TEERESTRIAL MAGNETISM. 707 



The values obtained by Koldewey in 1869 are, Inclination 

 79° 42', and the Total Intensity 5 ■ 8690 Gottingen units, that is, 

 11 '585 British units. 



In most of the expeditions to the Arctic regions the unifilar 

 magneiometer has been employed to determine the declination, 

 and the changes of declination, and also the earth's hori- 

 zontal magnetic force. Let F stand for the magnet which is 

 employed to determine the earth's horizontal force. For this 

 purpose it is necessary to determine the time of oscillation of the 

 magnet F, employed with its usual mounting, and to determine 

 it again when loaded with a ring or w^eight of known moment of 

 inertia. 



If t and t^ be the times of vibration of the magnet when free 

 and when loaded respectively, and I, Ij, be the moments of inertia 

 of the magnet and the weight added to it, then the observation 

 of the times t and t^ will give the moment of inertia of the magnet 

 by the formula 



If M be the magnetic moment of the magnet F, and X the 

 horizontal force of the earth, then the observation of the time of 

 vibration t will give the products MX, by the formula 



M 



The ratio ^ is given by the deflections produced by the magnet 



F when employed to produce deflections in another magnetic 

 needle. 



The formula is ^~^ where u is the deflection of the 



+ PM 



r" r 



suspended magnet, and r the distance between their centres. 



To determine the values p and q it is necessary to take observa- 

 tions for deflection at three different distances. (For details as to 

 the method see "Lloyd's Magnetism," p. 91, and "Admiralty 

 " Manual of Scientific Inquiry/' p. 96.) 



M 



A less approximate value of ^ is obtained by neglecting the 



fraction —4 in the above expression, in which case 

 M \ 7'^ sin u 



^~ 1 + ^ 



or - = 1 T^ sin u l\ — -^V where ^ is small. 

 A. V r^i r^ 



For this formula it is only necessary to take deflections at two 

 diflPerent distances ; but the results obtained will not be accurate 



unless -^ is very small. 



Y Y 2 



