[Illustration: Fig. 518.--Diagram of forces acting on the needle of a tangent galvanometer.] A simple form of tangent galvanometer is shown in fig. 516. The coil of this instrument consists of a simple circle of stout copper wire from ten to fifteen inches in diameter. At the center is delicately suspended a magnetized steel needle not exceeding one inch in length, and usually furnished with a light index of aluminum. When the galvanometer is in use, the plane of the ring must be vertical and in the magnetic meridian. A horizontal section through the middle of the instrument is shown in fig. 517. For simplicity, the coil is supposed to have but a single turn of wire, the circles surrounding the wire representing the magnetic lines of force. By extending the lines of force until they reach the needle, it will be seen that with a short needle, the deflecting force acts in an east and west direction when the galvanometer is placed with its coil in the magnetic meridian. If, in fig. 518, _ab_ represent the deflecting force acting on the N end of the needle, the component of this force that acts at a right angle to the needle will be _ab_ cos _x_ in which, _x_ is the angle of the deflection. The controlling force is _ad_ = H and when the needle is in equilibrium, the component _ae_ = H sin _x_ is equal and opposite to _ac_, hence _ab_ cos _x_ = H sin _x_ from which _ab_ = H(sin _x_ / cos _x_) = H tan _x_ Since _ab_ is proportional to the current, _ab_ = _k_ C = H tan _x_ in which _k_ is a constant depending upon the instrument. For any other current C', _k_ C' = H tan _x'_ hence C: C' = tan _x_ : tan _x'_ This means that the currents passing through the coil of a tangent galvanometer are proportional, not to the angle of deflection, but to the tangent of that angle. [Illustration: Fig. 519.--Diagram illustrating the tangent law. This is the law of the combined action of two magnetic fields upon a magnetic needle. If two magnetic fields be at right angles in direction as indicated in the figure, the resultant field is obtained by the parallelogram of forces and it makes an angle [theta] with one of the component fields such that tan [theta] = M + H where M and H are the strengths of the component fields. In the tangent galvanometer this principle is employed in the measurement of currents. A magnetic needle is pivoted in a field of known strength. The current to be measured is passed round a coil (or coils) which generates a field at right angles to the original field. The needle then lies along the direction of the resultant field, and by finding the tangent of its angle of deflection, and knowing the field strength produced by unit current in the coil, the current strength can be found.]