Constants of a Rectangular Galvanometer 



795 



by replacing each turn of the coil by a thin strip in breadth 

 equal to the over-all diameter of the wire, the error is 

 proportionately less and may be neglected. It is to be 

 remembered, however, as a consequence of the equivalence 

 of the coil and the current-sheet just mentioned, that the 

 breadth 2p of the coil-windings is to be interpreted as 

 meaning the total breadth of the coil measured from the 

 outside of the insulation of the first turn to the outside of 

 the insulation of the last turn. 



§ 10. If the galvanometer be constructed of several layers 

 of wire wound on a square frame and filling a rectangular 

 trough of breadth 2p perpendicular to the plane of the coil 

 and depth 2b parallel to the plane of the coil, its constant is 

 readily calculated by methods analogous to those of § 7. 

 Let 2d be the dimensions of the inner layer, as before. 



Fig. 5. 



"7 — ~ 



— -^ J- ^y 



Taking axes as shown in fig. 5, let dxdy be an element 

 of area whose coordinates are (x,y)* The current through 

 dxdy is in dxdy, where n is the number of turns of wire 

 per unit area. And the force at due to the " elementary" 

 square of side 2y is, by equation (ii.) 



d^= 



\indxdyif 

 * / a? + 2y 2 ~ 



u 2 +*/ 2 r 



T d+26 r»+p 



y 2 dx dy 



= Sin I (say) . 

 Hence, if N be the total number of turns^ 

 N = 4:npb 

 2NI 



and G = 



P b 



