, as the surfaces of the guard cells abutting on the air chamber are strongly cuticularized, and therefore impermeable.

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  • When the pinnate leaf of a Mimosa pudica, the so-called sensitive plant, is pinched or struck, the leaf droops rapidly and the leaflets become approximated together, so that their upper surfaces are in contact.

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  • Six sensitive hairs spring from the upper surface of the lobes, three from each; when one of these is touched the two lobes rapidly close, bringing their upper surfaces into contact and imprisoning anything which for the moment is between them.

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  • Davis, who classifies land surfaces in terms of the three factors - structure, process and time.

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  • In the north-east, French explorers have computed the altitudes of some mountains at figures which would make them the highest land surfaces of the western projection of Africa - from 6000 to 9000 ft.

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  • Throughout the whole of this vast area, their monotonous surfaces are diversified by only a few, and, for the most part, low, hilly tracts.

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  • Amongst the earliest mechanical contrivances of Fraunhofer was a machine for polishing mathematically uniform spherical surfaces.

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  • Immediately after taking his degree, he read to the Cambridge Philosophical Society a very novel memoir, " On the Transformation of Surfaces by Bending."

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  • Finally, the traditional circulus and titulus seem all but forgotten, the whole front and back surfaces of the mitre being ornamented with embroidered pictures or with arabesque patterns.

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  • In place of the six stamens we commonly find but one (two in Cypripedium), and that one is raised together with the stigmatic surfaces on an elongation of the floral axis known as the "column."

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  • In its medicinal use glycerin is an excellent solvent for such substances as iodine, alkaloids, alkalis, &c., and is therefore used for applying them to diseased surfaces, especially as it aids in their absorption.

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  • As so great a part of the whole surface of the kidney lies adjacent to external surfaces of the body, the remaining part which faces the internal organs is small; it consists of the left part of the under surface; it is level with the floor of the pericardium, and lies over the globular mass formed by the liver and convoluted intestine.

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  • Curiously enough, however, they differ from the cephalic Molluscan eye in the fact that, as in the vertebrate eye, the filaments of the optic nerve penetrate the retina, and are connected with the re surfaces of the nerve-end cells nearer the lens instead of with the opposite end.

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  • His first contributions to mathematical physics were two papers published in 1873 in the Transactions of the Connecticut Academy on "Graphical Methods in the Thermodynamics of Fluids," and "Method of Geometrical Representation of the Thermodynamic Properties of Substances by means of Surfaces."

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  • The platy minerals have also a perfect cleavage parallel to their flat surfaces, while the fibrous species often have two or more cleavages following their long axes; hence a schistose rock may split not only by separation of the mineral plates from one another but also by cleavage of the parallel minerals through their substance.

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  • When the foliation is undulose or sinuous the rocks are said to be crumpled, and have wavy splitting surfaces instead of nearly plane ones.

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  • The mineral has a very perfect cleavage parallel to the faces c and m, and the cleavage surfaces are perfectly smooth and bright.

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  • In process of time some of these banks, as in the case of Venice, raised themselves above the level of the water and became the true shore-line, while behind them lay large surfaces of water, called lagoons, formed partly by the fresh water brought down by the rivers, partly by the salt-water tide which found its way in by the channels of the river mouths.

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  • We find it retaining some traces of Byzantine influence in the decorated surfaces of applied marbles, and in the roundels of porphyry and verd antique, while it also retained certain characteristics of Gothic, as, for instance, in the pointed arches of the Renaissance facade in the courtyard of the ducal palace designed by Antonio Rizzo (1499).

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  • Maclaurin was the first to introduce into mechanics, in this discussion, the important conception of surfaces of level; namely, surfaces at each of whose points the total force acts in the normal direction.

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  • Obviously equimolecular surfaces are given by (Mv) 3, where M is the molecular weight of the substance, for equimolecular volumes are Mv, and corresponding surfaces the two-thirds power of this.

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  • This mode has some disadvantages attending it; such sheets are difficult to handle; the crustaceous species are liable to have their surfaces rubbed; the foliaceous species become so compressed as to lose their characteristic appearance; and the spaces between the sheets caused by the thickness of the specimen permit the entrance of dust.

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  • Between them the general theory of the complex variable, and of the various "infinite" processes of mathematical analysis, was established, while other mathematicians, such as Poncelet, Steiner, Lobatschewsky and von Staudt, were founding modern geometry, and Gauss inaugurated the differential geometry of surfaces.

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  • There is, of course, no sewerage system, the surfaces of the streets serving that purpose, and what garbage and refuse is not consumed by the dog scavengers washes down into the Tigris at the same place from which the water for drinking is drawn.

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

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  • The contact differences of potential at the interfaces of metals and electrolytes have been co-ordinated by Nernst with those at the surfaces of separation between different liquids.

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  • Double texture goods are made by uniting the rubber surfaces of two pieces of the coated material.

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  • The required thickness of the spread sheet is very often secured by the rubber-faced surfaces of two cloths being united before curing.

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  • Hence processes have been patented in which the objects to be plated are suspended in revolving drums between the anodes, the rotation of the drum causing the constant renewal of surfaces and affording a burnishing action at the same time.

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  • Very irregular surfaces may require the use of specially shaped anodes in order that the distance between the electrodes may be fairly uniform, otherwise the portion of the cathode lying nearest to the anode may receive an undue share of the current, and therefore a greater thickness of coat.

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  • Large metallic surfaces (especially external surfaces) are sometimes plated by means of a "doctor," which, in its simplest form, is a brush constantly wetted with the electrolyte, with a wire anode buried amid the hairs or bristles; this brush is painted slowly over the surface of the metal to be coated, which must be connected to the negative terminal of the electrical generator.

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  • For example, Wilde produced copper printing surfaces for calico printing-rollers and the like by immersing rotating iron cylinders as cathodes in a copper bath.

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  • The different kinds of mica vary from perfectly colourless and transparent - as in muscovite - through shades of yellow, green, red and brown to black and opaque - as in lepidomelane; the former have a pearly lustre and the latter a submetallic lustre on the cleavage surfaces.

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  • Sheets of mica very often show coloured rings and bands (Newton's rings), due to the interference of light at the surfaces of internal cleavage cracks.

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  • The hardness is 2 -3; smooth cleavage surfaces can be just scratched with the finger-nail.

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  • The outer surfaces of the mantle secrete' the shell, which is of the nature of a cuticle impregnated by calcareous salts.

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  • In the theory of surfaces we transform from one set of three rectangular axes to another by the substitutions 'X=' by+ cz, Y = a'x + b'y + c'z, Z =a"x+b"y-l-c"z, where X 2+Y2+Z2 = x2+ y2+z2.

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  • A stick of green wood is forced into it, and the vapours and gases set free expose new surfaces to the air, which at this temperature has only a mildly oxidizing effect.

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  • If V denote the potential, F the resultant force, X, Y, Z, its components parallel to the co-ordinate axes and n the line along which the force is directed, then - sn = F, b?= X, - Sy = Y, -s Surfaces for which the potential is constant are called equipotential surfaces.

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  • The resultant magnetic force at every point of such a surface is in the direction of the normal (n) to the surface; every line of force therefore cuts the equipotential surfaces at right angles.

