Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/143

different positions of equilibrium for different values of the force. Hence, by means of a mirror attached to the magnet and throwing a spot of light upon a photographic surface moved by clockwork, a curve may be traced, from which the intensity of the force at any instant may be determined according to a scale, which we may for the present consider an arbitrary one.

460.] In an observatory, where a continuous system of registration of declination and intensity is kept up either by eye observation or by the automatic photographic method, the absolute values of the declination and of the intensity, as well as the position and moment of the magnetic axis of a magnet, may be determined to a greater degree of accuracy.

For the declinometer gives the declination at every instant affected by a constant error, and the bifilar magnetometer gives the intensity at every instant multiplied by a constant coefficient. In the ex periments we substitute for $\delta$, $\delta +\delta _{0}$ where $\delta ^{\prime }$ is the reading of the declinometer at the given instant, and $\delta _{0}$ is the unknown but constant error, so that $\delta ^{\prime }+\delta _{0}$ is the true declination at that instant.

In like manner for $H$, we substitute $CH^{\prime }$ where $H^{\prime }$ is the reading of the magnetometer on its arbitrary scale, and $C$ is an unknown but constant multiplier which converts these readings into absolute measure, so that $CH^{\prime }$ is the horizontal force at a given instant.

The experiments to determine the absolute values of the quantities must be conducted at a sufficient distance from the declinometer and magnetometer, so that the different magnets may not sensibly disturb each other. The time of every observation must be noted and the corresponding values of $\delta ^{\prime }$ and $H^{\prime }$ inserted. The equations are then to be treated so as to find $\delta _{0}$, the constant error of the declinometer, and $C$ the coefficient to be applied to the readings of the magnetometer. When these are found the readings of both instruments may be expressed in absolute measure. The absolute measurements, however, must be frequently repeated in order to take account of changes which may occur in the magnetic axis and magnetic moment of the magnets.

461.] The methods of determining the vertical component of the terrestrial magnetic force have not been brought to the same degree of precision. The vertical force must act on a magnet which turns about a horizontal axis. Now a body which turns about a horizontal axis cannot be made so sensitive to the action of small forces as a body which is suspended by a fibre and turns about a vertical axis. Besides this, the weight of a magnet is so large compared