Online Encyclopedia
Search over 40,000 articles from the original, classic Encyclopedia Britannica, 11th Edition.
UNITS, PHYSICAL
Online EncyclopediaEncyclopedia Home :: TUM-VAN
del.icio.us it!
|
See also:UNITS, See also:PHYSICAL . In See also:order that our acquaintance with any See also:part of nature may become exact we must have not merely a qualitative but a quantitative knowledge of facts. Hence the moment that any See also:branch of See also:science begins to develop to any extent, attempts are made to measure and evaluate the quantities and effects found to exist. To do this we have to select for each measurable magnitude a unit or See also:standard of reference (Latin, unitas, unity), by comparison with which amounts of other like quantities may be numerically defined. There is nothing to prevent us from selecting these fundamental quantities, in terms of which other like quantities are to be expressed, in a perfectly arbitrary and See also:independent manner, and as a See also:matter of fact this is what is generally done in the See also:early stages of every science. We may, for instance, choose a certain length, a certain See also:volume, a certain See also:mass, a certain force or See also:power as our units of length, volume, mass, force or power, which have no See also:simple or See also:direct relation to each other. Similarly we may select for more See also:special measurements any arbitrary electric current, electromotive force, or resistance, and See also:call them our units. The progress of knowledge, however, is greatly assisted if all the measurable quantities are brought into relation with each other by so selecting the units that they are related in the most simple manner, each to the other and to one See also:common set of measurable magnitudes called the fundamental quantities. The progress of this co-ordination of units has been greatly aided by the See also:discovery that forms of physical See also:energy can be converted into one another, and that the See also:conversion is by definite See also:rule and amount (see ENERGY). Thus the See also:mechanical energy associated with moving masses can be converted into See also:heat, hence heat can be measured in mechanical energy units. The amount of heat required to raise one gramme of See also:water through 1° C. in the neighbourhood of to° C. is equal to See also:forty-two million ergs, the erg being the kinetic energy or energy of See also:motion associated with a mass of 2 grammes when moving uniformly, without rotation, with a velocity of 1 cm. per second. This number is commonly called the " mechanical See also:equivalent of heat," but would be more exactly described as the " mechanical equivalent of the specific heat of water at to° C." Again, the fact that the See also:maintenance of an electric current requires energy, and that when produced its energy can be wholly utilized in See also:heating a mass of water, enables us to make a similar statement about the energy required to maintain a current of one See also:ampere through a resistance of one See also:ohm for one second, and to define it by its equivalent in the energy of a moving mass. Physical units have therefore been selected with the See also:object of establishing simple relations between each of them and the fundamental mechanical units. Measurements based on such relations are called See also:absolute measurements. The science of See also:dynamics, as far as that part of it is concerned which deals with the motion and energy of material substances, starts from certain See also:primary See also:definitions concerning the measurable quantities involved. In constructing a See also:system of physical units, the first thing to consider is the manner in which we shall connect the various items. What, for instance, shall be the unit of force, and how shall it be determined by simple reference to the units of mass, length and See also:time? The See also:modern absolute system of physical measurement is founded upon dynamical notions, and originated with C. F. See also:Gauss. We are for the most part concerned in studying motions in nature; and even when we find bodies at See also:rest in See also:equilibrium it is because the causes of motion are balanced rather than absent. Moreover, the postulate which lies at the See also:base of all See also:present-See also:day study of physics is that in the ultimate issue we must seek for a mechanical explanation of the facts of nature if we are to reach any explanation intelligible to the human mind. Accordingly the See also:root of all science is the knowledge of the See also:laws of motion, and the enunciation of these laws by See also:Newton laid the See also:foundation of a more exact knowledge of nature than had been possible before. Our fundamental scientific notions are those of length, time, and mass. No metaphysical discussion has been able to resolve these ideas into anything simpler or to derive them from each other. Hence in selecting units for physical measurements we have first to choose units for the above three quantities. Fundamental Units.—Two systems of fundamental units are in common use: the See also:British system, having the yard and See also:pound as the standard units of length and mass, frequently termed the " See also:foot-pound-second " (F.P.S.) system; and the " centimetre-gramme-second " system (C.G.S.), having the centimetre and gramme as standard units of length and mass, termed the " metric " system. The fundamental unit of time is the same in both systems, namely, the " mean See also:solar second," 86,400 of which maker solar day (see TIME). Since these systems and the corresponding See also:standards, together with their factors of conversion, are treated in detail in the See also:article WEIGHTS AND See also:MEASURES, we need only See also:deal here with such units as receive special scientific use, i.e. other than in See also:ordinary commercial practice. The choice of a unit in which to See also:express any quantity is determined by the magnitude and proportional See also:error of the measurement. In See also:astronomy, where immense distances have to be very frequently expressed, a common unit is the mean See also:radius of the See also:earth's See also:orbit, the " astronomical unit " of length, i.e. 92,900,000 See also:miles. But while this unit serves well for the region of our solar system, its use involves unwieldy numerical coefficients when stellar distances are to be expressed. Astronomers have therefore adopted a unit of length termed the " See also:light See also:year," which is the distance traversed by light in a year; this unit is 63,000 times the mean radius of the earth's orbit. The relative merits of these units as terms in which astronomical distances may be expressed is exhibited by the values of the distance of the See also:star a Centauri from our earth, namely, 25,000,000,000,000 miles = 275,000 astronomical units = 4.35 light years. As another example of a physical unit chosen as a matter of convenience, we may refer to the magnitudes of the See also:wave-lengths of light. These quantities are extremely small, and admit of correct determination to about one part in ten-thousand, and range, in the visible spectrum, from about 6 