Unit sentence example

unit
  • The medical unit has healed me.
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  • This is Lieutenant George with the intel unit assigned to your command.
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  • Such a unit is independent of gravity or of any other quantity which varies with the locality.
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  • The married couple formed a unit as to external responsibility, especially for debt.
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  • No other regular army unit has a chance out here.
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  • As in Virginia, the county is the unit of government, though an unsuccessful attempt to introduce the township system was made in the first constitution.
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  • She strode to the clothing unit in the corner and ordered her a set.
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  • She turned toward the unit lifting her arms in delight.
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  • It would heal once he reached the main craft with the help of the medical unit but was useless in the meantime.
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  • The original method of charging adopted in Great Britain took the telephone instrument as the unit, charging a fixed annual rental independent of the amount of use to which the instrument was put.
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  • The factors Af (u-v cos i) and Bf (v sin i) give the frictional resistance to sinking, per unit length of the cable, in the direction of the length and transverse to the length respectively.
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  • In this primeval, or rather timeless because ever-proceeding, sacrifice, time itself, in the shape of its unit the year, is made to take its part, inasmuch as the three seasons - spring, summer and autumn - of which it consists, constitute the ghee (clarified butter), the offering-fuel and the oblation respectively.
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  • Besides, I rather like our little family unit, and the house certainly is big enough for us all.
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  • Between 1500 and 4000 metres the charge inside the unit tube is much less, only 0.000040.
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  • A window air conditioning unit hummed, and when he opened the door to the apartment, a surge of cool air invited them in.
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  • The ecclesiastical unit in episcopacy is a diocese, comprising many churches and ruled by a prelate; in congregationalism it is a single church, self-governed and entirely independent of all others; in Presbyterianism it is a presbytery or council composed of ministers and elders representing all the churches within a specified district.
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  • It is merely necessary to select some larger or smaller unit as the subject of observation--as criticism has every right to do, seeing that whatever unit history observes must always be arbitrarily selected.
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  • Taking i volt equal 1/300 of an electrostatic unit, we find M =0.000265.
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  • It is the seat of a justice of the peace, and is the electoral unit for the general council and the district council.
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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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  • With all its defective psychology, its barren logic, its immature technique, it emphasized two great and necessary truths, firstly, the absolute responsibility of the individual as the moral unit, and, secondly, the autocracy of the will.
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  • What if the basic unit was a couple, a relationship, and what if that relationship had an identity?
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  • A handheld GPS unit can settle any well-defined border issue.
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  • It was not long, however, before the party itself became divided on the fiscal question; and a Protectionist government coming into power, about half the Labour members gave it consistent support and enabled it to maintain office for about three years, the party as a political unit being thus destroyed.
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  • Each such unit is termed an "ommatidium."
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  • The fact that small nations can adopt standard treaties, laws, currencies, and international practices of larger countries means that a small economic unit can be viable.
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  • Whilst each unit of the lateral eye of Limulus has arhabdom of ten t pieces See fig.
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  • Alexander, became a unit of the Lettish army (Olai agreement on July 15 1919) to be formed by Gen.
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  • Gold is the nominal standard of value, the monetary unit being the gold milreis worth 2s.
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  • Hence we can separate the numbers from the common unit, and replace 3 lb - I - 5 lb - 7 lb +2 lb by (3+5-7+2) lb, the additions and subtractions being then performed by means of an addition-table.
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  • We may regard this as meaning the same as 5 X3 X7 lb, since 7 lb itself means 7 X 1 lb, and the lb is the unit in each case.
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  • We may therefore conveniently take as our unit, in place of x, a number y such that x=6y.
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  • For multiplication, for instance, we have the statement that, if P and Q are two quantities, containing respectively p and q of a particular unit, then p X Q = q X P; or the more abstract statement that p X q= q X p.
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  • The form (m+n)A=mA+nA follows at once from the fact that A is the unit with which we are dealing.
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  • We cannot solve the equation 7X =4s.; but we are accustomed to subdivision of units, and we can therefore give a meaning to X by inventing a unit w s.
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  • Here each member is a number, and the equation may, by the commutative law for multiplication, be written 2(x+I) - 4(x-2) This means that, whatever unit A we take, 2(x+ I) A Sand 5 4(x-2) A are equal.
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  • Thus, if we have an equation P=Q, where P and Q are numbers involving fractions, we can clear of fractions, not by multiplying P and Q by a number m, but by applying the equal multiples P and Q to a number m as unit.
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  • Taking any number n to be represented by a point on a line at distance nL from a fixed point 0, where L is a unit of length, we start with a series of points representing the integers I, 2, 3,.
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  • Every unit of the rth species which does not vanish is the product of r different units of the first species; two such units are independent unless they are permutations of the same set of primary units e i, in which case they are equal or opposite according to the usual rule employed in determinants.
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  • If E is any extensive unit, there is one other unit E', and only one, such that the (progressive) product EE' =- r.
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  • This unit is called the supplement of E, and denoted by IE.
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  • Now when r+s>n, the product E r E B is defined to be that unit of which the supplement is the progressive product IE,4E 8.
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  • It was with this corps that Dr. Elsie Inglis and a detachment of the Scottish Women's Hospitals served as medical unit.
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  • The corpus separatum became an independent unit under the League of Nations, the Croat suburb of Susak remaining in Yugoslavia and the Baros port being added as an outlet for Yugoslav trade.
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  • The analysis of the specific variations of organic form so as to determine what is really the nature and limitation of a single " character " or " individual variation," and whether two such true and strictly defined single variations of a single structural unit can actually " blend " when one is transmitted by the male parent and the other by the female parent, are matters which have yet to be determined.
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  • The force operative upon the positive half is parallel to OZ, and of amount per unit of area equal to - b 2 D = b 2 kD cos nt; and to this force acting over the whole of the plane the actual motion on the positive side may be conceived to be due.
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  • The unit of administration is the field cornetcy.
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  • The army corps was about to arrive, practically as a whole unit, in South Africa; but it was evident that the exigencies of the situation, and the widely divided areas of invasion, would at least defer the execution of the plan which had been formed for an invasion of the Orange Free State from Cape Colony.
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  • Under the currency law of the 31st of March 1879, the thousandth part of a kilogramme of gold was made the monetary unit and was called a bolivar, in honour of the Venezuelan liberator.
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  • Our starting-point in this, as in all departments of biological study, must be the biological unit, and it is to the alterations to which this is subject, under varying conditions of nutrition and stimulation, that the science of pathology must apply itself.
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  • According to our present knowledge of physiological and pathological processes, we must regard the cell as the ultimate biological unit - a unit of structure and a unit of function; this was first put forward by Schleiden in 1838, and by Schwann in 1839, but we owe to Virchow the full recognition of the fundamental importance of the living cell in all the processes of life, whether in health or disease.
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  • Moreover, the splendid building is nearly always a unit; seldom, unless accidentally, a component part of a broad effect.
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  • The walled city of London was a distinct political unit, although it owed a certain allegiance to that one of the kingdoms around it which was the most powerful for the time being.
