It would be a difficult matter to construct an instrument which should at once give the absolute value of the intensity, and its periodical changes ; but this object is readily attained by the application of the principle of the resolution of forces. For let 1' be the absolute value of the magnetic intensity, x and v its horizontal and vertical com ponents, 0 the inclination or dip : Then r = x sec 0 and r = x tan 0 Now, as we shall see, there is no difficulty in determining tho horizontal component x, and the inclination 0: hence, also, the vertical component Y and the total force r may be found.
Determination of the Hothontal Component of the Allognetic Force.— Thin element is obtained by a combination of two experiments made with an instrument called the Cnifilar Magnetometer. In the first experiment, the time of vibration of a suspended magnet is observed. In the second experiment we observe the amount of deflection which the same magnet produces in a second magnet suspended by a single thread.
Let T denote the time of vibration of a suspended magnet, deter mined much in the same way as the oscillation of a pendulum might be observed, that l7, by observing the time of the passing and repassing a fixed point on the magnet past a vertical line placed in the focus of a fixed telescope. Let et be the magnetie moment of the bar, K its moment of inertia, then by the principles of Dynamics we have fax= 0) Next let this same bar N a, be placed on a support in such a position that its axis lies in a straight line, passing through the centre of another magnet Si' s', suspended by a single thread, and its direction perpendicular to the axis of the latter magnet. Then the magnet Ns will deflect the magnet se s' from its normal position into a position N' s". Let u denote this angle of deflection N' c N", r the distance between the centres of the two magnets. Then the condition of equi librium will be given by the equation It is to be observed that the units of time, space, and mass referred to in these investigations, are by universal consent taken to bo, second, a foot, and a grain respectively.
But though we aro thus enabled to determine the absolute value of this horizontal component x, and, therefore, also the changes it under goes from time to time, yet it is not adapted to give those very minute changes which take place from hour to hour, and day to day. Such changes are called borary and diurnal variations ; and the instruments by which they are observed are called differential instruments. The variation in the horizontal force is denoted by the symbol .t x ; and is
observed by means of an instrument called a Bifilar .Magnetometer.
s is a magnet suspended by two threads hanging from a screw consists of a light magnet, N 5, with small holes at its extremities, across which fine threads are drawn in a horizontal position. Through the centre of the magnet is a knife-edge, C, perpendicular to the axis of the bar. This knife-edge is supported by two smooth agate planes, so as to free the motion of the magnet, as far as possible, from the effects of friction. The axis of the bar is placed in a position perpen dicular to the magnetic, meridian, thus rendering it. independent of the inclination or dip. A small shifting weight is attached to the magnet, and is so adjusted as to bring the axis lute a horizontal line for its normal position. Now it is evident that any change in the vertical force will deflect the bar from its horizontal position, and this deviation is viewed by means of two ordinary micrometers directed to the holes at N and 8. The change in the vertical force which corresponds to any number of revolutions of the micrometer screw may be found by absolute determination; hence, also, the changes due to one or more divisions are known—the zero reading of the micrometer corresponding to the normal position of the axis of the magnet, for which position the absolute value of the vertical component v has been carefully deter mined from the formula Y = x tan 8.
The Inclination or Dip is determined by means of a light magnet whose extremities taper to a point, and through the centre of which is a smooth cylindrical axle perpendicular to the plane iu which the axis of the magnet moves. This circle rests on two smooth agate planes, and thus the magnet moves freely in a vertical circle whose rim is graduated through each of the four quadrants from 0° to 90°. When used, the instrument is adjusted so that the plane of the graduated circle, together with the axis of the magnet, is in the plane of the magnetic meridian, previously determined. The needle now assumes the direction of the magnetic force at the place of observation, and the reading of the graduated circle opposite to either extremity of the magnet indicates the inclination of the axis of the needle to the horizon. In practice, the means of both readings are taken, and several pairs of observations made. These and many other precautions are adopted in order to eliminate, as far as possible, the mechanical defects in the instrument, and errors of observation.