In specifications, Murphy's Law supersedes Ohm's.
In specifications, Murphy's Law supersedes Ohm's.
_The Magnetic Circuit._--The phenomena presented by the electromagnet are interpreted by the aid of the notion of the magnetic circuit. Let us consider a thin circular sectioned ring of iron wire wound over with a solenoid or spiral of insulated copper wire through which a current of electricity can be passed. If the solenoid or wire windings existed alone, a current having a strength A amperes passed through it would create in the interior of the solenoid a magnetic force H, numerically equal to 4[pi]/10 multiplied by the number of windings N on the solenoid, and by the current in amperes A, and divided by the mean length of the solenoid l, or H = 4[pi]AN/10l. The product AN is called the "ampere-turns" on the solenoid. The product Hl of the magnetic force H and the length l of the magnetic circuit is called the "magnetomotive force" in the magnetic circuit, and from the above formula it is seen that the magnetomotive force denoted by (M.M.F.) is equal to 4[pi]/10 (= 1.25 nearly) times the ampere-turns (A.N.) on the exciting coil or solenoid. Otherwise (A.N.) = 0.8(M.M.F.). The magnetomotive force is regarded as creating an effect called magnetic flux (Z) in the magnetic circuit, just as electromotive force E.M.F. produces electric current (A) in the electric circuit, and as by Ohm's law (see ELECTROKINETICS) the current varies as the E.M.F. and inversely as a quality of the electric circuit called its "resistance," so in the magnetic circuit the magnetic flux varies as the magnetomotive force and inversely as a quality of the magnetic circuit called its "reluctance." The great difference between the electric circuit and the magnetic circuit lies in the fact that whereas the electric resistance of a solid or liquid conductor is independent of the current and affected only by the temperature, the magnetic reluctance varies with the magnetic flux and cannot be defined except by means of a curve which shows its value for different flux densities. The quotient of the total magnetic flux, Z, in a circuit by the cross section, S, of the circuit is called the mean "flux density," and the reluctance of a magnetic circuit one centimetre long and one square centimetre in cross section is called the "reluctivity" of the material. The relation between reluctivity [rho] = 1/µ magnetic force H, and flux density B, is defined by the equation H = [rho]B, from which we have Hl = Z([rho]l/S) = M.M.F. acting on the circuit. Again, since the ampere-turns (AN) on the circuit are equal to 0.8 times the M.M.F., we have finally AN/l = 0.8(Z/µS). This equation tells us the exciting force reckoned in ampere-turns, AN, which must be put on the ring core to create a total magnetic flux Z in it, the ring core having a mean perimeter l and cross section S and reluctivity [rho] = 1/µ corresponding to a flux density Z/S. Hence before we can make use of the equation for practical purposes we need to possess a curve for the particular material showing us the value of the reluctivity corresponding to various values of the possible flux density. The reciprocal of [rho] is usually called the "permeability" of the material and denoted by µ. Curves showing the relation of 1/[rho] and ZS or µ and B, are called "permeability curves." For air and all other non-magnetic matter the permeability has the same value, taken arbitrarily as unity. On the other hand, for iron, nickel and cobalt the permeability may in some cases reach a value of 2000 or 2500 for a value of B = 5000 in C.G.S. measure (see UNITS, PHYSICAL). The process of taking these curves consists in sending a current of known strength through a solenoid of known number of turns wound on a circular iron ring of known dimensions, and observing the time-integral of the secondary current produced in a secondary circuit of known turns and resistance R wound over the iron core N times. The secondary electromotive force is by Faraday's law (see ELECTROKINETICS) equal to the time rate of change of the total flux, or E = NdZ/dt. But by Ohm's law E = Rdq/dt, where q is the quantity of electricity set flowing in the secondary circuit by a change dZ in the co-linked total flux. Hence if 2Q represents this total quantity of electricity set flowing in the secondary circuit by suddenly reversing the direction of the magnetic flux Z in the iron core we must have Entry: ELECTROMAGNETISM
The difference between conduction through gases and through metals is shown in a striking way when we use potential differences large enough to produce the saturation current. Suppose we have got a potential difference between the plates more than sufficient to produce the saturation current, and let us increase the distance between the plates. If the gas were to act like a metallic conductor this would diminish the current, because the greater length would involve a greater resistance in the circuit. In the case we are considering the separation of the plates will _increase_ the current, because now there is a larger volume of gas exposed to the rays; there are therefore more ions produced, and as the saturation current is proportional to the number of ions the saturation current is increased. If the potential difference between the plates were much less than that required to saturate the current, then increasing the distance would diminish the current; the gas for such potential differences obeys Ohm's law and the behaviour of the gaseous resistance is therefore similar to that of a metallic one. Entry: A