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  • The potential due to a single pole of strength m at the distance r from the pole is V = m/ r, (7) the equipotential surfaces being spheres of which the pole is the centre and the lines of force radii.

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  • The equipotential surfaces are two series of ovoids surrounding the two poles respectively, and separated by a plane at zero potential passing perpendicularly through the middle of the axis.

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  • Whether the pericardium and the ventral sinus are made to expand simultaneously or all the movement is made by one only of the surfaces concerned, must depend on conditions of tension.

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  • A tendency is exhibited to the formation of a metasomatic as well as a prosomatic carapace by fusion of the tergal surfaces of the somites.

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  • Scorpions copulate with the ventral surfaces in contact.

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  • The finest, known from its polished surfaces as the "Mirror Tomb," is about 2 m.

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  • It serves for the thatching of roofs, for a papermaking material, for ornamenting small surfaces as a "strawmosaic," for plaiting into door and table mats, mattresses, &c., and for weaving and plaiting into light baskets, artificial flowers, &c. These applications, however, are insignificant in comparison with the place occupied by straw as a raw material for the straw bonnets and hats worn by both sexes.

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  • Later investigations by Fraunhofer, Airy and others have greatly widened the field, and under the head of " diffraction " are now usually treated all the effects dependent upon the limitation of a beam of light, as well as those which arise from irregularities of any kind at surfaces through which it is transmitted, or at which it is reflected.

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  • This strip is rapidly replaced, mainly by the connective tissue cells of the adjoining tissue growing across the temporary filled breach and firmly uniting the two cut surfaces.

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  • Hero also wrote Catoptrica (on reflecting surfaces), and it seems certain that we possess this in a Latin work, probably translated from the Greek by Wilhelm.

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  • It is, in fact, admitted that some of the glasses, most useful optically, the dense barium crown glasses, which are so widely used in modern photographic lenses, cannot be produced entirely free either from noticeable colour or from numerous small bubbles, while the chemical nature of these glasses is so sensitive that considerable care is required to protect the surfaces of lenses made from them if serious tarnishing is to be avoided.

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  • As the fractured surfaces of the glass in this condition are unsuitable for delicate examination a good deal of glass that passes this inspection has yet ultimately to be rejected.

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  • For the purpose of rendering this minute examination possible, opposite plane surfaces of the glass are ground approximately flat and polished, the faces to be polished being so chosen as to allow of a view through the greatest possible thickness of glass; thus in slabs the narrow edges are polished.

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  • Since the surfaces produced by rolling have subsequently to be ground and polished, it is essential that the glass should leave the rolling-table with as smooth a surface as possible, so that great care is required in this part of the process.

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  • By means of a rotating table either two surfaces of glass, or one surface of glass and one of cast iron, are rubbed together with the interposition of a powerful abrasive such as sand, emery or carborundum.

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  • This entire process must, obviously, be applied in turn to each of the two surfaces of the slab of glass.

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  • A vast quantity of small cups and paterae were made by this means in patterns which bear considerable resemblance to the surfaces of madrepores.

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  • On the other hand, infinitely thin films of silver which can be produced chemically on glass surfaces are absolutely opaque.

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  • The resultant force is therefore in the direction of the steepest pressure-gradient, and this is normal to the surface of equal pressure; for equilibrium to exist in a fluid the lines of force must therefore be capable of being cut orthogonally by a system of surfaces, which will be surfaces of equal pressure.

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  • Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force; n ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some function P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -V, such that the force in any direction is the downward gradient of V; and then dP dV (5) ax + Tr=0, or P+V =constant, in which P may be called the hydrostatic head and V the head of potential.

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  • With variation of temperature, the surfaces of equal pressure and density need not coincide; but, taking the pressure, density and temperature as connected by some relation,such as the gas-equation, the surfaces of equal density and temperature must intersect in lines lying on a surface of equal pressure.

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

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  • In 1785 appeared his Recherches theoriques et experimentales sur la force de torsion et sur l'elasticite des fils de metal, &c. This memoir contained a description of different forms of his torsion balance, an instrument used by him with great success for the experimental investigation of the distribution of electricity on surfaces and of the laws of electrical and magnetic action, of the mathematical theory of which he may also be regarded as the founder.

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  • Beads of baked earth, cylindrical and of all shapes, with smooth or polished surfaces, mostly black and red in colour, were chiefly in use.

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  • With the juice of some canes considerable difficulty is encountered in keeping the heating surfaces of the evaporators clean and free from incrustations, and cleaning by the use of acid has to be resorted to.

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  • The former bears two terminal suckers on the flattened dorsal and ventral surfaces, the latter six hooks near the tip of the tail.

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  • The action of frost is also very destructive to many stones, since the water within their cracks and crannies expands on freezing and splits off small pieces from their surfaces.

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  • Stomata occur on both surfaces of the leaves, and, with the peculiar hair structure render the microscopic appearance of the plant highly characteristic.

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  • This operation, performed in the garden by means of the spade, is carried on in the field on a larger scale by the plough,' which breaks the soil and by inverting the furrow-slice, exposes fresh surfaces to the disintegrating influence of air, rain and frost.

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  • The curved surfaces take the place of fl e the lens in fig.

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  • This condition may be cured completely, or greatly improved, by the use of lenses whose surfaces are segments of cylinders.

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  • In the encrusting type, which is found in a large proportion of the genera, the zooids are usually in a single layer, with their orifices facing away from the substratum; but in certain species the colony becomes multilaminar by the continued superposition of new zooids over the free surfaces of the older ones, whose orifices they naturally occlude.

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  • The undisguised touchec of the chisel tell a story of technical force and directness which could not be suggested by perfectly smooth surfaces.

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  • Electrified bodies exert mechanical forces on each other, creating or tending to create motion, and also induce electric charges on neighbouring surfaces.

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  • If we consider lines of electric force to be drawn from the boundaries of these areas, they will cut up the space round the conductor into tubular surfaces called tubes of electric force, and each tube will spring from an area of the conductor carrying a unit electric charge.

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  • In the next place we may consider the charged body to be surrounded by a number of closed surfaces, such that the potential difference between any point on one surface and the earth is the same.

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  • These surfaces are called "equipotential" or "level surfaces," and we may so locate them that the potential difference between two adjacent surfaces is one unit of potential; that is, it requires one absolute unit of work (I erg) to move a small body charged with one unit of electricity from one surface to the next.

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  • These enclosing surfaces, therefore, cut up the space into shells of potential, and divide up the tubes of force into electric cells.

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  • The potential of such a shell at any internal point is constant, and the equi-potential surfaces for external space are ellipsoids confocal with the ellipsoidal shell.

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  • We may describe, through all the points in an electric field which have the same potential, surfaces called equipotential surfaces, and these will be everywhere perpendicular or orthogonal to the lines of electric force.

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  • We can then establish some important properties of these tubes and surfaces.

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  • Every tube of electric force must therefore begin and end on electrified surfaces of opposite sign, and the quantities of positive and negative electricity on its two ends are equal, since the force E just outside an electrified surface is normal to it and equal to a/41r, where a is the surface density; and since we have just proved that for the ends of a tube of force EdS = E 1 dS', it follows that adS = a'dS', or Q = Q', where Q and Q' are the quantities of electricity on the ends of the tube of force.

