In the preceding paragraph it was tacitly assumed that the temperature was not widely different from that preilailing in rooms in which electrical measurements are usually made. Karnerlingh Onnes has shown, how ever, that the relation between resistance and temperature undergoes a remarkable change in the vicinity of the absolute zero. Experi menting, for example, with a coil consisting of 1,000 turns of fine lead wire, the two ends of which he had fused together, he found that, although the coil had a resistance of 734 ohms at the temperature of the laboratory, its re sistance appeared to totally vanish at 6° C. on the absolute scale. The coil was surrounded with liquid helium, and thereby cooled to 4.26° C. (absolute),— which is the boiling point of helium under atmospheric pressure,— and an electric current was then produced in it, by in duction. At the temperature of the laboratory this current would die out to practically noth ing within an extremely small fraction of a second after the removal of the exciting cause; but at the temperature of boiling helium the current persisted for many hours. It fell off, in fact, at the rate of less than 1 per cent per hour. If, however, the coil were lifted out of the helium, the current ceased abruptly as soon as the temperature rose to 6° C. (abso lute),— this being the points of the resistance of lead, above which the energy of the current was quickly dissipated in the form of heat, in the usual way. In another experiment Onnes used, a wire of solid mercury, the resistance of which, just be-. low the freezing point of mercury, was about 50 ohms. As the temperature of this wire was lowered, the resistance diminished regularly until it became reduced to 042 ohm at C. (absolute). Upon further cooling the resistance fell off abruptly at about 4.19° C (absolute), to 0.00001 ohm; and at 2.5° C. (absolute) the resistance of the mercury was only one ten-thousand-millionth of the mist ance observed at the freezing point of water. At 1.7° C. (absolute) a mercury wire will con duct a current having a density of 1,000 am peres per square millimeter, without showi any measurable difference of potential, and without developing heat. Ohm's law no longer holds, and the applied electromotive force may have to be increased a thousand fold, in order to realize a 10 per cent increase in the cur rent. When a metal exhibits these singular properties, by reason of being cooled to a tem perature lower than that at which its resist ance practically vanishes, it is said to be a (superconductor.* In the Citensiscit Weekblad (Amsterdam), Vol. XVI, p. 640, C A. Crom melin gives a historical and theoretical discus sion of the work of Kamerlingh Onnes along these lines, and appends a valuable bibliography bringing the subject up to 1919.
In the accurate measurement of electrical resistance, the device known as bridge) is employed. Ohm's law, which is one of the most fundamental principles in the science of electricity, states that in any circuit of con stant form, in which a constant electromotive force is acting and a uniform current is flowing, the current, resistance and electromotive force are connected by simple mathematical relation, which may be expressed in the following man ner: Let any two points in the circuit be selected, and let R be the resistance included be tween these points, as expressed in ohms. Let E be the electromotive force between these same points, as expressed in volts; and let C be the current between them, in amperes. Then the relation in question is C'==—, or E— CR.
To apply this principle to the measurement of resistances, let A and )3, in Fig. 2, be the two
points selected, and let the circuit be divided at these points, into the two branches AHB and AKB; the resistance of AH being P while that of NB is Q, that of AK is S and that of KB is T. The points H and K are to be connected, later, by means of a conductor, HGK, carrying a galvanometer, G; but for the moment the conductor HGK is assumed to be non-existent. Let us suppose that the difference in electromotive force between A arid B is E, while that between A and H is e. Then Ohm's law, when applied to the branch AHB as a whole, gives (P the cur rent flowing through the AHB. Sim ilarly, when applied to the section extending simply from A to H, Ohm's law gives e=mCiP. Eliminating C. from these two equations, we find that e, the electromotive force between the two points A and H, is equal to EP/(P Q). In the same way we may show that the differ ence of electromotive force between A and K in the branch AKB is equal to ES/(S ? T).
If the electromotive force between H and K is zero, then these two expressions are equal, and we have P/ (P -I-Q) =S/ (S T), which is equivalent to Cl/P.....T/S, or to PT... QS. If H and K are connected by a branch con ductor that includes a delicate galvanometer, G, then the galvanometer will indicate a current except when the electromotive force between H and K is zero; that is, it will show a current whenever the relation Pro= QS is not fulfilled. This arrangement of branch circuits, with a galvanometer bridging across from one of the branches to the other, constitutes "Wheatstone's bridge?' Its use for measuring resistances may be illustrated as follows: Let Q and T be two known resistances, and let P be the unknown resistance, whose value is to be determined. At S we introduce a "resistance box," which is merely a box containing an assortment of known resistances, so arranged that any or all of them can be conveniently thrown into the circuit or out of it. The resistance S is varied by trial until the galvanometer G ceases to show a deflection; and when this condition is fulfilled, we know that the equation PT = QS holds true. But we knew Q and T to start with, and we have determined S by trial ; so that we know three of the four resistances that enter the foregoing equation, and we can, there fore, calculate the fourth. Resistances may be determined, in this manner, with exceeding ac curacy. Consult for full details W. A. Price, 'Treatise on the Measurement of Electrical Re sistance) Ohm's law enables us to foresee, very easily, how the cells of a given battery must be ar ranged, in order to obtain the greatest possible current through a given, fixed conductor by which its terminals are to be joined. If the zinc electrode of each cell is joined to the car bon electrode of the next one, so that the cur rent has to pass through all the cells in succes sion, the battery is said to be arranged min series? The quantity of energy dissipated in the form of heat when a current traverses a con ducting circuit was investigated by Joule, and also by Lenz, Becquerel and others. It is found that the quantity of heat-energy set free in any given conductor in one second is pro portional (1) to the resistance of the conduc tor, and (2) to the square of the current that is flowing. If the resistance of the conductor is R ohms, and the current is C amperes, then the quantity of heat generated in T seconds will be 0.238 CRT calories; the "calorie' being defined as the quantity of heat required to raise the temperature of one gramme of water from 14° C. to 15° C. This is "Joule's law? Au.stir D. RISTEZN, PH.D.