_Practical Standards._--The practical measurement of resistivity involves many processes and instruments (see WHEATSTONE'S BRIDGE and OHMMETER). Broadly speaking, the processes are divided into _Comparison Methods_ and _Absolute Methods_. In the former a comparison is effected between the resistance of a material in a known form and some standard resistance. In the _Absolute Methods_ the resistivity is determined without reference to any other substance, but with reference only to the fundamental standards of length, mass and time. Immense labour has been expended in investigations concerned with the production of a standard of resistance and its evaluation in absolute measure. In some cases the absolute standard is constructed by filling a carefully-calibrated tube of glass with mercury, in order to realize in a material form the official definition of the ohm; in this manner most of the principal national physical laboratories have been provided with standard mercury ohms. (For a full description of the standard mercury ohm of the Berlin Physikalisch-Technische Reichsanstalt, see the _Electrician_, xxxvii. 569.) For practical purposes it is more convenient to employ a standard of resistance made of wire. Entry: A
KIRCHHOFF, GUSTAV ROBERT (1824-1887), German physicist, was born at Königsberg (Prussia) on the 12th of March 1824, and was educated at the university of his native town, where he graduated Ph.D. in 1847. After acting as _privat-docent_ at Berlin for some time, he became extraordinary professor of physics at Breslau in 1850. Four years later he was appointed professor of physics at Heidelberg, and in 1875 he was transferred to Berlin, where he died on the 17th of October 1887. Kirchhoff's contributions to mathematical physics were numerous and important, his strength lying in his powers of stating a new physical problem in terms of mathematics, not merely in working out the solution after it had been so formulated. A number of his papers were concerned with electrical questions. One of the earliest was devoted to electrical conduction in a thin plate, and especially in a circular one, and it also contained a theorem which enables the distribution of currents in a network of conductors to be ascertained. Another discussed conduction in curved sheets; a third the distribution of electricity in two influencing spheres; a fourth the determination of the constant on which depends the intensity of induced currents; while others were devoted to Ohm's law, the motion of electricity in submarine cables, induced magnetism, &c. In other papers, again, various miscellaneous topics were treated--the thermal conductivity of iron, crystalline reflection and refraction, certain propositions in the thermodynamics of solution and vaporization, &c. An important part of his work was contained in his _Vorlesungen über mathematische Physik_ (1876), in which the principles of dynamics, as well as various special problems, were treated in a somewhat novel and original manner. But his name is best known for the researches, experimental and mathematical, in radiation which led him, in company with R. W. von Bunsen, to the development of spectrum analysis as a complete system in 1859-1860. He can scarcely be called its inventor, for not only had many investigators already used the prism as an instrument of chemical inquiry, but considerable progress had been made towards the explanation of the principles upon which spectrum analysis rests. But to him belongs the merit of having, most probably without knowing what had already been done, enunciated a complete account of its theory, and of thus having firmly established it as a means by which the chemical constituents of celestial bodies can be discovered through the comparison of their spectra with those of the various elements that exist on this earth. Entry: KIRCHHOFF
_Resistivity of Mercury._--The volume-resistivity of pure mercury is a very important electric constant, and since 1880 many of the most competent experimentalists have directed their attention to the determination of its value. The experimental process has usually been to fill a glass tube of known dimensions, having large cup-like extensions at the ends, with pure mercury, and determine the absolute resistance of this column of metal. For the practical details of this method the following references may be consulted:--"The Specific Resistance of Mercury," Lord Rayleigh and Mrs Sidgwick, _Phil. Trans._, 1883, part i. p. 173, and R. T. Glazebrook, _Phil. Mag._, 1885, p. 20; "On the Specific Resistance of Mercury," R. T. Glazebrook and T. C. Fitzpatrick, _Phil. Trans._, 1888, p. 179, or _Proc. Roy. Soc._, 1888, p. 44, or _Electrician_, 1888, 21, p. 538; "Recent Determinations