Measured sentence example

measured
  • You're supposed to go down to be measured in the morning.
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  • "I know that man," he said in a cold, measured tone, evidently calculated to frighten Pierre.
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  • I must tell you, mon cher," he continued in the sad and measured tones of a man who intends to tell a long story, "that our name is one of the most ancient in France."
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  • Pierre was taken back to his place, and the rows of troops on both sides of the post made a half turn and went past it at a measured pace.
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  • She said in a measured tone.
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  • All kinds of energy are ultimately measured in terms of work.
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  • He was quickly measured and fitted and rejoined the others, relieved of a few more dollars.
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  • She opened the refrigerator door for him, releasing her breath in a measured dose.
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  • The amount of heat absorbed by the air could thus be measured, while the work done by it in expanding could be readily calculated.
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  • The speed of the ship can be roughly estimated from the speed of the engines; it is more accurately obtained by one or other of the various forms of log, or it may be measured by paying out continuously a steel wire over a measuring wheel.
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  • The ordinates of the curve give the strain in cwts., and the abscissae the distance in miles measured from the Canso end; as the strain is proportional to the depth, 18 cwts.
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  • This last circuit has a natural frequency of its own which is numerically measured by I/27r-!(CL), where C is the capacity of the condenser and L is the inductance of the circuit.
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  • Another method of charge, known as the " measured service rate," is de - signed to make the subscriber pay in proportion to the quality and quantity of the service he takes.
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  • The northern portion, measured from the Alps at the Monte Viso to the mouth of the Po, has a breadth of about 270 m., while the maximum breadth, from the Rocca Chiardonnet near Susa to a peak in the valley of the Isonzo, is 354 m.
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  • The Arab astronomers measured a degree on the plains of Mesopotamia, thereby deducing a fair approximation to the size of the earth.
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  • Then we will all go down together and Maria can get acquainted with her while you are measured for a dress.
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  • His tone was measured.
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  • "Why did you choose to come here?" he asked in a measured tone.
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  • "Are you all right?" he asked in a measured tone.
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  • The cell where she sat measured six by six with a grey bench.
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  • It was his turn to hear measured breathing beside him as Cynthia drifted off to sleep.
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  • Maybe it was because he was trying to control his emotions, but his kiss was measured.
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  • The fundamental conception that underlay all Berthelot's chemical work was that all chemical phenomena depend on the action of physical forces which can be determined and measured.
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  • According to one story, Archimedes was puzzled till one day, as he was stepping into a bath and observed the water running over, it occurred to him that the excess of bulk occasioned by the introduction of alloy could be measured by putting the crown and an equal weight of gold separately into a vessel filled with water, and observing the difference of overflow.
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  • If the actual crests of the excursions had been measured the figures in the second line would have been even larger.
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  • Eusebius in his Onomasticon uses it as a central point from which the distances of other towns are measured.
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  • The angle between two objects, such as stars or the opposite limbs of the sun, was measured by directing an arm furnished with fine " sights " (in the sense of the " sights " of a rifle) first upon one of the objects and then upon the other (q.v.), or by employing an instrument having two arms, each furnished with a pair of sights, and directing one pair of sights upon one object and the second pair upon the other.
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  • Few persons can see with the naked eye - much less measure - more than six stars of the Pleiades, although all the stars measured by Maestlin have been seen with the naked eye by a few individuals of exceptional powers of eyesight.
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  • Sir William Herschel was the first astronomer who measured position angles; the instrument he employed is described in Phil.
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  • The end-plane of this cylinder receives the pressure of the micrometer screw, so that by turning the small drum-head the coincidence-reading of the movable web with the fixed web can be changed, and thus any given angle can be measured with different FIG.
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  • Its fundamental principle is that, by a combination of glass scales with a micrometer screw, " the chief part of the distance to be measured is read off on the scale; the fractional part of the scalespace is not estimated but measured by the screw."
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  • This is about a semitone below the Diapason Normal, and a just minor third lower than the St Jacobi organ in the same city (1688), measured by Herr Schmahl, a' 489.2.
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  • Thus if the instrument depends on the pressure or suction effect alone, and this pressure or suction is measured against the air pressure in an ordinary room, in which the doors and windows are carefully closed and a newspaper is then burnt up the chimney, an effect may be produced equal to a wind of io m.
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  • A metal vessel was placed in a calorimeter and air forced into it, the amount of energy expended in compressing the air being measured.
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  • The arc measured was 3° 7' 3" in length; and the work consisted of two measured bases connected by a series of triangles, one north and the other south of the equator, on the meridian of Quito.
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  • 1738, Pierre Louis Moreau de Maupertuis, Alexis Claude Clairaut, Charles Etienne Louis Camus, Pierre Charles Lemonnier and the Swedish physicist Celsius measured an arc of the meridian in Lapland.
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  • The measurement of a coast-line is difficult, because the length will necessarily be greater when measured on a largescale map where minute irregularities can be taken into account.
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  • It is usual to distinguish between the general coast-line measured from point to point of the headlands disregarding the smaller bays, and the detailed coast-line which takes account of every inflection shown by the map employed, and follows up river entrances to the point where tidal action ceases.
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  • Density of population is measured by the average number of people residing on a unit of area; but in order to compare one part of the world with another the average should, strictly speaking, be taken for regions of equal size or of equal population; and the portions of the country which are permanently uninhabitable ought to be excluded from the calculation.'
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  • In the log-glass the time is measured by running sand, which, however, is apt to be affected by the humidity of the atmosphere.
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  • In Germany, therefore, the importance of the Moravians must be measured, not by their numbers, but by their influence upon other Christian bodies.
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  • The rate at which work is done on a particular axle is measured by the product where T is the torque or turning moment exerted on the axle by the motor or mechanism applied to it for this purpose, and is the angular velocity of the axle in radians per second.
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  • - Gradients are measured either by stating the number of feet horizontally, G say, in which the vertical rise is I ft., or by the vertical rise in too ft.
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  • The difference between the horizontal distance and the distance measured along the rail is so small that it is negligible in all practical calculations.
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  • The difference of pressure between the outside air and the smoke-box gases may be measured by the difference of the water levels in the limbs of a U tube, one limb being in communication with the smokebox, the other with the atmosphere.
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  • The area of the diagram may be measured, but it is usually more convenient to calculate the number of B.Th.U.
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  • More original, perhaps, is the argument in the immediately preceding work, The Destiny of Man, viewed in the Light of his Origin (1884), which is, in substance, that physical evolution is a demonstrated fact; that intellectual force is a later, higher and more potent thing than bodily strength; and that, finally, in most men and some "lower animals" there is developed a new idea of the advantageous, a moral and non-selfish line of thought and procedure, which in itself so transcends the physical that it cannot be identified with it or be measured by its standards, and may or must be enduring, or at its best immortal.
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  • Known quantities of the solutions are taken, and the temperature of each is accurately measured before mixing, the solutions having been allowed as far as possible to adjust themselves to the same temperature.
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  • The chemical symbols stand for quantities measured in grammes, and heat-evolution is reckoned as positive, heat-absorption as negative.
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  • In the interior of the chain the rain is far less, and the quantity of precipitation is so small in Tibet that it can be hardly measured.
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  • The drought of 1898 was interrupted by copious rains in June, and these falling on a warm soil led to a rapid growth of grass and, as measured by yield per acre, an exceedingly heavy crop of hay.
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  • His own reception at the Speculative Debating Society, where he first measured his strength in public conflict, was calculated to produce selfdistrust.
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  • There are many fine trees in Scotland; one near Roseneath, figured by Strutt in his Sylva Britannica, then measured more than 22 ft.
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  • Orthodox theology has never, in any of the confessions, ventured beyond the circle which the mind of Origen first measured out.
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  • Of special interest are cockroachlike forms, with two pairs of similar membranous wings and a long ovipositor, and gigantic insects allied to the Odonata, that measured 2 ft.
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  • A breach of the covenant to repair gives the landlord an action for damages which will be measured by the estimated injury to the reversion if the action be brought during the tenancy, and by the sum necessary to execute the repairs, if the action be brought later.
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  • The depth of the middle portion of the lake has not yet been measured, but must exceed 500 fathoms. It was expected that an underground ridge would be found connecting Olkhon with Svyatoi Nos; but depths exceeding 622 fathoms have been sounded even along that line.
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  • It is sometimes assumed that this is measured perfectly by the standard deviation,' which is obtained by taking the squares of the differences between the average and the individual prices, summing them and extracting the square root.
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  • Who has hitherto here with certainty measured the realm of the possible and the real?
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  • By means of this instrument the time occupied in the flow of a measured quantity of the oil through a small orifice at a given temperature is measured.
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  • Plans of attack were sketched: routes were traced: distances were measured; and finally in 1163 there came the impulse from within which turned these plans into action.
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  • In their simplest form they consist of a wire through which passes the current to be measured, some arrangement being provided for measuring the small expansion produced by the heat generated in the wire.
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  • A known fraction of the current is then indicated and measured.
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  • In constructing a hot-wire instrument for the measurement of high frequency currents it is necessary to make the working wire of a number of fine wires placed in parallel and slightly separated from one another, and to rpass the whole of the current to be measured through this strand.
