240 MEASUREMENT OF CURRENTS. 



Lastly, in order to proceed to the case of a coil, we will substitute 



a 2 

 for the principal factor 2?r , which represents the action of the 



coil on the axis at the distance x, the value of G given by 

 equation (12) of (729). 



The value of the factor D being thus calculated from the 

 dimensions of the coil and the distance of the needle, with the 

 corrections for the deflections and for the length of the needle, 

 the equations of equilibrium are then for the needle 



(29) IMD cos (8 + 8') = MH sin 8, 

 and for the coil 



(30) HIS cos 8' + IMD cos (8 + 8') = C sin 8' ; 



they only differ from equations (25) and (26) by the substitution 

 of D for G. 



In order to determine directly the term of correction relative 

 to the magnetisation of the needle, it is sufficient to fix it in its 

 original position, and observe the fresh deflection 8 l of the coil. 



Equation (30) gives, in that case, 8 = 0, 



CtanS^HIS 



we shall get from it the ratio - , as a function of the angles 



rib 



8, 8', and 8 l by an expression similar to equation (28). 



We should calculate in a similar way by the formulas of (795) 

 the experiments for the case in which the needle is in the mean 

 plane of the coil. 



To construct such an instrument, the coil is mounted so as to 

 be movable about a vertical axis provided with a graduated circle. 

 The needle is placed in a case itself movable about a vertical axis, 

 and supported by a carriage which slides along a divided scale. 

 The divided scale can finally also rotate about the same axis as_ 

 the mounting of the coil. 



It will easily be seen that these various arrangements enable us, 

 either directly or with rotations of 90 and appropriate reversals, 

 i, To place the mean plane of the coil in the meridian; 2, To 