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  • The 1st division, under major-general Crealock, advanced along the coast belt and was destined to act as a support to the 2nd division, under major-general Newdigate, which with Wood's flying column, an independent unit, was to march on Ulundi from Rorke's Drift and Kambula.
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  • The pressure at any point cf a plane in the interior of a fluid is the intensity of the normal thrust estimated per unit area of the plane.
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  • The pressure of the air is a convenient unit to employ in practical work, where it is called an " atmosphere "; it is made the equivalent of a pressure of one kg/cm'; and one ton/inch 2, employed as the unit with high pressure as in artillery, may be taken as 150 atmospheres.
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  • Hence the space variation of the pressure in any direction, or the pressure-gradient, is the resolved force per unit volume in that direction.
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  • The absolute unit of force is employed here, and not the gravitation unit of hydrostatics; in a numerical application it is assumed that C.G.S.
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  • As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of time considered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium.
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  • If homogeneous liquid is drawn off from a vessel so large that the motion at the free surface at a distance may be neglected, then Bernoulli's equation may be written H = PIP--z - F4 2 / 2g = P/ p +h, (8) where P denotes the atmospheric pressure and h the height of the free surface, a fundamental equation in hydraulics; a return has been made here to the gravitation unit of hydrostatics, and Oz is taken vertically upward.
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  • The ner of 600 and the sar of 3600 were formed from the soss or unit of 60, which corresponded with a degree of the equator.
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  • The practical unit of quantity of electricity, the coulomb, is named after him.
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  • A very usual size of cistern forming a convenient unit is one that will hold 20 tons of char.
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  • The coinage formerly was the caroub and piastre (the latter worth about 6d.), but in 1891 the French reformed the coinage, substituting the franc as a unit, and having the money minted at Paris.
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  • The monetary unit is the Peruvian pound (libra) which is uniform in weight and fineness with the British pound sterling.
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  • With him the unit is termed "digitus"; when multiplied by ten it becomes the "articulus"; while the combination of the articulus and the digitus is the "numeras compositus."
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  • Until recently these spherical lenses were numbered in terms of their focal length, the inch being used as the unit.
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  • Owing principally to differences in the length of the inch in various countries this method had great inconveniences, and now the unit is the refractive power of a lens whose focal length is one metre.
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  • This unit is called a "dioptric" (usually written "D").
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  • The town (or township) is the unit of local government, the county being recognized only for judicial purposes and to a certain extent in the appointment by central administrative boards.
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  • On the one hand, his whole formulation of Evolution in mechanical terms urges him in the direction of materialism, and he attempts to compose the mind out of homogeneous units of consciousness (or" feeling ")" similar in nature to those which we know as nervous shocks; each of which is the correlative of a rhythmical motion of a material unit or group of such units "(§ 62).
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  • In the next place we must notice that electrification is a measurable magnitude and in electrostatics is estimated in terms of a unit called the electrostatic unit of electric quantity.
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  • The unit of mechanical force in the " centimetre, gramme, second " (C.G.S.) system of units is the dyne, which is approximately equal to 1/981 part of the weight of one gramme.
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  • A very small sphere is said then to possess a charge of one electrostatic unit of quantity, when it repels another similar and similarly electrified body with a force of one dyne, the centres being at a distance of one centimetre, provided that the spheres are in vacuo or immersed in some insulator, the dielectric constant of which is' taken as unity.
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  • This provides us with a definition of a unit of electric force, for it is the strength of an electric field at that point where a small conductor carrying a unit charge is acted upon by unit mechanical force, assuming the dielectric constant of the surrounding medium to be unity.
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  • If we consider a very small conductor charged with a unit of positive electricity to be placed in an electric field, it will move or tend to move under the action of the electric force in a certain direction.
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  • We may define the term potential difference otherwise by saying that it is the work done in carrying a small conductor charged with one unit of electricity from one point to the other in a direction opposite to that in which it would move under the electric forces if left to itself.
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  • Suppose then that we have a conductor charged with electricity,we may imagine its surface to be divided up into small unequal areas, each of which carries a unit charge of electricity.
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  • If we consider lines of electric force to be drawn from the boundaries of these areas, they will cut up the space round the conductor into tubular surfaces called tubes of electric force, and each tube will spring from an area of the conductor carrying a unit electric charge.
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  • Hence the charge on the conductor can be measured by the number of unit electric tubes springing from it.
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  • These surfaces are called "equipotential" or "level surfaces," and we may so locate them that the potential difference between two adjacent surfaces is one unit of potential; that is, it requires one absolute unit of work (I erg) to move a small body charged with one unit of electricity from one surface to the next.
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  • Accordingly the number of electric cells into which the space round is cut up is equal to twice the energy stored up, or each cell contains half a unit of energy.
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  • By the surface density of electrification on a conductor is meant the charge per unit of area, or the number of tubes of electric force which spring from unit area of its surface.
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  • The potential of a conductor has already been defined as the mechanical work which must be done to bring up a very small body charged with a unit of positive electricity from the earth's surface or other boundary taken as the place of zero potential to the surface of this conductor in question.
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  • The quantity of electricity which must be given to the sphere to raise it to unit potential is therefore R electrostatic units.
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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 unit of electrostatic capacity is therefore that of a sphere of I cm.
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  • This unit is too small for practical purposes, and hence a unit of capacity 900,000 greater, called a microfarad, is generally employed.
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  • If, however, we defined the strength of the source by the statement that the strength divided 1 The beginner is often puzzled by the constant appearance of the factor 47r in electrical theorems. It arises from the manner in which the unit quantity of electricity is defined.
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  • A tube so chosen that EdS for one section has a value unity, is called a unit tube, since the product of force and section is then everywhere unity for the same tube.
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  • Since the potential of a conductor is defined to be the work required to move a unit of positive electricity from the surface of the earth or from an infinite distance from all electricity to the surface of the conductor, it follows that the work done in putting a small charge dq into a conductor at a potential v is v dq.
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  • Suppose that the dielectric has a constant K, then we must multiply both sides by K and the expression for the energy per unit of volume of the field is equivalent to z DE where D is the displacement or polarization in the dielectric.
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  • The customary unit of expenditure is the threepenny-bit or "tickey."
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  • He therefore employed the corresponding expression for a cycle of infinitesimal range dt at the temperature t in which the work dW obtainable from a quantity of heat H would be represented by the equation dW =HF'(t)dt, where F'(t) is the derived function of F(t), or dF(t)/dt, and represents the work obtainable per unit of heat per degree fall of temperature at a temperature t.
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  • If we consider any short length of the stream bounded by two imaginary cross-sections A and B on either side of the plug, unit mass of the fluid in passing A has work, p'v', done on it by the fluid behind and carries its energy, E'+ U', with it into the space AB, where U' is the kinetic energy of flow.
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  • If two diatomic molecules, having each 5 degrees of freedom, combine to form a molecule with 6 degrees of freedom, we should have n = 2, or the energy lost would be 2pc per unit mass.
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  • The total entropy of the system is found by multiplying the entropy per unit mass of the substance in each state by the mass existing in that state, and adding the products so obtained.
