CHAPTER VIII.

THE COMPARISON OF RESISTANCES.

WE give here some account of methods for the com

parison of the resistances of conductors in which steady currents are kept flowing. In most cases the conductor to be compared is arranged in a particular way in connection with other conductors, which are then adjusted so as to render the current through a certain conductor of the system zero. From the known relation of the resistances of the other conductors the required comparison is deduced.

The form of galvanometer generally employed in the measurement of resistances is the reflecting galvanometer invented by Sir William Thomson, one arrangement of which is shown in Fig. 42. For most purposes the ordinary form of the instrument can be used. In this a mirror of silvered glass to which the needle-magnets are cemented at the back is hung within a cylindrical cell about half a centimetre in diameter. The ends of the cylinder are closed by glass plates from four to five millimetres apart, held in brass rings which can be screwed out or in so as to increase or diminish the length of the cell. The mirror is hung by a piece of a single silk fibre passed through a small hole in the cylindrical

surface of the chamber and fixed there with a little shellac. The mirror is only of slightly smaller diameter than the cylinder in which it hangs, so that in this

arrangement the fibre is very short, rendering it necessary in cases in which deflections have to be read off to allow for the effects of torsion. The cylindrical chamber is

FIG. 42.

screwed into one end of a cylinder of slightly greater diameter which fits the hollow core of the coil, and is called the galvanometer-plug. When the plug is in position the mirror hangs freely within its cell, with therefore the point of suspension on the highest generating line of the cylinder. Deflections of the needle are observed either by the Poggendorff telescope method, or, and much more generally, by the ordinary projection method described on pp. 7 and 8 above.

The weight of the needle and mirror is under one grain, and hence the period of free vibration of the suspended system about any position of equilibrium is short. The needle is also made to come quickly to rest by the smallness of the chamber in which it hangs. Since the mirror nearly fills the whole cross-section of the cell, the air damps the motion of the mirror to a very great extent even when the cell has its largest volume. The mirror may be made quite dead-beat," ," that is, to come to rest without oscillation, by screwing in the front and back of the cell until the space is sufficiently limited.

In instruments in which it is desirable to avoid effects of torsion the galvanometer coil is made in two lengths which are fixed end to end, with a narrow space between them to receive the suspension piece. This piece forms a chamber in which the needle hangs between the two halves of the coil, and gives a length of fibre which at shortest is equal to the radius of the outer case of the coil, and which can obviously be made as long as is desired. The part of the hollow core at the needle is closed in front and at back by glass plates carried by brass rings, These can be screwed in or out by a key from without so as to diminish or increase the size of the chamber, and

thus render the needle system more or less nearly "deadbeat."

We shall suppose the galvanometer set up so that the deflections are read by the ordinary deflection method. It is only necessary to arrange that the needles when no current is flowing in the wires shall hang parallel to the plane of the coils. This is done as follows. A straight thin knitting wire of steel is magnetized and hung by a single silk fibre of a foot or so in length. This can easily be done by taking a sufficiently long single fibre of silk and forming a double loop on one end by doubling twice and knotting. In this double loop, made widely divergent, the steel wire is laid horizontally, and the single end of the fibre is attached to a support carried by a convenient stand, which is then placed so that the wire takes up a position in the direction of the horizontal component of the magnetic field where the needle is to be placed. A line can now be drawn parallel to the wire on the table beneath it. All that is necessary then is to place the galvanometer so that the front and back planes of the coil are vertical and parallel to this line, and adjust the lamp and scale as described above.

It is sufficient for our present purpose to state that if the needles be so small as in the Thomson reflecting galvanometer, and torsion can be neglected, the current in the coil may be taken as proportional to the tangent of the deflection angle, and therefore if that angle be not greater than three or four degrees the current may, with an error not greater than ✈ per cent., be taken as proportional to the deflection simply.

The galvanometer should be made as sensitive as possible by diminishing the directive force on the needle as

far as is practicable without rendering the needle unstable. This is easily done by placing magnets near the coil so that the needle hangs, when the current in the coil is zero, in a very weak magnetic field. That the field has been weakened by any change in disposition of the magnets, made in the course of the adjustment, will be shown by a lengthening of the period of free vibration of the needle when deflected for an instant by a magnet and allowed to return to zero. The limit of instability has been reached when the position of the spot of light for zero current changes from place to place on the scale, and the intensity of the field must then be slightly raised to make the zero position of the needle one of stable equilibrium.

Although not absolutely essential, except when accurate readings of deflections are required, it is always well when the field is produced by magnets, to arrange them so that the field at the needle is nearly uniform. It may therefore be produced by two or more long magnets placed parallel to one another at a little distance apart symmetrically with respect to the centre of the needle above or below it, and with their like poles turned in the same directions; or a long magnet placed horizontally with its centre over the needle, and mounted on a vertical rod so that it can be slided up or down to give the required sensibility, may be used.

Sensibility is sometimes obtained by the use of astatic galvanometers, but these are rarely necessary and are more troublesome to use than the ordinary non-astatic instrument.

For the comparison of the resistances of conductors other resistances the relations of which are known are employed. These are generally coils of insulated wire