RESISTANCES TO THE CUREENT.—It is found that the dimensions and material of substances included in the circuit exercise an important influence on the strength of the current. It is of the greatest importance to ascertain the relative amount of the resist ance offered by conductors of various forms and materials. The rheostat, invented by Wheatstone, is generally employed for this purpose, and for this object is constructed so as to introduce or withdraw a considerable amount of highly resisting wire from the circuit without stopping the current. It is shown in fig. 7. Two cylinders, Cc C, about 6 in. in length, and 1 in. in diameter, are placed parallel to each other, both being movable round their axis. One of them, C', is of brass, the other, C, is of well dried wood. The wooden cylinder has a spiral groove cut into it, making forty turns to the inch, in which is placed a fine metallic wire. One end of the wire is fixed to a brass ring, which is seen in the figure at the further end of the wooden cylinder; and its other end is attached to the nearer end (not seen in the figure) of the brass cylinder, C'. The brass ring just mentioned is connected with the binding screw, S, by a strong metal spring. The further end of the cylinder C', has a similar connection with the binding screw, S'. The key. H, fits the project ing staple of either cylinder, and can consequently turn both. As the brass cylinder, C, is turned in the same direction as the hands of a watch, it uncoils the wire from the wooden cylinder,. C, making it thereby revolve in the same way. When the wooden cylinder is turned contrary to the bands of a watch, the reverse takes place. The num ber of revolutions is shown by a scale placed between the two, and the fraction of a revolution is shown by a pointer moving on the graduated circle, P. When the bind ing screws, S and S', are included within a circuit, say S with the positive, and S"with the negative pole, the current passes along the wire, on the wooden cylinder, 0, till it comes to the point where the wire crosses to the brass cylinder, C'; it then passes up the cylinder, C', to the spring and binding screw, S'. The resistance it encounters within the rheostat is met only in wire, for as soon as it reacbes the large cylinder, C', the resistance it encounters up to S' may be considered as nothing. When the rheostat is to be used, the whole of the wire is wound on the wooden cylinder; C, the binding screws are put into the circuit of a constant cell or battery along with a galvanometer, astatic or tangent. If, now, the resistances of two wires are to be tested, the galva nometer is read before the first is put in the circuit. After it is introduced, in conse quence of the increased resistance offered by it, the needle falls back, and then as much of the rheostat wire is unwound as will bring the needle back 4o its former place. The quantity of wire thus uncoiled in the rheostat is shown by the scales, and is manifestly equal in power to the introduced wire. The first is then removed, the rheostat
readjusted, and the second wire included, and the same unwinding goes on as before. To fix our ideas, let the quantity of wire unwound in the first case be 40 in., and in the second case CO in.; 40 in. of the rheostat wire offer as much resistance to the current as the first wire, and 60 in. of it as much as the second. We have thus 40 to CO as the ratio of the resistances of the two wires. The wire of the rheostat, from its limited length, can only be comparable with small resistances; and where great resistances are to be measured, supplementary resistance coils of wires, of a known number of ohms, are introduced into the circuit, or removed from it, as occasion requires, leaving to the rheostat to give, as it were, only the fractional readings. This being premised, it will be easily understood how the following results have been ascertained. It is proved, for instance, that the resistances of 'wires of the same material, and of 'uniform thickness, are in the direct ratio of their lengths, and in the inverse ratio of the squares of their diame ters. Thus a wire of a certain length offers twice the resistance of its half, thrice of its third, and so forth. wires of the same metal, diameters stand in the ratio of 1, 2, 3, etc., offer resistances which stand to each other as 1, 4, etc.; there fore, the longer the wire the greater the resistance; the thicker the wire the less the resistance. The same holds true of liquids, but not with the same exaet-Dess. For this reason, the larger the plates of a galvanic pair, and the nearer they are placed to each other, the less will' be the resistance offered to the current by the intervening liquid. The following table of the resistances, expressed in ohms. offered by a wire one meter long and one millimeter in diameter at 0' centigrade, has been determined by Dr. Mathiessen: Silver annealed, 0.01937; copper annealed, 0.02057; gold annealed, 0.02650; aluminum annealed, 0.03751; zinc, 0.07244; platinum annealed, 0.1166; iron annealed, 0.1251; tin, 0.1701; lead, 0.2526; mercury, 1.2247; German silver, 0.2695. With copper at 82° F. as 1, the following liquids stand thus! Saturated solution of the sulphate of copper, At 48' F„ 16,885,520; ditto of chloride of sodium at 56' F., 2,903, 638; sulphate of zinc, 15,861,207; sulphuric acid, diluted to Itr, itt 63° F., 1,032,020; nitric acid, at 55° F., 976,000; distilled water, at 59° F., 6,754,208.000. The slightest admixture of a foreign metal alters the resistance very decidedly: i per cent of iron in copper wire increases the resistance more than 25 per cent. It has been found also that the resistance offered by a wire increases. as its temperature rises. It is almost needless to add, that the conducting powers of metals are inversely as their specific resistances, the least resisting being the best conducting.