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  • In the Knox and Boss mills, which are also employed for the amalgamation of silver ores, the grinding is effected between flat horizontal surfaces instead of conical or curved surfaces as in the previously described forms.

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  • One of the greatest difficulties in the treatment of gold by amalgamation, and more particularly in the treatment of pyrites, arises from the so-called " sickening " or " flouring " of the mercury; that is, the particles, losing their bright metallic surfaces, are no longer capable of coalescing with or taking up other metals.

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  • The gold and other metals are precipitated on the under surfaces of the turnings and fall to the bottom of the compartment as a black slime.

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  • The vertebrae of the neck unite by nearly flat surfaces, the humerus has lost the foramen, or perforation, at the lower end, and the third trochanter to the femur may also be wanting.

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

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  • It may be that the study of such sums, which he found in the works of Diophantus, prompted him to lay it down as a principle that quantities occurring in an equation ought to be homogeneous, all of them lines, or surfaces, or solids, or supersolidsan equation between mere numbers being inadmissible.

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  • The heights to which the liquids rise, measured in each case by the distance between the surfaces in the reservoirs and in the tubes, are inversely proportional to the densities.

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  • The former contrivances consist essentially of levers or cams with toothed surfaces or gripping shoes mounted upon transverse axes attached to the sides of the cage, whose function is to take hold of the guides and support the cage in the event of its becoming detached from the rope.

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  • Third and fourth digits of both feet almost equally developed, and their terminal phalanges flattened on their inner or contiguous surfaces, so that each is not symmetrical in itself, but when the two are placed together they form a figure symmetrically disposed to a line drawn between them.

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  • To promote smoothness of action, the rubbing surfaces are lubricated.

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  • The maintenance of the conditions of steadiness implied in equation (I) depends upon the constancy of F, and therefore of the coefficient of friction µ between the rubbing surfaces.

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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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  • At first the heat-motion will be confined to molecules near the rubbing surfaces of the two bodies, but, as already explained, these will in time set the interior molecules into motion, so that ultimately the heat-motion will become spread throughout the whole mass.

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  • Mineral, vegetable and animal substances, by means of tools and apparatus of stone, wood and bone - tools for cutting, or edged tools; tools for abrading and smoothing the surfaces of substances, like planes, rasps and sandpaper; tools for striking, that is, pounding for the sake of pounding, or for crushing and fracturing violently; perforating tools; devices for grasping and holding firmly.

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  • The colour is usually pale bronze-yellow, often rather lighter than that of pyrites; on freshly fractured surfaces of pure marcasite the colour is tin-white, but this rapidly tarnishes on exposure to air.

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  • A third group, of increasing importance, comprises cases in which curves or surfaces arise out of the application of graphic methods in engineering, physics and statistics.

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  • The process of unrolling is analytical, but the unrolled area can be measured by methods not applicable to other surfaces.

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  • The curved surfaces of the cylinder and of the cone are developable surfaces; i.e.

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  • The theorems are of use, not only for finding the volumes or areas of solids or surfaces of revolution, but also, conversely, for finding centroids or centres of gravity.

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  • In the ordinary case three of the four lateral surfaces of the prismoid are at right angles to the two ends.

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  • In special cases two of these three lateral surfaces are equally inclined to the third.

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  • Many of the oceanic islets are composed of coral limestone, which in this way becomes phosphatized; others are igneous, consisting of trachyte or basalt, and these rocks are also phosphatized on their surfaces but are not so valuable, inasmuch as the presence of iron or alumina in any quantity renders them unsuited for the preppration of artificial manures.

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  • All sections of the 1 The surfaces formed by revolving a circle about any chord also received attention at the hands' of the Greeks.

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  • The pillars composing it are close-fitting and for the most part somewhat irregular hexagons, made up of articulated portions varying from a few inches to some feet in depth, and concave or convex at the upper and lower surfaces.

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  • With the single exception of the Indian sloth-bear, all the species have forty-two teeth, of which the incisors and canines closely resemble those of purely carnivorous mammals; while the molars, and especially the one known as the " sectorial " or " carnassial," have their surfaces tuberculated so as to adapt.

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  • We may now, as is somewhat the more natural course in the terrestrial application, take axes (x,y,z) which move with the matter; but the current must be invariably defined by the flux across surfaces fixed in space, so that we may say that relation (i) refers to a circuit fixed in space, while (ii) refers to one moving with the matter.

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  • Sodium is excreted by all the mucous surfaces and by the liver and kidneys.

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  • In 1714 Ditton published his Discourse on the Resurrection of Jesus Christ; and The New Law of Fluids, or a Discourse concerning the Ascent of Liquids in exact Geometrical Figures, between two nearly contiguous Surfaces.

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  • The junction of the edges of the silver and copper-blend was treated with a flux of borax and the whole was submitted to the heat of a furnace until the silver was seen to be melting, when it was instantly removed, care being taken to avoid pressing upon the upper or lower surfaces, as the liquid silver in that case would have been squeezed out from between the two enclosing plates and the operation ruined.

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  • Festschrift zum 70ten Geburtstage von Ernst Haeckel, 19(34) has restored the conditions existing in the lagoons and atoll reefs of the Jurassic sea of Solnhofen in Bavaria; he has traced the process of gradual accumulation of the coral mud now constituting the fine lithographic stones in the inter-reef region, and has recognized the periodic laying bare of the mud surfaces thus formed; he has determined the winds which carried the dust particles from the not far distant land and brought the insects from the adjacent Jurassic forests.

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  • Long droughts are common in many parts of the country, and on the barren surfaces of the plateau the rains drain away rapidly, leaving but slight beneficial results.

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  • Twinned crystals are not common, but the presence of polysynthetic twinning is sometimes shown by fine striations running diagonally or obliquely across the cleavage surfaces.

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  • Large masses with a coarse or fine granular structure are of common occurrence; the fractured surfaces of such masses present a spangled appearance owing to the numerous bright cleavages.

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  • If the refractive index is, for instance, the same for both in the case of green light, and a source of white light is viewed through the mixture, the green component will be completely transmitted, while the other colours are more or less scattered by multiple reflections and refractions at the surfaces of the powdered substance.

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  • It is very rapidly absorbed from raw surfaces and may thereby cause fatal consequences.

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  • Although composed chiefly of crystalline rocks, which are commonly associated with a rugged landscape, and although possessing a greatly deformed structure, which must at some ancient period have been associated with strong relief, the upland as a whole is gently rolling, and the inter-stream surfaces are prevailing plateau-like in their evenness, with altitudes of 1400 to 1600 ft.

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  • Hoofs of the two middle toes with their contiguous surfaces flattened.

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  • When hardened in situ its shape is that of a right-angled, triangular prism showing five surfaces - superior, anterior, inferior, posterior and right lateral which represents the base of the prism.

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  • The peritoneal surfaces in the region of the liver should then be wiped clean, and the abdominal wound closed, except for the passage through it of a gauze drain.