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  • If J', J" represent the values of the function for unit mass of the substance of specific volumes v' and v" in the two states at temperature 0 and pressure and if a mass m is in the state v', and 1-m in the.
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  • The original settlement on the Palatine, like its neighbour on the Quirinal, was an agricultural community, whose unit both from the legal and religious point of view was not the individual but the household.
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  • By the method of empirical psychology, he examined man first as a unit in himself and secondly in his wider relations to the larger units of society and the universe of mankind.
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  • With drums beating and colours flying, every unit within call went forward for the final effort.
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  • The characters thus composed, though so simple as to their basal unit, are appallingly complex in their elaboration.
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  • The word is also used as a unit of linear measurement of the magnifying power of a lens or microscope.
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  • Other standards of reference may be used in special connexions; for example, the Earth is the usual unit for expressing the relative density of the other members of the solar system.
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  • It may be noted that if comparison be made with water at 4°, the relative density is the same as the absolute density, since the unit of mass in the C.G.S.
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  • The unit of local government is the " hundred," which corresponds to the township of Pennsylvania.
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  • According to the constitution of 1831 the unit of representation in the legislature was the county; inasmuch as the population of New Castle county has exceeded after 1870 that of both Kent and Sussex, the inequality became a cause of discontent.
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  • Although the three formed a unit at one stage it may seem doubtful whether two so closely related chapters as 1 Chron.
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  • The commissioners' court of five members, including the presiding judge, attends to county business matters, the county being the unit of local government.
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  • The smallest unit of matter with which physical phenomena are concerned is the molecule.
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  • Let a mixture of gases contain per unit volume v molecules of the first kind, v' of the second kind, and so on.
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  • The number of molecules of the first kind of gas, whose components of velocity lie within the ranges between u and u+du, v and v+dv, w and w+dw, will, by formula (5), be v?l (h 3 m 3 /7 3)e hm (u2+v2+w2)dudvdw (9) per unit volume.
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  • This is equivalent to a steady pressure p i per unit area where +0 pi - zfff v J 1 (h3m3/ir3)e hm(u2+v2+w2)mu2dudvdw.
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  • Clearly the integral is the sum of the values of mu g for all the molecules of the first kind in unit volume, thus p=v mu l +v'm'u 2 +...
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  • As in all other languages, so in those of aboriginal America, the sentence is the unit.
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  • In all parts of the western hemisphere society was organized on cognate kinship, real or artificial, the unit being the clan.
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  • Before the development of pneumatic chemistry, air was regarded as a distinct chemical unit or element.
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  • With some modifications introduced by Jefferson, notably the adoption of a higher unit of value (the dollar instead of one-tenth of a cent), this plan constitutes the basis of the present American system.
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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 failure seems (§ 2) to be due to difficulty in realizing the numerical expression of an area or a solid in terms of a specified unit, while the same difficulty does not arise in the case of linear measure or liquid measure, where the number of units can be ascertained by direct counting.
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  • But catholicity of feeling is inherent in the congregational idea of the church, inasmuch as it knows no valid use of the term intermediate between the local unit of habitual Christian fellowship and the church universal.
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  • Let E be the bulk modulus of elasticity, defined as increase of pressure = decrease of volume per unit volume where the pressure increase is so small that this ratio is constant, w the small increase of pressure, and - (dy/dx) the volume decrease, then E=e/(- dy/dx) or w Æ= - dy/dx (I) This gives the relation between pressure excess and displacement.
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  • Then, as we shall prove later, the vibrations of the string may be represented by the travelling of two trains in opposite directions each with velocity /tension=mass per unit length each half the height of the train represented in fig.
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  • We certainly do not wish to measure its loudness, and even if we did it might be difficult to fix on any unit of noisiness.
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  • Probably we should be driven to a purely physical unit, the stream of energy proceeding in any direction, and if the noise were great enough we might measure it possibly by the pressure against a surface.
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  • We shall first investigate the velocity with which a disturbance travels along a string of mass m per unit length when it is stretched with a constant tension T, the same at all points.
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  • Kuropatkin, who had taken command of the army, saw from the first that he would have Kuro- to gain three months, and disposed his forces as they patkin's came on the scene, unit by unit, in perfect accord plan.
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  • Let K be the breaking strength of a bar per unit of section, when it is loaded once gradually to breaking.
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  • Generally the influence line is drawn for unit load.
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  • Repeating the process for other positions, we get the influence line Aghb, for the shear at C due to unit load anywhere on the girder.
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  • The loads at D', E, due to unit weight on the rail girder are (p-n)/p and n/p. The reaction at B' is {(p- n)xi+n(xi+p)}' /pi.
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  • The true catenary is that assumed by a chain of uniform weight per unit of length, but the form generally adopted for suspension bridges is that assumed by a chain under a weight uniformly distributed relatively to a horizontal line.
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  • At the age of nineteen he invented an electromagnetic engine, and in the course of examining its performance dissatisfaction with vague and arbitrary methods of specifying elec rical quantities caused him to adopt a convenient and scie tific unit, which he took to be the amount of electricity req ired to decompose nine grains of water in one hour.
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  • The lowest administrative unit was the political sub-district (Bezirk) under an official (Bezirkshauptmann), who united nearly all the administrative functions which were divided among the various ministries according to their attributions.
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  • He further made the cohort the military unit instead of the maniple, and his cavalry and light-armed troops were drawn from foreign countries, so that it may be said that Marius was the originator of the mercenary army.
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  • The tical (baht) is the unit of currency and also the unit of weight.
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  • The unit of linear measure is the wall, which is subdivided into wah or sauk, a wah or kup, and into 9 1 6 wah or niew.
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  • The unit of land measure is the rai, which is equal to 400 square wah, and is subdivided into four equal ngan.
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  • The usual definition of the component current in any direction, as the net amount of electrons which crosses, towards the positive side, an element of surface fixed in space at right angles to that direction, per unit area per unit time, here gives no definite result.
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  • In the present case the total dielectric contribution to this current works out to be the change per unit time in the electric separation in the molecules of the element of volume, as it moves uniformly with the matter, all other effects being compensated molecularly without affecting the propagation.
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  • Thus the diocese, hitherto a simple unit, became an elaborately articulated whole.
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  • The symbol (alp) which is known as Legendre's symbol, and denotes the positive or negative unit which is the remainder when au s (-1) is divided by a prime number p, does not appear in this memoir, but was first used in the Essai sur la theorie des nombres.
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  • In an extended table of S, the value is interpolated for unit increment of velocity.
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  • In 1908 the General Assembly passed a law providing for annual direct primary elections (outside of Baltimore; and making the Baltimore special primary law applicable to state as well as city officials), but, as regards state officers, making only a slight improvement upon previous conditions inasmuch as the county or district is the unit and the vote of county or district merely " instructs " delegates to the party's state nominating convention, representation in which is not strictly in proportion to population, the rural counties having an advantage over Baltimore; no nomination petition is required.
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  • It will be seen that communes do not correspond with any natural unit.
