238 



wires. The same maj' be said about ray own observations with 

 quartz fibres. Generally (he deflection actually observed is some 

 3—5 times smaller than we onglit to expect from the theory. The 

 explanation is found when we consider the behaviour of silver strings 

 of 16.5 microns and of copper strings of 15 microns diameter. These 

 wires still give vibrations when the tension is reduced as far as 

 possible, but in every case the frequency is about 1.5 to 2.1 

 times greater than that calculated from formula (1). With a silver 

 string of 16.5 (i and 53 mm length I could not reduce the frequency 

 under 20 per second instead of 14 as calculated. When magnified 

 47 times 1 microampere caused a deflection of 1.31 millimeter; the 

 string being placed in a field of 14000 Gauss. The theoretical value 

 is 3.7 millimetres with 14 vibrations, which would come to about 

 1.8 millimeters with 20 vibrations. As there may be a slight difïer- 

 ence between the figure taken for the diameter and the actual 

 diameter, the agreement may be considered not unsatisfactory, the 

 more so as the value of I'^ must also be considered as merely an 

 approximate one. Finally we must state that the string was not an 

 entirely straight one, and that in being mounted it had probablj' 

 retained a slight torsional stress. 



In a few other observations of the same kind with wires of 

 difFerent material I found a deflection of 8.1 mm where 9.1 mm 

 was expected ; also one of 36 mm, where 40 had been calculated. 

 Generally speaking, the agreement was by far the best with the 

 thicker wires. Yet in all cases the agreement was close enough to 

 allow an extension of the theorj' to the sensitiveness for small 

 potential differences. 



From the formula (4) we find an expression for the sensibility 

 for small potential differences by dividing both parts by iv, the 

 resistance of the string : 



h HI* 



- = - ■ ■ , . . (5) 



iiv 6jTEd*io 



This formula gives the deflection in centimeters of the middle 

 part of the string when a potential difference of 10 Volts is applied 

 to the terminals. But with this formula we have not taken count 

 of the damping. The movement of the string in the Einthoven 

 galvanometer is damped partly by air friction, partly by electro- 

 magnetically generated counter-electromotive force. In the following 

 cases we shall consider only the electromagnetic damping, which 

 with thick wires greatly exceeds the air resistance. As the electro- 

 magnetic damping is caused by the number of the lines of force 



