String Galvanometer of JEinthoven. 



209 



The mechanical force exerted upon an element of the 

 string ds, due to the mutual action of the current I and the 

 field H, is always perpendicular both to the field and the 

 direction of the elementary current, that is, it is in the 

 direction of the normal to the curve assumed by the string, 



IT 



and its value is HIds. Hence in (1) and (2) ^ = -; HI 

 takes the place of F, and we have 



/7T 



— -- 1 = 0, and T x = a constant throughout the (3) 

 as 



and 



length of the string, 



r = 



HI 



or r cc 



H 



W 



The curve assumed by the string carrying a steady direct 

 current when the field is uniform is, therefore, the arc of a 

 circle, and since the deflexions employed in practice are very 

 small compared with the length of the string, the radius of 

 curvature is correspondingly large. Let OL, figure 2, repre- 

 sent the chord of the string which forms the arc OBL with 





Fig. 2. 









* 



3 





o^ 





> " 



y^ 



^ 





c } 



P 



/ i 



y 





0' 



centre at 0', showing a small deflexion y at the centre of 

 the length. With 0' as origin, and abscissae parallel with 

 OL, the equation of the circle is 



Transferring the origin to 0, so that OL becomes the axis 

 of a, by putting 



x » m - g 



and jf = y + p, 



where 0'C = p, the equation of the circle is 



x 2 -lv+y 2 + 2p!, = (5) 



Phil Mag. S. 6. Vol. 28. No. 164. Aug. 1914. P 