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  • The unit among the Mahommedans is the douar, a tribal division administered by a cadi.
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  • The dates printed in heavy type are certain, at least within a unit.
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  • Hence the Pacific basin may be regarded as a stable and homogeneous geographical unit, clearly marked off round nearly all its margin by steep sharp slopes, extending in places through the whole known range of elevation above sea-level and of depression below it - from the Cordilleras of South America to the island chains of Siberia and Australia.
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  • The monetary unit is the gold colon weighing 778 gramme, 900 fine, and thus worth about 23d.
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  • The International Geodetic Committee have adopted the metre as their unit of measurement.
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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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  • The usual arrangement by countries has been mainly abandoned in favour of following out each unit as a whole, without recurring to it separately for every locality.
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  • Vases may also be found bearing such relations to one another as to show their unit of volume.
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  • Another defect in the evidence of coins is that, when one variety of the unit of weight was once fixed on for the coinage, there was (barring the depreciation) no departure from it, because of the need of a fixed value, and hence coins do not show the range and character of the real variations of units as do buildings, or vases, or the actual commercial weights.
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  • Buildings at Persepolis, all of nearly the same age, vary in unit 1 in 450 (25).
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  • Hence we see that if one unit is derived from another it may be possible, by the similarity or difference of the forms of the curves, to discern whether it was derived by general consent and recognition from a standard in the same condition of distribution as that in which we know it, or whether it was derived from it in earlier times before it became so varied, or by some one action forming it from an individual example of the other standard without any variation being transmitted.
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  • It should be borne in mind that in early times the larger values, such as minae, would be transmitted by commerce, while after the introduction of coinage the lesser values of shekels and drachmae would be the units; and this needs notice, because usually a borrowed unit was multiplied or divided according to the ideas of the borrowers, and strange modifications thus arose.
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  • Sir C. Warren has derived a primitive unit from a proportion of the human body, by ascertaining the probable mean height of the ancient people in Egypt, and so thereby has derived a standard from the stature of man.
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  • It is curious, however, to find that an ancient nation of the East, so wise in geometrical proportions, should have followed what by modern experience may be regarded as an inverse method, that of obtaining a unit of length by deducing it through weights and cubic measure, rather than by deriving cubic measure through the unit of length.
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  • This unit is also recorded by cubit lengths scratched on a tomb at Beni Hasan (44), and by dimensions of the tomb of Ramessu IV.
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  • Babylonia had this unit nearly as early as Egypt.
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  • Asia Minor had this unit in early times-in the temples of Ephesus 20.55, Samos 20.62; Hultsch also claims Priene 20.90, and the stadia of Aphrodisias 20.67 and Laodicea 20.94.
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  • In Greece it is the most usual unit, occurring in the Propylaea at Athens 12.44, temple at Aegina 12.40, Miletus 12.51, the Olympic course 12.62, &c. (18); thirteen buildings giving an average of 12.45, mean variation .06 (25), = (3/5)ths of 20.75, m.
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  • On the Egyptian cubits a small cubit is marked as about 17 in., which may well be this unit, as (5/6)ths of 20.6 is 17.2; and, as these marks are placed before the 23rd digit or 17.0, they cannot refer to 6 palms, or 17.7, which is the 24th digit, though they are usually attributed to that (33).
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  • As a unit of 1.013, decimally multiplied, is most commonly to be deduced from the ancient Persian buildings, we may take 25.34 as the nearest approach to the ancient Persian unit.
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  • The Egyptian cubits have an arm at 15 digits or about 10.9 marked on them, which seems like this same unit (33).
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  • Apparently the same unit is found (18) at Heraclea in Lucania, 21.86; and, as the general foot of the South Italians, or Oscan foot (18), best defined by the 100 feet square being (3/10)ths of the jugerum, and therefore = 10.80 or half of 21.60.
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  • The Gallic leuga, or league, is a different unit, being 1.59 British miles by the very concordant itinerary of the Bordeaux pilgrim.
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  • In Roman times the artaba remained (Didymus), but 1/6 was the usual unit (name unknown), and this was divided down to 1/24 or 1/144 artaba (35) -- thus producing by 1/12 artaba a working equivalent to the xestes and sextarius (35).
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  • A few barrel weights are found at Karnak, and several egg-shaped shekel weights at Gebelen (44); also two cuboid weights from there (44) of 1 and 10 utens are marked as 6 and 60, which can hardly refer to any unit but the heavy shekel, giving 245.
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  • On the Aegean coast it often occurs in early coinage (17) -- at Lampsacus 131-129, Phocaea 256-254, Cyzicus 252-247, Methymna 124.6, &c. In later times it was a main unit of North Syria, and also on the Euxine, leaden weights of Antioch,(3), Callatia and Tomis being known (38).
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  • At Corinth the unit was evidently the Assyrian and not the Attic, being 129.6 at the earliest (17) (though modified to double Attic, or 133, later) and being divided by 3, and not into 2 drachms. And this agrees with the mina being repeatedly found at Corcyra, and with the same standard passing to the Italian coinage (17) similar in weight, and in division into 1/3 -- the heaviest coinages (17) down to 400 B.C. (Terina, Velia, Sybaris, Posidonia, Metapontum, Tarentum, &c.) being none over 126, while later on many were adjusted to the Attic, and rose to 134.
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  • It is usually the case that a unit lasts later in trade than in coinage; and the prominence of this standard in Italy may show how it is that this mina (18 unciae = 7400) was known as the "Italic" in the days of Galen and Dioscorides (2).
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  • If this unit haS any connexion with the kat, it is that a kat of gold is worth 15 shekels or 1/4 mina of silver; this agrees well with the range of both units, only it must be remembered that 129 was used as gold unit, and another silver unit deduced from it.
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  • The silver bars found at Troy averaging 2744, or 1/3 mina of 8232, have been attributed to this unit (17); but no division of the mina in 1/3 is to be expected, and the average is rather low.
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  • That this unit (commonly called Phoenician) is derived from the 129 system can hardly be doubted, both being so intimately associated in Syria and Asia Minor.
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  • Hence the 224 unit seems to have been formed from the 129, after the main families or types of that had arisen.
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  • Under the Ptolemies, however, it became the great unit of Egypt, and is very prominent in the later literature in consequence (18, 35).
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  • The "argenteus" (as Revillout transcribes a sign in the papyri) (35) was of 5 shekels, or 1090; it arose about 440 B.C., and became after 160 B.C. a weight unit for copper.
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  • From Phoenicia this naturally became the main Punic unit; a bronze weight from Iol (18), marked 100, gives a drachma of 56 or 57 (224-228); and a Punic inscription (18) names 28 drachmae = 25 Attic, and therefore 57 to 59 grains (228-236); while a probably later series of 8 marble disks from Carthage (44) show 208, but vary from 197 to 234.
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  • That this unit is quite distinct from the Persian 86 grains is clear in the Egyptian weights, which maintain a wide gap between the two systems. Next, in Syria three inscribed weights of Antioch and Berytus (18) show a mina of about 16,400, or 200 x 82.
