TANGENT GALVANOMETER. 211 



they give by addition 



/8-8' \ TT 8 + 8' 8-8' 

 IG cos I ha ) = H tan cos 



If the difference 8 - 8' is so small that its square may be neglected, 

 the angle a is of the same order of magnitude, and we have sensibly 



TT g [ SV 



(10) I = tan -. 



When this simplification is inadmissible, equations (9) give 



_ H 2 (tan 8' - tan S) 2 + 4 tan 2 8 tan 2 8' 

 G 2 (tan 8' + tan 8) 2 



In both cases the mean of the deflections to the right and to the ' \~ 



left is taken as the value of G. 



835. If the needle is on a pivot, the friction, however small it is, 

 prevents it, in strict accuracy, from attaining its position of equili- 

 brium, and by no method can this cause of error be altogether 

 corrected. It is lessened by taking a very light needle, and making 

 it rest, by means of a polished agate cap, on a very fine steel point. 

 When the needle, through a very small angle, is deflected from its 

 position of equilibrium, it should revert to it within the limits of the 

 errors of reading. 



It is generally preferable to suspend the needle by a thread, 

 although the centring is less accurate. If the torsion of the wire 

 is not a negligeable quantity, it may be readily eliminated. When 

 the current is suppressed, the needle only sets exactly in the mag- 

 netic meridian provided the wire is without torsion. Let us assume 

 that it deflects through an angle /? ; if # is the angle through which 

 the wire must be twisted to bring the needle into the meridian, and 

 C is the coefficient of the wire, we have 



MHsin oS =C(0 -/3 ). 



If we turn the needle at the top through an angle 0, the needle 

 turns through an angle /?, and makes then the angle ft + /3 Q with the 



p 2 



