Page:Elementary Text-book of Physics (Anthony, 1897).djvu/372

358 this form it consists of a circular conductor set up in the earth's magnetic field, so that its plane is parallel with the lines of force, and having a small magnet placed at its centre. The magnet is free to swing in the horizontal plane. If the current $$i$$ be sent through the circuit, the couple which it will exert on the magnet, on the supposition that the magnet is so short that the force at its poles is the same as that at its centre, is $$\frac{2\pi i M}{r} \cos \phi$$ (§ 396), where $$M$$ represents the magnetic moment of the magnet, and $$\phi$$ the angle made by the axis of the magnet with the direction of the lines of force. The couple exerted by the field upon the magnet and tending to turn it in the opposite sense is $$HM \sin \phi,$$ where $$H$$ represents the horizontal intensity of the earth's magnetism. Equilibrium will obtain, and the magnet will be at rest, when these couples are equal, or when $$\frac{2\pi i M}{r} \cos \phi = HM \sin \phi.$$ From this equation we obtain The current is therefore proportional to the tangent of the angle of deflection. All the quantities in this expression for current, except $$H,$$ are either numbers or lengths and may be directly measured; and $$H$$ may be determined in absolute units (§ 244). The tangent galvanometer therefore permits of the determination of current strength in absolute units.

In the more complicated forms of the instrument, the dimensions and position of its parts are so adjusted that the corrections rendered necessary by the impossibility of fulfilling the conditions assumed in the simple case may be either calculated or avoided.

Weber's electro-dynamometer is an instrument with fixed coils like those of the tangent galvanometer, but with a small suspended coil substituted for the magnet. The small coil is usually suspended by the two fine wires through which the current is introduced into it, and, the moment of torsion of this so-called bifilar suspension enters into the expression for the current strength. The same current is sent through the fixed and the movable coils, and a