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  • Farther west the same unit occurs in several Greek weights (44) which show a mina of 7800 to 8310, mean 8050/100 = 80.5.
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  • But we are now able to prove that it was an independent system -- (1) by its not ranging usually over 200 grains in Egypt before it passed to Greece; (2) by its earliest example, perhaps before the 224 unit existed, not being over 208; and (3) by there being no intermediate linking on of this to the Phoenician unit in the large number of Egyptian weights, nor in the Ptolemaic coinage, in which both standards are used.
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  • So we have thus a weight of 207-191 in Egypt on marked weights, joining therefore completely with the Aeginetan unit in Egypt of 199 to 186, and coinage of 199, and strongly connected with Syria, where a double mina of Sidon (18) is 10,460 or 50 x 209.2.
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  • Ionia (197); while the coinage of Aegina, (17, 12), which by its wide diffusion made this unit best known, though a few of its earliest staters go up even to 207, yet is characteristically on the lower of the two groups which we recognize in Egypt, and thus started what has been considered the standard value of 194, or usually 190, decreasing afterwards to 184.
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  • In the Hellenic coinage it varies (18) from a maximum of 200 at Pharae to 192, usual full weight; this unit occupied (17) all central Greece, Peloponnesus and most of the islands.
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  • Hence, although the two groups overlap owing to their nearness, it is impossible to regard them as all one unit.
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  • The type of the grouping is not alike in different places, showing that no distinct families had arisen before the diffusion of this unit in Egypt; but the usual range is 65.5 to 69.0.
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  • Next it is found at Troy (44) in three cases, all high examples of 68.2 to 68.7; and these are very important, since they cannot be dissociated from the Greek Attic unit, and yet they are of a variety as far removed as may be from the half of the Assyrian, which ranges there from 123.5 to 131; thus the difference of unit between Assyrian and Attic in these earliest of all Greek weights is very strongly marked.
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  • At Athens a low variety of the unit was adopted for the coinage, true to the object of Solon in depreciating debts; and the first coinage is of only 65.2, or scarcely within the range of the trade weights (28); this seems to have been felt, as, contrary to all other states, Athens slowly increased its coin weight up to 66.6, or but little under the trade average.
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  • This unit passed also into Italy, the libra of Picenum and the double of the Etrurian and Sicilian libra (17); it was there divided in unciae and scripulae (44), the mean of 6 from Italy and Sicily being 6600; one weight (bought in Smyrna) has the name "Leitra" on it.
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  • The "tola" (180 grains) is properly the Government unit of weight for currency; and 80 tolas make the "Government seer."
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  • For engineering and manufacturing purposes the more important linear gauges are, however, now used, adjusted to some fundamental unit of measure as the inch; although in certain trades, as for wires and flat metals, gauges continue to be used of arbitrary scales and of merely numerical sizes, having no reference to a legal unit of measure; and such are rarely accurate.
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  • Instruction in the principles of the metric system, and in the advantages to be gained from uniformity in the method of forming multiples and sub-multiples of the unit, are, under this Code, to be given to the scholars in Standards IV., V., VI.
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  • By a law of the 9th of December 1904, promulgated by an executive decree of the 25th of March 1905, the gold standard was adopted, and the silver peso, 9027 fine and containing 24.438 grammes of pure silver, was made the monetary unit with a valuation of .75 grammes of gold.
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  • Kutais is divided into seven districts, of which the chief towns, with their populations in 1897, are Kutais, capital of the province (q.v.); Lailashi (834), chief;town of Lechgum, of which Svanetia makes a separate administrative unit; Ozurgeti (4694); Oni, chief town of Racha; Senaki (Ioi); Kvirili, of Sharopan district; Zugdidi; and two semi-military districts - Batum (28,512) with Artvin (7000) and Sukhum-kaleh (7809).
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  • A voltmeter isan instrument for measuring difference of electric potential in terms of the unit called a volt.
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  • Since there are 8760 hours in a year, if such an instrument were connected continuously to the circuit it would take up energy equal to 263,000 watt-hours, or 260 Board of Trade units per annum, If the cost of production of this energy was only one penny per unit, the working expenses of keeping such a voltmeter in connexion with a circuit would therefore be more than £i per annum, representing a capitalized value of, say, £io.
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  • The curia voted as a single unit and thus furnished the type for that system of group-voting which runs through all the later organization of the popular assemblies.
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  • The silver peso, or dollar, of 100 centavas is the monetary unit, weighs 25 grammes.
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  • New England is a unit, though a diversified unit.
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  • As in the north-east, so in the south-west, the crystalline belt widens and gains in height; but while New England is an indivisible unit, the southern crystalline belt must be subdivided The Southinto a higher mountain belt on the north-west, 60 m.
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  • The plains are by no means a simple unit; they are of diverse structure and of various stages of erosional development.
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  • The relative excess of males in each unit of population has not constantly progressed, but has been continuous.
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  • In the Southern states the county is the local administrative unit, and in addition to its original judicial and financial functions it has now also control over public schools, the care of the poor and the construction and mana,gement of roads.
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  • For in such a construction every point of the figure is obtained by the intersection of two straight lines, a straight line and a circle, or two circles; and as this implies that, when a unit of length is introduced, numbers employed, and the problem transformed into one of algebraic geometry, the equations to be solved can only be of the first or second degree, it follows that the equation to which we must be finally led is a rational equation of even degree.
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  • One cannot even describe the climate of a single province, like Ontario or British Columbia, as a unit, as it varies so greatly in different parts.
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  • This difference is very large compared with the smallness of the unit.
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  • The permanent committee of the Paris International Congress of 1900, which was held for the purpose of unification of the numerotage of counts, unanimously decided - (a) With reference to cotton, silk and other textiles spun from fibres, that they should be based on a fixed weight and variable length, the unit being one metre to one gramme.
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  • The length of skein adopted was 450 metres and the unit of length the half decigramme.
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  • The quantity N may serve to fix the third fundamental unit.
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  • In Ine's Laws (cap. 70) we find a list of payments specified for a unit of ten hides, perhaps the normal holding of a twelfhynde man - though on the other hand it may be nothing more than a mere fiscal unit in an aggregate of estates.
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  • The unit was the sulung (aratrum) or ploughland (from sulk, " plough"), the fourth part of which was the geocled or geoc (jugum), originally a yoke of oxen.
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  • The hide itself, which was the regular unit in the other kingdoms, usually contained 120 acres in later times and was divided into four girda (virgatae) or yardlands.
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  • By the time of Ine, however, pending, pen(n)ing (" penny "), had already come into use for the latter, while, owing to the temporary disappearance of a gold coinage, scilling had come to denote a mere unit of account.
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  • It was, however, a variable unit, for the Kentish shilling contained twenty sceattas (pence), while the Mercian contained only four.
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  • In Northumbria a totally different monetary system prevailed, the unit being the terms, which contained three sceattas or pence.
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  • In the former case the mancus was the usual unit of calculation.
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  • Generally speaking, however, each tribe formed a political unit in itself, and the combinations brought together from time to time in the hands of powerful kings were liable to fall to pieces after the first disaster.
