String Galvanometer of Einthoven. 223 



term only and the form of the string is a simple curve 

 of sines. 



This result may be obtained by so altering the field 

 distribution along the string as to make the string assume 

 the sine form. The conditions for this result may be 

 examined by the general differential equations of the string 

 (1) and (2). The equation of the string should he 



3/=J/osin™ (62) 



The force applied to the element of the string is always 

 perpendicular to the string, so cos% = 0, and the string 

 tension is constant at all points as was the case with the uni- 

 form field. By (4) we have 



T v 1 

 f= TE 



and, as r the radius of curvature is now variable, it follows 

 that H must vary inversely as r, the coefficient being con- 

 stant. The general expression for the radius of curvature 

 of any curve is 



Mm 



dx 2 

 Applying this to the sine curve (62), 



. 7TX 



sin T 



= 12^0 



z**°r\ . 7T 



1+ _ yo » COB ._J 



And since in practice -y y is a very small quantity 



compared with unity, the second term in the bracket may be 

 dropped, giving 



H = YT #o sin- l" ( bJ ) 



for the field distribution, which is as expected a curve of 

 sines having the maximum field at the centre of the string. 



This points to a possible improvement in the string 

 galvanometer to be brought about by tapering the pole- 

 pieces to increase the air-gap from the centre towards the 



