# Unit Sentence Examples

The medical

**unit**has healed me.This is Lieutenant George with the intel

**unit**assigned to your command.Such a

**unit**is independent of gravity or of any other quantity which varies with the locality.The married couple formed a

**unit**as to external responsibility, especially for debt.No other regular army

**unit**has a chance out here.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.She strode to the clothing

**unit**in the corner and ordered her a set.It would heal once he reached the main craft with the help of the medical

**unit**but was useless in the meantime.She turned toward the

**unit**lifting her arms in delight.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.AdvertisementThe 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.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.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.Besides, I rather like our little family

**unit**, and the house certainly is big enough for us all.Between 1500 and 4000 metres the charge inside the

**unit**tube is much less, only 0.000040.AdvertisementThe 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.A window air conditioning

**unit**hummed, and when he opened the door to the apartment, a surge of cool air invited them in.Taking i volt equal 1/300 of an electrostatic

**unit**, we find M =0.000265.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.'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.AdvertisementWolfer'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.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.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.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.Each of them was an independent

**unit**, and in none was there any town or community politically separate from the tribe as a whole.AdvertisementSome 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.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.Rates and taxes on land are mostly levied according to a uniform system of assessment, the

**unit**of which is called a Tonde Hartkorn.The

**unit**of the Danish monetarysystem, as of the Swedish and Norwegian, is the krone (crown), equal to is.Where the

**unit**was mentioned, neither the date of the event nor the locality in which it occurred was to be specified.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.The largest administrative

**unit**is that of the county, but the areas of counties may be adapted to meet various public or political requirements.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.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.The river is navigable below Charjui, and takes its place as an important

**unit**in the general scheme of Russian frontier communications.The solar day is the fundamental

**unit**of time, not only in daily life but in astronomical practice.Within the separate provinces the administrative

**unit**is the district, of which there are 249 in India.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.There is no administrative

**unit**below the subdivision or tahsil.The village still remains as the agricultural

**unit**, and preserves its independence for revenue purposes in most parts of the country.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.As the land tax forms the mainstay of the imperial revenue, so the ryot or cultivator constitutes the

**unit**of the social system.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.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.The currency of Mauritius is rupees and cents of a rupee, the Indian rupee (=16d.) being the standard

**unit**.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.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.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**.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.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.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.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.In Any Case It Is Necessary To Define A Thermometric

**Unit**Of Class (1).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**.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.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.This Is Really Only An Absolute

**Unit**In Disguise, And Evades The Essential Point.Which Is The Selection Of A Standard Temperature For The Water Thermometric

**Unit**.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.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.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.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.Thought as form would thus be a factor or an element in a composite

**unit**.The

**unit**for logic is the concept taken for granted.Its

**unit**, the logical concept, is a manipulated product and the process of manipulation may be called abstraction.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**.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.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.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.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.In other words, a

**unit**line, drawn in any direction whatever, must have - r for its square.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.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.Suppose, for simplicity, the factor-lines to be each of

**unit**length.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.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.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.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.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.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).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.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.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.The monetary

**unit**is the silver peso or dollar of too cents, which weighs 25 grammes, .900 fine.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.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.The tension is constant, and the pressure per

**unit**length varies as the curvature.The practical

**unit**or standard of mass must, from the nature of the case, be the mass of some particular body, e.g.The

**unit**of force implied in (I) is that which produces**unit**momentum in**unit**time.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.The

**unit**of acceleration is the acceleration of a point which gains**unit**velocity in**unit**time; it is accordingly denoted by LT2.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.Ihe number which expresses a physical quantity of any particular kind will of course vary inversely as the magnitude of the corresponding

**unit**.This shows that mechanical energy is lost at the rate 2 F per

**unit**time.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.Application of Force to Mechanism.Forces are applied in units of weight; and the

**unit**most commonly employed in Britain is the pound avoirdupois.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.The

**unit**of energy is the same with the**Unit**of work.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.The ordinary British

**unit**of moment is a foot-pound; but it is to be remembered that this is a foot-pound of a different sort from the**unit**of energy and work.Moment of Friction.The work performed in a

**unit**of time in overcoming the friction of a pair of surfaces is the product of the friction by the velocity of sliding of the surfaces over each other, if that is the same throughout the whole extent of the rubbing surfaces.When the relative motion of the rubbing surfaces is one of rotation, the work of friction in a

**unit**of time, for a portion of the rubbing surfaces at a given distance from the axis of rotation, may be found by multiplying together the friction of that portion, its distance from the axis, and the angular velocity.To express this symbolically, let dii represent the area of a portion of a pair of rubbing surfaces at a distance r from the axis of their relative rotation; p the intensity of the normal pressure at du per