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  • A much better form of electromagnetic ammeter can be constructed on a principle now extensively employed, which consists in pivoting in the strong field of a permanent magnet a small coil through which a part of the current to be measured is sent.
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  • The instrument can therefore be graduated by passing through it known and measured continuous currents, and it then becomes available for use with either continuous or alternating currents.
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  • The potential difference of the ends of the low resistance is at the same time measured on the potentiometer, and the quotient of this potential difference by the known value of the low resistance gives the true value of the current passing through the ammeter.
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  • Either common salt or strong brine in measured quantity is added to the charge, and, the soap being insoluble in such salt solution, a separation of constituents takes place: the soap collects on the surface in an open granular condition, and the spent lye sinks to the bottom after it has been left for a short time to settle.
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  • Another curious theorem proposed by Bouilland in 1625 as a substitute for Kepler's second law is that the angular motion of the body as measured around the empty focus F' is (approximately) uniform.
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  • Thus, the equation 2112+02 =2H20 not only represents that certain definite weights of hydrogen and oxygen furnish a certain definite weight of the compound which we term water, but that if the water in the state of gas, the hydrogen and the oxygen are all measured at the same temperature and pressure, the volume occupied by the oxygen is only half that occupied by the hydrogen, whilst the resulting water-gas will only occupy the same volume as the hydrogen.
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  • In quantitative analysis the methods can be subdivided into: (a) gravimetric, in which the constituent is precipitated either as a definite insoluble compound by the addition of certain reagents, or electrolytically, by the passage of an electric current; (b) volumetric, in which the volume of a reagent of a known strength which produces a certain definite reaction is measured; (c) colorimetric, in which the solution has a particular tint, which can be compared with solutions of known strengths.
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  • Kopp, begun in 1842, on the molecular volumes, the volume occupied by one gramme molecular weight of a substance, of liquids measured at their boiling-point under atmospheric pressure, brought to light a series of additive relations which, in the case of carbon compounds, render it possible to predict, in some measure, the cornposition of the substance.
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  • Now the value of K, -y being measured in dynes and M being the molecular weight of the substance as a gas, is in general 2.121; this value is never exceeded, but in many cases it is less.
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  • The capillary tube can be raised or lowered at will by running a magnet outside the tube, and the heights of the columns are measured by a cathetometer or micrometer microscope.
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  • Near Seathwaite, below Styhead Pass, the largest annual rainfall in the British Isles is recorded, the average (1870-1899) being 133.53 in., while 173.7 was measured in 1903 and 243.98 in.
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  • Ephesians has been called "the crown of St Paul's writings," and whether it be measured by its theological or its literary interest and importance, it can fairly dispute with Romans the claim to be his greatest epistle.
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  • These orthodromic distances are of course shorter than those measured along a loxodromic line, which intersects all parallels at the same angle.
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  • Distances such as these can be measured only on a topographical map of a fairly large scale, for on general maps many of the details needed for that purpose can no longer be represented.
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  • Nearly all these instruments register the revolution of a small wheel of known circumference, which is run along the line to be measured.
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  • It was upon a map based upon such a source that Eratosthenes (276-196 B.C.) measured the distance between Syene and Alexandria which he required for his determination of the length of a degree.
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  • Having determined the difference of latitude between Alexandria and Syene which he erroneously believed to lie on the same meridian, and obtained the distance of those places from each other from the surveys made by Egyptian geometers, he concluded that a degree of the meridan measured 700 stadia.'
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  • Ptolemy were translated into Arabic, and in 827, in the reign of the caliph Abdullah al Mamun, an arc of the meridian was measured in the plain of Mesopotamia.
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  • In France, in the meantime, an arc of the meridian had been measured (1669-1670) by Jean Picard, numerous longitudes had been observed between 1672 and 1680 by the same, and by Phil.
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  • The year 1784 marks the beginning of the ordnance survey, for in that year Major-General Roy measured a base line of 27,404 ft.
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  • Six additional base lines were measured up to 1849, including the Lough Foyle, in 1827-1828, and that on Salisbury Plain, in 1849.
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  • It was measured at the shoulder, bending the head gently down.
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  • It was in connexion with these latter inquiries that he devised his phosphoroscope, an apparatus which enabled the interval between exposure to the source of light and observation of the resulting effects to be varied at will and accurately measured.
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  • Some of the earliest adherents indulged in extravagances of no measured kind.
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  • The capital sum per section was fixed, in round figures, at 54,000,000 francs (£2,160,000), subject to adjustment when the section was completed and its actual length definitely measured up. A minimum net price of 812% was fixed for the realization of these securities on the market.
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  • One of the highest peaks hitherto measured is at Tiningnertok, on the Lindenov Fjord, in 60° 35' N., which is 7340 ft.
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  • The Petermann Spitze, near the shore of Franz Josef Fjord, measured by Payer and found to be 11,000 ft., has hitherto been considered to be the highest mountain in Greenland, but according to Nathorst it " is probably only two-thirds as high as Payer supposed," perhaps between 8000 and 9000 ft.
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  • On the view of the process of conduction described above, the amount of electricity conveyed per second is measured by the product of the number of ions, known from the concentration of the solution, the charge carried by each of them, and the velocity with which, on the average, they move through the liquid.
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  • The concentration is known, and the conductivity can be measured experimentally; thus the average velocity with which the ions move past each other under the existent electromotive force can be estimated.
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  • (2) As the concentration of the solutions increases, the ionization as measured electrically and the dissociation as measured osmotically might decrease more or less together, though, since the thermodynamic theory only holds when the solution is so dilute that the dissolved particles are beyond each other's sphere of action, there is much doubt whether this second relation is valid through any appreciable range of concentration.
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  • It is found that divergence has begun before the concentration has become great enough to enable freezing points to be measured with any ordinary apparatus.
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  • The chemical activity of a substance is a quantity which may be measured by different methods.
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  • If the chemical changes which occur in the cell were allowed to take place in a closed vessel without the performance of electrical or other work, the change in energy would be measured by the heat evolved.
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  • By the American photographs the distances between the centres of Venus and the sun, and the angles between the line adjoining the centres and the meridian, could be separately measured and a separate result for the parallax derived from each.
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  • On these occasions the actual parallax would be six times greater than that of the sun, and could therefore be measured with much greater precision than in the case of any other planet.
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  • The velocity of light (q.v.) has been measured with all the precision necessary for the purpose.
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  • The strength or intensity of a magnetic field at any point is measured by the force in dynes which a unit pole will experience when placed at that point, the direction of the field being the direction in which a positive pole is urged.
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  • The total magnetic induction or flux corresponds to the current of electricity (practically measured in amperes); the induction or flux density B to the density of the current (number of amperes to the square centimetre of section); the magnetic permeability to the specific electric conductivity; and the line integral of the magnetic force, sometimes called the magnetomotive force, to the electro-motive force in the circuit.
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  • - Intensity of magnetization is most directly measured by observing the action which a magnetized body, generally a long straight rod, exerts upon a small magnetic needle placed near it.
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  • The induction of the magnetization may be measured by observing the force required to draw apart the two portions of a divided rod or ring when held together by their mutual attraction.
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  • If the pull is measured in pounds and the area in square inches, the formula may be written B =1317 X iI P/S +H.
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  • Ewing has described an arrangement in which the test bar has a soft-iron pole piece clamped to each of its ends; the pole pieces are joined by a long well-fitting block of iron, which is placed upon them (like the " keeper " of a magnet), and the induction is measured by the force required to detach the block.
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  • In the magnetic balance of du Bois (Magnetic Circuit, p. 346) the uncertainty arising from the presence of a joint is avoided, the force measured being that exerted between two pieces of iron separated from each other by a narrow air-gap of known width.
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  • The intensity of a field may be measured by the rotation of the plane of polarization of light passing in the direction of the magnetic force through a transparent substance.
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  • As the source of monochromatic light a bright sodium burner is used, and the rotation, which is exactly proportional to H, is measured by an accurate polarimeter.
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  • The difference of the ballastic throws taken with the two coils measured the intensity of the field in the space around the iron, and it also enabled a correction to be made for the nonferrous space between the iron neck and the centre of the thickness of'the inner coil.
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  • The value of the residual induction which persisted when the bobbin was drawn out was added to that of the induction measured, and thus the total induction in the iron was determined.
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  • Honda, measured the changes of length of various metals shaped in the form of ovoids instead of cylindrical rods, and determined the magnetization curves for the same specimens; a higher degree of accuracy was thus attained, and satisfactory data were provided for testing theories.
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  • Bidwell," who, adopting special precautions against sources of error by which former work was probably affected, measured the changes of thermo-electric force for iron, steel, nickel and cobalt produced by magnetic fields up to I Soo units.
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  • The increase in wealth may best be measured by the rise in assessed valuation.
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  • In the graphic method of representation the sign - may be taken as denoting a reversal of direction, so that, if + 3 represents a length of 3 units measured in one direction,-3 represents a length of 3 units measured in the other direction.
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  • The principle underlying this expression is probably to be found in the fact that it measured the limits of their attainments in algebra, for they were unable to solve equations of a higher degree than the quadratic or square.
