237 



the current strength in Webers (^ 10 am|)ere) and / the length ot 

 the wire in centimeters. If we put this value for P in 3): 



Hd* 

 h = ......... (4 



giving the deflection of the middle of a string clamped at the ends 

 without tension, and of a length / and a diameter d, placed in a 

 magnetic field //, as soon as a current of i Weber passes through 

 the string. We need hardly insist on the fact that this formula 

 gives the absolute limit for the sensibility for small currents. 



The next table II shows this limit for strings made of different 

 materials. For the dimensions of the string we again take 10 cm 

 and 1 micron, for the current-strength lO-^-' Weber (10"^^ ampere), 

 for the field intensity 10000 Gauss. The last column gives the 

 deflection in millimeters if the absolute deflection of the middle 

 be magnified 1000 times. We can use the figures of this column, 

 if we wish to calculate the possible deflection with strings of other 

 dimensions in a field of a different strength, and when observed 

 magnified to another scale. The deflections are proportional to the 

 fourth power of the length and the inverse of the diameter of the 

 string. 



TABLE II. 



1 



98100000 



De- \v^ mo-x,d=ui I 



flection^ /^ 10cm, /= 10-13 Weber J 



Cii 



Au 

 Al 

 Pt 



11000 

 7500 

 7500 

 6750 



16500 



4916.10-20 

 7210.10-20 

 7210.10-20 

 8012.10-20 

 3277.10-20 



49. 16 mm 

 72.10 „ 

 72.10 „ 

 80.12 „ 

 32.77 „ 



The figures in the last column may also serve to calculate figures 

 for existing strings. With an aluminium string of 2 microns and 

 56 millimeters' length in a field of about 16000 Gauss, 1 found a 

 deflection of 0.40 millimeters for 10—^- ampere, which took place 

 in about 20 seconds. From the figure in the table we calculate that 

 the deflection ought to be 1.20 millimetres. In Binthovkn's publica- 

 tions on silvered quartz fibres we equally find figures about the 

 possible sensibility, the order of which does not disagree greatly 

 with the theoretically possible deflection if we take for the sensitive- 

 ness with silvered quartz fibres the same value as in the case of silver 