to 4 ten-millionths of a See also:metre. Since their values are determined to four significant figures, it is desirable to choose a unit which represents the value as an integer number; the unit is therefore a ten-thousandmillionth of a metre, termed a " tenth metre," since it is io 10 metres. Sometimes the thousand-millionth of a metre, the " micromillimetre," denoted by µµ, serves as a unit for wave lengths. Another relatively See also:minute unit is the " micron," denoted by µ, and equal to orie-millionth of a metre; it is especially used by bacteriologists. Units in See also:Mechanics. --The quantifies to be measured in mechanics (q.v.) are velocity and See also:acceleration, dependent on the units of length and time only, momentum, force, energy or See also:work and power, dependent on the three fundamental units. The unit of velocity in the British system is r foot, i yard, or r mile per second; or the time to which the distance is referred may be expressed in See also:hours, days, &c., the choice depending upon the actual magnitude of the velocity or on See also:custom. Thus the muzzle velocity of a See also:rifle or See also:cannon shot is expressed in feet per second, whereas the See also:speed of a See also:train is usually expressed in miles per See also:hour. Similarly, the unit on the metric system is s metre, or any decimal multiple thereof, per second, per hour, &c. Since acceleration is the See also:rate of increase of velocity per unit time, it is obvious that the unit of acceleration depends solely upon the units chosen to express unit velocity; thus if the unit of velocity be one foot per second, the unit of acceleration is one foot per second per second, if one metre per second the unit is one metre per second per second, and similarly for other units of velocity. Momentum is defined as the product of mass into velocity; unit momentum is therefore the momentum of unit mass into unit velocity; in the British system the unit of mass may be the pound, ton, &c., and the unit of velocity any of those mentioned above; and in the metric system, the gramme, kilogramme, &c., may be the unit of mass, while the metre per second, or any other metric unit of velocity, is the remaining See also:term of the product. Force, being measured .by the See also:change of momentum in unit time, is expressed in terms of the same units in which unit momentum is defined. The common British unit is the poundal," the force which in one second retards or accelerates the velocity of a mass of one pound by one foot per second. The metric (and scientific) unit, named the " dyne," is derived from the centimetre, gramme, and second. The poundal and dyne are related as follows:—r poundal= 13,825.5 dynes. A common unit of force, especially among See also:engineers, is the " See also:weight of one pound," by which is meant the force equivalent to the gravitational attraction of the earth on a mass of one pound. This unit obviously depends on gravity; and since this varies with the See also:latitude and height of the See also:place of observation (see EARTH, FIGURE oF), the " force of one pound " of the engineer is not See also:constant. Roughly, it equals 32.17 poundals or 98o dynes. The most frequent uses of this engineer's unit are to be found in the expressions for pressure, especially in the boilers and cylinders of See also:steam engines, and in structures, such as See also:bridges, See also:foundations of buildings, &c. The expression takes the See also:form: pounds per square foot or See also:inch, meaning a force equivalent to so many pounds' weight distributed over a square foot or inch, as the See also:case may be. Other units of pressure (and therefore special units of force) are the " See also:atmosphere " (abbreviated atmo "), the force exerted on unit See also:area by the See also:column of See also:air vertically above it; the " millimetre or centimetre of See also:mercury," the usual scientific units, the force exerted on unit area by a column of mercury one millimetre or centimetre high; and the " foot of water," the column being one foot of water. All these units admit of ready conversion:—I atmo -s-- 76o mm. mercury—32 feet of water =1,013,600 dynes. Energy of work is measured by force acting over a distance. The scientific unit is the " erg," which is the energy expended when a force of one dyne acts over one centimetre. This unit is too small for measuring the quantity of energy associated, for instance, with engines; for such purposes a unit ten-million times as See also:great, termed the " See also:joule," is used. The British absolute unit is the " poundal-foot." As we noticed in the case of units of force, common-See also:life experience has led to the introduction of units dependent on See also:gravitation, and therefore not invariable; the common British See also:practical unit of this class is the " foot-pound "; in the metric system its congener is the " kilogramme-metre." Power is the rate at which force does work; it is therefore expressed by " units of energy per second." The metric unit in use is the " See also:watt," being the rate equal to one joule per second. Larger units in practical use are: " kilowatt,' equal to See also:I000 See also:watts; the corresponding energy unit being the kilowatt-second, and 3600 kilowatt-seconds or I kilowatt-hour called a " See also:Board of See also:Trade unit " or a " See also:kelvin." This last is a unit of energy, not power. In British See also:engineering practice the common unit of power is the " See also:horse-power " (I-P), which equals 55o foot-pounds performed per second, or 33,000 foot-pounds per minute; its equivalent in the metric system is about 746 watts, the ratio varying, however, with gravity. Units of Heat.—In studying the phenomena of heat, two measurable quantities immediately present themselves: (1) temperature or thermal potential, and (2) quantity of heat. Three arbitrary scales are in use for measuring temperature (see See also:THERMOMETRY), and each of these scales affords units suitable for the expression of temperature. On the Centigrade See also:scale the unit, termed a " Centigrade degree," is one-hundredth of the See also:interval between the temperature of water boiling under normal barometric pressure_ (76o mm. of mercury) and that of melting See also:ice; the " See also:Fahrenheit degree " is one-hundredand-eightieth, and the " See also:Reaumur degree " is one-eightieth of the same difference. In addition to these scales there is the " thermo-dynamic scale," which, being based on dynamical reasoning, admits of correlation with the fundamental units. This subject is discussed in the articles See also:THERMODYNAMICS and THERMOMETRY. Empirical units of " quantity of heat " readily suggest them-selves as the amount of heat necessary to heat a unit mass of any substance through unit temperature. In the metric system the unit, termed a " calorie," is the quantity of heat required to raise a gramme of water through one degree Centigrade. This quantity, however, is not constant, since the specific heat of water varies with temperature (see See also:CALORIMETRY). In defining the calorie, therefore, the particular temperatures must be specified; consequently there are several calories