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  • If we put for shortness 7 for the quantity under the last circular function in (I), the expressions (i), (2) may be put under the forms u sin T, v sin (T - a) respectively; and, if I be the intensity, I will be measured by the sum of the squares of the coefficients of sin T and cos T in the expression u sin T +v sin (T - a), so that I =u 2 +v 2 +2uv cos a, which becomes on putting for u, v, and a their values, and putting f =Q .
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  • Let x, y, z be the co-ordinates of any particle of the medium in its natural state, and, 7 7, the displacements of the same particle at the end of time t, measured in the directions of the three axes respectively.
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  • Primary, secondary and spurious bows were formed, and their radii measured; a comparison of these observations exhibited agreement with Airy's analytical values.
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  • It was a square piece of woollen stuff about a foot longer than the height of the wearer, and equal in breadth to twice the span of the arms measured from wrist to wrist.
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  • Guncottons are examined for degree of nitration by the nitrometer, in which apparatus they are decomposed by sulphuric acid in contact with mercury, and all the nitrogen is evolved as nitric oxide, NO, which is measured and the weight of its contained nitrogen calculated.
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  • Another heat test, that of Will, consists in heating a weighed quantity of the guncotton in a stream of carbon dioxide to 130° C., passing the evolved gases over some red-hot copper, and finally collecting them over a solution of potassium hydroxide which retains the carbon dioxide and allows the nitrogen, arising from the guncotton decomposition, to be measured.
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  • As the rods make their measured strokes one of the miners, starting from the surface, steps on the first platform as it rises to the surface landing and is then lowered on the down stroke.
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  • The pressure is measured by a " water-gauge " and the velocity of flow by an " anemometer."
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  • The value of any property is measured by its annual profits.
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  • In the case of a developed mine its life may be predicted in many cases with absolute certainty - as when the extent of the mineral deposit and the volume of mineral can be measured.
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  • The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.
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  • It is usually essential that some parts of the apparatus shall be made to acquire a temperature identical with the temperature to be measured.
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  • The electromotive force thus generated is measured by a galvanometer, the scale of which is divided and figured so that the temperature may be-directly read.
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  • - These qualities can be readily judged by inspection of the glass in pieces of considerable thickness, and they may be quantitatively measured by means of the spectro-photometer.
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  • Processes of annealing, or very gradual cooling, are intended to relieve these strains, but such processes are only completely effective when the cooling, particularly through those ranges of temperature where the glass is just losing the last traces of plasticity, is extremely gradual, a rate measured in hours per degree Centigrade being required.
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  • In the absence of a medium the inertia of the body to transtion is the same in all directions, and is measured by the (3) But the change of the resultant momentum F of the medium as.
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  • The amount measured at Dhala at the extreme south of the plateau at an elevation of 4800 ft.
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  • Such a furnace, to take a current of 4 H.P. (say, of 60 amperes and so volts), measured externally about 6 by 6 by 7 in., and the electrodes were about o 4 in.
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  • In 1764, with the aid of his assistant, William Irvine (1743-1787), he further measured the latent heat of steam, though not very accurately.
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  • His eminence as a man of science must be measured by his only original work in that department, - the construction, namely, of the new science of society.
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  • Its axes measured 505 and 404 ft.
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  • The year 1881 saw the nation divided into political parties and within measured distance of constitutional government.
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  • The threads extend only to the outlines of each figure, and it follows that every part of the pattern has a rim of minute holes like pierced lines separating postage stamps in a sheet, the effect being that the design seems to hang suspended it1 the groundlinked into it, as the Japanese term implies.i A specimen of this nature recently manufactured by Kawashimas weavers measured 20 ft.
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  • It is the point from which all distances in Japan are measured.
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  • Roberts-Austen pointed out that surfusion might be easily measured in metals and in alloys by the sensitive method of recording pyrometry perfected by him.
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  • Dahms in the case of salts, could be measured in the lead-tin alloys.
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  • Its high coefficient of thermal expansion, coupled with its low freezing point, renders it a valuable thermometric fluid, especially when the temperatures to be measured are below - 39° C., for which the mercury thermometer cannot be used.
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  • If the two small conducting spheres are placed with centres at a distance d centimetres, and immersed in an insulator of dielectric constant K, and carry charges of Q and Q' electrostatic units respectively, measured as above described, then the mechanical force between them is equal to QQ'/Kd 2 dynes.
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  • Hence the charge on the conductor can be measured by the number of unit electric tubes springing from it.
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  • For by the definition of potential it follows that the electric force in any direction at any point is measured by the space rate of change of potential in that direction or E = + dVldx.
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  • If we consider the charge of a conductor to be measured by the number of tubes of electric force which proceed from it, then, since each tube must end on some other conductor, the above statement is equivalent to saying that the charges at each end of a tube of electric force are equal.
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  • I It is an interesting fact that Cavendish measured capacity in " globular inches," using as his unit the capacity of a metal ball, in.
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  • The electric force outward from that point is - dV/dn, where do is a distance measured along the outwardly drawn normal, and the force within the surface is zero.
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  • With this definition of temperature 0, if the heat H is measured in work units, the expression of Carnot's principle for an infinitesimal cycle of range do reduces to the simple form dW/d9=H/0.
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  • In the notation of the calculus the relations become - dH/dp (0 const) = odv /do (p const) (4) dH/dv (0 const) =odp/do (v const) The negative sign is prefixed to dH/dp because absorption of heat +dH corresponds to diminution of pressure - dp. The utility of these relations results from the circumstance that the pressure and expansion co efficients are familiar and easily measured, whereas the latent heat of expansion is difficult to determine.
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  • The value of the specific heat s at constant volume can also be measured in a few cases, but it is generally necessary to deduce it from that at constant pressure, by means of relation (6).
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  • A continuous stream of gas, supplied at a constant pressure and temperature, is forced through a porous plug, from which it issues at a lower pressure through an orifice carefully surrounded with non-conducting material, where its temperature is measured.
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  • The condition in this form can be readily applied provided that the external work dW can be measured.
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  • The intensity of emigration is measured not by the absolute number of emigrants, but by the number of emigrants to the total population.
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  • It has come to be fully accepted that when we use such a phrase as "the age of the world" we are dealing with a period that must be measured not in thousands but in millions of years; and that to the age of man must be allotted a period some hundreds of times as great as the five thousand and odd years allowed by the old chronologists.
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  • The result of the contest was never in doubt, however, for the geological evidence, once it had been gathered, was unequivocal; and by about the middle of the century it was pretty generally admitted that the age of the earth must be measured by an utterly different standard from that hitherto in vogue.
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  • The substance whose volume is to be determined is placed in the cup PE, and the tube PC is immersed in the vessel of mercury D, until the mercury reaches the mark P. The plate E is then placed on the cup, and the tube PC raised until the surface of the mercury in the tube stands at M, that in the vessel D being at C, and the height MC is measured.
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  • The vapour density is calculated by the following formula: D - W(1 +at) X587,780 (p-s) V in which W =weight of substance taken, V =volume of air expelled, a= 1/273 = .003665, t and p = temperature and pressure at which expelled air is measured, and s= vapour pressure of water at 1°.
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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 small interval between the adjacent limbs was then measured with a wire micrometer.
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  • Jupiter was measured on eleven nights in the months of June and July 1794; from these measures Schur derives the values 35"39 and 37".94 for the polar and equatorial diameter respectively, at mean distance, corresponding with a compression 1/14.44.
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  • In 1812 Bessel measured with it the angle between the components of the double star 61 Cygni and observed the great comet of 1811.
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  • Complete rotation of the head is obviously impossible because of the interference of the declination axis with the rods, and therefore, in some angles, objects cannot be measured in two positions of the circle.
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  • 2 The diameter of Venus was measured with one of these heliometers at the observatory of Breslau by Brandes in 1820 (Berlin Jahrbuch, 1824, p. 064).
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  • The eye-piece is fixed in the axis, and the segments are symmetrically displaced from the axis each by an amount equal to half the angle measured.
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  • In Bessel's heliometer this would amount to a difference of o oat h of an inch when an angle of 1 ° is measured.
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  • Modern heliometers made with cylindrical slides measure angles over 2°, the images remaining as sharp and perfect as when the smallest angles are measured.
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  • But the method is not available if the separation is to be measured by screws; it is found, in that case, that the direction of the final motion of turning of the screw must always be such as to produce motion of the segment against gravity, otherwise the " loss of time " is apt to be variable.
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  • Thus the simple connexion of the two screws by cogwheels to give them automatic opposite motion is not an available method unless the separation of the segments is independently measured by scales.
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  • This lens is divided and mounted like a heliometer objectglass; the separation of the lenses produces the required double image, and is measured by a screw.
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  • By a scale attached to the sliding tube the magnifying power of the eye-piece was deduced, and this combined with the angle of the prism employed gave the angle measured.
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  • The intensity of gravity at the surface of the sea far from land has been measured on several occasions.
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  • Hecker took the opportunity of a voyage from Hamburg to La Plata, and in 1904 and 1905 of voyages in the Indian and Pacific Oceans to determine the local attraction over the ocean by comparing the atmospheric pressure measured by means of a mercurial barometer and a boiling-point thermometer, and obtained results similar to Scott Hansen's.
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  • " Nero " in 1899 found 5269 fathoms in 12° 43' N., 1 45° 49' E., the greatest depth yet measured.
