104 ELEMENTARY LESSONS ON [CHAP. n. 



124. Now, let us suppose that the deflection 8 were 

 produced by a magnetic force applied at right angles to 

 the magnetic meridian, and tending to draw the pole A 

 in the direction R A. The length of the line R T multi- 

 plied by the new force will be the " moment " of the 

 new couple tending to twist the magnet into the direction 

 E W. Now, if the needle has come to rest in equilibrium 

 between these two forces, it is clear that the two oppos- 

 ing twists are just equal and opposite in power, or that 

 the moment of one couple is equal to the moment of the 

 other couple. Hence, the force in the direction W E 

 will be to the force in the direction S N in the same 

 ratio as P Q is to R T, or as P O is to R O. 



Or, calling this force f, 



/: H = PO : RO 

 Or /=Hg 



But P O = A R and 4 = tan 8 hence 

 /= H tan 8; 



or, in other words, the magnetic force which, acting at 

 right angles to the meridian, produces on a magnetic 

 needle the deflection 8, is equal to the horizontal force of 

 the earths magnetism at that point, multiplied by the 

 tangent of the angle of deflection. Hence, also, two 

 different magnetic forces acting at right angles to the 

 meridian would severally deflect the needle through 

 angles whose tangents are proportional to the forces. 



This very important theorem is applied in the con- 

 struction of certain galvanometers (see Art. 1 99). 

 _.. The name Magnetometer is given to any magnet 

 specially arranged as an instrument for the purpose 

 of measuring magnetic forces by the deflections they 

 produce. The methods of observing the absolute 

 values of magnetic forces in dynes or other abstract 

 units of force will be explained in the Note at the end of 