particularized by special designations:—(r) conventional or common gramme-calorie, the heat required to raise I gramme of water between 150° C. and 17° C. through 1° C.; (2) " mean or See also:average gramme calorie," one-hundredth of the See also:total heat required to raise the temperature of I gramme of water from o° C. to See also:roe C.; (3) " zero gramme calorie," the heat required to raise r gramme of water from o° C. to I° C. These units are thus related: common calorie= 1.987 mean calories= 0.992 zero calories. A unit in common use in thermo-See also:chemistry is the See also:major calorie, which refers to one kilogramme of water and I° C. In the British system the common unit, termed the " British Thermal Unit " (B.Th.U.), is the amount of heat required to raise one pound of water through one degree Fahrenheit. A correlation of these units of quantity of heat with the fundamental units of mass, length and time attended the recognition of the fact that heat was a form of energy; and their quantitative relationships followed from the experimental determinations of the so-called " mechanical equivalent of heat," i.e. the amount of mechanical energy, expressed in ergs, joules, or foot-pounds, equivalent to a certain quantity of heat (cf. CALORIMETRY). These results show that a See also:gram-calorie is equivalent to about 4.2 joules, and a British thermal unit to 78o foot-pounds. See also:Electrical Units.—The next most important units are the electrical units. We are principally concerned in electrical work with three quantities called respectively, electric current, electromotive force, and resistance. These are related to one another by Ohm's See also:law, which states that the electric current in a See also:circuit is directly as the electromotive force and inversely as the resistance, when the current is unvarying and the temperature of the circuit constant. Hence if we choose units for two of these quantities, the above law defines the unit for the third. Much discussion has taken place over this question,. The choice is decided by the nature of the quantities themselves. Since resistance is a permanent quality of a substance, it is possible to select a certain piece of See also:wire or See also:tube full of mercury, and declare that its resistance shall be the unit of resistance, and If the substance is permanent we shall possess an unalterable standard or unit of resistance. For these reasons the practicalunit of resistance, now called the See also:international ohm, has been selected as one of the above three electrical units. It has now been decided that the second unit shall be the unit of electric current. As an electric current is not a thing, but a See also:process, the unit current can only be reproduced when desired. There are two available methods for creating a standard or unit electric current. If an unvarying current is passed through a neutral See also:solution of See also:silver nitrate it decomposes or electrolyses it and deposits silver upon the negative See also:pole or See also:cathode of the electrolytic See also:cell. According to See also:Faraday's law and all subsequent experience, the same current deposits in the same time the same mass of silver. Hence we may define the unit current by the mass of silver it can liberate per second. Again, an electric current in one circuit exerts mechanical force upon a magnetic pole or a current in another circuit suitably placed, and we may measure the force and define by it a unit electric current. Both these methods have been used. Thirdly, the unit of electromotive force may be defined as equal to the difference of potential between the ends of the unit of resistance when the unit of current flews in it. Apart, however, from the relation of these electrical units to each other, it has been found to be of great importance to establish a simple relation between the latter and the absolute mechanical units. Thus an electric current which is Absolute passed through a conductor dissipates its energy as electrical heat, and hence creates a certain quantity of heat units. per unit of time. Having chosen our units of energy and related unit of quantity of heat, we must so choose the 'Init of current that when passed through the unit of resistance it shall dissipater unit of energy in 1 unit of time. A further See also:consideration has weight in selecting the See also:size of the units, namely, that they must be of convenient magnitude for the ordinary measurements. The founders of the British modern system of practical electrical units were a Assoclacommittee appointed by the British Association in tioa 1861, at the See also:suggestion of See also:Lord Kelvin, which made its units. first See also:report in 1862 at See also:Cambridge (see B. A. Report). The five subsequent reports containing the results of the See also:committee's work, together with a large amount of most valuable matter on the subject of electric units, were collected in a volume edited by Prof. Fleeming Jenkin in 1873, entitled Reports of the Committee on Electrical Standards. This committee has continued to sit and report annually to the British Association since that date. In their second report in 1863 (see B.A. Report, See also:Newcastle-on-See also:Tyne) the committee recommended the See also:adoption of the absolute system of electric and magnetic units on the basis originally proposed by Gauss and See also:Weber, namely, that these units should be derived from the fundamental dynamical units, but assuming the units of length, mass and time to be the metre, gramme and second instead of the millimetre, milligramme and second as proposed by Weber. Considerable See also:differences of See also:opinion existed as to the choice of the fundamental units, but ultimately a suggestion of Lord Kelvin's was adopted to select the centimetre, gramme, and second, and to construct a system of electrical units (called the C.G.S. system) derived from the above fundamental units. On this system the unit of force is the dyne and the unit of work the erg. The dyne is the See also:uniform force which when acting on a mass of r gramme for I second gives it a velocity of I centimetre per second. The erg is the work done by I dyne when acting through a distance of I centimetre in its own direction. The electric and magnetic units were then derived, as previously suggested by Weber, in the following manner: If we consider two very small See also:spheres placed with centres I centimetre apart in air and charged with equal quantities of See also:electricity, then if the force between these bodies is I dyne each See also:sphere is said to be charged with I unit of electric quantity on the electrostatic system. Again, if we consider two isolated magnetic poles of equal strength and consider them placed r centimetre apart in air, then if the force between them is r dyne these poles are said to have a strength of I unit on the electromagnetic system. Unfortunately the committee did not take into See also:account the fact that in the first case the force between the electric charges depends upon and varies inversely as the di-electric constant of the See also:medium in which the experiment is made, and in the second case it depends upon the magnetic See