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  • The transparency of sea-water has frequently been measured at sea by the simple expedient of sinking white-painted disks and noting the depth at which they become invisible as the measure of the transparency of the water.
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  • The former determination is made by driving out the dissolved gases from solution and collecting them in a Torricellian vacuum, where the volume is measured after the carbonic acid has been removed.
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  • The oxygen is then absorbed by some appropriate means, and the volume of the nitrogen measured directly, that of the oxygen being given by difference.
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  • Dickson and others leave no doubt, for example, that the variations in the intensity of the Gulf Stream, whether these be measured by the change in the strength of the current or in the heat stored in the water, produce great variations in the character of the weather of northern Europe.
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  • Each stalactite, stalagmite and pilaster was measured, numbered, and removed in sections.
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  • In driving levels it is necessary to cut grooves vertically parallel to the walls, a process known as shearing; but the most important operation is that known as holing or kirving, which consists in cutting a notch or groove in the floor of the seam to a depth of about 3 ft., measured back from the face, so as to leave the overhanging part unsupported, which then either falls of its own accord within a few hours, or is brought down either by driving wedges along the top, or by blasting.
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  • For flat ropes the drum or bobbin consists of a solid disk, of the width of the rope fixed upon the shaft, with numerous parallel pairs of arms or horns, arranged radially on both sides, the space between being just sufficient to allow the rope to enter and coil regularly upon the preceding lap. This method has the advantage of equalizing the work of the engine throughout the journey, for when the load is greatest, with the full cage at the bottom and the whole length of rope out, the duty required in the first revolution of the engine is measured by the length of the smallest circumference; while the assistance derived from gravitating action of the descending cage in the same period is equal to the weight of the falling mass through a height corresponding to the length of the largest lap, and so on, the speed being increased as the weight diminishes, and vice versa.
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  • The general theory of this kind of brake is as follows: - Let F be the whole frictional resistance, r the common radius of the rubbing surfaces, W the force which holds the brake from turning and whose line of action is at a perpendicular distance R from the axis of the shaft, N the revolutions of the shaft per minute, co its angular velocity in radians per second; then, assuming that the adjustments are made so that the engine runs steadily at a uniform speed, and that the brake is held still, clear of the stops and without oscillation, by W, the torque T exerted by the engine is equal to the frictional torque Fr acting at the brake surfaces, and this is measured by the statical moment of the weight W about the axis of revolution; that is T =Fr=WR...
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  • The power of a motor is measured by the rate at which it works, and this is expressed by Tw =T 60N in foot-pounds per second.
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  • The ratio p is given by e"` e, where e= 2.718; µ is the coefficient of friction and 0 the angle, measured in radians,, subtended by the arc of contact between the rope and the wheel.
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  • The moments of the components of these actions and reactions in a plane to which the axis of rotation is at right angles are the two aspects of the torque acting, and therefore the torque acting on B through the shaft is measured by the torque required to hold A still.
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  • From to 30 H.P. may be measured at loo revs.
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  • Every part of a machine transmitting force suffers elastic defor mation, and the force may be measured indirectly by measuring the deformation.
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  • P and p may be measured directly by leading the belt round two freely hanging guide pulleys, one in the tight, the other in the slack part of the belt, and adjusting loads on them until a stable condition of running is obtained.
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  • The force Q, usually measured by a spring, required to maintain the beam in its central position is proportional to (P - p).
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  • When a shaft is driven by means of gearing the driving torque is measured by the product of the resultant pressure P acting between the wheel teeth and the radius of the pitch circle of the wheel fixed to the shaft.
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  • If, therefore, the motor is mounted on a cradle free to turn about knife-edges, the reacting torque is the only torque tending to turn the cradle when it is in a vertical position, and may therefore be measured by adjusting weights to hold the cradle in a vertical position.
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  • It is by the help of numbers that concrete quantities are practically measured and calculated.
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  • The law of equipartition shows that the various mean energies of different kinds are all equal, each being measured by the quantity 1/4h.
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  • (16) Let a quantity dQ of energy, measured in work units, be absorbed by the gas from some external source, so that its pressure, volume and temperature change.
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  • (3) While in the ancient church the language used in excommunicating had been carefully measured, we find an amazing recklessness in the phraseology employed by the medieval clergy.
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  • Professor Putnam measured for the World's Columbian Exposition 1700 living Indians, and the results have been summed up by Boas.
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  • If now the telescope be directed on the target and this level be brought to the centre of its run, the angle of sight can be read - if afterwards any range ordered is put on the sight and the gun truly layed, this bubble will be found in the centre of its run - so that if thereafter the target becomes obscured the gun can be relayed by elevating till the bubble is in the centre of its run, or at a completely concealed target the angle of sight can, if the range and difference of level are known or can be measured from somewhere near the gun, be put on by means of the micrometer screw, and the gun subsequently layed by putting the range in yards or degrees on the sight drum and elevating or depressing till the bubble is central.
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  • At nightfall the Army of the North lay concentrated "in a square whose sides measured 12 m.
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  • The distance between two points can, at any rate in theory, be measured directly, by successive applications of the unit of measurement.
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  • But an area or a volume cannot generally be measured by successive applications of the unit of area or volume; intermediate processes are necessary, the result of which is expressed by a formula.
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  • The first group comprises such subjects as land-surveying; here the measurements in the elementary stages take place in a plane, and the consideration of volumes necessarily constitutes a later stage; and the figures to be measured are mostly not movable, so that triangulation plays an important part.
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  • The second group comprises the mechanic arts, in which the bodies to be measured are solid bodies which can be handled; in these cases plane figures appear mainly as sections of a solid.
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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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  • Suppose, for instance, that we require the area of a circular grass-plot of measured diameter.
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  • As a matter of fact, no grass-plot is truly circular; and it might be found that if the breadth in various directions were measured more accurately the want of circularity would reveal itself.
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  • Thus the inaccuracy in taking the measured diameter as the datum is practically of the same order as the inaccuracy in taking the grass-plot to be circular.
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  • Suppose, for instance, that in the example given in § 20 the diameter as measured is is ft.
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  • 7 let base BC=2a, and let h be the distance, measured at right angles to BC, from the middle point of BC to AD.
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  • The area of the trapezette, measured from the lower bounding ordinate up to the ordinate corresponding to any value of x, is some function of x.
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  • Suppose, for instance, that u is of degree not exceeding 3 in x, and of degree not exceeding 3 in y, that it contains terms in x3y3, x 3 y 2, x2y3, &c.; and suppose that the edges parallel to which x and y are measured are of lengths 2h and 3k, the briquette being divided into six elements by the plane x=xo+h and the planes y = yo+k, y = yo+2k, and that the 12 ordinates forming the edges of these six elements are given.
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  • For the purpose of measuring resistances up to a few thousand ohms, the most convenient appliance is a Wheatstone's Bridge (q.v), but when the resistance of the conductor to be measured is several hundred thousand ohms, or if it is the resistance of a so-called insulator, such as the insulating covering of the copper wires employed for distributing electric current in houses and buildings for electric lighting, then the ohmmeter is more convenient.
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  • The tangent of the angle of deflection 0 of this needle measured from its position, when the shunt coil is disconnected, is equal to the ratio of the voltage of the dynamo to the current through the insulator.
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  • One of these coils is in series with the armature circuit and with the insulation or high resistance to be measured.
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  • These two quadrants are interconnected by the high resistance to be measured, and, therefore, themselves differ in potential.
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  • The period of Algol, as measured by its eclipses, is subject to complex irregularities.
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  • An obvi us method of determining the velocity of sound in air consists in starting some sound, say by firing a gun, and stationing an observer at some measured distance from the gun.
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  • But when the wind is steady its effect may be eliminated by " reciprocal " observations, that is, by observations of the time of passage of sound in each direction over the measured distance..
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  • The times were measured by pendulum clocks.
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  • When the interval between a flash and a report is measured, the personal equations for the two arrivals are, in all probability, different, that for the flash being most likely less than that for the sound.
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  • The time between the breaks could be measured in seconds by the clock signals, and in fractions of a second by the tuning-fork record.
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  • The intensity of the stream of energy passing per second through a square centimetre when a given pure tone is sounded is more definite and can be measured.
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  • In the one, the energy of vibration of the source is measured, and the rate at which that energy decreases is observed.
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  • The difference in loss in the two cases measured the energy given up to and sent out by the resonator as sound.
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  • He used a spherical Helmholtz resonator resounding to the tone to be measured.
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  • We may represent the displacement due to one of the trains by y l =a sin 2 i (24) where x is measured as in equation (16) from an ascending node as A in fig.
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  • If d is measured for two gases in succession for the same frequency N, we have 72 p 2P1 d22 71 p i p s d12' where the suffixes denote the gases to which the quantities relate.
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  • When a known temperature was attained the sounder was excited, and d 2 and d 1 could be measured.
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  • Formerly each nation took its own capital or principal observatory as the standard meridian from which longitudes were measured.
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  • Large sections of the old history are devoted to the religion and politics of the ten tribes, which are altogether unintelligible and uninteresting when measured by a strictly Levitical standard; and in general the whole problems and struggles of the prophetic period turn on points which had ceased to be cardinal in the life of the New Jerusalem, which was no longer called to decide between the claims of the Word of Yahweh and the exigencies of political.