**unit**of area; and f the coefficient of friction.Friction of Teeth.Let N be the normal pressure exerted between a pair of teeth of a pair of wheels; s the total distance through which they slide upon each other; n the number Of pairs of teeth which pass the plane of axis in a

**unit**of time; then nf NI (63)The quantity of work whic produces a British

**unit**of heat (or so much heat as elevates the temperature of one pound of pure water, at or near ordinary atmospheric temperatures, by 1 F.) is 772 foot-pounds.Its moment is found by multiplying the normal pressure between the rolling surfaces by an arm, whose length depends on the nature of the rolling surfaces, and the work lost in a

**unit**of time in overcoming it is the product of its moment by the angular velocity of the rolling surfaces relatively to each other.To say that it displaced the centre of gravity in politics and commerce, substituting the ocean for the Mediterranean, dethroning Italy from her seat of central importance in traffic, depressing the eastern and elevating the western powers of Europe, opening a path for Anglo-Saxon expansiveness, forcing philosophers and statesmen to regard the Occidental nations as a single group in counterpoise to other groups of nations, the European community as one

**unit**correlated to other units of humanity upon this planet, is truth enough to vindicate the vast significance of these discoveries.The type of religion found in these documents is that of Geneva, the

**unit**being the self-governing congregation, and the great aim of the system the pure preaching of the Word.Hence his measurements are all directly comparable with modern electrostatic measurements in which the

**unit**of capacity is that of a sphere r centimetre in radius.Maxwell never committed himself to a precise definition of the physical nature of electric displacement, but considered it as defining that which Faraday had called the polarization in the insulator, or, what is equivalent, the number of lines of electrostatic force passing normally through a

**unit**of area in the dielectric. A second fundamental conception of Maxwell was that the electric displacement whilst it is changing is in effect an electric current, and creates, therefore, magnetic force.This ultimate

**unit**of electric quantity Professor Johnstone Stoney called an electron.'The subject was pursued by Thomson and the Cambridge physicists with great mathematical and experimental ability, and finally the conclusion was reached that in a high vacuum tube the electric charge is carried by particles which have a mass only a fraction, as above mentioned, of that of the hydrogen atom, but which carry a charge equal to the

**unit**electric charge of the hydrogen ion as found by electrochemical researches.The British sovereign is the current gold coin, the

**unit**of the bronze and silver coinage being the piastre (13 penny).The crowd rather than the individual is the thinking

**unit**.What if the basic

**unit**was a couple, a relationship, and what if that relationship had an identity?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.A handheld GPS

**unit**can settle any well-defined border issue.Whilst each

**unit**of the lateral eye of Limulus has arhabdom of ten t pieces See fig.Alexander, became a

**unit**of the Lettish army (Olai agreement on July 15 1919) to be formed by Gen.Gold is the nominal standard of value, the monetary

**unit**being the gold milreis worth 2s.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.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.We may therefore conveniently take as our

**unit**, in place of x, a number y such that x=6y.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.The form (m+n)A=mA+nA follows at once from the fact that A is the

**unit**with which we are dealing.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.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.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**.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,.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.If E is any extensive

**unit**, there is one other**unit**E', and only one, such that the (progressive) product EE' =- r.This

**unit**is called the supplement of E, and denoted by IE.It was with this corps that Dr. Elsie Inglis and a detachment of the Scottish Women's Hospitals served as medical

**unit**.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.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.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.The

**unit**of administration is the field cornetcy.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.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.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.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.Moreover, the splendid building is nearly always a

**unit**; seldom, unless accidentally, a component part of a broad effect.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.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.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.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.Hence the space variation of the pressure in any direction, or the pressure-gradient, is the resolved force per

**unit**volume in that direction.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.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.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.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.The practical

**unit**of quantity of electricity, the coulomb, is named after him.A very usual size of cistern forming a convenient

**unit**is one that will hold 20 tons of char.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.The monetary

**unit**is the Peruvian pound (libra) which is uniform in weight and fineness with the British pound sterling.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."Until recently these spherical lenses were numbered in terms of their focal length, the inch being used as the

**unit**.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.This

**unit**is called a "dioptric" (usually written "D").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.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).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.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.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.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.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.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.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.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.Hence the charge on the conductor can be measured by the number of

**unit**electric tubes springing from it.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.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.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.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.The quantity of electricity which must be given to the sphere to raise it to

**unit**potential is therefore R electrostatic units.I It is an interesting fact that Cavendish measured capacity in " globular inches," using as his

**unit**the capacity of a metal ball, in.The

**unit**of electrostatic capacity is therefore that of a sphere of I cm.This

**unit**is too small for practical purposes, and hence a**unit**of capacity 900,000 greater, called a microfarad, is generally employed.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.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.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.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.The customary

