Physics. — ''The Limit of Sensitidenesa in the String galvanometer." 

 Bv Prof. I. K. A. Wekthejm Sai.omonsoin. 



(Communicated in the meeting of June 29, 1918). 



In Einthoven's stringgalvanometer tlie deflectioiial constant is 

 subjected to the same law as holds good in the movable needle- 

 and movable coil galvanometer: it is proportional to the square of 

 the periodic time of the movable part. In the string instruments 

 the duration of the oscillations is modified by altering the tension 

 of the string. The sensitiveness tinallj' depends on this tension as 

 well as on the dimension and material of the string, and lastlj' on 

 the strength of the magnetic field. 



The tension of the string can only be altered within certain limits. 

 The upper limit is given by a tensile stress exceeding the elastic 

 strength. The lower limit is the total absence of tension. But even 

 when no pull is exerted, the string can still vibrate transversally. 

 The frequency of the vibrations it then makes, is a function of the 

 dimensions of the wire and two properties of the material i.e. density 

 and the elasticity-modulus, and may be represented by 



m' d I /E 

 = ^7,1/ -•..-. . • (1) 



N 



g 



in which N denotes the frequency, / the length, d the diameter of 

 the string, g being the density and E Young's modulus, whereas 

 m is the smallest root of the transcendental equation co^mco5/M»=3 1. 

 The value 7/1 = 4.730... (Rayleigh On sound I. Art. 174). 



As we may discard the influence of temperature on the elasticity, 

 this formula gives the lowest frequency for transvei'se vibrations 

 obtainable in strings, which in a definite material and with given 

 dimensions cannot be lessened. We may therefore say that the 

 periodic time of the string in the Einthoven galvanometer, and 

 consequently the sensitiveness of the latter is limited by the impos- 

 sibilitj- to lessen the frequency ; and as the elasticity of the material 

 is responsible for transverse vibrations which might occur in a 

 perfectly relaxed wire, the true limit of the sensitiveness is to be 

 found in the elasticity, and as we shall see also in the density and 

 specific resistance of the material of the strings. 



With the formula (i) we can always calculate the minimum of 



