THE MEASUREMENT OF ELECTRIC RESISTANCE

209*.] In the present state of electrical science, the determination of the electric resistance of a conductor may be considered as the cardinal opera- tion in electricity, in the same sense that the determination of weight is the cardinal operation in chemistry.

The reason of this is that the determination in absolute measure of other electrical magnitudes, such as quantities of electricity, electromotive forces, currents, &c., requires in each case a complicated series of operations, in- volving generally observations of time, measurements of distances, and de- terminations of moments of inertia, and these operations, or at least some of them, must be repeated for every new determination, because it is impossible to preserve a unit of electricity, or of electromotive force, or of current, in an unchangeable state, so as to be available for direct comparison. But when the electric resistance of a properly shaped conductor of a prop- erly chosen material has been once determined, it is found that it always re- mains the same for the same temperature∗ , so that the conductor may be used as a standard of resistance, with which that of other conductors can be com- pared, and the comparison of two resistances is an operation which admits of extreme accuracy.

When the unit of electrical resistance has been fixed on, material copies of this unit, in the form of ‘Resistance Coils,’ are prepared for the use of electricians, so that in every part of the world electrical resistances may be expressed in terms of the same unit. These unit resistance coils are at present the only examples of material electric standards which can be preserved, copied, and used for the purpose of measurement. Measures of electrical capacity, which are also of great importance, are still defective, on account of the disturbing influence of electric absorption.

210*.] The unit of resistance may be an entirely arbitrary one, as in the case of Jacobi’s Etalon, which was a certain copper wire of 22·4932 grammes ∗ [Recent observations have shewn that it is far from easy to find a material satisfying this condition.]UNIT OF RESISTANCE.

weight, 7·61975 metres length, and 0·667 millimetres diameter. Copies of this have been made by Leyser of Leipsig, and are to be found in different places. According to another method the unit may be defined as the resistance of a portion of a definite substance of definite dimensions. Thus, Siemens’ unit is defined as the resistance of a column of mercury of one metre long, and one square millimetre section, at the temperature 0°C.

211*.] Finally, the unit may be defined with reference to the electrostatic or the electromagnetic system of units. In practice the electromagnetic system is used in all telegraphic operations, and therefore the only systematic units actually in use are those of this system.

In the electromagnetic system a resistance is a quantity homogeneous with a velocity, and may therefore be expressed as a velocity.

212*.] The first actual measurements on this system were made by Weber, who employed as his unit one millimetre per second. Sir W. Thomson after- wards used one foot per second as a unit, but a large number of electricians have now agreed to use the unit of the British Association, which professes to represent a resistance which, expressed as a velocity, is ten millions of metres per second. The magnitude of this unit is more convenient than that of Weber’s unit, which is too small. It is sometimes referred to as the B.A. unit, but in order to connect it with the name of the discoverer of the laws of resistance, it is called the Ohm.

213*.] To recollect its value in absolute measure it is useful to know that ten millions of metres is professedly the distance from the pole to the equator, measured along the meridian of Paris. A body, therefore, which in one second travels along a meridian from the pole to the equator would have a velocity which, on the electromagnetic system, is professedly represented by an Ohm. I say professedly, because, if more accurate researches should prove that the Ohm, as constructed from the British Association’s material standards, is not really represented by this velocity, electricians would not alter their standards∗ , but would apply a correction. In the same way the metre is pro- fessedly one ten-millionth of a certain quadrantal arc, but though this is found not to be exactly true, the length of the metre has not been altered, but the

[Electricians have scarcely acted up to this principle in the reform of the Ohm.]STANDARD RESISTANCE COILS.

dimensions of the earth are expressed by a less simple number. According to the system of the British Association, the absolute value of the unit is originally chosen so as to represent as nearly as possible a quantity derived from the electromagnetic absolute system.

214*.] When a material unit representing this abstract quantity has been made, other standards are constructed by copying this unit, a process capa- ble of extreme accuracy—of much greater accuracy than, for instance, the copying of foot-rules from a standard foot. These copies, made of the most permanent materials, are distributed over all parts of the world, so that it is not likely that any difficulty will be found in obtaining copies of them if the original standards should be lost. But such units as that of Siemens can with- out very great labour be reconstructed with con- siderable accuracy, so that as the relation of the Ohm to Siemens unit is known, the Ohm can be reproduced even without having a standard to copy, though the labour is much greater and the accuracy much less than by the method of copying.

Finally, the Ohm may be reproduced by the electromagnetic method by which it was origi- nally determined. This method, which is con- siderably more laborious than the determina- tion of a foot from the seconds pendulum, is probably inferior in accuracy to that last men- tioned. On the other hand, the determination of the electromagnetic unit in terms of the Ohm with an amount of accuracy corresponding to the progress of electrical science, is a most im- portant physical research and well worthy of be- Fig. 44. ing repeated.

The actual resistance coils constructed to represent the Ohm were madeFORMS OF RESISTANCE COILS. 199 of an alloy of two parts of silver and one of platinum in the form of wires from ·5 millimetres to ·8 millimetres diameter, and from one to two metres in length. These wires were soldered to stout copper electrodes. The wire itself was covered with two layers of silk, imbedded in solid paraffin, and enclosed in a thin brass case, so that it can be easily brought to a temperature at which its resistance is accurately one Ohm. This temperature is marked on the insulating support of the coil. (See Fig. 44.)