**unit**of expenditure is the threepenny-bit or "tickey."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.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.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.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.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.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.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.With drums beating and colours flying, every

**unit**within call went forward for the final effort.The characters thus composed, though so simple as to their basal

**unit**, are appallingly complex in their elaboration.The word is also used as a

**unit**of linear measurement of the magnifying power of a lens or microscope.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.The

**unit**of local government is the " hundred," which corresponds to the township of Pennsylvania.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.Although the three formed a

**unit**at one stage it may seem doubtful whether two so closely related chapters as 1 Chron.The commissioners' court of five members, including the presiding judge, attends to county business matters, the county being the

**unit**of local government.The smallest

**unit**of matter with which physical phenomena are concerned is the molecule.Let a mixture of gases contain per

**unit**volume v molecules of the first kind, v' of the second kind, and so on.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.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.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 +...As in all other languages, so in those of aboriginal America, the sentence is the

**unit**.In all parts of the western hemisphere society was organized on cognate kinship, real or artificial, the

**unit**being the clan.Before the development of pneumatic chemistry, air was regarded as a distinct chemical

**unit**or element.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.The distance between two points can, at any rate in theory, be measured directly, by successive applications of the

**unit**of measurement.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.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.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.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 Ã†= - dy/dx (I) This gives the relation between pressure excess and displacement.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.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.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.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.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.Let K be the breaking strength of a bar per

**unit**of section, when it is loaded once gradually to breaking.Generally the influence line is drawn for

**unit**load.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.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.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.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.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.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.The tical (baht) is the

**unit**of currency and also the**unit**of weight.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.The

**unit**of land measure is the rai, which is equal to 400 square wah, and is subdivided into four equal ngan.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.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.Thus the diocese, hitherto a simple

**unit**, became an elaborately articulated whole.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.In an extended table of S, the value is interpolated for

**unit**increment of velocity.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.It will be seen that communes do not correspond with any natural

**unit**.The

**unit**among the Mahommedans is the douar, a tribal division administered by a cadi.The dates printed in heavy type are certain, at least within a

**unit**.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.The monetary

**unit**is the gold colon weighing 778 gramme, 900 fine, and thus worth about 23d.The International Geodetic Committee have adopted the metre as their

**unit**of measurement.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.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.Vases may also be found bearing such relations to one another as to show their

**unit**of volume.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.Buildings at Persepolis, all of nearly the same age, vary in

**unit**1 in 450 (25).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.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.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.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.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.Babylonia had this

**unit**nearly as early as Egypt.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.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.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).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**.The Egyptian cubits have an arm at 15 digits or about 10.9 marked on them, which seems like this same

**unit**(33).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.The Gallic leuga, or league, is a different

**unit**, being 1.59 British miles by the very concordant itinerary of the Bordeaux pilgrim.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).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.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).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.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).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.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.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.Hence the 224

**unit**seems to have been formed from the 129, after the main families or types of that had arisen.Under the Ptolemies, however, it became the great

**unit**of Egypt, and is very prominent in the later literature in consequence (18, 35).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.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.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.Farther west the same

**unit**occurs in several Greek weights (44) which show a mina of 7800 to 8310, mean 8050/100 = 80.5.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.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.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.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.Hence, although the two groups overlap owing to their nearness, it is impossible to regard them as all one

**unit**.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.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.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.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.The "tola" (180 grains) is properly the Government

**unit**of weight for currency; and 80 tolas make the "Government seer."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.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.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.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).A voltmeter isan instrument for measuring difference of electric potential in terms of the

**unit**called a volt.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.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.The silver peso, or dollar, of 100 centavas is the monetary

**unit**, weighs 25 grammes.New England is a

**unit**, though a diversified**unit**.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.The plains are by no means a simple

**unit**; they are of diverse structure and of various stages of erosional development.The relative excess of males in each

**unit**of population has not constantly progressed, but has been continuous.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.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.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.This difference is very large compared with the smallness of the

**unit**.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.The length of skein adopted was 450 metres and the

**unit**of length the half decigramme.The quantity N may serve to fix the third fundamental

**unit**.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.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.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.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.It was, however, a variable

**unit**, for the Kentish shilling contained twenty sceattas (pence), while the Mercian contained only four.In Northumbria a totally different monetary system prevailed, the

**unit**being the terms, which contained three sceattas or pence.In the former case the mancus was the usual

**unit**of calculation.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.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.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.That would provide a useful name for an important geographical

**unit**, but is too misleading.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.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.Hence the osmotic pressure is measured by the work done per

**unit**change of volume of the solution.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.