direction of their resultant . The current in the coil causes the compass needle to rotate by an angle : From tangent law, , i.e. or or , where is called the Reduction Factor of the tangent galvanometer. One problem with the tangent galvanometer is that its resolution degrades at both high currents and low currents. The maximum resolution is obtained when the value of is 45°. When the value of is close to 0° or 90°, a large percentage change in the current will only move the needle a few degrees. Geomagnetic field measurement A tangent galvanometer can also be used to measure the magnitude of the horizontal component of the geomagnetic field. When used in this way, a low-voltage power source, such as a battery, is connected in series with a rheostat, the galvanometer, and an ammeter. The galvanometer is first aligned so that the coil is parallel to the geomagnetic field, whose direction is indicated by the compass when there is no current through the coils. The battery is then connected and the rheostat is adjusted until the compass needle deflects 45 degrees from the geomagnetic field, indicating that the magnitude of the magnetic field at the center of the coil is the same as that of the horizontal component of the geomagnetic field. This field strength can be calculated from the current as measured by the ammeter, the number of turns of the coil, and the radius of the coils. Astatic galvanometer Unlike the tangent galvanometer, the astatic galvanometer does not use the Earth's magnetic field for measurement, so it does not need to be oriented with respect to the Earth's field, making it easier to use. Developed by Leopoldo Nobili in 1825, it consists of two magnetized needles parallel to each other but with the magnetic poles reversed. These needles are suspended by a single silk thread. The lower needle is inside a vertical current sensing coil of wire and is deflected by the magnetic field created by the passing current, as in the tangent galvanometer above. The purpose of the second needle is to cancel the dipole moment of the first needle, so the suspended armature has no net magnetic dipole moment, and thus is not affected by the earth's magnetic field. The needle's rotation is opposed by the torsional elasticity of the suspension thread, which is proportional to the angle. Mirror galvanometer To