Page:Elementary Text-book of Physics (Anthony, 1897).djvu/374

360 '''304. Resistance.'''—As in the discussion of § 274, we may define the ratio of the electromotive force to the current in any circuit as the resistance in that circuit. The electromagnetic unit of resistance is the resistance of that circuit in which unit electromotire force gives rise to unit current, when both these quantities are measured in electromagnetic units.

In practice another unit of resistance is used, called the ohm. The true ohm contains 109 C. G. S. electromagnetic units. The dimensions of resistance in the electromagnetic system are $$[r] = \left[ \frac{e}{i} \right] = LT^{-1}.$$

The standard of resistance, usually called the B. A. unit, determined by the committee of the British Association, has a resistance somewhat less than the true ohm as it is here defined. In practical work resistances are used which have been compared with this standard. The Electrical Congress of 1884 defined the legal ohm to be "the resistance of a column of mercury of one square millimetre section and of 106 centimetres of length at the temperature of freezing." This definition has since been modified by increasing the length of the mercury column to 106.3 cm. The legal ohm contains 1.0112 B.A. units. Boxes containing coils of wire of definite resistance, so arranged that by different combinations of them any desired resistance may be introduced into a circuit, are called resistance boxes or rheostats.

305. Kirchhoff's Laws.—In circuits which are made up of several parts, forming what may be called a network of conductors, there exist relations among the electromotive forces, currents, and resistances in the different branches, which have been stated by Kirchhoff in a way which admits of easy application.

Several conventions are made with regard to the positive and negative directions of currents. In considering the currents meeting at any point, those currents are taken as positive which come up to the point, and those as negative which move away from it. In travelling around any closed portion of the network, those currents are taken as positive which are in Wie direction of motion, and those