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  • During his first period of discovery, besides the induction of electric currents, Faraday established the identity of the electrification produced in different ways; the law of the definite electrolytic action of the current; and the fact, upon which he laid great stress, that every unit of positive electrification is related in a definite manner to a unit of negative electrification, so that it is impossible to produce what Faraday called "an absolute charge of electricity" of one kind not related to an equal charge of the opposite kind.
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  • It is found that this gives a consistent result; that is to say, if by an experiment with two particles A and B we get the ratio of their masses, and by an experiment with B and a third particle C we get the ratio of the masses of B and C, and thus the ratio of the masses of A and C, we should get the same ratio by a direct experiment with A and C. For the numerical measure of mass that of some standard body is chosen as a unit, and the masses of other bodies are obtained by comparison with this.
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  • That would provide a useful name for an important geographical unit, but is too misleading.
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  • If in unit mass of any phase we have n components instead of one we must know the amount of n - I components present in that unit mass before we know the exact composition of it.
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  • Let us Freezing freeze out unit mass of solvent from a solution at its freezing point T - dT and remove the ice, which is assumed to be the ice of the pure solvent.
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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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  • Let us imagine unit mass of solution of volume V confined in a cylinder ABC between a fixed vapour sieve B and a solid piston A A B C FIG.
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  • Callendar has shown that the variation of vapour pressure of a solution with pressure is given by the expression V'dP = vdp, where V' is the change in volume of the solution when unit mass of solvent is mixed with it.
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  • The chief difficulty lies in the determination of the quantity V', the change in volume the solution under the pressure Po when unit mass of solvent is mixed with it.
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  • In the equation dP/dT= X/T(v 2 - v 1), P is the osmotic pressure, T the absolute temperature and X the heat of solution of unit mass of the solute when dissolving to form a volume v2 - v1 of saturated solution in an osmotic cylinder.
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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 quantity of substance which diffuses through unit area in one second may be taken as proportional to the difference in concentration between the fluids at that area and at another parallel area indefinitely near it.
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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 resistance offered by the liquid, and therefore the force F, required to drive one grammemolecule through the liquid with unit velocity is the sum of the corresponding quantities for the individual ions.
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  • Now the velocities u and v of the opposite ions under unit potential gradient, and therefore U and V under unit force, are known from electrical data.
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  • In the Heraeum at Olympia, it may be remarked, the unit adopted was not this Olympian foot, but an older one of 0.297 metre, and in the temple of Zeus an Attic foot of 1.08 English foot was used.
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  • Assuming the materials to be of equal tensile strength per unit of area - hard-drawn copper is stronger, but has a lower conductivity - the adoption of aluminium thus leads to a reduction of 52% in the weight, a gain of 60% in the strength, and an increase of 26% in the diameter of the conductor.
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  • When the price of aluminium is less than double the price of copper aluminium is cheaper than copper per unit of electric current conveyed; but when insulation is necessary, the smaller size of the copper wire renders it more economical.
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  • The level at which it is desired to keep the water in these ditches constitutes the unit of water measurement for the polder, and is called the polder's zomer peil (Z.P.) or summer water-level.
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  • Owing to the shrinkage of the soil in reclaimed lands, however, that is, lands which have been drained after fen or other reclamation, the sides of the polder are often higher than the middle, and it is necessary by means of small dams or sluices to make separate water-tight compartments (afpolderingen), each having its own unit of measurement.
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  • Large size has here, as in most metallurgical operations, not only its usual advantage of economy of installation, labour and administration per unit of product, but the further very important one that it lessens the proportion which the outer heat-radiating and hence heatwasting surface bears to the whole.
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  • In this system there is for each ingot and each mould only one handling in which it is moved as a separate unit, the mould from one train to the other, the ingot from its train into the furnace.
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  • In the other movements, all the moulds and ingots of a given charge of steel are grouped as a train, which is moved as a unit by a locomotive.
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  • Here each mould and each ingot was handled as a separate unit twice, instead of only once as in the car casting system; the ingots radiated away great quantities of heat in passing naked from the converting mill to the soaking furnaces, and the heat which they and the moulds radiated while in the converting mill was not only wasted, but made this mill, open-doored as it was, so intolerably hot, that the cost of labour there was materially increased.
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  • Increase in Production.-In 1810 the Unit d States made about 7%, and in 1830, 1850 and 1860 not far fr m io% of the world's production of pig iron, though, indeed, in 1820 their production was only about one-third as great as in 1810.
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  • This class of skin is the most expensive fur in the world, reckoning values by a square foot unit.
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  • He holds, apparently, that the foundation of all the science of number is the fact that each element of conscious experience is presented as a unit, and adds that we are capable of considering any fact or collection of facts as a unit.
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  • The writers of the Scottish school, Reid in particular, did undoubtedly indicate some of the weaknesses in Hume's fundamental conception, and their attempts to show that the isolated feeling cannot be taken as the ultimate and primary unit of cognitive experience are efforts in the right direction.
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  • The provinces are governed by a governor nominated by the king, the canton is a judicial division for marking the limit of the jurisdiction of each juge de paix, and the commune is the administrative unit, possessing self-government in all local matters.
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  • They are bound by place and the unit is the individual community.
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  • It must be a unit, its forces constant and its totality an organic whole.
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  • The " rate of transmission of heat " is here understood to mean the quantity of heat transferred in unit time through unit area of cross-section of the substance, the unit area being taken perpendicular to the lines of flow.
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  • The " gradient of temperature " is the fall of temperature in degrees per unit length along the lines of flow.
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  • In this case it is generally more convenient to consider as unit of heat the thermal capacity c of unit volume, or that quantity which would produce a rise of one degree of temperature in unit volume of the soil or substance considered.
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  • If Q is expressed in terms of this unit in equation (I), it is necessary to divide by c, or to replace k on the right-hand side by the ratio k/c. This ratio determines the rate of diffusion of temperature, and is called the thermometric conductivity or, more shortly, the diffusivity.
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  • No calorimetric observations are required, but the results are obtained in terms of the thermal capacity of unit volume c, and the measurements give the diffusivity klc, instead of the calorimetric conductivity k.
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  • The heat transmitted through the plane x is equal per unit area of surface to the product of k by the mean temperature gradient (de /dx) and the interval of time, T - T'.
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  • The magnitude of the stress per unit area parallel to the direction of flow is evidently proportional to the velocity gradient, or the rate of change of velocity per cm.
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  • The Illinois State Convention of the Republican party, held at Decatur on the 9th and 10th of May 1860, amid great enthusiasm declared Abraham Lincoln its first choice for the presidential nomination, and instructed the delegation to the National Convention to cast the vote of the state as a unit for him.
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  • The unit of the terman system of local government is the commune (Geineinde, or more strictly Ortsgemeinde).
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  • The unit is the mark (I shilling)the tenth part of the imperial gold coin (Krone=crown), of which last 139& are struck from a pound of pure gold.
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  • Wolfer's frequencies with data obtained by other observers for areas of sun-spots, and his figures show unquestionably that the unit in one or other set of data must have varied appreciably from time to time.