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  • Many indications of ice action are found in these islands; striated surfaces are to be seen on the cliffs in Eday and Westray, in Kirkwall Bay and on Stennie Hill in Eday; boulder clay, with marine shells, and with many boulders of rocks foreign to the islands (chalk, oolitic limestone, flint, &c.), which must have been brought up from the region of Moray Firth, rests upon the old strata in many places.

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  • Many of them, like ungulates, are specialized for swift running, and have unusually long limbs, with ridges developed on the articular surfaces of the lower bones; the clavicles are more or less reduced; the thorax is more compressed than usual, with a narrower breast-bone; and there is a marked tendency to the reduction or loss of the lateral toes, more especially in the hind limb.

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  • The remaining rodents, which include two families - the picas (Ochotonidae) and the hares and rabbits (Leporidae) - constitute a second sub-order, the Duplicidentata, differing from all the foregoing groups in possessing two pairs of incisors in the upper jaw (of which the second is small, and placed directly behind the large first pair), the enamel of which extends round to their postericr surfaces.

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  • In machinery, abrasion between moving surfaces has to be prevented as much as possible by the use of suitable materials, good fitting and lubrication.

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  • The members of both groups appear to have a power like that possessed by geckos of clinging to vertical surfaces of rocks and trees by the soles of their feet.

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  • Further, in the free surface the solutions of an involatile solute in a volatile solvent, through which surface the vapour of the solvent alone can pass, and in the boundary of a crystal of pure ice in a solution, we have actual surfaces which are in effect perfectly semipermeable.

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  • If the height be not too great, we may assume the density of the vapour to be uniform, and write the difference in vapour pressure at the surfaces of the solvent and of the solution as p - p' = hgo-.

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  • Brucine is a local anaesthetic. Strychnine enters the blood as such, being freely absorbed from mucous surfaces or when given hypodermically.

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  • Experience shows that, although spherical pebbles are to be avoided, Portland cement adheres tightly to smooth flint surfaces, and that rough stones often give a less compact concrete than smooth ones on account of the difficulty of bedding them into the matrix when laying the concrete.

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  • The only geometry known to the Egyptian priests was that of surfaces, together with a sketch of that of solids, a geometry consisting of some simple quadratures and elementary cubatures, which they had obtained empirically.

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  • The coping of garden walls is important, both for the preservation of the walls and for throwing the rain-water off their surfaces.

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  • They are less economical, however, owing to loss of heat from their exposed surfaces.

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  • The damping of all absorbent surfaces, such as the floors or bare walls, &c., is frequently necessary several times a day in the growing season, so as to keep up a humid atmosphere; hence the advantage of laying the floors a little rounded, as then the water draws off to the sides against the kerbstone, while the centre remains dry for promenaders.

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  • Many fungi (Phallus, Agaricus, Fumago, &c.) when strongly growing put out ribbon-like or cylindrical cords, or sheet-like mycelial plates of numerous parallel hyphae, all growing together equally, and fusing by anastomoses, and in this way extend long distances in the soil, or over the surfaces of leaves, branches, &c. These mycelial strands may be white and tender, or the outer hyphae may be hard and black, and very often the resemblance of the subterranean forms to a root is so marked that they are termed rhizomorphs.

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  • The same laws apply to the individual hyphae and their branches as to simple sporophores, and as long as the conidia, sporangia, gametes, &c., are borne on their external surfaces, it is quite consistent to speak of these as compound sporophores, &c., in the sense described, however complex they may become.

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  • The rough appearances of physical facts, their outlines, surfaces and so on, are the data of observation, and only by a method of approximation do we gradually come near to such propositions as are laid down in pure geometry.

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  • The ideas of perfect lines, figures and surfaces have not, according to him, any existence.

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  • They are occasionally adulterated with the leaves of Inula Conyza, ploughman's spikenard, which may be distinguished by their greater roughness, their less divided margins, and their odour when rubbed; also with the leaves of Symphytum officinale, comfrey, and of Verbascum Thapsus, great mullein, which unlike those of the foxglove have woolly upper and under surfaces.

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  • This extraordinary diamond weighed 30254 carats (13 lb) and was clear and water white; the largest of its surfaces appeared to be a cleavage plane, so that it might be only a portion of a much larger stone.

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  • If the plate is thin, it is necessary to measure the thickness with great care, and it is necessary to assume that the temperatures of the surfaces are the same as those of the media with which they are in contact, since there is no room to insert thermometers in the plate itself.

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  • Hall proposed to overcome this difficulty by coating the plate thickly with copper on both sides, and deducing the difference of temperature between the two surfaces of junction of the iron and the copper from the thermo-electric force observed by means of a number of fine copper wires attached to the copper coatings at different points of the disk.

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  • The advantage of the thermo-junction for this purpose is that the distance between the surfaces of which the temperature-difference is measured, is very exactly defined.

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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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  • The isothermal surfaces are coaxial cylinders.

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  • If the thickness of the glass is small compared with the diameter of the tube, say one-tenth, equation (1) may be applied with sufficient approximation, the area A being taken as the mean between the internal and external surfaces.

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  • Unfortunately the method cannot be applied to good conductors, like the metals, because the difference of temperature between the surfaces may be five or ten times less than that between the water and steam in contact with them, even if the water is ener-, TABLE I.

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  • From the surfaces of all objects there are continually flowing thin filmy images exactly copying the solid body whence they originate; and these images by direct impact on the organism produce (we need not care to ask how) the phenomena of vision.

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  • The surfaces are not in the least subdued by a general breadth of style, as in the last period; but, on the contrary, revel in the full detail of variety.

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  • It was full of delicate variety in the surfaces, and of elaborated close-packed lines of hair and ornaments.

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  • For dressing flat surfaces three wooden pegs (102) of equal length were used; a string was stretched between the tops of two, and the third peg was set on the point to be tested and tried against the string.

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  • This is of blocks of limestone whose faces follow the natural cleavages, and only dressed where needful; part is hammer-dressed, but most of the surfaces are adze-dressed.

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  • The facing of the cloven surfaces was done by hammer-dressing, using rounded masses of quartzose hornstone, held in the hand without any handle.

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  • In the latter age granite surfaces were ground, hieroglyphs were chipped out and polished by copper tools fed with emery; outlines were graved by a thick sheet of copper held in the hand, and sawed to and fro with emery.

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  • Large ring-stands also were brought in, to support jars, so that the damp surfaces should not touch the dusty ground.

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  • In tracing the tonus of neurons to a source, one is always led link by link against the current of nerve force - so to say, "up stream" - to the first beginnings of the chain of neurons in the sensifacient surfaces of the body.

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  • These aggregations or colonies, as they are termed, may attached to muddy surfaces by rhizoids; Caulerpa, on the other, assume the form of a plate, a ring, a solid sphere, a hollow sphere, presents a remarkable instance of the way in which much the same a perforate sphere, a closed net, or a simple or branched filament.

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  • Gaps then appear in the apposed surfaces, usually at the isthmus; the entire protoplasts either pass out to melt into one another clear of the old walls, or partly pass out and fuse without complete detachment from the old walls.

