424 The Magnetic Fidd produced by Electric Currents [CH. xm 



the current be increased by an amount di, and let the corresponding change 

 in 6 be d6, then from equation (417), 



iG\ GH 



7/1 



so that if i is large, -yr is small. Thus, although the instrument may be 

 cw 



used for the measurement of large currents, the measurements cannot be 

 effected with much accuracy. 



A second defect of the instrument is caused by the circumstance that 

 the field produced by the current is not absolutely uniform near the centre 

 of the coil. If a is the radius of the coil, and 6 the distance of either pole 

 of the magnet from its centre, the poles will be in a part of the field in 



which the intensity differs from that at the centre of the coil by terms of 



53 

 the order of . For instance, if the magnet is one inch long, while the 



coil has a diameter of 10 inches, the intensity of the field will be different 

 from that assumed, by terms of the order of (j 1 ^) 3 , so that the reading will be 

 subject to an error of about one part in a thousand. 



By replacing the single coil of the tangent galvanometer by two or more 

 parallel coils, it is possible to make the field, in the region in which the 

 magnet moves, as uniform as we please. It is therefore possible, although 

 at the expense of great complication, to make a tangent galvanometer which 

 shall read to any required degree of accuracy. 



The Sine Galvanometer. 



494. The sine galvanometer differs from the tangent galvanometer in 

 having its coil adjusted so that it can be turned about a vertical axis. 

 Before the current is sent through the coil, the instrument is turned until 

 the needle is at rest in the plane of the coil. The coil is then in the direc- 

 tion of the earth's field at the point. 



As soon as a current is sent through the coil, the needle is deflected, as 

 in the tangent galvanometer. The coil is now slowly turned in the direction 

 in which the needle has moved, until it overtakes the needle, and as soon 

 as the needle is again at rest in the plane of the coil, a reading is taken, 

 giving the angle through which the coil has been turned. Let be this 

 angle, then the earth's field may be resolved into components, H cos 6 in 

 the plane of the coil arid H sin 6 at right angles to this plane. Since the 

 needle rests in the plane of the coil, the latter component must be just 

 neutralised by the field set up by the current, this being, as we have seen, 

 entirely at right angles to the plane of the coil. We accordingly have 



