TERRESTRIAL MAGNETISM 311 



In using the last method, a graduated horizontal cross bar 

 about a metre long is fixed at right angles to, and just under, the 

 torsion box. A carriage slides along this bar to carry the deflect- 

 ing magnet, and the distance d is read on the scale of the bar. 

 To measure a short magnet provided with a mirror is suspended 

 in the torsion box of Fig. 224 to serve as the deflected magnet. 

 A telescope with a scale attached replaces the telescope used in 

 the declination experiment to fix the position of this deflected 

 magnet. The deflected magnet is first suspended and its position 

 is observed when the deflecting magnet is not acting. The reading 

 of the horizontal circle at the base of the instrument is also to be 

 taken. The deflecting magnet is then put in position at a distance 

 indicated as d on the bar scale and the instrument, with the 

 telescope, is turned round until the deflected magnet appears in the 

 same position in the field of the telescope. The horizontal scale 

 at the base is again read, and the difference in readings gives 

 the deflection 0. If the observed d were the actual d this would 

 suffice in so far as the simple formula holds. But the centre of the 

 magnet may not coincide with the index mark on the carriage. 

 The deflected magnet is therefore turned end for end. The deflec- 

 tion is now reversed and the mean value eliminates error of 

 centering of the deflecting magnet. The graduation of the bar 

 may not date from a point exactly under the centre of the deflected 

 magnet. The deflecting magnet is therefore moved on its carriage 

 to the other side of the bar to the distance marked as d, and the 

 deflections are again taken with the magnet in its last position on 

 the carriage and when it is turned end for end. We have then 

 four values of the deflection, and the mean eliminates the errors 

 considered. 



But the formula for the deflecting force - is only approxi- 

 mate. A nearer approximation is given by * 



where P depends on the distribution of magnetisation along the 

 magnet. We may eliminate P by taking another value of the 

 deflection 0' at another distance d' and it is easily found that 



H 2 (d* - 



M == d 5 sin - d 6 sin & ' 



TT 



The error in the determination of ^ is a minimum if the value 



7/ 



of -r is about 1 *3. 

 a 



* Maxwell, Electricity and Magnetism, vol. ii., 3rd ed., p. 106. 



