SCIENCE AND PRACTICE. 



241 



needle occupying the apex of a cone having the circular 

 current for a base, the tangents of the angles of deflection 

 are almost strictly proportional to the intensities, when the 

 height of the cone is equal to a quarter of the diameter of 

 the base. 



17. Sine Galvanometers. When the needle is deflected from 

 the magnetic meridian by the action of the ring or coil, we 

 have seen that the force n c with which the earth's mag- 

 netism strives to bring the needle back to the line n s is 

 equal to the product of the directive force, M, of the earth's 

 magnetism on the needle and the sine of the angle of 

 deflection, or 



n c M sin. a, 



and n' c=n d. M sin. a is therefore the value of each of the 

 forces which pull in opposite directions 

 and between which the needle comes to 

 rest. If the convolutions of the ring, 

 which have been hitherto supposed to 

 remain in the same plane, be turned 

 round the vertical axis of the galvano- 

 meter in the direction of the needle, the 

 latter will be deflected still farther from 

 the meridian, but always through a less 

 angle than that through which the coil is 

 turned after it. Hence, in time, a point 

 is reached where the plane of the coil 

 coincides with the direction of the needle, 8i 

 or they are parallel to each other. 



Let this be now the position of things 

 in Fig. 124, the needle in the position n 

 parallel to it having been turned through the angle a ; 

 the force with which the coil deflects the needle is now not 

 only at right angles to its own plane, but also to the direc- 

 tion of the needle, and is represented, directly, by the line 

 n d, which is also the expression of the current moving in 

 the coil, whilst that part of the earth's magnetism which 

 balances this force is n c, as before. 



R 



Fig. 124. 

 and the coil 