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  • The thallus is somewhat spherical and unicellular, exhibiting a distinction between anterior and posterior extremities, and dorsal and ventral surfaces.

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  • A very few species, like Chroolepus, which grows on rock surfaces, are comparable with the land plants which have been termed xerophilous.

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  • The drama of the subject has in this instance not interested him at all, but only the forms and designs of the figures, the realization of the quality of flesh surfaces by the subtlest use of the graving-tool known to him, and the rendering, by methods of which he had become the greatest of all masters, of the richness and intricacy of the forest background.

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  • The hind feet have six pads on their inferior surfaces, and the colour is dull grizzled brown above and greyish white below.

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  • The tail is about half the length of the head and body, and the hind feet are long and powerful, although not webbed, and have five rounded pads on their lower surfaces.

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  • A cement for Derbyshire spar and china, &c., is composed of 7 parts of rosin and i of wax, with a little plaster of Paris; a small quantity only should be applied to the surfaces to be united, for, as a general rule, the thinner the stratum of a cement, the more powerful its action.

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  • Japanese cement, for uniting surfaces of paper, is made by mixing rice-flour with water and boiling it.

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  • The coat is remarkable for its density and compactness; the general colour of the head and upper parts being clove-brown, with more or less white or whitish grey on the under parts and inner surfaces of the limbs, while there is also some white above the hoofs and on the muzzle, and there may be whitish rings round the eyes; there is a white area in the region of the tail, which includes the sides but not the upper surface of the latter; and the tarsal tuft is generally white.

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  • These alluvial terraces form a strip of low fertile land between the edge of the sea and the rising ground of the interior, and among the western fjords sometimes supply the only arable soil in their neighbourhood, their flat green surfaces presenting a strong contrast to the brown and barren moors that rise from them.

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  • Oxygen may be applied locally as a disinfectant to foul and diseased surfaces by the use of the peroxide of hydrogen, which readily parts with its oxygen; a solution of hydrogen peroxide therefore forms a valuable spray in diphtheria, tonsillitis, laryngeal tuberculosis and ozaena.

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  • The volcanic character of the region is likewise responsible for large areas of barren surfaces.

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  • The line of permanent snow is much higher on the plateau side in both ranges, the precipitation being greater on the outer sides - those facing the forested lowlands - and the terrestrial radiation being greater from the barren surfaces of the plateau.

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  • Their lower articular surfaces, instead of being pulley-like, with deep ridges and grooves, as in other Artiodactyla, are simple, rounded and smooth.

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  • The terminal phalanges are small and nodular, not flattened on their inner or opposed surfaces, and not completely encased in hoofs, but bearing nails on their upper surface only.

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  • These bones, although separate, have their adjacent surfaces more closely applied than is the case in the latter; while in this and the earlier genera the terminal toe-bones indicate that the foot was of the normal hoofed type.

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  • The abundance in which iron is found in so many places, its great strength, its remarkable ductility and malleability in a red-hot state, and the ease with which two heated surfaces of iron can be welded together under the hammer combine to make it specially suitable for works on a large scale where strength with lightness are required - things such as screens, window-grills, ornamental hinges and the like.

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  • Bright surfaces are protected with oil or with lacquer.

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  • Until Newton's discovery of the different refrangibility of light of different colours, it was generally supposed that object-glasses of telescopes were subject to no other errors than those which arose from the spherical figure of their surfaces, and the efforts of opticians were chiefly directed to the construction of lenses of other forms of curvature.

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  • James Gregory, in his Optica Promota (1663), discusses the forms of images and objects produced by lenses and mirrors, and shows that when the surfaces of the lenses or mirrors are portions of spheres the images are curves concave towards the objective, but if the curves of the surfaces are conic sections the spherical aberration is corrected.

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  • Comparisons of light grasp derived from small, fresh, carefully silvered surfaces are sometimes given which lead to illusory results, and from such experiments Foucault claimed superiority for the silvered speculum over the object-glass.

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  • Equatorials of types A, B, C and D have the advantage of avoiding interposed reflecting surfaces, but they involve inconveniences from the continual motion of the eye-piece and the consequent necessity for providing elaborate observing stages or rising floors.

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  • In those of type E the eye-piece has a fixed position and the observer may even occupy a room maintained at uniform temperature, but he must submit to a certain loss of light from one or more reflecting surfaces, and from possible loss of definition from optical imperfection or flexure of the mirror or mirrors.

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  • The shape of the universe may thus be compared to that of a grindA stone or lens, the sun being situated about midway between the two surfaces.

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  • When the two metal surfaces are connected for a short time with the terminals of some source of electromotive force, such as an electric machine, an induction coil or a voltaic battery, electric energy is stored up in the condenser in the form of electric strain in the glass, and can be recovered again in the form of an electric discharge.

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  • For this purpose they are made by Moscicki in the form of glass tubes partly coated by silver chemically deposited on the glass on the inner and outer surfaces.

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  • All the lugs on one side are connected together, and so also are all the lugs on the other side, and the two sets of tin foils separated by sheets of mica constitute the two metallic surfaces of the Leyden jar condenser.

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  • In the theory of surfaces, in hydrokinetics, heat-conduction, potentials, &c., we constantly meet with what is called " Laplace's operator," viz.

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  • The Cambrian rocks previ-, ously described are all such as would result from deposition, in comparatively shallow seas, of the products of degradation of land surfaces by the ordinary agents of denudation.

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  • Evidences of shallow water conditions arc abundant; very frequently on the bedding surfaces of sandstones and other rocks we find cracks made by the sun's heat and pittings caused by the showers that fell from the Cambrian sky, and these records of the weather of this remote period are preserved as sharply and clearly as those made only to-day on our tidal reaches.

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  • The precise value of X will vary with the nature and condition of the surfaces in contact.

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  • For instance, the position of a theodolite is fixed by the fact that its rounded feet rest in contact with six given plane surfaces.

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  • Again, the normal pressure between two surfaces disappears from the equation, provided the displacements be such that one of these surfaces merely slides relatively to the other.

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  • It is evident, in the first place, that in any displacement common to the two surfaces, the work of the two equal and opposite normal pressures will cancel; moreover if, one of the surfaces being fixed, an infinitely small displacement shifts the point of contact from A to B, and if A be the new position of that point of the sliding body which was at A, the pro jectior of AA on the normal at A is of the second order.

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  • For the virtual work of two equal anc opposite forces will cancel in any displacement which is commor to the two surfaces; whilst, if one surface be fixed, the displace ment of that point of the rolling surface which was in contact with the other is of the second order.

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  • In other cases the safety of the joint against displacement by sliding depends on its power of exerting friction, and that power depends on the law, known by experiment, that the friction between two surfaces bears a constant ratio, depending on the nature 01 the surfaces, to the force by which they are pressed together.

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  • In order that the surfaces which abut at the Joint JK maybe pressed together, the resistance required by the conditions of equilibrium CR, must be a thrust and not a pull; and in that case the force by which the surfaces are pressed together is equal and opposite to the normal component CP of the resistance.