also:permeability of the medium in which the magnetic poles exist. To put it in other words, they assume that the See also:dielectric constant of the circumambient medium was unity in the first case, and that the permeability was also unity in the second case. The result of this choice was that two systems of measurement were created, one depending upon the unit of electric quantity so chosen, called the electrostatic system, and the other depending upon the unit magnetic pole defined as above, called the electromagnetic system of C.G.S. units. Moreover, it was found that in neither of these systems were the units of very convenient magnitude. Hence, finally, the committee adopted a third system of units called the practical system, in which convenient decimal multiples or fractions of the electromagnetic units were selected and named for use. This system, moreover, is not only consistent with itself, but may be considered to be derived from a system of dynamical units in which the unit of length is the earth quadrant or ro million metres, the unit of mass is Io 11 of a gramme and the unit of time is i second. The units on this system have received names derived from those of eminent discoverers. Moreover, there is a certain relation between the size of the units for the same quantity on the electrostatic (E.S.) system and that on the electromagnetic (E.M.) system, which depends upon the velocity of light in the medium in which the measurements are supposed to be made. Thus on the E.S. system the unit of electric quantity is a point See also:charge which at a distance of r cm. acts on another equal charge with a force of r dyne. The E.S. unit of electric current is a current such that I E.S. unit of quantity flows per second across each See also:section of the circuit. On the E.M. system we start with the See also:definition that the unit magnetic pole is one which acts on another equal pole at a distance of r cm. with a force of 1 dyne. The unit of current on the E.M. system is a current such that if flowing in circular circuit of r cm. radius each unit of length of it will See also:act on a unit magnetic pole at the centre with a force of r dyne. This E.M. unit of current is much larger than the E.S. unit defined as above. It is v times greater, where v = 3 X r o10 is the velocity of light in air expressed in See also:ems. per second. The See also:reason for this can only be understood by considering the dimensions of the quantities with which we are concerned. If L, M, T denote length, mass, time, and we adopt certain sized units of each, then we may measure any derived quantity, such as velocity, acceleration, or force in terms of the derived dynamical units as already explained. Suppose, however, we alter the size of our selected units of L, M or T, we have to consider how this alters the corresponding units of velocity, acceleration, force, &c. To do this we have to consider their dimensions. If the unit of velocity is the unit of length passed over per unit of time, then it is obvious that it varies directly as the unit of length, and inversely as the unit of time. Hence we may say that the dimensions of velocity are L/T or LT-'; similarly the dimensions of acceleration are L/T2 or LT-2, and the dimensions of a force are MLT-2. For a See also:fuller explanation see above (UNITS, DIMENSIONS OF), or See also:Everett's Illustrations of the C.G.S. System of Units. Accordingly on the electrostatic system the unit of electric quantity is such that f= q2/Kd2, where q is the quantity of Flectro- the two equal charges, d their distance, f the mechanical staticand force or stress between them, and K the dielectric electro- constant of the dielectric in which they are See also:im- magnetic mersed. Hence since f is of the dimensions MLT-2, q2 units. must be of the dimensions of KML3T-2, and q of the dimensions M1 LIT 'KI. The dimensions of K, the dielectric constant, are unknown. Hence, in accordance with the suggestion of See also:Sir A. Rucker (Phil. Mag., See also:February 1889), we must treat it as a fundamental quantity. The dimensions of an electric current on the electrostatic system are therefore those of an electric quantity divided by a time, since by current we mean the quantity of electricity conveyed per second. Accordingly current on the E.S. system has the dimensions MiLIT-2KI. We may obtain the dimensions of an electric current on the magnetic system by observing that if two circuits traversed by the same or equal currents are placed at a distance from each other, the mechanical force or stress between two elements of the circuit, in accordance with Ampere's law (see ELECTRO-See also:KINETICS), varies as the square of the current C, the product of the elements of length ds, ds' of the circuits, inversely as the square of their distance d, and directly as the permeability p of the medium in which they are immersed. Hence C2dr ds'g/d2 must be of the dimensions of a force or of the dimensions MLT-2. Now, ds and ds' are lengths, and d is a length, hence the dimensions of electric current on the E.M. system must be MlLIT 'p 1. Accordingly the dimensions of current on the E.S. system are MILIT-2 K1, and on the E.M. system they are M1LIT' 1, where u and K, the permeability and di- electric constant of the medium, are of unknown dimensions, and therefore treated as fundamental quantities. The ratio of the dimensions of an electric current on the two systems (E.S. and E.M.) is therefore LT 1K'µ1. This ratio must be a See also:mere numeric of no dimensions, and therefore the dimensions of SKµ must be those of the reciprocal of a velocity. We do not know what the dimensions of u and K are separately, but we do know, therefore, that their product has the dimensions of the reciprocal of the square of a velocity. Again, we may arrive at two dimensional expressions for electromotive force or difference of potential. Electrostatic difference of potential between two places is measured by the mechanical work required to move a small conductor charged with a unit electric charge from one place to the other against the electric force. Hence if V stands for the difference of potential between the two places, and Q for the charge on the small conductor, the product QV must be of the dimensions of the work or energy, or of the forceXlength, or of ML2T-2. But Q on the electrostatic system of measurement is of the dimensions MILlT-'KI ; the potential difference V must be, therefore, of the dimensions MiLiT 'KI. Again, since by Ohm's law and Joule's law electromotive force multiplied by a current is equal to the power expended on a circuit, the dimensions of electromotive force, or, what is the same thing, of potential difference, in the electromagnetic system of measurement must be those of power divided by a current. Since mechanical power means rate of doing work, the dimensions of power must be ML2T-3. We have already seen that on the electromagnetic system the dimensions of a current are MiLIT 'p 1 • therefore the dimensions of electromotive force or potential on the electromagnetic system must be MILIT-2µI. Here again we find that the ratio of the dimensions on the electrostatic system to the dimensions on the electromagnetic system is L-1TK 1p 1. In the same manner we