of the Absolute Resistance of Mercury," R. T. Glazebrook, _Electrician_, 1890, 25, pp. 543 and 588. Also see J. V. Jones, "On the Determination of the Specific Resistance of Mercury in Absolute Measure," _Phil. Trans._, 1891, A, p. 2. Table IV. gives the values of the volume-resistivity of mercury as determined by various observers, the constant being expressed (a) in terms of the resistance in ohms of a column of mercury one millimetre in cross-section and 100 centimetres in length, taken at 0° C.; and (b) in terms of the length in centimetres of a column of mercury one square millimetre in cross-section taken at 0° C. The result of all the most careful determinations has been to show that the resistivity of pure mercury at 0° C. is about 94,070 C.G.S. electromagnetic units of resistance, and that a column of mercury 106.3 centimetres in length having a cross-sectional area of one square millimetre would have a resistance at 0° C. of one international ohm. These values have accordingly been accepted as the official and recognized values for the specific resistance of mercury, and the definition of the ohm. The table also states the methods which have been adopted by the different observers for obtaining the absolute value of the resistance of a known column of mercury, or of a resistance coil afterwards compared with a known column of mercury. A column of figures is added showing the value in fractions of an international ohm of the British Association Unit (B.A.U.), formerly supposed to represent the true ohm. The real value of the B.A.U. is now taken as .9866 of an international ohm. Entry: TABLE
_The Characteristic Curve for Discharge through Gases._--When a current of electricity passes through a metallic conductor the relation between the current and the potential difference is the exceedingly simple one expressed by Ohm's law; the current is proportional to the potential difference. When the current passes through a gas there is no such simple relation. Thus we have already mentioned cases where the current increased as the potential increased although not in the same proportion, while as we have seen in certain stages of the arc discharge the potential difference diminishes as the current increases. Thus the problem of finding the current which a given battery will produce when part of the circuit consists of a gas discharge is much more complicated than when the circuit consists entirely of metallic conductors. If, however, we measure the potential difference between the electrodes in the gas when different currents are sent through it, we can plot a curve, called the "characteristic curve," whose ordinates are the potential differences between the electrodes in the gas and the abscissae the corresponding currents. By the aid of this curve we can calculate the current produced when a given battery is connected up to the gas by leads of known resistance. Entry: _
In metallic conduction it is found that the current is proportional to the applied electromotive force--a relation known by the name of Ohm's law. If we place in a circuit with a small electromotive force an electrolytic cell consisting of two platinum electrodes and a solution, the initial current soon dies away, and we shall find that a certain minimum electromotive force must be applied to the circuit before any considerable permanent current passes. The chemical changes which are initiated on the surfaces of the electrodes set up a reverse electromotive force of polarization, and, until this is overcome, only a minute current, probably due to the slow but steady removal of the products of decomposition from the electrodes by a process of diffusion, will pass through the cell. Thus it is evident that, considering the electrolytic cell as a whole, the passage of the current through it cannot conform to Ohm's law. But the polarization is due to chemical changes, which are confined to the surfaces of the electrodes; and it is necessary to inquire whether, if the polarization at the electrodes be eliminated, the passage of the current through the bulk of the solution itself is proportional to the electromotive force actually applied to that solution. Rough experiment shows that the current is proportional to the excess of the electromotive force over a constant value, and thus verifies the law approximately, the constant electromotive force to be overcome being a measure of the polarization. A more satisfactory examination of the question was made by F. Kohlrausch in the years 1873 to 1876. Ohm's law states that the current C is proportional to the electromotive force E, or C = kR, where k is a constant called the conductivity of the circuit. The equation may also be written as C = E/R, where R is a constant, the reciprocal of k, known as the resistance of the circuit. The essence of the law is the proportionality between C and E, which means that the ratio E/C is a constant. But E/C = R, and thus the law may be tested by examining the constancy of the measured resistance of a conductor when different currents are passing through it. In this way Ohm's law has been confirmed in the case of metallic conduction to a very high degree of accuracy. A similar principle was applied by Kohlrausch to the case of electrolytes, and he was the first to show that an electrolyte possesses a definite resistance which has a constant value when measured with different currents and by different experimental methods. Entry: II