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  • The extremities of the diameter perpendicular to a small circle are called the "poles" of that circle, and the distance from the pole to the circle, measured by the arc of the great circle through the pole, is the "polar distance" of the small circle.
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  • R=wx (I+x2/4Y2) Let i be the angle between the tangent at any point having the co-ordinates x and y measured from the vertex, then 3..
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  • 72 with arcs of the length 1,, l2, l3, &c., and with the radii r1, r 2, &c. (note, for a length 2l 1 at each end the radius will be infinite, and the curve must end with a straight line tangent to the last arc), then let v be the measured deflection of this curve from the straight line, and V the actual deflection of the bridge; we have V = av/b, approximately.
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  • The effect of such folds is often exaggerated by thrusts, and faulting of this sort is prominent in the southern section, where the existence of over-thrusts measured by several miles has been established.
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  • Gounelle measured the velocity of electricity.
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  • The current to be measured is passed through the coils of the electromagnet, then enters the mercury disk at the centre, flows through it radially in all directions, and emerges at the periphery.
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  • The rotation of the mercury is detected and measured by means of a small vane of platinum wire immersed in it, the shaft of this vane being connected by an endless screw with a counting mechanism.
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  • The current to be measured passes transversely across the disk and causes it to revolve in the magnetic field; at the same time the copper brake, geared on the same shaft, revolves in the field and has local or eddy currents produced in it which retard its action.
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  • The current to be measured passes through the fixed field-coils, whilst through the armature passes a shunt current obtained by connecting the brushes across the supply mains through a constant resistance.
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  • In these circumstances the number of rotations made by the armature in a given time is proportional to the product of the strength of the current flowing through the armature and that flowing through the field-coils, the former being the current to be measured.
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  • Below this pendulum let there be placed another coil through which passes the current to be measured; then when currents pass through these coils the pendulum of the second clock will be either accelerated or retarded relatively to the other clock, since the action of gravity is supplemented by that of an electric attraction or repulsion between the coils.
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  • If the difference of the number of oscillations made by the two pendulums in a given time is small compared to the number made by either of them separately, then it is easy to show that the power given to the circuit is measured by the gain or loss of one clock over the other in a given time, and can therefore be indicated on a counting mechanism or registering dials.
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  • The current in the shunt coil lags 90 degrees behind the impressed electromotive force of the circuit to be measured; hence if the main current is in step with the potential difference of the terminals of the supply mains, which is the case when the supply is given wholly to electric lamps, then the field due to the main coil differs from that due to the shunt coil by 90 degrees.
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  • They were measured by the meridian-passages of the limiting stars, and varied in amplitude from 2° 42' to 30° 24'.
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  • This fact, however, is the sole outcome of the history of a thousand years; a poor result, if measured by the standard of the rich history of the Western world, yet large enough not to exclude the hope of a new development.
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  • When in Egypt he measured the pyramids, and, finding that the angles formed by the sides of the largest were in the direction of the four cardinal points, he concluded that this position must have been intended, and also that the poles of the earth and meridians had not deviated since the erection of those structures.
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  • In point of fact some form of revelation or oracle appears to have existed in every great shrine of Canaan and Syria,' and the importance of this element in the cultus may be measured from the fact that at Hierapolis it was the charge of the chief priest, just as in the Levitical legislation.
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  • Abandoning therefore all a priori theoretical assumption, Bashforth set to work to measure experimentally the velocity of shot and the resistance of the air by means of equidistant electric screens furnished with vertical threads or wire, and by a chronograph which measured the instants of time at which the screens were cut by a shot flying nearly horizontally.
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  • The equations of motion are now, the co-ordinates x and y being measured in feet, 2 (26) - -rr- - C, dt2 dty - g' * These numbers are taken from a part omitted here of the abridged ballistic table.
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  • =0.504, the upper figure 55.01 denoting the specific volume of the charge measured in cubic inches per lb, filling the chamber in a state of gas, the product of the two numbers 55.01 and 0.504 being 2 7.73; and the chamber capacity C =1 3' 2 5 X 55.01 =730 cub.
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  • Buell's failure to appreciate political considerations as a part of strategy justified his recall, but the value of his work, like that of McClellan, can hardly be measured by marches and victories.
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  • This is given somewhat as follows: the distance represented by the square root of a negative quantity cannot be measured in the line backwards or forwards, but can be measured in the same plane above the line, or (as appears elsewhere) at right angles to the line either in the plane, or in the plane at right angles thereto.
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  • By such an arrangement the potential difference can be measured of any amount from o to 1.5 volts.
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  • It has been in use for measuring corn, potatoes, &c., from a very early date; the value varying locally and with the article measured.
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  • He became a member of the speculative society, where he measured himself in debate with Scott, Brougham, Francis Horner, the marquess of Lansdowne, Lord Kinnaird and others.
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  • The principle on which the instrument works is as follows: Suppose any circuit, such as an electric motor, lamp or transformer, is receiving electric current; then the power given to that circuit reckoned in watts is measured by the product of the current flowing through the circuit in amperes and the potential difference of the ends of that circuit in volts, multiplied by a certain factor called the power factor in those cases in which the circuit is inductive and the current alternating.
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  • Hence this power can be measured by the torsion which must be applied to the movable coil of the wattmeter to hold it in the normal position against the action of the forces tending to displace it.
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  • Measured by the value of the product, flour and grist mill products rose from third in rank in 1900 to first in rank in 1905, from $13,017,043 to $18,007,786, or 38.3%; and chewing and smoking tobacco and snuff fell during the same period from first to third in rank, from $14,948,192 to $13,117,000, or 12.3%; in 1900 Kentucky was second, in 1905 third, among the states in the value of this product.
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  • He was the first, in 1867, to examine the spectrum of the aurora borealis, and detected and measured the characteristic bright line in its yellow green region; but he was mistaken in supposing that this same line, which is often called by his name, is also to be seen in the zodiacal light.
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  • In the absence of the actual standards of ancient times the units of measure and of weight have to be inferred from the other remains; hence unit in this division is used for any more or less closely defined amount of length or weight in terms of which matter was measured.
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  • With the first instrument of this kind, having objectives of 1 5 inch aperture, he measured the brightness of 4260 stars, including all stars down to the 6th magnitude between the North Pole and - 30° declination.
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  • The great teocalli of Huitzilopochtli in the city of Mexico stood in an immense square, whence radiated the four principal thoroughfares, its courtyard being enclosed by a square, of which the stone wall, called the coatepantli or serpent-wall from its sculptured serpents, - measured nearly a quarter of a mile on each side.
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  • The menhir of Men-er-H`roeck (Fairy stone), which was broken into four pieces by lightning in the 18th century, previously measured about 67 ft.
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  • Cotton goods, the manufacture of which was introduced in 1804, increased in value only slightly during the last decade of the 19th century, from $21,958,002 to $22,998,249, but from 1900 to 1905 their value increased 28.4%, or to $29,540,770; except in 1900 the manufacture of cotton goods had long ranked first, measured by the value of the product, among the state's manufacturing industries.
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  • In order to find the amount of dispersion caused by any given prism, the deviations produced by it on two rays of any definite pure colours may be measured.
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  • It is more useful than (1), as the refractive indices may be measured with a prism of any convenient angle.
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  • In these instruments the potential difference between two points is measured by the electric current produced in a wire connecting to two points.
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  • In any case of potential difference measurement it is essential not to disturb the potential difference being measured; hence it follows that in electrokinetic voltmeters the wire connecting the two points of which the potential difference is to be measured must be of very high resistance.
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  • In this case a highresistance wire is connected between the points of which the potential difference is required, and from some known fraction of this resistance wires are brought to an electrostatic voltmeter, or to a movable coil electromagnetic voltmeter, according as the voltage to be measured is alternating or continuous.
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  • The city on the river side of the Tigris extended about 21 m., its north wall measured 7000 ft., the eastern wall was nearly 3 m.
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  • As an alternative method it may be decomposed by hydrogen peroxide in alkaline solution and the amount of evolved oxygen measured: 2K 3 Fe(NC) 5 + 2KHO + H 2 O 2 = 2K 4 Fe(NC) 6 + 2H,0 + 02.
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  • The greatness of the thickness, as it has been measured, is also due in part to the oblique position in which the beds of sediment were originally deposited.
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  • If maximum thicknesses of its several parts in different localities, as usually measured, are added together, the total would approach or reach 25,000 ft.; but the strata of any one region have scarcely more than half this thickness, and the average is much less.
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  • The thickness of the system in the west is great, the formations of each of the several stages mentioned above running into thousands of feet, as thicknesses are commonly measured.
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  • Thus the heaviest measured rainfall east of the Mississippi is on the southern Appalachians; while in the west, where observations are as yet few at high level stations, the occurrence of forests and pastures on the higher slopes of mountains which rise from desert plains clearly testifies to the same rule.
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  • Measured by the gross value of products, wholesale slaughtering and meat packing was the most important industry in 1903.
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  • The traffic on these, measured in units moved one mile, was 28,797,781,231 passenger-miles, and 214,340,129,523 freight miles.
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  • It measured 282 ft.
