( 2J4 ) 



The unit of virtual resistance (or better of the virtual resistance 

 coefficient) ^) r is the force of 1 micrampere resisting the motion of 

 the string when the image of the string moves with a velocity of 

 1 mm. distance per 1 mm, of time. The unit of sensitiveness c is 

 the sensitiveness with which a force of 1 micrampere causes a 

 deflection of the image of 1 mm. 



These units are constant as long as the field intensity H between 

 the poles of the electromagnet, the length / of the quartz thread, 

 the magnification h of the image of the string and the speed V of 

 the recording plane remain unchanged. 



If the string is strongly stretched and is suddenly passed by a 

 constant current, it will perform damped oscillations. We have then 

 the condition which we will in the fii-st place consider more closely 

 and which is expressed by formula (2): 



^ I y/ 4:711 



To this case also the following formulae (4) and (5) apply: 



T = 2jr \/^. (4) 



''='\/' + i <'> 



Here means the period which we would obtain without damping, 



whereas T represents the real period with damping. 



A z=z Ign k, (6) 



cc ct 

 k being the damping ratio, ^• = — = — =: etc. in which ffj, «j, «, 



are the deflections with damping. 



From the formulae (4), (5) and (6) follows: 



m = (7) 



c [39,5 + 4 (Z^nA;)*} ^ ' 



As the period T is expressed in millimetres, the value of ??z changes 

 if the velocity V of the recording plane is changed. In our measure- 

 ments V was nearly always 500 mm. per second. Only with a few 

 photograms the sliding frame had a different velocity, so that with 

 these a reduction will have to be applied in order to render the 

 values of m comparable. 



1) The word "resistance coefficient" expresses the meaning of r better than the 

 word resistance. But the latter is simpler and is also used as a coefficient in the 

 theory of electricity, where it denotes ohmic resistance. In this paper we shall 

 repeatedly use "resistance" instead of "resistance coefficient". 