may recover from fundamental facts and relations the dimensions of every electric and magnetic quantity on the two systems, starting in one case from electrostatic phenomena and in the other case from electromagnetic or magnetic. The electrostatic dimensional expression will always involve K, and the electromagnetic dimensional expression will always involve p, and in every case the dimensions in terms of K are to those in terms of p for the same quantity in the ratio of a power of LT-'K1µ1. This therefore confirms the view that whatever may be the true dimensions in terms of fundamental units of µ and K, their product is the inverse square of a velocity. Table I. gives the dimensions of all the See also:principal electric and magnetic quantities on the electrostatic and electromagnetic systems. It will be seen that in every case the ratio of the dimensions on the two systems is a power of LT-'K'1µ1, or of a velocity multiplied by the square root of the product K and p; in other words, it is the product of a velocity multiplied by the geometric mean of K and p. This quantity i/s/Kµ must therefore be of the dimensions of a velocity, and the questions arise, What is the absolute value of this velocity? and, How is it to be determined? The See also:answer is, that the value of the velocity in See also:concrete See also:numbers maybe obtained by measuring the magnitude of any electric quantity in two ways, one making use only of electrostatic phenomena, and the other only of electromagnetic. To take one instance :—It is easy to show that the electrostatic capacity of a sphere suspended in air or in vacuo at a great distance from other conductors is given by a number equal to its radius in centimetres. Suppose such a sphere to be charged and discharged rapidly with electricity from any source, such as a See also:battery. It would take electricity from the source at a certain rate, and would in fact act like a resistance in permitting the passage through it or by it of a certain quantity of electricity per unit of time. If K is the capacity and n is the number of discharges per second, then nK is a quantity of the dimensions of an electric conductivity, or of the reciprocal of a resistance. If a conductor, of which the electrostatic capacity can be calculated, and which has associated with it a commutator that charges and discharges it n times per second, is arranged in one branch of a See also:Wheatstone's See also:Bridge, it can be treated and measured as if it were a resistance, and its equivalent resistance calculated in terms of the resistance of all the other branches of the bridge (see Phil. Mag., 1885, 20, 258). Accordingly, we have two methods of measuring the capacity of a conductor. One, the electrostatic method, depends only on the measurement of a length, which in the case of a sphere in See also:free space is its radius; the other, the electromagnetic method, deter-mines the capacity in terms of the quotient of a time by a resistance. The ratio of the electrostatic to the electromagnetic value of the same capacity is therefore of the dimensions of a velocity multiplied by a resistance in electromagnetic value, or of the dimensions of a velocity squared. This particular experimental measurement has been carried out carefully by many observers, and the result has been always to show that the velocity v which expresses the ratio is very nearly equal to 30 thousand million centimetres per second; v =nearly 3 X 10'0. The value of this important constant can be determined by experiments made to measure electric quantity, potential, resistance or capacity, both in electrostatic and in electromagnetic measure. For details of the various methods employed, the reader must be referred to standard See also:treatises on Electricity and See also:Magnetism, where full particulars will be found (see See also:Maxwell, See also:Treatise on Electricity and Magnetism, vol. ii. ch. xix. 2nd ed.; also Mascart and See also:Joubert, Treatise on Electricity and Magnetism, vol. ii. ch. viii., Eng. trans. by See also:Atkinson).
Table II. gives a See also:list of some of these determinations of v, with references to the See also:original papers.
It will be seen that all the most See also:recent values, especially those in which a comparison of capacity has been made, approximate to 3 X tO'0 centimetres per second, a value which is closely in See also:accord with the latest and best determinations of the velocity of light.
We have in the next place to consider the question of Practical practical electric units and the determination and units. construction of concrete standards. The committee of the British Association charged with the See also:duty of arranginga system of absolute and magnetic units settled also on a system of practical units of convenient magnitude, and gave names to them as follows:-
Io9 absolute electromagnetic units of resist-
ance = I ohm
Ios „ „ units of electro-
See also:motive force = r volt
th of an „ unit of current =1 ampere
-i,° th of an „ „ unit of quantity = I See also:coulomb
Io-9 „ ,,
units of capacity=1 farad Io is ,,
11
units of capacity =1microfarad
Since the date when the preceding terms were adopted, other multiples of absolute C.G.S. units have received practical names, thus:
Io7 ergs or absolute C.G.S. units of energy = I joule Io7 ergs per second or C.G.S. units of power = I watt
•Io9 absolute units of inductance = r See also: As the unit of capacity, the International Farad, which is the capacity of a See also:condenser charged to a potential of one international volt by one international coulomb of electricity. " As a unit of work, the Joule, which is equal to Io7 units of work in the C.G.S. System, and which is represented sufficiently well for practical use by the energy expended in one second by an international ampere in an international ohm. " As a unit of power, the Watt, which is equal to Io7 units of power in the C.G.S. System, and which is represented sufficiently well for practical use by the work done at the rate of one joule per second. As the unit of inductance, the Henry, which is the See also:induction in a circuit when an electromotive force induced in this circuit is one international volt, while the inducing current varies at the rate of one ampere per second.” Neither the weber nor the gauss has received very See also:general adoption, although recommended by the Committee of the British Association on Electrical Units. Many different suggestions have been made as to the meaning to be applied to the word " gauss.” The practical electrical engineer, up to the present, prefers to use one ampere-turn as his unit of magnetomotive force, and one See also:line of force as the unit of magnetic flux, equal respectively to Io/47r times and I times the C.G.S. absolute units. Very frequently the kiloline,” equal to woo lines of force, is now used as a unit of magnetic flux. Quantity. See also:Symbol. Dimensions Dimensions Ratio of E.S to on the Electro- on the Electro- static System magnetic EM. E.S. System E.M.
Magnetic per-) (µ) L 2 Ts K 1 µ L Tz K i µ
meability . (H) Li Mi T KI L i MI T u I L T' KI µi
Magnetic
force o r
See also: Weber and Electrodynamisc he Quantity 3•Io7XIo'o
R. Kohlrausch Massbeslimmungen
and Pogg. See also:Ann.
