WEBER'S TANGENT GALVANOMETER. 239 



middle P of the needle in respect of the axis and of a right line 

 in the mean plane of the coil for its new position, we have first 



y = d sin 8', 

 x = d cos 8'. 



If the deflection 8 is very small, the components X and Y at 

 the point P of the action of the coil, which we suppose reduced 

 to the winding of mean radius a for unit current, may be calculated 

 as in 736. 



The expression for the couple produced on an infinitely small 

 needle is 



M ~Xcos(S + S') + Ysin(5 + S')~=M cos(8 + 8') ~X + Y tan (8 + S')~ . 



Replacing X and Y by their expansion in series as function of y, 

 and disregarding terms of a higher order than the second, we have 



2 U 



[cos 8' tan (8 + 8') 



If the needle is at some distance from the coil, we may in the 

 term of correction replace u by d, the sines and tangents by their 

 corresponding angles, and neglect the product of the square of the 



a 2 



deflection by the ratio ; we then get 

 d 2 ' 



X + Y tan (8 + 8') = 2^ |~i +^8'(8 - 8')1 . 



To allow for the length of the needle, this result is multiplied by 

 usual factor (746), which re 

 We get then the expression 



the usual factor (746), which reduces sensibly to i 3 . 



in which we shall replace u 2 by x 2 + a 2 = d* cos 2 8' + a 2 . 



