Constants of a Rectangular Galvanometer 



'91 



we have 



G = 



4 \/c 2 + d 2 ^k-d 2 + d 2 



cd 



(k-d)d 



which is easily seen to be a minimum when c — d. To avoid 

 cumbersome algebra, the square is chosen to illustrate several 

 o£ the theorems discussed below. There is no difficulty 

 whatever in extending the discussion to a rectangle. 



§ 4. But even so, for a given length o£ winding the square 

 shape is more advantageous as regards field-intensity at its 

 centre o£ symmetry than the circle. 



For at the centre of the circle we have 



a 

 And if a wire of length 2ira be formed into a square 



G 



, _4 v /2_16v/2 



giving 



ira/± 



ira 



g := i ^ 2 - 1 . 15 



<§ 5. It is desirable to discuss the variation in the field at 

 points near the centre of the square, as it is, of course, 

 necessary that the field in this neighbourhood shall be constant 

 to the first order of small quantities. 



Fiff. 2. 



/\ 



/ ^ 





T 



xcf c r 



Let us find an expression for the force at a point P on 

 the horizontal axis of a square of side 2c } and at a small 



3F 2 



