( 228 ) 



tensions of the quartz tliread were used, varying from 1 to 324. 

 That ^^itll smaller tensions of the string than were used above, 

 the proportionality l)et\veen the velocity of the string and the 

 frictional resistance of the air, is maintained, has been sufiiciently 

 proved on a former occasion ^). A standardising curve with a sensi- 

 tiveness of 1 mm. detlection for !()-'" Ampere, was recorded on 

 a photographic plate, which moved with a velocity of 10 mm. per 

 second. After the sensitiveness had been reduced ten times and the 

 speed of the plate had been ten times increased another standardising 

 curve was written. This latter shows the same shape as the former, 

 both curves can be so superposed that they coincide over nearly their 

 whole length. 



So we may say that the tensions may vary from 1 to nearly 3000, 

 the value of I'a being oidy slightly altered. 



Let us now consider the amount of the electromagnetic damping, 

 expressed by ru. The value of ru is nothing else than the pondero- 

 motive force which the string experiences by its motion in the mag- 

 netic field when the velocity of the image of the string is unity. 



If this ponderomotive force is rendered in the [_nuii — m.4] system, 

 it is expressed by a certain number of micramperes with the given 

 length of the thread and the given intensity of the field. 



The calculation can be made in tiie following way. 



The electromotive force E, generated in a wire, which is perpen- 

 dicular to the lines of force of a homogeneous magnetic field, and 

 is displaced with a velocity of t\ centimetres per second in a direction 

 which at the same time is perpendicular to its length and to the 

 lines of force, is 



in which / means the length of the wire in centimetres and H the 



intensity of the field in C. G. S. units. 



When the middle part of the string moves with a velocity v^, 



the average velocity of all the parts of the string may be put 



2 



V, = 0,B37 i\, so that for the electromotive force e, generated by 



jt 



a deflection of the c[uartz thread, we may write 



6 = 0,637*', ///X 10-8 Fo/« (19) 



Moreover we have 



1) See these "Proceedings" 6, p. 107, 1903. 