_Galvanism._--For treatment by galvanism a large battery is needed, the simplest form being known as a "patient's battery," consisting of a variable number of dry cells arranged in series. The cells used are those of Leclanché, with E.M.F. (or voltage) of 1.5 and an internal resistance of .3 ohm. Thus the exact strength of the current is known; the number of cells usually employed is 24, and when new give an E.M.F. of about 36 volts. By using the formula C = E/R, where E is the voltage of the battery, R the total resistance of battery, electrodes and the patient's skin and tissues, and C the current in amperes, the number of cells required for any particular current can be worked out. The resistance of the patient's skin must be made as low as possible by thoroughly wetting both skin and electrodes with sodium bicarbonate solution, and keeping the electrodes in very close apposition to the skin. A galvanometer is always fitted to the battery, usually of the d'Arsonval type, with a shunt by means of which, on turning a screw, nine-tenths of the inducing current can be short-circuited away, and the solenoid only influenced by one-tenth of the current which is being used on the patient. In districts where electric power is available the continuous current can be used by means of a switchboard. A current of much value for electrotherapeutic purposes is the sinusoidal current, by which is meant an alternating current whose curve of electromotive force, in both positive and negative phase, varies constantly and smoothly in what is known as the sine curve. In those districts supplied by an alternating current, the sinusoidal current can be obtained from the mains by passing it through various transformers, but where the main supply is the direct or constant current, a motor transformer is needed. Entry: ELECTROTHERAPEUTICS
_Faraday's Views._--The two-fluid theory may be said to have held the field until the time when Faraday began his researches on electricity. After he had educated himself by the study of the phenomena of lines of magnetic force in his discoveries on electromagnetic induction, he applied the same conception to electrostatic phenomena, and thus created the notion of lines of electrostatic force and of the important function of the dielectric or non-conductor in sustaining them. Faraday's notion as to the nature of electrification, therefore, about the middle of the 19th century came to be something as follows:--He considered that the so-called charge of electricity on a conductor was in reality nothing on the conductor or in the conductor itself, but consisted in a state of strain or polarization, or a physical change of some kind in the particles of the dielectric surrounding the conductor, and that it was this physical state in the dielectric which constituted electrification. Since Faraday was well aware that even a good vacuum can act as a dielectric, he recognized that the state he called dielectric polarization could not be wholly dependent upon the presence of gravitative matter, but that there must be an electromagnetic medium of a supermaterial nature. In the 13th series of his _Experimental Researches on Electricity_ he discussed the relation of a vacuum to electricity. Furthermore his electrochemical investigations, and particularly his discovery of the important law of electrolysis, that the movement of a certain quantity of electricity through an electrolyte is always accompanied by the transfer of a certain definite quantity of matter from one electrode to another and the liberation at these electrodes of an equivalent weight of the ions, gave foundation for the idea of a definite atomic charge of electricity. In fact, long previously to Faraday's electrochemical researches, Sir H. Davy and J.J. Berzelius early in the 19th century had advanced the hypothesis that chemical combination was due to electric attractions between the electric charges carried by chemical atoms. The notion, however, that electricity is atomic in structure was definitely put forward by Hermann von Helmholtz in a well-known Faraday lecture. Helmholtz says: "If we accept the hypothesis that elementary substances are composed of atoms, we cannot well avoid concluding that electricity also is divided into elementary portions which behave like atoms of electricity."[16] Clerk Maxwell had already used in 1873 the phrase, "a molecule of electricity."[17] Towards the end of the third quarter of the 19th century it therefore became clear that electricity, whatever be its nature, was associated with atoms of matter in the form of exact multiples of an indivisible minimum electric charge which may be considered to be "Nature's unit of electricity." This ultimate unit of electric quantity Professor Johnstone Stoney called an _electron_.