CHAP, in.] ELECTRICITY AND MAGNETISM. 165 



small its poles are never far from the centre, and hence 

 never protrude into the regions where the magnetic force 

 is irregular. Whatever magnetic force the current in 

 the coil can exert on the needle is exerted normally to 

 the plane of the ring, and therefore at right angles to 

 the magnetic meridian. Now, it was proved in Art. 124 

 that the magnetic force which, acting at right angles to 

 the meridian, produces on a magnetic needle the de- 

 flection 8 is equal to the horizontal force of the earth's 

 magnetism at that place multiplied by the tangent of the 

 angle of deflection. Hence a current flowing in the coil 

 will turn the needle aside through an angle such that the 

 tangent of the angle of deflection is proportional to the 



strength of the current. j% 

 jf 



EXAMPLE. Suppose a certain battery gave a deflection of 

 15 on a tangent galvanometer, and another battery 

 yielding a stronger current gave a deflection of 30. The 

 strengths currents are not in the proportion of 15 : 30, 

 but in the proportion of tan 15 to tan 30. These 

 values must be obtained from a Table of natural tangents 

 like that given on p. 1 1 1 , from which it will be seen 

 that the ratio between the strengths of the currents is 

 268 : -577, or about 10 : 22. 



Or, more generally, if current C produces deflection 5, and 

 current C' deflection 5', then 



C : C' = tan d : tan d' 



To obviate reference to a table of figures, the circular 

 scale of the instrument is sometimes graduated into 

 tangent values instead of being divided into equal 

 degrees of arc. Let a tangent O T be drawn to the 

 circle, as in Fig. 90, and along this line let any number 

 of equal divisions be set off, beginning at O. From 

 these points draw back to the centre. The circle will 

 thus be divided into a number of pieces, of which those 

 near O are nearly equal, but which get smaller and 

 smaller away from O. These unequal pieces correspond 



