Prof. A. Schuster on Magnetic Precession. 315 



quantity of positive electricity in unit volume the current- 

 density is 2qu, so that 



4^ 2 w 2 = i 2 , 

 /. 2g*p = m. 



The momentum of positive electricity will be ?nu or q/ii. 



If a mass moves relatively to a body which is rotating, we 

 may treat the effect of the rotation as being the same as 

 that due to certain fictitious forces. These fictitious forces 

 are of two kinds. The first, depending on the square of the 

 angular velocity and commonly called centrifugal force, will 

 act equally on positive and negative electricity, and cannot 

 therefore produce any effect on the distribution of electric 

 currents. The second force depends on the relative velocity, 

 it will therefore have opposite effects on positive and 

 negative electricity, in other words it will be equivalent to an 

 electromotive force. Its direction is at right angles both to 

 the direction of relative velocity and to the axis of rotation, and 

 its intensity per unit mass is equal to 2cov r sin ^, where co is 

 the angular velocity, v r the vector representing the relative 

 velocity, and % the angle between v r and the axis of rotation. 

 The direction of the force is such that the displacement of the 

 body through a right angle in the direction of rotation would 

 bring the direction of the force into the plane containing the 

 axis of rotation and the direction of relative velocity. 



If electric currents are confined to the surface of a sphere 

 rotating with an angular velocity ro, we may calculate the 

 components of electromotive force produced by the rotation 

 o£ the sphere, but it is only the tangential components which 

 will produce any effect. For any point on the earth which 

 has a colatitude 0, the horizontal components will be the 

 same, as if the angular velocity were (o cos 6 about the vertical. 

 If the flow is from north to south, the force will be to the 

 west in the northern hemisphere, and its intensity per unit 

 volume will be 2m© cos 0u$, u s denoting the velocity to the 

 south. For flow u-$ from west to east the force will be 

 2m&>'cos#KE and act from north to south in the northern 

 hemisphere. Hence, if w T e take the directions to south and 

 to east as the positive directions the two forces will be 

 — 2m© cos 6 us and + 2mco cos 6 « E - These are the forces per 

 unit volume; to obtain the forces per unit quantity of electri- 

 city we divide by g, and replacing the velocities of flow by 

 the current-densities we have for the two componems 



Y2 