xcix., August 10,
1856
1867 Lord Kelvin Report of British Potential 2-81 X1o'o
1868 and W. F. See also: See also:Soc., 1868, p. 643 1872 Lord Kelvin and Phil. Trans. Roy. „ z'89 XIo10 Dugald M'Kich- Soc.. 1873, p. 409 1878 an See also:lawn. Soc. Tel. Eng. Capacity 2.94 X1010 W. E. See also:Ayrton and 188o J. See also:Perry vol. viii. p. 126 Potential 2.955X I010 Lord Kelvin and Phil. Mag., 188o, vol. Shida x. P. 431 1881 A. G. Stoletow . Soc. See also:Franc. de Phys., Capacity 2.99 Xioto 188r 1882 F. Exner . Wien. Ber., 1882 Potential 2-92 X into 1883 Sir J. J. See also:Thomson Phil. Trans. Roy. Capacity 2.963X See also:row Soc., 1883, p. 707 1884 I. Klemencic Journ. Soc. Tel. Eng., ii 3.019 X 1010 I887, p. 162
1888 F. Himstedt . . Electrician, See also: Roy. Inst., 1889 Potential 3'094Xlolo 1889 H. A. See also:Rowland , Phil..Mag., 1888 Quantity 2.981XroIo 1889 E. B. See also:Rosa Phil. Mag., 1889 Capacity 3.~XIO10 1890 Sir J. J. Thomson Phil. Trans., 1890 2995X1010 1887 and G. F. C. Searle Wied. Ann. 1897 Alternating 3.o15X 1010 M. E. Maltby. . currents In connexion with the numerical values in the above definitions much work has been done. The electrochemical equivalent of silver or the weight in grammes deposited per second by r C.G.S. electromagnetic unit of current has been the subject of much See also:research. The following determinations of it have been given by various observers: Name. Value. Reference. E. E. N. Mascart . 0.011156 Journ. de physique, 1884, (2), 3, 283. F. and W. Kohlrausch . o•oi 1183 Wied. Ann., 1886, 27, I. Lord See also:Rayleigh and Mrs 0.011179 Phil. Trans. Roy. Soc., See also:Sedgwick 1884, 2, 411. J. S. H. Pellat and 0.011192 Journ. de Phys., 1890, (2), A. Potier 9, 381. Karl Kahle 0.011183 Wied. Ann., 1899, 67, I. G. W. Patterson and 0.011192 Physical See also:Review, 1898, 7, K. E. Guthe 251. J. S. H. Pellat and S. A. o•ot 1195 Comptes rendus, 1903, Leduc 136, 1649. Although some observers have urged that the 0.01119 is nearer to the true value than o•o1118, the preponderance of the See also:evidence seems in favour of this latter number and hence the value per ampere-second is taken as o•oolISoo gramme. The exact value of the electromotive force of a See also:Clark cell has also been the subject of much research. Two forms of cell are in use, the simple tubular form and the H-form introduced by Lord Rayleigh. The See also:Berlin Reichsanstalt has issued a specification for a particular H-form of Clark cell, and its E.M.F. at 15° C. is taken as 1.4328 international volts. The E.M.F. of the cell set up in accordance with the British Board of Trade specification is taken as 1.434 international volts at 15° C. The detailed specifications are given in See also:Fleming's See also:Hand-See also:book for the Electrical Laboratory and Testing See also:Room (1901), vol. i. See also:chap. 1; in the same book will be found copious references to the scientific literature of the Clark cell. One objection to the Clark cell as a concrete standard of electromotive force is its variation with temperature and with slight impurities in the mercurous sulphate used in its construction. The Clark cell is a voltaic cell made with mercury, mercurous sulphate, See also:zinc sulphate, and zincas elements, and its E.M.F. decreases o.o8 % per degree Centigrade with rise of temperature. In 1891 Mr Weston proposed to employ cadmium and cadmium sulphate in place of zinc and zinc sulphate and found that the temperature coefficient for the cadmium cell might be made as See also:low as 0.004 % per degree Centigrade. Its E.M.F. is, however, 1•o184 international volts at 20 C. For details of construction and the literature of the subject see Fleming's Handbook for the Electrical Laboratory, vol. i. chap. i.
In the British Board of Trade laboratory the ampere and the volt are not recovered by immediate reference to the electrochemical equivalent of silver or the Clark cell, but by means of See also:instruments called a standard ampere See also:balance and a standard See also:loo-volt electrostatic See also:voltmeter. In the standard ampere balance the current is determined by weighing the attraction between two coils traversed by the current, and the ampere is defined to be the current which causes a certain attraction between the coils of this standard form of ampere balance. The form of ampere balance in use at the British Board of Trade electrical standards See also:office is described in Fleming's Handbook for the Electrical Laboratory, vol. i., and that constructed for the British See also:National Physical Laboratory in the report of the Committee on Electrical Standards (Brit. Assoc. See also:Rep., 1905). This latter See also:instrument will recover the ampere within one-thousandth part. For a further description of it and for full discussion of the present position of knowledge respecting the values of the international practical units the reader is referred to a See also:paper by Dr F. A. See also:Wolff read before the International Electrical Congress at St See also: Inst. Elec. Eng. Lond., 1904-5, 34, 190, and 35, 3).