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  • Conditions of Stiffness and Strength.After the arrangement of the pieces of a structure and the size and figure of their joints or surfaces of contact have been determined so as to fulfil the conditions of stabilityconditions which depend mainly on the position and direction of the resultant or total load on each piece, and the relative magnitude of the loads on the different piecesthe dimensions of each piece singly have to be adjusted so as to fulfil the conditions of stiffness and strengthconditions which depend not only on the absolute magnitude of the load on each piece, and of the resistances by which it is balanced, but also on the mode of distribution of the load over the piece, and of the resistances over the joints.

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  • Points, lines and surfaces have no independent existence, and consequently those divisions of this chapter which relate to their motions are only preliminary to the subsequent divisions, which relate to the motions of bodies.

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  • In the wheel and axle, motion is received and transmitted by two cylindrical surfaces of different radii described about their common fixed axis of turning, their velocity-ratio being that of their radii.

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  • The whole of the foregoing reasonings are applicable, not merely when A and B are actual regular cones, but also when they are the osculating regular cones of a pair of irregular conical surfaces, having a common apex at 0.

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  • That for a pair of turning pieces with parallel axes, and for a turning piece and a shifting piece, the line of contact is straight, and parallel to the axes or axis; and hence that the rolling surfaces are either plane or cylindrical (the term cylindrical including all surfaces generated by the motion of a straight line parallel tO itself).

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  • The pitch-surfaces of a pair of toothed wheels are the ideal smooth surfaces which would have the same comparative motion by rolling contact that the actual wheels have by the sliding contact of their teeth.

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  • Teeth of Bevel- Wheels.The acting surfaces of the teeth of bevel-wheels are of the conical kind, generated by the motion of a line passing through the common apex of the pitch-cones, while its extremity is carried round the outlines of the cross section of the teeth made by a sphere described about that apex.

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  • Describe the figures of teeth for the developed arcs as for a pair of spur-wheels; then wrap the developed arcs on the cones, so as to make them coincide with the pitch-circles, and trace the teeth on the conical surfaces.

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  • At the point of contact of the screws their threads must be parallel; and their line of connection is the common nerpendicular to the acting surfaces of the threads at their point 0f contact.

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  • Reuleaux has shown that the relative motion of any pair of nonadjacent links of a kinematic chain is determined by the rolling together of two ideal cylindrical surfaces (cylindrical being used here in the general sense), each of which may be assumed to be formed by the extension of the material of the link to which it corresponds.

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  • These surfaces have contact at the instantaneous axis, which is now called the instantaneous axis of the two links concerned.

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  • To find the form of these surfaces corresponding to a particular pair of non-adjacent links, consider each link of the pair fixed in turn, then the locus of the instantaneous axis is the axode corresponding to the fixed link, or, considering a plane of motion only, the locus of the instantaneous centre is the ceotrode corresponding to the fixed link.

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  • Unguents.The most important kind of resistance in machines is the friction or rubbing resistance of surfaces which slide over each other.

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  • The total pressure exerted between the rubbing surfaces is the resultant of the normal pressure and of the friction, and its obliquity, or inclination to the common perpendicular of the surfaces, is the angle of repose formerly mentioned in 14, whose tangent is the coefficient of friction.

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  • Moment of Friction.The work performed in a unit of time in overcoming the friction of a pair of surfaces is the product of the friction by the velocity of sliding of the surfaces over each other, if that is the same throughout the whole extent of the rubbing surfaces.

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  • If that velocity is different for different portions of the rubbing surfaces, the velocity of each portion is to be multiplied by the friction of that portion, and the results summed or integrated.

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  • When the relative motion of the rubbing surfaces is one of rotation, the work of friction in a unit of time, for a portion of the rubbing surfaces at a given distance from the axis of rotation, may be found by multiplying together the friction of that portion, its distance from the axis, and the angular velocity.

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  • The total moment of friction of a pair of rotating rubbing surfaces is the sum or integral of the moments of friction of their several portions.

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  • To express this symbolically, let dii represent the area of a portion of a pair of rubbing surfaces at a distance r from the axis of their relative rotation; p the intensity of the normal pressure at du per unit of area; and f the coefficient of friction.

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  • Let N be the total pressure sustained by a flat pivot of the radius r; if that pressure be uniformly distributed, which is the case when the rubbing surfaces of the pivot and its step are both true planes, the intensity of the pressure is pN/irr2 (60)

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  • Between the concave spherical surfaces of those cups is placed a steel 0 ball, being either a complete sphere or a lens having convex surfaces of a somewhat less radius p i than the concave surfaces of the cups.

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  • Rolling Resistance.By the rolling of two surfaces over each other without sliding a resistance is caused which is called sometimes rolling friction, but more correctly rolling resistance.

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  • Its moment is found by multiplying the normal pressure between the rolling surfaces by an arm, whose length depends on the nature of the rolling surfaces, and the work lost in a unit of time in overcoming it is the product of its moment by the angular velocity of the rolling surfaces relatively to each other.

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  • The first of these usually carries a ventral tube, furnished with paired eversible sacs which assist the insects in walking on smooth surfaces, and perhaps serve also as organs for breathing.

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  • A notable feature of Finland are the asar or narrow ridges of morainic deposits, more or less reassorted on their surfaces.

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  • For the nature and method of preparing these surfaces see respectively Engraving (and allied articles), Lithography and Typography.

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  • Greater power was obtained at a smaller expenditure of labour, and it allowed of larger and heavier surfaces being printed.

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  • Two-colour machines, usually made with one feed, that is, with only one cylinder, but with two printing surfaces, and two sets of inking apparatus one at each end of the machine.

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  • As its name implies, the type bed and impression platen are both flat surfaces as in the hand-press, but as they are self-inking and are easily driven, the average output is about moo copies per hour, and but one operator is required, whereas two men at a handpress can produce only 250 copies in the same time.

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  • As the name implies, these presses are so constructed that both printing surfaces and paper to duplicate the type pages and to run several machines at the same time, thus producing copies with far greater rapidity.

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  • The inking arrangements are placed at the two extreme ends of these four drums or cylinders, thus being near the type surfaces in each case.

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  • In "autogenous soldering" two pieces of metal are united by the melting of the opposing surfaces, without the use of a separate fusible alloy or solder as a cementing material.

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  • Henry Wilde, in 1875, in depositing copper on iron printing-rollers, recognized this principle and rotated the rollers during electrolysis, thereby renewing the surfaces of metal and liquid in mutual contact, and imparting sufficient motion to the solution to prevent stratification; as an alternative he imparted motion to the electrolyte by means of propeller blades.

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  • When applied to broken skin or exposed surfaces it coagulates the albumen in the discharges, forming a protecting layer or coat.

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  • The desert regions of the north include comparatively large areas of plains and gently sloping surfaces, traversed by ranges of barren hills.

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  • Consequently the monochromatic class includes the aberrations at reflecting surfaces of any coloured light, and at refracting surfaces of monochromatic or light of single wave length.

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  • Two " astigmatic image surfaces " correspond to one object plane; and these are in contact at the axis point; on the one lie the focal lines of the first kind, on the other those of the second.

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  • Systems in which the two astigmatic surfaces coincide are termed anastigmatic or stigmatic.

