210 Dr. A. C. Crehore on the Tlwory of the 



And from the properties of the circle, 



Hence the radius 



v_ , ;vo 



^+f (6) 



This expression for the radius together with that already 

 found in (4) gives the tension 



\ $Vn 2 / 



In practice the deflexions are small and the second term 

 may be omitted, giving 



T I= ™ (7) 



This expression involves three quantities Z, I, and y , which 

 may be accurately and easily measured. H and T x are not as 

 readily measured directly. If, however, H is determined for 

 one string and one strength of field, it remains the same for 

 any other string. The tension cannot be measured directly 

 with a fine quartz fibre, but if a fine wire is substituted for 

 the fibre, the upper end being fastened to the same point as 

 the fibre, and the lower end passed through a V-groove held 

 in the same position as the lower end of the fibre, weights 

 may be suspended from the wire and the tension thus 

 directly measured. By this device the field strength is found 

 from (7), and it has the advantage that the average value is 

 measured in just the same position as the fibre occupies, 

 so that when the fibre is replaced its tension is indirectly 

 measured by a knowledge of H. 



The order of magnitude of the deflexion and the radius of 

 curvature may be obtained from an actual case. With a 

 magnification of 900, and a deflexion of the shadow of the 

 centre of the string of 3 cm., and length of string 14 cm., the 



deflexion y = qaa = '00333 cm. ; and ^— = 7350 cm. The 



radius of the arc formed by the string is therefore 73 # 5 

 metres. 



Solving (5) for y and using the positive sign before the 

 radical, we find as the equation of the circular arc formed by 

 the string 



y = — p -f ( — # 2 -f fa -f p 2 )*. 