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  • Wolf and Wolfer have, however, aimed persistently at securing a definite standard, and there are several reasons for believing that the change of unit has been in the auroral rather than the sun-spot frequency.
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  • Each of the territories was a separate political unit with a separate history, and some of them had a historic claim to a large amount of selfgovernment; in many the old feudal estates had survived till 1848.
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  • As in India, the village with its lands and cultivation was constituted the unit of assessment, and the provinces were divided into districts under native headmen responsible for the collection of the tax, and its payment to the paramount chief, who in turn rendered the assigned share to district and village chiefs, to the officers of state recognized by government and to the government itself.
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  • Each of them was an independent unit, and in none was there any town or community politically separate from the tribe as a whole.
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  • Some further details are to be found in documents preserved by the archaeologist Maqrizi, from which it appears that the sum for which each district was responsible was distributed over the unit in such a way that artisans and tradesmen paid at a rate similar to that which was enforced on those employed in agriculture.
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  • Each neuron or nerve cell is a morphologically distinct and discrete unit connected functionally but not structurally with its neighbours, and leading its own life independently of the destiny of its neighbours.
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  • Rates and taxes on land are mostly levied according to a uniform system of assessment, the unit of which is called a Tonde Hartkorn.
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  • The unit of the Danish monetarysystem, as of the Swedish and Norwegian, is the krone (crown), equal to is.
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  • Where the unit was mentioned, neither the date of the event nor the locality in which it occurred was to be specified.
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  • Since alite is a solid solution and, although an individual mineral, is not a chemical unit, the proportion of tricalcium silicate to tricalcium aluminate in a given specimen of alite will vary; but, whatever the proportions, each of these substances will react in its characteristic manner according to the equations given above.
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  • The largest administrative unit is that of the county, but the areas of counties may be adapted to meet various public or political requirements.
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  • And finally, there are a series of variations, amongst which no doubt are the mutations of de Vries and the disintegrations and recombinations of the unit factors with which Mendel and his followers have worked, in which the external or environmental factor is most remote from the actual result.
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  • Their experimental work shows that many facts of inheritance correspond with the theory that the essential fabric of an organism is a mosaic of unit characters.
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  • The river is navigable below Charjui, and takes its place as an important unit in the general scheme of Russian frontier communications.
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  • The solar day is the fundamental unit of time, not only in daily life but in astronomical practice.
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  • Within the separate provinces the administrative unit is the district, of which there are 249 in India.
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  • The system of partitioning, and also the nomenclature, vary in the different provinces; but generally it may be said that the subdivision or tahsil is the ultimate unit of administration.
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  • There is no administrative unit below the subdivision or tahsil.
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  • The village still remains as the agricultural unit, and preserves its independence for revenue purposes in most parts of the country.
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  • The prevailing system throughout the Madras presidency is the ryotwari, which takes the cultivator or peasant proprietor as its rent-paying unit, somewhat as the Bengal system takes the zamindar.
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  • As the land tax forms the mainstay of the imperial revenue, so the ryot or cultivator constitutes the unit of the social system.
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  • The village system is well described, each little rural unit seeming to be an independent republic. Megasthenes remarked the exemption of the husbandmen (Vaisyas) from war and public services, and enumerates the dyes, fibres, fabrics and products (animal, vegetable and mineral) of India.
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  • Apart from this, the chief meaning, the word is used of the malt refuse of brewing and distilling, and of many hard rounded small particles, resembling the seeds of plants, such as "grains" of sand, salt, gold, gunpowder, &c. "Grain" is also the name of the smallest unit of weight, both in the United Kingdom and the United States of America.
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  • The currency of Mauritius is rupees and cents of a rupee, the Indian rupee (=16d.) being the standard unit.
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  • The specific heat of a substance is sometimes defined as the thermal capacity of unit mass, but more often as the ratio of the thermal capacity of unit mass of the substance to that of unit mass of water at some standard temperature.
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  • The two definitions are identical, provided that the thermal capacity of unit mass of water, at a standard temperature, is taken as the unit of heat.
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  • In the practical use of the instrument it is not necessary to know both the latent heat of fusion of ice and the change of volume which occurs on melting; it is sufficient to determine the change of volume per calorie, or the quantity of mercury which is drawn into the bulb of the apparatus per unit of heat added.
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  • In order to be independent of the accuracy of the thermometer employed for observing the initial temperature of the water introduced, it has been usual to employ water at ioo° C., adopting as unit of heat the " mean calorie," which is one-hundredth part of the heat given up by one gramme of water in cooling from ioo° to o° C. The weight of mercury corresponding to the mean calorie has been determined with considerable care by a number of observers well skilled in the use of the instrument.
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  • It is generally employed to denote the number of units of mechanical work or energy which, when completely converted into heat without loss, would be required to produce one heat unit.
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  • A more convenient unit of work or energy, in practice, on account of the smallness of the erg, is the joule, which is equal to 10.7 ergs, or one watt-second of electrical energy.
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  • On account of its practical convenience, and its close relation to the international electrical units, the joule has been recommended by the British Association for adoption as the absolute unit of heat.
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  • Many Of The Uncertainties In The Reduction Of Older Experiments, Such As Those Of Regnault, Arise From Uncertainty In Regard To The Unit In Terms Of Which They Are Expressed, Which Again Depends On The Scale Of The Particular Thermometer Employed In The Investigation.
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  • We May Probably Take The Tabulated Values As Showing Correctly The Rate Of Variation Between 110° And 190° C., But The Values In Terms Of Any Particular Thermal Unit Must Remain Uncertain To At Least 0.5% Owing To The Uncertainties Of The Thermometry.
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  • Assoc. Report, 1899, with a slight modification Specific Heat Of Water In Terms Of Unit At 20° C. 4.180 Joules to allow for the increase in the specific heat below 20° C. This was estimated in 1899 as being equivalent to the addition of the constant quantity 0.020 to the values of the total heat h of the liquid as reckoned by the parabolic formula (5).
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  • The unit of comparison in the following table is taken as the specific heat of water at 20° C. for the reasons given below.
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  • This unit is taken as being 4.180 joules per gramme-degree-centigrade on the scale of the platinum thermometer, corrected to the absolute scale as explained in the article Thermometry, Which Has Been Shown To Be Practically Equivalent To The Hydrogen Scale.
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  • This Unit Has The Advantage Of Being Independent Of Thermometry, But The Applicability Of These Methods Is Limited To Special Cases, And The Relation Of The Units To Other Units Is Difficult To Determine.
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  • In Any Case It Is Necessary To Define A Thermometric Unit Of Class (1).
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  • But As The Hydrogen Thermometer Is Not Directly Available For The Majority Of Experiments, It Is Necessary To Use A Secondary Standard For The Practical Definition Of The Unit.
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  • The Primary Consideration In The Definition Of A Unit Is To Select That Method Which Permits The Highest Order Of Accuracy In Comparison And Verification.
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  • For This Reason The Definition Of The Thermal Unit Will In The End Probably Be Referred To A Scale Of Temperature Defined In Terms Of A Standard Platinum Thermometer.