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  • If the above errors be eliminated, the two astigmatic surfaces united, and a sharp image obtained with a wide aperture - there remains the necessity to correct the curvature of the image surface, especially when the image is to be received upon a plane surface, e.g.

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  • Spherical aberration and changes of the sine ratios are often represented graphically as functions of the aperture, in the same way as the deviations of two astigmatic image surfaces of the image plane of the axis point are represented as functions of the angles of the field of view.

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  • Rather smaller than a squirrel, with dusky brown fur, the tarsier has immense eyes, large ears, a long thin tail, tufted at the end, a greatly elongated tarsal portion of the foot, and disk-like adhesive surfaces on the fingers, which doubtless assist the animal in maintaining its position on the boughs.

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  • The sandy zone along the coast is nearly barren, but behind this is a more elevated region with broken surfaces and sandy soil which is amenable to cultivation and produces fruit and most tropical products when conditions are favourable.

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  • He found that a magnetic needle, made to oscillate over nonferruginous surfaces, such as water, glass, copper, &c., falls more rapidly in the extent of its oscillations according as it is more or less approached to the surface.

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  • The wood, like that of other species, is applicable to many purposes - as for the seats of Windsor chairs, turnery, &c. The grain in very old trees is sometimes undulated, which suggested the name of curled maple, and gives beautiful effects of light and shade on polished surfaces.

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  • In the rat-kangaroos, or kangaroo-rats, as they are called in Australia, constituting the sub-family Potoroinae, the first upper incisor is narrow, curved, and much exceeds the others in length; the upper canines are persistent, flattened, blunt and slightly curved, and the first two premolars of both jaws have large, simple, compressed crowns, with a nearly straight or slightly concave free cutting-edge, and both outer and inner surfaces usually marked by a series of parallel, vertical grooves and ridges.

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  • He attributed this force, however, not to any general property of the surfaces of liquids, but to the fatty part of the soap which he supposed to separate itself from the other constituents of the solution, and to form a thin skin on the outer face of the bubble.

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  • The tension of the surface separating two liquids which do not mix cannot be deduced by any known method from the tensions of the surfaces of the liquids when separately in contact with air.

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  • If three fluids which do not mix are in contact with each other, the three surfaces of separation meet in a line, straight or curved.

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  • The three angles between the tangent planes to the three surfaces of separation at the point 0 are completely determined by the tensions of the b o a three surfaces.

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  • For if in the triangle abc the side ab is taken so as to represent on a given scale the tension of the surface of contact of the fluids a and b, and if the other sides be and ca are taken so as to represent on the same scale the tensions of the surfaces between b and c and between c and a respectively, then the condition of equilibrium at 0 for the corresponding tensions R, P and Q is that the angle ROP shall be the supplement of abc, POQ of bca, and, therefore, QOR of cab.

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  • Thus the angles at which the surfaces of separation meet are the same at all parts of the line of concourse of the three fluids.

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  • If four fluids, a, b, c, d, meet in a point 0, and if a tetrahedron AB CD is formed so that its edge AB represents the tension of the surface of contact of the liquids a and b, BC that of b and c, and so on; then if we place this tetrahedron so that the face ABC is normal to the tangent at 0 to the line of concourse of the fluids abc, and turn it so that the edge AB is normal to the tangent plane at 0 to the surface of contact of the fluids a and b, then the other three faces of the tetrahedron will be normal to the tangents at 0 to the other three lines of concourse of the liquids, an the other five edges of the tetrahedron will be normal to the tangent planes at 0 to the other five surfaces of contact.

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  • If no one of these tensions is greater than the sum of the other two, the drop will assume the form of a lens, the angles which the upper and lower surfaces of the lens make with the free surface of A and with each other being equal to the external angles of the triangle of forces.

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  • But when the surface-tension of A exceeds the sum of the tensions of the surfaces of contact of B with air and with A, it is impossible to construct the triangle of forces, so that equilibrium becomes impossible.

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  • The edge of the drop is drawn out by the surface-tension of A with a force greater than the sum of the tensions of the two surfaces of the drop. The drop, therefore, spreads itself out, with great velocity, over the surface of A till it covers an enormous area, and is reduced to such extreme tenuity that it is not probable that it retains the same properties of surface-tension which it has in a large mass.

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  • This drop will not spread out like the first drop, but will take the form of a flat lens with a distinct circular edge, showing that the surface-tension of what is still apparently pure water is now less than the sum of the tensions of the surfaces separating oil from air and water.

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  • Operating in this way there is no difficulty in obtaining surfaces upon which a drop of water spreads, although from causes that cannot always be traced, a certain proportion of failures is met with.

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  • If the distance between the inner surfaces of the plates is a, and if the mean height of the film of fluid which rises between them is h, the weight of fluid raised is pghla.

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  • Moreover, a different behaviour is observed when the surfaces are slightly dusted over.

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  • The bubble, in fact, has two surfaces, an outer and an inner surface, both exposed to air.

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  • It has, therefore, a certain amount of surface-energy depending on the area of these two surfaces.

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  • Since in the case of thin films the outer and inner surfaces are approximately equal, we shall consider the area of the film as representing either of them, and shall use the symbol T to denote the energy of unit of area of the film, both surfaces being taken together.

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  • Hence the equation of work and energy is p dV = Tds (6) 41rpr 2 dr = 8zrrdrT (7) p = 2T/r (8) This, therefore, is the excess of the pressure of the air within the bubble over that of the external air, and it is due to the action of the inner and outer surfaces of the bubble.

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  • We must remember that since the film has two surfaces the surface-tension of the film is double the tension of the surface of the liquid of which it is formed.

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  • This equation, which gives the pressure in terms of the principal radii of curvature, though here proved only in the case of a surface of revolution, must be true of all surfaces.

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  • If we suppose that upon the whole the air cannot be removed, so that the mean distance between the opposed surfaces remains constant, the electric attractions tend to produce an instability whereby the smaller intervals are diminished while the larger are increased.

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  • Extremely local contacts of the liquids, while opposed by capillary tension which tends to keep the surfaces flat, are thus favoured by the electrical forces, which moreover at the small distances in question act with exaggerated power.

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  • It would seem that the surfaces, coming into collision within a fraction of a second of their birth, would still be subject to further contamination from the interior.

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  • Now let us consider the surfaces of revolution formed by this system of catenaries revolving about the directrix of the two catenaries of equal tension.

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  • The mean curvature of these surfaces is therefore convex towards the axis.

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  • The mean curvature of these surfaces is, therefore, concave towards the axis.

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  • And of all Arizona it should be said that owing to the extreme dryness of the air, evaporation from moist surfaces is very rapid,' so that the high temperatures here are decidedly less oppressive than much lower temperatures in a humid atmosphere.

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  • These forms are termed by Fischer Metatrophic, because they require various kinds of organic materials obtained from the dead remains of other organisms or from the surfaces of their bodies, and can utilize and decompose them in various ways (Polytrophic) or, if monotrophic, are at least unable to work them up. The true parasites - obligate parasites of de Bary - are placed by Fischer in a third biological group, Paratrophic bacteria, to mark the importance of their mode of life in the interior of living organisms where they live and multiply in the blood, juices or tissues.

