CHAP, v.] ELECTRICITY AND MAGNETISM. 281 



NOTE ON MEASUREMENT OF EARTH'S MAGNETIC 

 FORCE IN ABSOLUTE UNITS. 



325a. The intensity of the earth's magnetic force at any place is 

 the force with which a magnet-pole of unit strength is attracted. 

 As explained in Art. 138, it is usual to measure the horizontal 

 component H of this force, and from this and the cosine of the 

 angle of dip to calculate the total force I, as the direct deter- 

 mination of the total force is surrounded with difficulties. To 

 determine H in absolute (or C.G.S.) units, it is necessary to 

 make two observations with a magnet of magnetic moment M ; 

 (the magnetic moment being, as mentioned in Art. 313, the 

 product of its length into the strength of one of its poles). In 

 one of these observations the product MH is determined by a 



method of oscillations ; in the second the quotient jj i s deter- 

 mined by a particular method of deflection. The square root of 

 the quantity obtained by dividing the latter by the former will, 

 of course, give H. 



(i.) Determination ofMH. The time / of a complete oscilla- 

 tion to-and-fro of a magnetic bar is 



t 27T 



where K is the "moment of inertia of the magnet, and g the 

 acceleration of gravity (in centimetres per second) at the place. 

 This formula is, however, only true for very small arcs of 

 vibration. By simple algebra it follows that 



--, 



** . 



Of these quantities / is ascertained by a direct observation of 

 the time of oscillation of the magnet hung by a torsionless fibre ; 

 and K can be either determined experimentally or by one of the 

 following formulae : 



For a round bar K w ( __ . SLY 



\I2 4/ 



(/2 _L l^\ 

 - / ' 



where w is the weight of the bar in grammes, / its length, a 



