491-493] Galvanometers 423 



Before use, the instrument is placed so that the plane of the coil contains 

 the lines of magnetic force of the earth's field. The needle accordingly rests 

 in the plane of the coil. When the current is allowed to flow in the coil 

 a new field is originated, the lines of force being at right angles to the 

 plane of the coil, and the needle will now place itself so as to be in equi- 

 librium under the field produced by the superposition of the two fields the 

 earth's field and the field produced by the current. 



As the needle can only move in a horizontal plane, we need consider 

 only the horizontal components of the two fields. Let H, as usual, denote 

 the horizontal component of the earth's field. Let i be the current flowing 

 in the coil, measured in electromagnetic units, let a be the radius and let n 

 be the number of turns of wire. Near the centre of the coil the field 

 produced by the current is, by 489, a uniform field at right angles to 



the plane of the coil, of intensity - . The total 



CL 



horizontal field is therefore compounded of a field of 

 strength H in the plane of the coil, and a field of 



strength - - at right angles to it. 



FIG. 129. 

 The resultant will make an angle 6 with the plane 



of the coil, where 



/27mA 



' (416), 



lirin 



and the needle will set itself along the lines of force of the field. Thus the 

 needle will, when in equilibrium, make an angle with the plane of the 

 coil, where 6 is given by equation (416). If we observe 6 we can determine 

 i from equation (416). We have 



(417), 



where G is a constant, known as the galvanometer constant, its value 



T . 2?m 

 being - . 





The instrument is called the tangent-galvanometer from the circum- 

 stance that the current is proportional to the tangent of the angle 6. 



The tangent-galvanometer has the advantage that all currents, no matter 

 how small or how great, can be measured without altering the adjustment 

 of the instrument. A disadvantage is that the readings are not very sensi- 

 tive when the currents to be measured are large only a very small change 

 in the reading is produced by a considerable change in the current. Let 