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  • The Specific Heat At 4° Could Be Accurately Determined At The Mean Over The Range O° To 8° Keeping The Jacket At O° C. But The Change Appears To Be Rather Rapid Near O°, The Temperature Is Inconveniently Low For Ordinary Calorimetric Work, And The Unit At 4° Would Be So Much Larger Than The Specific Heat At Ordinary Temperatures That Nearly All Experiments Would Require Reduction.
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  • This Is Really Only An Absolute Unit In Disguise, And Evades The Essential Point.
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  • Which Is The Selection Of A Standard Temperature For The Water Thermometric Unit.
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  • The Most Practical Unit Is The Calorie At 15° Or 20° Or Some Temperature In The Range Of Ordinary Practice.
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  • According To The Elementary Kinetic Theory Of An Ideal Gas, The Molecules Of Which Are So Small And So Far Apart That Their Mutual Actions May Be Neglected, The Kinetic Energy Of Translation Of The Molecules Is Proportional To The Absolute Temperature, And Is Equal To 3/2 Of Pv, The Product Of The Pressure And The Volume, Per Unit Mass.
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  • A unit of length, which is often used in measuring stellar distances, is the light year or distance that light travels in a year; it is rather less than six billion miles.
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  • If it is merely the aggregate of the stars, each star or small group of stars may be a practically independent unit, its birth and development taking place without any relation to the evolution of the whole.
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  • Thus the figure represents a section the (ideally simplified) uni verse cut perpendicular to C P' D the planes AB and CD between which the stars are contained, 1 This number is the 3/2th power of the ratio of the brightness of stars differing by a unit magnitude.
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  • Thought as form would thus be a factor or an element in a composite unit.
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  • The unit for logic is the concept taken for granted.
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  • Its unit, the logical concept, is a manipulated product and the process of manipulation may be called abstraction.
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  • That the unit for logic is the concept and not the judgment has proved a stumblingblock to those of Lotze's critics who are accustomed to think in terms of the act of thought as unit.
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  • The act of judgment " which refers an ideal content (recognized as such) to a reality beyond the act " is the unit for logic. Grammatical subject and predicate necessarily both fall under the rubric of the adjectival, that is, within the logical idea or ideal content asserted.
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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 directed line whose length is a, and which makes an angle 0 with the real (positive) unit line, is expressed by a (cos 0+i sin e), where i is regarded as +1,/ - 1.
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  • Its length is, therefore, the product of the lengths of the factors, and its inclination to the real unit is the sum of those of the factors.
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  • In other words, a unit line, drawn in any direction whatever, must have - r for its square.
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  • We may state, in passing, that every quaternion can be represented as a (cos 0+ 7 sin 9), - where a is a real number, 6 a real angle, and it a directed unit line whose square is - 1.
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  • He saw that he could get a hint from the simpler case, already thoroughly discussed, provided the two factor lines were in one plane through the real unit line.
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  • Suppose, for simplicity, the factor-lines to be each of unit length.
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  • Also, if 0 be the angle between them, and x", y", z" the direction-cosines of a line perpendicular to each of them, we have xx' +yy'+zz' =cos 0, yz' - zy" = x" sin 0, &c., so that the product of two unit lines is now expressed as - cos0+ (ix" +jy" +kz") sin 0.
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  • Hence, and in this lies the main element of the symmetry and simplicity of the quaternion calculus, all systems of three mutually rectangular unit lines in space have the same properties as the fundamental system i, j, k.
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  • Again a unit point p. may be regarded as by multiplication changing (a) from octonion to point-plane-scalar, (b) from point-plane-scalar to octonion, (c) from plane-scalar to linear element, (d) from linear element to plane-scalar.
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  • The quantity required per unit mass of the substance is termed the latent heat of vaporization.
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  • The total heat of the saturated vapour at any temperature is usually defined as the quantity of heat required to raise unit mass of the liquid from any convenient zero up to the temperature considered, and then to evaporate it at that temperature under the constant pressure of saturation.
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  • It is equivalent, as Callendar (loc. cit.) points out, to supposing that the variation of the specific heat is due to the formation and solution of a mass w/(v-w) of vapour molecules per unit mass of the liquid.
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  • The unit of heat assumed in the table is the calorie at 20° C., which is taken as equal to 4.180 joules, as explained in the article Calorimetry.
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  • The rapidity of the movement has not been exceptional in Arkansas, but the size of its average farm, less in 1850 than that of the other cotton states, was in 1900, 93.1 acres (108.8 for white farmers alone, 49 o for blacks alone), which was even less than that of the North Atlantic states (96.5 acres, the smallest sectional unit of the Union).
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  • The unit of inquiry was the Hundred (a subdivision of the county which had then an administrative entity), and the return for each Hundred was sworn to by twelve local jurors, half of them English and half Normans.
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  • Stock ranches, tobacco plantations, and hay and grain farms, average from Boo to 530 acres, and counteract the tendency of dairy farms, beet plantations, orchards, vegetable gardens and nurseries to lower the size of the farm unit still further.
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  • Since the movements of the magnet are always small, the rotation of the magnet is proportional to the change in H, so long as M and the couple, 0, corresponding to unit twist of the suspension system remain constant.
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  • The monetary unit is the silver peso or dollar of too cents, which weighs 25 grammes, .900 fine.
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  • Its separation was due to growing consciousness of the Gospels as a unit of sacred records, to which Acts stood as a sort of appendix.
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  • In most questions of pure statics we are concerned only with the ratios of the various forces which enter into the problem, so that it is indifferent what unit of force is adopted.
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  • The tension is constant, and the pressure per unit length varies as the curvature.
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  • The practical unit or standard of mass must, from the nature of the case, be the mass of some particular body, e.g.
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  • The unit of force implied in (I) is that which produces unit momentum in unit time.
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  • Thus the unit of velocity is that of a point describing the unit of length in the unit of time; it may be denoted by LTi, this symbol indicating that the magnitude of the unit in question varies directly as the unit of length and inversely as the unit of time.
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  • The unit of acceleration is the acceleration of a point which gains unit velocity in unit time; it is accordingly denoted by LT2.
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  • The unit of work on the same principles is ML2T2, and itis to be noticed that this is identical with the unit of kinetic energy.
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  • Ihe number which expresses a physical quantity of any particular kind will of course vary inversely as the magnitude of the corresponding unit.
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  • This shows that mechanical energy is lost at the rate 2 F per unit time.
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  • Then the variation of the cubic contents of the vessel in a unit of time by reason of the motion of one piston is Va.
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  • Application of Force to Mechanism.Forces are applied in units of weight; and the unit most commonly employed in Britain is the pound avoirdupois.
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  • The unit of work commonly used in Britain is a resistance of one pound overcome through a distance of one foot, and is called a foot-pound.
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  • The unit of energy is the same with the Unit of work.
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  • The unit of power, called conventionally a horse-power, is 550 foot-pounds per second, or 33,000 foot-pounds per minute, or 1,980,000 foot-pounds per hour.