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  • He summed up his results in the general statement that "hydrogen, the alkaline substances, the metals and certain metallic oxides are attracted by negatively electrified metallic surfaces, and repelled by positively electrified metallic surfaces; and contrariwise, that oxygen and acid substances are attracted by positively electrified metallic surfaces and repelled by negatively electrified metallic surfaces; and these attractive and repulsive forces are sufficiently energetic to destroy or suspend the usual operation of elective affinity."

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  • Among his most remarkable works may be mentioned his ten memoirs on quantics, commenced in 1854 and completed in 1878; his creation of the theory of matrices; his researches on the theory of groups; his memoir on abstract geometry, a subject which he created; his introduction into geometry of the "absolute"; his researches on the higher singularities of curves and surfaces; the classification of cubic curves; additions to the theories of rational transformation and correspondence; the theory of the twenty-seven lines that lie on a cubic surface; the theory of elliptic functions; the attraction of ellipsoids; the British Association Reports, 1857 and 1862, on recent progress in general and special theoretical dynamics, and on the secular acceleration of the moon's mean motion.

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  • Usually it is found on the British coast encrusting rocks exposed at low tides, or on the flat surfaces formed by sandbanks overlying clay, the latter kind of colonies being known locally as "scalps."

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  • No machine, however light and powerful, will ever fly whose travelling surfaces are not properly fashioned and properly applied to the air.

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  • It must launch itself in the ocean of air, and must extract from that air, by means of its travelling surfaces - however fashioned and however applied - the recoil or resistance necessary to elevate and carry it forward.

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  • Extensive inert surfaces indeed are contra-indicated in a flying machine, as they approximate it to the balloon, which, as has been shown, cannot maintain its position in the air if there are air currents.

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  • These appliances as indicated should not be unnecessarily expanded, but when expanded they should, wherever practicable, be converted into actively moving flying surfaces, in preference to fixed or inert dead surfaces.

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  • As there are active and passive surfaces in the flying animal, so there are, or should be, active and passive surfaces in the flying machine.

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  • The active surfaces in flying creatures are always greatly in excess of the passive ones, from the fact that the former virtually increase in proportion to the spaces through which they are made to travel.

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  • Nature not only distinguishes between active and passive surfaces in flying animals, but she strikes a just balance between them, and utilizes both.

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  • She regulates the surfaces to the strength and weight of the flying creature and the air currents to which the surfaces are to be exposed and upon which they are to operate.

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  • As a rule she reduces the passive surfaces of the body to a minimum; she likewise reduces as far as possible the actively moving or flying surfaces.

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  • While, however, diminishing the surfaces of the flying animal as a whole, she increases as occasion demands the active or wing surfaces by wing movements, and the passive or dead surfaces by the forward motion of the body in progressive flight.

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  • They can be moved, and the angles made by their under surfaces with the horizon adjusted.

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  • He also explained that all wings act upon a common principle, and that they present oblique, kite-like surfaces to the air, through which they pass much in the same way that an oar passes through water in sculling.

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  • This twisting is in a great measure owing to the manner in which the bones of the wing are twisted upon themselves, and the spiral nature of their articular surfaces - the long axes of the joints always intersecting each other b FIG.

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  • To meet these peculiarities the insect, bird and bat are furnished with extensive flying surfaces in the shape of wings, which they apply with singular velocity and power to the air, as levers of the third order.

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  • If, however, the bird is fairly launched in space and a stiff breeze is blowing, all that is required in many instances is to extend the wings at a slight upward angle to the horizon so that the under parts of the wings present kite-like surfaces.

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  • While, therefore, there is apparently no correspondence between the area of the wing and the animal to be raised, there is, except in the case of sailing insects, birds and bats, an unvarying relation as to the weight and number of oscillations; so that the problem of flight would seem to resolve itself into one of weight, power, velocity and small surfaces, versus buoyancy, debility, diminished speed and extensive surfaces - weight in either case being a sine qua non.

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  • The existence of such a law is very encouraging so far as artificial flight is concerned, for it shows that the flying surfaces of a large, heavy, powerful flying machine will be comparatively small, and consequently comparatively compact and strong.

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  • The kite-like surfaces and angles made by the wing with the horizon (a, b) during the down strokes are indicated at c d e f g, j k l m, - those made during the up strokes being indicated at g h i.

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  • The kite-like surfaces referred to in natural flight are those upon which the constructors of flying machines very properly ground their hopes of ultimate success.

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  • These surfaces may be conferred on artificial wings, aeroplanes, aerial screws or similar structures; and these structures, if we may judge from what we find in nature, should be of moderate size and elastic. The power of the flying organs will be increased if they are driven at a comparatively high speed, and particularly if they are made to reverse and reciprocate, as in this case they will practically create the currents upon which they are destined to rise and advance.

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  • The angles made by the kite-like surfaces with the horizon should vary according to circumstances.

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  • They were all constructed on a common principle, and were provided with extensive flying surfaces in the shape of rigid aeroplanes inclined at an upward angle to the horizon, and more or less fixed on the plan advocated by Henson.

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  • When the aerodrome rose to the surface, it was found that while the front sustaining surfaces had been broken by their impact with the water, yet the rear ones were comparatively uninjured.

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  • Chanute in America confined his endeavours to the production of automatic stability, and made the surfaces movable instead of the man.

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  • The rudder for lateral steering was placed about 21 metres behind the main surfaces and was formed of two vertical pivoted aeroplanes.

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  • A, B, Main supporting surfaces.

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  • After much litigation it has now been established that this provision does not give the council an absolute property in the soil of the street, but merely such a qualified property in the surfaces as enables them to exercise control.

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  • In mathematics, the "caustic surfaces" of a given surface are the envelopes of the normals to the surface, or the loci of its centres of principal curvature.

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  • Jacobi, he extended these results to curves and surfaces of unequal order.

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  • Plucker himself worked out the theory of complexes of the first and second order, introducing in his investigation of the latter the famous complex surfaces of which he caused those models to be constructed which are now so well known to the student of the higher mathematics.

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  • Where surfaces in riveted work come in contact they shall be painted before assembling.

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  • Nevertheless, holding that every dimension has a principle of its own, he rejected the derivation of the elemental solids - pyramid, octahedron, icosahedron and cube - from triangular surfaces, and in so far approximated to atomism.

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  • In size they vary between wide limits, from minute sparkling points encrusting rock surfaces and often so thickly clustered together as to produce a drusy effect, to large single crystals measuring a yard in length and diameter and weighing half a ton.

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  • The equations of surfaces of equal angular motion would be of the form r =R (i --6 cos 2 0), where e is proportional to the square of the angular motion, supposed small, and R increases as e diminishes.

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  • The fact is that radiation is not a superficial phenomenon but a molar one, and Stefan's law, exact though it be, is not an ultimate theory but only a convenient halting-place, and the radiations of two bodies can only be compared by it when their surfaces are similar in a specific way.

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  • One characteristic of such surfaces is fixity, which has no trace of parallel in the sun.

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  • On the upheaval of such rocks above the sea-level, fresh water from rainfall began to flow over their exposed surfaces, and, so far as the strata were permeable, to lie in their interstices upon the salt water.