802 Mr. A. Ferguson on the Construction and 



e 



This expression, then, gives the force at the centre of the 

 square due to the quadrant KPS. The force due to the two 

 linear elements RQ, QS, is (fig. 10) easily seen to be given by 



p_ 2 sin (yjr + <f>) _ 2 sin ^ 

 c c 



2 _ 2{c-a ) 

 \/2c qc 



2 2(c-a) 



Hence 



V'2c c\ / 2cVc — a 



= a/2 1 a_ = ft 



"c '2(T Cv /2* 



For the case of a single turn of wire wound on a square of 

 semi-side 20 cm., if we assume as an outside value a = l mm., 



then k= ^-r, and 



200 ' 



whence it easily follows that the error in the estimation of 

 the galvanometer constant due to the curvature at the corners 

 in this case amounts to less than one part in half-a-million, 

 and is therefore quite negligible. 



§ 15. It remains to consider the effect of temperature 

 changes on the value of the galvanometer constant. If we 

 assume 



G=G„(l + /30, 



then /3 may be defined as the increase in the value of the 

 galvanometer constant per unit field per uuit rise in tempe- 

 rature, due to the increase in dimensions of the rectangle. 

 Therefore, if a be the linear coefficient of expansion of the 

 material of the rectangle, we have 



G = ^Jl+^l 



c d 