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  • If measured to the head of Peace river the Mackenzie has a length of more than 2000 m., and it provides more than 1000 m.
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  • If we wish the successive divisions of the scale to correspond to equal increments in the density of the corresponding liquids, then the volumes of the instrument, measured up to the successive divisions of the scale, must form a series in harmonical progression, the lengths of the divisions increasing as we go up the stem.
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  • Ostwald (ibid., 1900, 35, pp. 33, 204) has observed that on dissolving chromium in dilute acids, the rate of solution as measured by the evolution of gas is not continuous but periodic. It is largely made as ferro-chrome, an alloy containing about 60-70% of chromium, by reducing chromite in the electric furnace or by aluminium.
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  • When the agreed-on weight is on the drum, the silk is drawn across the face of the drum parallel with its axle, and pulled off in form of a sheet, and is called a lap. This lap is thin, but presents the fibres of silk now joined and overlapped in a continuous form, the length measured by the circumference of the drum.
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  • Perot's number is now definitely adopted to define the Angstrom, and need never be altered, for should at some future time further researches reveal a minute error, it will be only necessary to change slightly the temperature or pressure of the air in which the wave-length is measured.
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  • If a source of light be placed behind the auxiliary slit a parallel beam of light will pass within the collimator and fall on the slit the width of which is to be measured.
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  • From the measured distances of the diffraction bands the width of the slit may be easily deduced.
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  • P. Lewis,' lines as far as 11,500 having been measured by the latter.
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  • The most complete hydrogen spectrum is that measured by Evershed 8 in the flash spectrum observed during a total solar eclipse, and contains thirty-one lines, all of which agree with considerable accuracy with the formula, if the frequency number n is calculated correctly by reducing the wave-length to vacuo.9 It is a characteristic of Balmer's formula that the frequency approaches a definite limit as s is increased, and it was soon discovered that in several other spectra besides hydrogen, series of lines could be found, which gradually come nearer and nearer to each other as they become fainter, and approach a definite limit.
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  • Wood has in that case measured as many as 50 lines belonging to this series.
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  • The distance between the lines measured on the frequency scale does not, according to the equation, increase indefinitely from the head downwards, but has a maximum which, in Pickering's form as written above, is reached when (s +, u) 2 = 3a.
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  • Experimentally we should be confined to a strict investigation of absorption spectra, because in the electric discharge temperature has no definite meaning, and variations of pressure and density are not easily measured.
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  • Curiously enough this is also approximately the ratio of the displacements found by Humphreys in the trunk series, the side branch and main branch in the order named, in cases where these displacements have been measured.
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  • Hemsalech 1 have measured the velocity with which the luminous molecules are projected from metallic poles when a strong spark is passed through the air interval which separates the poles.
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  • In the case of some metals, notably bismuth, the velocity measured was different for different lines, which seems intelligible only on the supposition that the metal vapour consists of different vibrating systems which can differ with different velocities.
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  • Preston that all the lines of the same series show identical effects when measured on the frequency scale, arfrl the fact recently announced by Runge 3 that even in the more complicated cases mentioned some simple relation between the distances of the components exists.
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  • He had specially prepared himself, as he thought, for "teaching imaginative men, and political men, and legal men, and scientific men who bear the world in hand"; and he did not attempt to win their attention to abstract and worn-out theological arguments, but discussed the opinions, the poetry, the politics, the manners and customs of the time, and this not with philosophical comprehensiveness, not in terms of warm eulogy or measured blame, but of severe satire varied by fierce denunciation, and with a specific minuteness which was concerned primarily with individuals.
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  • He was a man of strong personality, of measured utterance, "civil" (says Penn) "beyond all forms of breeding."
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  • It remains to consider the measurement of the declination and the horizontal component, these two elements being generally measured with the same instrument, which is called a unifilar magnetometer.
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  • - Two small square temples, of a common westernprovincial type, were in the east of the town; the cella of the larger measured 42 ft.
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  • A spherical angle is a particular dihedral angle; it is the angle between two intersecting arcs on a sphere, and is measured by the angle between the planes containing the arcs and the centre of the sphere.
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  • The angle between a line and a curve (mixed angle) or between two curves (curvilinear angle) is measured by the angle between the line and the tangent at the point of intersection, or between the tangents to both curves at their common point.
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  • Galileo measured time for the purpose of his experiments by the flow of water through a small hole under approximately constant conditions, which was of course a very old method.
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  • Measured on the Euphrates, this would be from the place where the river, having bored its way through the rocks, issues on to the high plain a little above Samsat (Samosata) only 1 500 ft.
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  • Measured on the Tigris Mesopotamia would stretch from some where between Jeziret-ibn-`Omar and Mosul to somewhere below Tekrit.
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  • The number F is called the number of degrees of freedom of the system, and is measured by the excess of the number of unknowns over the number of variables.
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  • The relative lowering of vapour pressure of the solution compared with that of the solvent is measured by the ratio of the extra mass absorbed from the solvent bulbs to the total mass absorbed from both series of bulbs.
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  • Now the work done by allowing a small quantity of solvent to enter reversibly into an osmotic cylinder is measured by the product of the osmotic pressure into the change in volume.
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  • Hence the osmotic pressure is measured by the work done per unit change of volume of the solution.
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  • A quantity of gas measured by its molecular weight in grammes when confined in a volume of one litre exerts a pressure of 22.2 atmospheres, and thus the osmotic pressure of a dilute solution divided by its concentration in gramme-molecules per litre has a corresponding value.
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  • But we have seen that the depression of dT of the freezing point of a dilute solution is measured by TPdv/L.
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  • Frazer, who have made direct measurements of osmotic pressure of solution of cane-sugar, have also measured the freezing points of corresponding solutions.
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  • If the heat of solution be measured in a calorimeter, no work is done, so that, if we call this calorimetric heat of solution L, the two quantities are connected by the relation L = X+P(v - v).
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  • If l is the heat of dilution per unit change of volume in a calorimeter where all the energy goes to heat, the change in internal energy U is measured by ldv.
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  • The first to make systematic experiments on the free diffusion of dissolved substances with no separating membrane was Thomas Graham (1804-1869), who immersed in a large volume of water a wide-mouthed bottle containing a solution, and after some time measured the quantity of substance which had diffused into the water.
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  • This constant can be measured experimentally, and for such a substance as sugar or water comes out about 0.3 at 20° C., the unit of time being the day.
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  • The great court measured 300 ft.
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  • The following figures for the years 1904 and 1905 show that its trade is still rapidly increasing: - The growth of its commerce in recent times may be measured by a comparison of the following figures.
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  • The island, which belongs to Turkey, is of considerable size: Pliny says that the coast-line measured 1122 Roman miles, and the area has been estimated at 150 sq.
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  • In 1761 he announced the discovery of an epic on the subject of Fingal, and in December he published Fingal, an Ancient Epic Poem in Six Books, together with Several Other Poems composed by Ossian, the Son of Fingal, translated from the Gaelic Language, written in the musical measured prose of which he had made use in his earlier volume.
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  • In the intravascular coagulation experiments above described, all the rabbits were carefully weighed, and the amount of nucleoproteid injected until coagulation occurred was measured.
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  • The south side, running nearly due east and west, is about equally long, if measured from the end of the west wall to the point which the east wall would touch when produced due south in a straight line from the place at which it was demolished to make way for " Nero's house."
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  • The east side, measured to a point just behind the treasure-houses, is the shortest, about 200 yds.
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  • It was apparently a square building, of which each side measured 100 Olympian feet, with a south-west aspect.
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  • An entire skull, obtained from the Lower Pliocene beds of Eppelsheim, Hesse-Darmstadt, in 1836, measured 41ft.
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  • The area is subject 1 At Maastricht, however, a portion lies on the left bank of the river, measured, according to the treaty with Belgium, 19th of April 1839, art.
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  • The States of Holland had, in the years that followed the truce of 1609, measured their strength with that of the StatesGeneral, but the issue had been decided conclusively in favour of the federal authority by the sword of Maurice.
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  • The general order of merit of a given variety or specimen of iron or steel may be measured by the degree to which it combines strength and hardness with ductility.
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  • The combination of ductility, which lessens the tendency to break when overstrained or distorted, with a very high limit of elasticity, gives it great value for shafting, the merit of which is measured by its endurance of the repeated stresses to which its rotation exposes it whenever its alignment is not mathematically straight.
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  • When, in the course of centuries, the exhaustion of richer ores shall have forced us to mine, crush and concentrate mechanically or by magnetism the ores which contain only 2 or 3% of iron, then the cost of iron in the ore, measured in terms of the energy needed to mine and concentrate it, will be comparable with the actual cost of the copper in the ore of the copper-mines of to-day.
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  • In short, a very large part of the earth's coal supply is known and measured, but its iron ore supply is hardly to be guessed.
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  • The system of human sacrifices, practised among the Ashanti until the closing years of the 19th century, was founded on a sentiment of piety towards parents and other connexions - the chiefs believing that the rank of their dead relatives in the future world would be measured by the number of attendants sent after them.
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  • They criticized in no measured terms the current medicine of the time, and exposed the practical ignorance, the pomposity, and the greed of those who practised it.
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  • Thus in December 1906 a new island of mud was thrown up, and measured 3 07 by 217 yds.
