57 MAGNETIC FIELD. 



is eliminated by difference. This is the experiment of Biot and 

 Savart (444). 



For greater strictness, it may be observed that the effective 

 magnetic moment of the needle, which is M (i+<H) in the ter- 

 restrial field, becomes M [i + <(H + F)] in the field H + F. If this 

 latter is of the order of the terrestrial field, the numbers of oscil- 

 lations N and N, relative to to the two experiments, give 



N'-Ng F I+< H2H + F) 



or, replacing H + F in the term of correction by its approximate 

 value, 



N 2 " 



The number N' of oscillations in the field H + F' gives an 

 analogous equation, and we finally get 



F M'-N'T 'N'-N i 



When the field F, instead of being parallel to the terrestrial 

 field, makes with it a small angle a, the resultant field R is given 

 by the equation 



The error made in taking R = H-f F is of the same order as 

 the square of the angle of deflection, and may therefore be neg- 

 lected provided the sum H + F is not very small, which would 

 correspond to two opposite fields. 



1142. METHODS OF TORSION. The magnetic needle being 

 suspended by a metal wire the coefficient of which is C, and 

 situate at first in the magnetic meridian, the torsion w is measured 

 which is necessary to bring it into a determinate direction. If it 

 is near the transverse position (721) the induced magnetisation 

 gives from symmetry a zero couple, and rigid magnetism alone 

 comes in. If w is the rotation of the milled head, and 6 the 



