the Unipolar Induction of the Earth. 497 



passed over by the conductor, and the angle which the direc- 

 tion of movement makes with the lines of force. Now, as we 

 have already said, the positions of the lines of force and the 

 intensity of the magnetic field are independent of the circum- 

 stance whether the magnet is, or is not, in rotation on its axis. 

 It follows, therefore, that the electromotive force of induction 

 produced in the moving conductor is altogether independent of 

 the rotation of the magnet on its axis. 



After this preliminary exposition we may pass on to the 

 principal subject of this memoir. 



§3. 



If we only w T ish to calculate roughly and in general terms 

 the effect of the unipolar induction of the earth, we may assume, 

 for the reason considered in the memoir quoted, that the mag- 

 netic phenomena of our globe are produced by a magnet which 

 traverses the centre of the earth at an angle of 17° with the 

 axis of rotation. For the following argument we may suppose, 

 for the sake of greater simplicity, without introducing any 

 error affecting the result, that the magnet imagined is coinci- 

 dent with the axis of rotation. The magnitude of the uni- 

 polar inductive action of the earth upon a vertical prism of 

 unit section and length Ar, situated at the equator in the 

 neighbourhood of the terrestrial surface, may then be deter- 

 mined as follows : — 



Let r be the radius of the earth, 2p the distance between 

 the poles of the terrestrial magnet, M the magnetic intensity 

 of these poles, co the velocity of rotation of a point upon the 

 surface of the earth under the equator, and k a constant, we 

 obtain, by the method explained in the memoir quoted, as the 

 value of the force a, by which unipolar induction tends to urge 

 the aether (positive electricity) of the prism Ar in the direc- 

 tion of the terrestrial radius, 



_2kMpcoAr /n 



*~(r 2 + p 2 )f ' 



In this equation k, M, and p are unknown quantities. If we 

 suppose that the radius of the equation is ^-q longer than that 

 of the axis, co will be equal to 466 metres per second, the time 

 of rotation of the earth being 23 hours 56 minutes. 



The horizontal component of terrestrial magnetism under 

 the equator exercises upon a magnetized needle capable of 

 motion in a horizontal plane, and forming the angle u with the 

 magnetic meridian, a directive force, which, when the poles 

 are distant 2\ from each other and have an intensity //,, may 