[18] The formulation of electrical theory as far as regards operations in space free from matter was immensely assisted by Maxwell's mathematical theory. Oliver Heaviside after 1880 rendered much assistance by reducing Maxwell's mathematical analysis to more compact form and by introducing greater precision into terminology (see his _Electrical Papers_, 1892). This is perhaps the place to refer also to the great services of Lord Rayleigh to electrical science. Succeeding Maxwell as Cavendish professor of physics at Cambridge in 1880, he soon devoted himself especially to the exact redetermination of the practical electrical units in absolute measure. He followed up the early work of the British Association Committee on electrical units by a fresh determination of the ohm in absolute measure, and in conjunction with other work on the electrochemical equivalent of silver and the absolute electromotive force of the Clark cell may be said to have placed exact electrical measurement on a new basis. He also made great additions to the theory of alternating electric currents, and provided fresh appliances for other electrical measurements (see his _Collected Scientific Papers_, Cambridge, 1900). Entry: C
It is assumed as a first approximation that the heat-loss is proportional to the rise of temperature _d[theta]_, provided that _d[theta]_ is nearly the same in both cases, and that the distribution of temperature in the apparatus is the same for the same rise of temperature whatever the flow of liquid. The result calculated on these assumptions is given in the last column in joules, and also in calories of 20° C. The heat-loss in this example is large, nearly 4.5% of the total supply, owing to the small flow and the large rise of temperature, but this correction was greatly reduced in subsequent observations on the specific heat of water by the same method. In the case of mercury the liquid itself can be utilized to conduct the electric current. In the case of water or other liquids it is necessary to employ a platinum wire stretched along the tube as heating conductor. This introduces additional difficulties of construction, but does not otherwise affect the method. The absolute value of the specific heat deduced necessarily depends on the absolute values of the electrical standards employed in the investigation. But for the determination of relative values of specific heats in terms of a standard liquid, or of the variations of specific heat of a liquid, the method depends only on the constancy of the standards, which can be readily and accurately tested. The absolute value of the E.M.F. of the Clark cells employed was determined with a special form of electrodynamometer (Callendar, _Phil. Trans._ A. 313, p. 81), and found to be 1.4334 volts, assuming the ohm to be correct. Assuming this value, the result found by this method for the specific heat of water at 20° C. agrees with that of Rowland within the probable limits of error. Entry: SPECIFIC
_Diffusion of Electrolytes and Contact Difference of Potential between Liquids._--An application of the theory of ionic velocity due to W. Nernst[7] and M. Planck[8] enables us to calculate the diffusion constant of dissolved electrolytes. According to the molecular theory, diffusion is due to the motion of the molecules of the dissolved substance through the liquid. When the dissolved molecules are uniformly distributed, the osmotic pressure will be the same everywhere throughout the solution, but, if the concentration vary from point to point, the pressure will vary also. There must, then, be a relation between the rate of change of the concentration and the osmotic pressure gradient, and thus we may consider the osmotic pressure gradient as a force driving the solute through a viscous medium. In the case of non-electrolytes and of all non-ionized molecules this analogy completely represents the facts, and the phenomena of diffusion can be deduced from it alone. But the ions of an electrolytic solution can move independently through the liquid, even when no current flows, as the consequences of Ohm's law indicate. The ions will therefore diffuse independently, and the faster ion will travel quicker into pure water in contact with a solution. The ions carry their charges with them, and, as a matter of fact, it is found that water in contact with a solution takes with respect to it a positive or negative potential, according as the positive or negative ion travels the faster. This process will go on until the simultaneous separation of electric charges produces an electrostatic force strong enough to prevent further separation of ions. We can therefore calculate the rate at which the salt as a whole will diffuse by examining the conditions for a steady transfer, in which the ions diffuse at an equal rate, the faster one being restrained and the slower one urged forward by the electric forces. In this manner the diffusion constant can be calculated in absolute units (HCl = 2.49, HNO3 = 2.27, NaCl = 1.12), the unit of time being the day. By experiments on diffusion this constant has been found by Scheffer, and the numbers observed agree with those calculated (HCl = 2.30, HNO3 = 2.22, NaCl = 1.11). Entry: W