TANGENT GALVANOMETER. 213 



from this follows 



IMG cos cos 



2 



HM sin cos ( - - - /3 + C 



When the angles a and /3 Q are very small, this is also the case 

 with the difference 8 5', and we have sensibly 



8 + 8' 



T H 8 + 8' 

 (n) I = tan + 



G 2 8 + 8' 



cos 



If the deflections themselves, 8 and 8', are very small, we may 

 again write 



H 8 + 8' 8 + 8' 



I = tan +e . 



G 2 2 



836. From what we have seen above (746), the factor of cor- 

 rection y, relative to a needle of magnetic length 2/, the middle of 

 which is on the axis at a distance x from the centre of the coil, has 

 the following value, if we confine ourselves to quantities of the 

 second order, 



3 a 2 - 4*2 ; . / 2 



an expression in which a is the mean radius of the coil, and u the 

 distance Ja 2 + x 2 . Equation (8) gives then, to the same degree of 

 approximation, 



i i 



8 + 8' 



or, for a needle in the centre of the coil, 



8 + 8' 