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  • Religion was with him all and in all - that by which all besides was measured, and to whose interests all else was subordinated.
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  • Based upon the Confession of Faith of 1560, this document denounced the pope and the doctrines of the Roman Catholic Church in no measured terms. It was adopted by the General Assembly, signed by King James VI.
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  • If the inherent energy of the principle of population (supposed everywhere the same) is measured by the rate at which numbers increase under the most favourable circumstances, surely the force of less favourable circumstances, acting through prudential or altruistic motives,, is measured by the great difference between this maximum rate and those which are observed to prevail in most European countries.
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  • The area A from which the heat is collected need not be the whole surface of the plate, but a measured central area where the flow is most nearly uniform.
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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 actual tempera ture of the metal itself can then be observed by inserting thermometers or thermo-couples at measured distances from the centre.
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  • The heat transmitted should be measured calorimetrically, and not in terms of the uncertain emissivity.
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  • The heat transmitted was measured by observing the difference of temperature between the inflow and the outflow, and the weight of water which passed in a given time.
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  • The temperature at different heights was measured by iron wires forming thermo-junctions with the mercury in the inner tube.
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  • The heat-flow through the central column amounted to about 7.5 calories in 54 seconds, and was measured by continuing the tube through the iron plate into the bulb of a Bunsen ice calorimeter, and observing with a chronometer to a fifth of a second the time taken by the mercury to contract through a given number of divisions.
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  • This can be measured graphically without any knowledge of the law of variation of the surface temperature, or of the laws of propagation of heat waves.
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  • Ang3trom's value for iron, when corrected for obvious numerical errors, and for the probable variation of c, becomes Iron, k =0.164 (1-0.0013 0), but this is very doubtful as c was not measured.
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  • The thermal capacity and electrical conductivity were measured at various temperatures on the same specimens of metal.
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  • The advantage is that the quantities of heat are measured directly in absolute measure, in terms of the current, and that the results are independent of a knowledge of the specific heat.
    0
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  • The last expression in terms of k/k' is very simple, but the first is more useful in practice, as the quantities actually measured are E, C, 1, q, and the difference of temperature.
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  • The current C was measured in the usual way by the difference of potential on a standard resistance.
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  • "If a man's fame," says KOppen, "can be measured by the number of hearts who revere his memory, by the number of lips who have mentioned, and still mention him with honour, Asoka is more famous than Charlemagne or Caesar."
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  • They went back to the later period of Plato's thought, the period when Plato endeavoured to combine his doctrine of Ideas with the Pythagorean number-theory, and identified the Good with the One, the source of the duality of the Infinite and the Measured (rd .bretpov and 71-pas) with the resultant scale of realities from the One down to the objects of the material world.
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  • One of the publishers to whom Johnson applied for employment measured with a scornful eye that athletic though uncouth frame, and exclaimed, "You had better get a porter's knot and carry trunks."
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  • His wrath was excited in no measured terms against the re-marriage of his old friend Mrs Thrale, the news of which he heard this summer.
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  • Azimuths were also measured at Jan Mayen for 338 auroral bands, the mean being 22.0° W., or 7.9° to the east of the magnetic meridian.
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  • Dividing the whole number of arcs, 156, whose angular velocities were measured into three numerically equal groups, according to their altitude, the following were the results in minutes of arc per second of time (or degrees per minute of time): - Each group contained auroras which appeared stationary.
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  • If an auroral arc represented a definite selfluminous portion of space of small transverse dimensions at a uniform height above the ground, its height could be accurately determined by observations made with theodolites at the two ends of a measured base, provided the base were not too short compared to the height.
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  • C. C. Baly (21), making use of the observations of the Russian expedition in Spitsbergen in 1899, accepts as the wave-lengths of the three principal auroral lines 557 o, 4276 and 3912; and he identifies all three and ten other auroral lines ranging between 5570 and 3707 with krypton lines measured by himself.
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  • Thus the differences in the wave-lengths of presumably the same lines as measured by different Arctic observers may be only partly due to unfavourable observational conditions.
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  • Roda Island contains a mosque built by Kait Bey, and at its southern extremity is the Nilometer, by which the Cairenes have for over a thousand years measured the rise of the river.
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  • Weighis and Measures.The metrical system of weights and measures is in official but not in popular use, except in the foreign quarters of Cairo, Alexandria, &c. The most common Egyptian measures are the fitr, or space measured by the extension of the thumb and first finger; the shibr, or span; and the cubit (of three kinds 224, 25 and 263/4 in.).
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  • Twice during this period Denmark and Sweden measured their strength in the open field, on the first occasion in the " Scandinavian Seven Years' War " (1562-70), on the second in the " Kalmar War " (1611-13), and on both occasions Denmark prevailed, though the temporary advantage she gained was more than neutralized by the intense feeling of hostility which the unnatural wars, between the two kindred peoples of Scandinavia, left behind them.
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  • The measurements of a female, taken in the flesh, were head and body 4 ft., tail 172 in.; but a large individual measured 6 ft.
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  • The term was first used by Musschenbroek to denote an instrument wherein the expansion of a metal rod measured the temperature.
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  • From east to west it measured 258 ft., the nave is 69 ft.
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  • Wallace, whilst insisting that the range of observed and measured variation was much larger in proportion to the size of the organisms or parts of organism affected than was generally believed, leaned to the Darwinian view in excluding from the normal factors in the origin of species variations of the extremer ranges of magnitude.
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  • Such differentiation may be measured by determining the correlation between the position or the time of production and the character of the organs produced, the methods by which the correlation is measured being those described in the article Error, Law Of.
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  • Professor Pearson has measured this correlation.
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  • We may therefore conclude that for large classes of characters, both animal and vegetable, the variability of an individual, as measured by the standard deviation of its undifferentiated but repeated organs, is a constant fraction of the variability of its race, as measured by the standard deviation of the corresponding series of organs produced by all the individuals of its race.
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  • The kind of selection involved may then be measured by comparing those animals which pair with the general body of adults.
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  • This kind of selection, called by Pearson "reproductive" or "genetic" selection, may be measured by finding the correlation between the characters of the individuals which pair and the number of young.
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  • This kind of selection is measured by the correlation between deviation of either mate from the type, and deviation of the other.
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  • Any line parallel to the axis is a diameter, and the parameter of any diameter is measured by the focal chord drawn FIG.
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  • When the other ten were aggrieved Jesus declared that greatness was measured by service, not by rank; and that the Son of Man had come not to be served but to serve, and to give His life to ransom many other lives.
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  • He flourished about 625 B.C. Several of the ancients ascribe to him the invention of the dithyramb and of dithyrambic poetry; it is probable, however, that his real service was confined to the organization of that verse, and the conversion of it from a mere drunken song, used in the Dionysiac revels, to a measured antistrophic hymn, sung by a trained body of performers.
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  • Measured by the records of other men equally successful as political leaders, there seems little of this nature to criticize severely.
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  • This point, by a line measured down the valley, but not following the winding of the river, is about 1050 m.
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  • First, the entire area of the district, whether cultivated or uncultivated, and of each field within the district is accurately measured.
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  • Each field is measured, and an assessment placed upon it according to the quality of the soil without any attempt to fix the actual average produce.
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  • James Bradley, on 27th December 1722, actually measured the diameter of Venus with a telescope whose objectglass had a focal length of 2124 ft.
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  • He has never seen more perfect optical definition in any of the many telescopes he has employed, and certainly never measured a celestial object in such favourable conditions of physical comfort.
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  • The interval between the true trails, measured at right angles to the direction of the trails, obviously corresponds to the difference of zenith distance of the two stars.
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  • A calorimeter is any piece of apparatus in which heat is measured.
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  • Quantities of heat may be measured indirectly in a variety of ways in terms of the different effects of heat on material substances.
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  • The thermal capacity of a body is measured by the quantity of heat required to raise its temperature one degree, and is necessarily proportional to the mass of the body for bodies of the same substance under similar conditions.
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  • The Method of Mixture consists in imparting the quantity of heat to be measured to a known mass of water, or some other standard substance, contained in a vessel or calorimeter of known thermal capacity, and in observing the rise of temperature produced, from which data the quantity of heat may be found as explained in all elementary text-books.
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  • In the latter case two steady currents of water at different temperatures, say o° and too° are passed through an equalizer, and the resulting temperature measured without mixing the currents, which are then separately determined by weighing.
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  • This difficulty was overcome by the invention of the Bunsen calorimeter, in which the quantity of ice melted is measured by observing the diminution of volume, but the successful employment of this instrument requires considerable skill in manipulation.
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  • In addition to its great theoretical interest, this method possesses the advantage of being frequently the most accurate in practical application, since energy can be more accurately measured in other forms than in that of heat.
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  • The Torque Was Measured By Weights 0 And P Suspended By Silk Ribbons Passing Over The Pulleys N And Round The Disk Kl.
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  • The Frictional Generation Of Heat In A Metallic Wire Conveying A Current Can Be Measured In Various Ways, Which Correspond To Slightly Different Methods.
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  • The Duration Of An Experiment Was About Ten Minutes, And The Product Of The Mean Current And The Time, Namely Ct, Was Measured By The Weight Of Silver Deposited In A Voltameter, Which Amounted To About 0.56 Gramme.
