( 212 ) 



to the motion of the quartz wire, increases proportionally to the 

 velocity of motion of the wire. 



This assumption, which is justified on theoretical grounds, will later 

 appear to be also practically proved by the results of analysis. 



If we assume it to be true, we must also expect the motion of 

 the string to be completely determined by the laws that govern the 

 motion of an oscillating body with electromagnetic damping. For 

 electromagnetic damping, as in our case the air-damping, develops 

 a resistance, increasing proportionally to the velocity of the moving 

 body. In the string galvanometer both electromagnetic and air-damping 

 occur. They can be expressed in the same units and their combined 

 effect is always equal to the effect of eitlier of them, if only in the 

 latter case the amount is made equal to the sum of the two, taken 

 separatel3\ In olher words: if Va represents the resistance through 

 air-damping ^) and ri the resistance through electromagnetic damping, 

 we may reckon for the total damping resistance : 



r^ra-\rn (1) 



The laws of motion of an oscillating body with electromagnetic 



damping are e. g. extensively dealt with in Kohlrausch' textbook *). 



They agree with the laws determining the charge or discharge of a 



condenser through a conductor having resistance and self-induction, 



Avhich are found in various textbooks on electricity '). The formulae 



given in the above-mentioned works form the foundation of our 



further calculations. 



If we denote by : 



m the virtual mass of the image of the string, 



r the virtual resistance, damping the motion of the string, 



c the sensitiveness of the galvanometer for constant currents, 



two conditions may present themselves. In the first the motion is 



oscillatory and 



4m 



(2) 



<v 



in the second condition the motion is aperiodic and 



^>\/- <^) 



1) Besides the air-damping and the ordinary electromagnetic damping still other, 

 very feeble, damping influences are active, which may however be neglected here. 

 They will be dealt with in chapter 7. 



2) Lehrbuch der praktischen Physik, S. 448. 1901. 



3) Vide e.g. J. A. Fleming. The alternate current transformer. London. I, p. 370. 1890. 



