the Unipolar Induction of the Earth. 499 



§4. 



(a) A round steel magnet, 125 millim. long and 10 millim. 

 in diameter, concentrically surrounded by a cylinder of brass, 

 was fixed in a vertical position upon a rotatory apparatus, by 

 means of which the magnet and cylinder could be put into 

 uniform rotation about their common axis. Two brass springs 

 press upon the cylinder, the one above one of the poles, the 

 other midway between the poles. These springs were con- 

 nected with a galvanometer, the deviations of which were read 

 by means of a telescope and scale in the usual manner. The 

 radius p of the cylinder was 0175 metre, and /, or half the 

 distance between the poles, was fixed at 0*062 metre. When 

 the magnet with its envelope performed five complete revolu- 

 tions per second, a current was obtained which gave a constant 

 deflection of 102*0 divisions of the scale. The resistance in 

 the entire circuit was 21*4 ohms. With a resistance of 

 100,000 ohms, one Daniell cell gave a deflection of 419*5 

 divisions. Consequently the electromotive force of unipolar 



5*2033 

 induction was D = A, where D denotes, as usual, the 



electromotive force of a Daniell cell. 



(b) In order to determine the ratio between the magnetic 

 moment of this same steel magnet and the horizontal compo- 

 nent of the earth's magnetism, the magnet was placed, as de- 

 scribed above, at right angles to the magnetic meridian, so as 

 to produce a deflection in a small magnetized needle suspended 

 by a silk fibre, the deviation of this needle being read in the 

 ordinary way by means of reflection. The observations (which 

 were made in the court of the buildings of the Academy of 

 Sciences, to avoid all disturbing influences of magnetic sub- 

 stances) gave the following results: — 



For a = 0'724 metre we obtain u=2° 41' 5", 

 For a= 1*046 „ „ u = 0° 52' 20 v ; 



whence we have in the first case - — ^ = 56*19 metres, and in 



a 6 



cot IjL 



the second — g— = 57'40 metres, giving a mean of 56*8 metres. 



The horizontal intensity of terrestrial magnetism at the 

 equator may be taken as twice that at Stockholm; and the 

 above calculation being for a point on the earth's surface at 

 the equator, this result must be multiplied by 2, giving 113*6 

 metres. 



According to the values given for I and p, __ will be 