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  • The Peculiar Advantage Of The Electric Method Of Callendar And Barnes, Already Referred To, Is That The Specific Heat Itself Is Determined Over A Range Of 8° To 10° At Each Point, By Adding Accurately Measured Quantities Of Heat To The Water At The Desired Temperature In An Isothermal Enclosure, Under Perfectly Steady Conditions, Without Any Possibility Of Evaporation Or Loss Of Heat In Transference.
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  • In The Case Of Solids And Liquids Under Ordinary Conditions Of Pressure, The External Work Of Expansion Is So Small That It May Generally Be Neglected; But With Gases Or Vapours, Or With Liquids Near The Critical Point, The External Work Becomes So Large That It Is Essential To Specify The Conditions Under Which The Specific Heat Is Measured.
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  • The determination of stellar parallaxes is a matter of great difficulty on account of the minuteness of the angle to be measured, for in no case does the parallax amount to I"; moreover, there is always an added difficulty in determining an annual change of position, for seasonal instrumental changes are liable to give rise to a spurious effect which will also have an annual period.
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  • Henderson at the Cape of Good Hope measured the parallax of a Centauri, but his resulting value 1" was considerably too high.
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  • The quantity determined by these methods is the relative parallax between the star measured and the stars with which it is compared.
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  • Although the parallaxes hitherto measured have added greatly to our general knowledge of stellar distances and absolute luminosities of stars, a collection of results derived by various observers choosing specially selected stars is not suitable for statistical discussion.
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  • Regarded as a linear velocity, the parallactic motion is the same for all stars, being exactly equal and opposite to the solar motion; but its amount, as measured by the corresponding angular displacement of the star, is inversely proportional to the distance of the star from the earth, and foreshortening causes it to vary as the sine of the angular distance from the apex.
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  • To arrive at some estimate of the speed of the solar motion, we may consider the motions of those stars whose parallaxes have been measured, and whose actual linear speed is accordingly known (disregarding motion in the line of sight).
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  • We may conveniently distinguish the two drifts as the slow-moving and fast-moving drifts respectively; but it should be remembered that, since these motions are measured relatively to the sun, this distinction is not physically significant.
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  • After that event the city walls, which measured about three quarters of a mile each way, were razed, wide streets were made, the course of the river straightened, electric lighting and tramways introduced and a good water service supplied.
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  • The importance of these acts cannot be over-estimated as supplying a legal standard of efficiency by which all prisons could be measured.
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  • A new committee sat in 1863, and in its report again remarked in no measured terms upon the many and wide differences that still existed in the gaols of Great Britain as regards construction, diet, labour and general discipline, "leading to an inequality, uncertainty and inefficiency of punishment productive of the most prejudicial results."
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  • This plan had originated with Captain Maconochie, at one time superintendent in Norfolk Island, who had recommended that the punishment inflicted upon criminals should be measured, not by time, but by the amount of labour actually performed.
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  • This industry was to be measured by marks earned by hard labour at the public works, after a short probational term of close "separate" confinement.
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  • He measured arms with Habib, and was slain.
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  • Kant's influence, then, upon subsequent logic is least of all to be measured by his achievement in his professed contribution.
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  • The energy stored up in the jar in joules is expressed by the value of CV 2, where C is the capacity measured in farads and V the potential difference of the coatings in volts.
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  • Owing to the variation in the value of the dielectric constant of glass with the temperature and with the frequency of the applied electromotive force, and also owing to electric glow discharge from the edges of the tin foil coatings, the capacity of an ordinary Leyden jar is not an absolutely fixed quantity, but its numerical value varies somewhat with the method by which it is measured, and with the other circumstances above mentioned.
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  • In the case of time, measured from the Christian era, this distinction is at once given.by the letters A.D.
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  • His constructions are based on the idea that the imaginaries d - 1 represent a unit line, and its reverse, perpendicular to the line on which the real units 1 are measured.
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  • The quantity of heat so measured is the total heat of the vapour reckoned from the final temperature of the calorimeter, and the heat of the liquid h must be subtracted from the total heat measured to find the latent heat of the vapour at the given temperature.
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  • To find the total heat H of a vapour, we have H =E+p(v - b), where the intrinsic energy E is measured from the selected zero 9 0 of total heat.
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  • But it must be remarked that the superheat of the steam in these experiments is only I or 2%° of the total heat measured.
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  • A similar objection applies, though with less force, to Regnault's main experiments between 125° and 225° C., giving the value S =0.475, in which the superheat (on which the value of S depends) is only one-sixteenth of the total heat measured.
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  • That of Biot is far more complicated and troublesome, but admits greater accuracy of adaptation, as it contains five constants (or six, if 0 is measured from an arbitrary zero).
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  • The reason for adopting this method is that the specific volume of a saturated vapour cannot be directly measured with sufficient accuracy on account of the readiness with which it condenses on the surface of the containing vessel.
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  • The specific volumes of superheated vapours may, however, (19) be measured with a satisfactory degree of approximation.
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  • The drainage basin measured from the water-partings of the enclosing mountains is some three times as great.
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  • The light reflected from the fixed mirror traces a straight line on the paper, serving as a base line from which the variations in declination are measured.
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  • The value of this constant angle is obtained by comparing the record with the value for the declination as measured with a magnetometer.
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  • Balard determined the volume composition of the gas by decomposition over mercury on gentle warming, followed by the absorption of the chlorine produced with potassium hydroxide, and then measured the residual oxygen.
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  • The progress made through even this darkest age may be measured by the difference between the army of Rollo and that which William the Conqueror gathered for the invasion of England.
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  • 36, if OA, OB, OC be three mutually perpendicular lines in the solid, we may denote by O the angle which OC makes with a fixed direction OZ, by ~ the azimuth of the plane ZOC measured from some fixed plane through OZ, and by f~ the inclination of the plane COA to the plane ZOC In fig.
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  • This is the axis of the required screw; the amount of the translation is measured by the projection of AB or BC or CD on the axis; and the angle of rotation is given, by the inclination of the aforesaid bisectors.
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  • Successive half-turns about parallel axes a, b are equivalent to a translation measured by double the distance between these axes in the direction from a to 1,.
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  • We infer that on our reckoning the force of gravity on a mass m is to be measured by mg, the momentum produced per second when this force acts alone.
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  • The distance h1+h2, which occurs in the first term on the right hand can be measured directly.
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  • If x be measured upwards from the lower end, the horizontal component of the tension P at any point will be Pay/ax, approximately, if y denote the lateral displacement.
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  • Relations between Polygons of Loads and of Resistances.In a structure in which each piece is supported at two joints only, the well-known laws of statics show that the directions of the gross load on each piece and of the two resistances by which it is supported must lie in one plane, must either be parallel or meet in one point, and must bear to each other, if not parallel, the proportions of the sides of a triangle respectively parallel to their directions, and, if parallel, such proportions that each of the three forces shall be proportional to the distance between the other two,all the three distances being measured along one direction.
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  • In order to allow for the finite stiffness and strength of materials, the least distance of the centre of resistance inward from the nearest edge of the joint is made to bear a definite proportion to the depth of the joint measured in the same direction, which proportion is fixed, sometimes empirically, sometimes by theoretical deduction from the laws of the strength of materials.
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  • The pitch of a screw is the distance, measured parallel to its axis, between two successive turns of the same thread or helical projection.
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  • A condition equivalent to the above, and necessarily connected with it, is, that at each pair of points of contact the inclinations of the curves to their radii-vectores shall be equal and contrary; or, denoting by r1, rf the radii-vectores at any given pair of points of contact, and s the length of the equal arcs measured from a certain fixed pair of points of contact dri/ds= drm/ds; (18)
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  • The distance, measured along the pitch-circle, from the face of one tooth to the face of the next, is called the pitch., The pitch and the number of teeth in wheels are regulated by the following principles:
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  • To find the length of the path of contact on either side of the pitch-point I, it is to be observed that the distance between the fronts of two successive teeth, as measured along PiIPi, is less than the pitch in the ratio of cos obliquity: I; and consequently that, if distances equal to the pitch be marked off either way from I towards P~ and Pi respectively, as the extremities of the path of contact, and if, according to Principle IV.
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  • The spare between two teeth, measured on the pitch-circle, is made about ~th part wider than the thickness of the tooth on the pitch-circle-that is to say, Thickness of tooth =~ pitch; Width of space =Iis pitch.
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  • The pitch or axial pitch of a screw has the meaning assigned to it in that section, viz, the distance, measured parallel to the axis, between the corresponding points in two successive turns of the same thread.
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  • If, therefore, the screw has several equidistant threads, the true pitch is equal to the divided axial pitch, as measured between two adjacent threads, multiplied by the number of threads.
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  • If a helix be described round the screw, crossing each turn of the thread at right angles, the distance between two corresponding points on two successive turns of the same thread, measured along this normal helix, may be called the normal pitch; and when the screw has more than one thread the normal pitch from thread to thread may be called the normal divided pitch.
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  • Let r1 be the radius of the large end of each, ri that of the small end, r, that of the middle; and let Ii be the sagitta, measured perpendicular to the axes, of the arc by whose revolution each of the conoids is generated, or, in other words, the bulging of the conoids in the middle of their length.
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