The construction of the international ohm or practical unit of resistance involves a knowledge of the specific resistance of mercury. Numerous determinations of this constant have been made. The results are expressed either in terms .of the length in cm. of the column of pure mercury of 1 sq. mm. in section which at o° C. has a resistance of so' C.G.S. electromagnetic units, or else in terms of the weight of mercury in grammes for a column of constant cross-sectional area and length of 100.3 cm. The latter method was adopted at the British Association See also:Meeting at See also:Edinburgh in 1892, but there is some uncertainty as to the value of the See also:density of mercury at o° C. which was then adopted. Hence it was proposed by See also:Professor J. Viriamu See also: Roy. Inst. vol. 14, part iii. p. 6os). For the length of the mercury column defining the ohm as above, Lord Rayleigh in 1882 found the value 106.27 cm., and R. T. Glazebrook in the same year the value 106.28 cm. by a different method, while another determination by Lord Rayleigh and Mrs Sedgwick in 1883 gave Io6.22 cm. Viriamu Jones in 1891 gave the value I06.3o cm., and one by W. E. Ayrton in 1897 by the same method obtained the value 106.27 to Io6.28 cm. Hence the specific resistance of mercury cannot be said to be known to part in 50,000, and the absolute value of the ohm in centimetres per second is uncertain to at least that amount. (See also J. Viriamu Jones, " On a Determination of the International Ohm in Absolute Measure,” Brit. Assoc. Report, 1894.) The above-described practical system based on the C.G.S. See also:double system of theoretical units labours under several very great disadvantages. The practical system is derived from and connected with an abnormally large unit of length (the earth quadrant) and an absurdly small unit of mass. Also in consequence of the manner in which the unit electric quantity and magnetic pole strength are defined, a coefficient, 47r, makes its See also:appearance in many practical equations. For example, on the present system the magnetic force H in the interior of a See also:long See also:spiral wire of N turns per centimetre of length when a current of A amperes circulates in the wire is 47r AN/Io. Again, the electric displacement or induction D through a unit of area is connected with the electric force E and the dielectric constant K by the See also:equation D = KE/47r. In numerous electric and magnetic equations the constant 47r makes its appearance where it is apparently meaningless. A system of units in which this constant is put into its right place by appropriate definitions is called a rational system of electric units. Several physicists have proposed such systems. Amongst others that of Professor G. Giorgi especially deserves mention. GiorgPs We have seen that in expressing the dimensions of system oi electric and magnetic qualities we cannot do so simply electrical by reference to the units of length, mass and time, units. but must introduce a See also:fourth fundamental quantity. This we may take to be the dielectric constant of the See also:ether or its magnetic permeability, and thus we obtain two systems of Rational system of electrical units. measurement. Professor Giorgi proposes that the four fundamental quantities shall be the units of length, mass, time and electrical resistance, and takes as the concrete units or standards the metre, kilogramme, second and ohm. Now this proposal not only has the See also:advantage that the theoretical units are identical with the actual practical concrete units, but it is also a rational system. Moreover, the present practical units are unaltered; the ampere, volt, coulomb, weber, joule and watt remain the actual as well as theoretical units of current, electromotive force, quantity, magnetic flux, work and power. But the unit of magnetic force becomes the ampere-turn per metre, and the unit of electric force the volt per metre; thus the magnetic units are measured in terms of electric units. The numerical value of the permeability of ether or air becomes 47r X 10-7 and the dielectric constant of the ether or air becomes r,/4srX9Xio9; their product is therefore 1/(3Xro8)2, which is the reciprocal of the square of the velocity of light in metres per second. For a discussion of the Giorgi proposals, see a paper by Professor M. See also:Ascoli, read before the International Electrical Congress at St Louis, 1904 (Journ. Inst. Elect. Eng. Lond., 1904, 34, 176). It can hardly be said that the present system of electrical units is entirely satisfactory in all respects. Great difficulty would of course be experienced in again altering the accepted practical concrete units, but if at any future time a See also:reformation should be possible, it would be desirable to See also:bear in mind the recommendations made by See also:Oliver Heaviside with regard to their rationalization. The British Association Committee defined the strength of a magnetic pole by reference to the mechanical stress between it and another equal pole: hence the British Association unit magnetic pole is a pole which at a distance of one centimetre attracts or repels another equal pole with a force of one dyne. This, we have seen, is an imperfect definition, because it omits all reference to the permeability of the medium in which the experiment takes place; but it is also unsatisfactory as a starting-point for a system of units for another reason. The important quantity in connexion with polar magnets is not a mechanical stress between the free poles of different magnets, but the magnetic flux emanating from, or associating with, them. From a technical point of view this latter quality is far more important than the mechanical stress between the magnetic poles, because we mostly employ magnets to create induced electromotive force, and the quantity we are then mostly concerned with is the magnetic flux proceeding from the poles. Hence the most natural definition of a unit magnet pole is that pole from which proceeds a total magnetic flux of one unit. The definition of one unit of magnetic flux must then be that flux which, when inserted into or withdrawn from a conducting circuit of one turn having unit area and unit conductivity, creates in it a flow or circulation of one unit of electric quantity. The definition of a unit magnetic pole ought, therefore, to have been approached from the definition of a unit of electric quantity. On the C.G.S. or British Association system, if a magnetic filament has a pole strength m—that is to say, if it has a magnetization I, and a section s, such that Is equals m—then it can be shown that the total flux emanating from the pole is 4,rm. The See also:factor 47r., in consequence of this definition, makes its appearance in many practically important expressions. For instance, in the well-known magnetic equation connecting the vector values of magnetization 1. magnetic force H and magnetic flux density B, where we have the equation B=H+4irI, the appearance of the quantity 47r disguises the real physical meaning of the equation. The true remedy for this difficulty has been suggested by Heaviside to be the substitution of rational for irrational formulae and definitions. Neavt- He proposes to restate the definition of a unit magnetic See also:side's pole in such a manner as to remove this constant 47r rational from the most frequently employed equations. His start- system. See also:ing-point is a new definition according to which a unit magnetic pole is said to have a strength of m units if it attracts or repels another equal pole placed at a distance of d centimetres with a force of m2/47d2 dynes. It follows from this definition that a rational unit magnetic pole is weaker or smaller than the irrational or British Association unit pole in the ratio of1/y4ir to I, or .28205 to I. The magnetic force due to a rational pole of strength m at a distance of d centimetres being m/47rd2 units, if we suppose a magnetic filament having a pole of strength m in rational units to have a smaller sphere of radius r described See also:round its pole, the magnetic force on the See also:surface of this sphere is m/47rr2 units, and this is therefore also the numerical value of the flux density. Hence the total magnetic flux through the surface of the sphere is 4ar2Xm/47r2 units =m units; and therefore the number which denotes the total magnetic flux coming out of the pole of strength in in rational units is also m. The Heaviside system thus gives us an obvious and natural definition of a unit magnetic pole, namely, that it is a pole through which proceeds the unit of magnetic flux. It follows, therefore, that if the intensity of magnetization of the magnetic filament is I and the section is s, the total flux traversing the centre of the magnet is Is units; and that if the filament is an endless or poleless See also:iron filament magnetized uniformly by a resultant See also:external magnetic force H, the flux density will be expressed in rational units by the equation B = I +H. The physical meaning of this equation is that the flux per square centimetre in the iron is simply obtained by adding together the flux per square centimetre, if the iron is supposed to be removed, and the magnetization of the iron at that place. On the rational system, since the unit pole strength has been decreased in the ratio of I to 1/1,/ 47r, or of 3.5441 to i, when compared with the magnitude of the present irrational unit pole, and since the unit of magnetic flux is the total flux proceeding from a magnetic pole, it follows that Heaviside's unit of magnetic flux is larger than the C.G.S. unit of magnetic flux in the ratio of 3.5441 to 1. It will be seen, therefore, that the Heaviside rational units are all incommeasurable with the practical units. This is a great barrier to their adoption in practice, because it is impossible to discard all the existing resistance coils, ammeters, voltmeters, &c., and equally impossible to recalibrate or readjust them to read in Heaviside units. A suggestion has been made, in modification of the Heaviside system, which would provide a system of rational practical units not impossible of adoption. It has been pointed out by J. A. Fleming that if in place of the ampere, ohm, watt, joule, farad and coulomb, we employ the dekampere, dekohm, the dekawatt, the dekajoule, the dekafarad and the dekacoulomb, we have a system of practical units such that measurements made in these units are equal to measurements made in Heaviside rational units when multiplied by some power of 47r. Moreover, he has shown that this power of 47r, in the case of most units, varies inversely as the power under which appears in the See also:complete dimensional expression for the quantity in electromagnetic measurement. Thus a current measured in Heaviside rational units is numerically equal to (4,r)= times the same current measured in dekamperes, and in the electromagnetic dimensional expression for current, namely, LIMIT-1µl, µ appears as 1.1-1. If, then, we consider the permeability of the ether to be numerically 47r instead of unity, the measurement of a current in dekamperes will be a number which is the same as that given by reckoning in Heaviside rational units. In this way a system of Rational Practical Units (R.P. Units) might be constructed as follows: The R.P. Unit of Magnetic Force =47r X the C.G.S. Unit. Magnetic See also:Polarity = i/47r X Magnetic Flux = t „ Magnetomotive Force = I Electric Current = t Electric Quantity = t Electromotive Force = to, Resistance = to8 Inductance = io8 „ Power = to8 „ Work = 108 Capacity = lo-8 „ All except the unit of magnetic force and magnetic polarity are commensurable with the corresponding C.G.S. units, and in multiples which form a convenient practical system. Even the rational systems already mentioned do not entirely fulfil the ideal of a system of physical units. There are certain constants of nature which are fundamental, invariable, and, as far as we know, of the same magnitude in all parts of the universe. One of these is the mass of the See also:atom, say of See also:hydrogen. Another is the length of a wave of light of particular refrangibility emitted by some atom, say one of the two yellow lines in the spectrum of See also:sodium or one of the hydrogen lines. Also a time is fixed by the velocity of light in space which is according to the best measurement very See also:close to 3X Io1° ems. per sec. Another natural unit is the so-called constant of gravitation, or the force in dynes due to'the attraction of two spherical masses each of r gramme with centres at a distance of r cm. Very approximately this is equal to 648 X lo 1° dynes. Another natural electrical 11 unit of great importance is the electric charge represented by 1 See also:electron (see ELECTRICITY). This according to the latest determination is nearly 3.4 X Io '0 electrostatic units of quantity on the C.G.S. system. Hence, 2930 million electrons are equal to I E.S. unit of quantity on the C.G.S. system, and the quantity called 1 coulomb is equal to 879X1016 electrons. In round numbers 9X 1o1' electrons make 1 coulomb. The electron is nature's unit of electricity and is the charge carried by r hydrogen See also:ion in See also:electrolysis (see See also:CONDUCTION, ELECTRIC, § Liquids). Accordingly a truly natural system of physical units would be one which was based upon the electron, or a multiple of it, as a unit of electric quantity, the velocity of light or fraction of it as a unit of velocity, and the mass of an atom of hydrogen or multiple of it as a unit of mass. An approximation to such a natural system of electric units will be found discussed in chap. 17 of a book on The Electron Theory, by E.E. See also:Fournier d'Albe (London, 1906), to which the reader is referred. See J. Clerk Maxwell, Treatise on Electricity and Magnetism, vol. ii. chap. x. (3rd ed., See also:Oxford, 1892) ; E. E. N. Mascart and J. Joubert, Treatise on Electricity and Magnetism, See also:translation by E. Atkinson, vol. i. chap. xi. (London, 1883) ; J. D. Everett, Illustrations of the C.G.S. System of Units (London, 1891); See also:Magnus Maclean, Physical Units (London, 1896) ; Fleeming Jenkin, Reports on Electrical Standards (London, 1873); Reports of the British Association Committee on Electrical Units from 1862 to present date; J. A. Fleming, A Handbook for the Electrical Laboratory and Testing-Room (2 vols., London, 1901); Lord Rayleigh, Collected Scientific Papers, vol. ii. (1881–87) ; A. See also:Grey, Absolute Measurements in Electricity and Magnetism, vol. ii. part ii. chap. ix. p. 15o (London, 1893) ; Oliver Heaviside, Electromagnetic Theory, 1. 116 (London, 1893) ; Sir A. W. Rucker, " On the Suppressed Dimensions of Physical Quantities," Proc. Phys. Soc. Lond. (1888), 10, 37; W. See also:Williams, " On the Relation of the Dimensions of Physical Quantities to Directions in Space," Proc. Phys. Soc. Lond. (1892), II, 257; R. A. See also:Fessenden, " On the Nature of the Electric and Magnetic Quantities," Physical Review (See also:January 1900). (J. A. Additional information and CommentsThere are no comments yet for this article.
» Add information or comments to this article.
Please link directly to this article:
Highlight the code below, right click, and select "copy." Then paste it into your website, email, or other HTML. Site content, images, and layout Copyright © 2006 - Net Industries, worldwide. |
|
|
[back] UNITS, DIMENSIONS OF |
[next] UNIVERSAL LANGUAGES |