( 255 ) 



to the tension so that we may say that the increments of the tension are 



proportional to the increments of the length, which must be expected fora 



stretched elastic thread. For increments in length of ratios : 1 : 2 the 



/Mil /1\ 



increments m tension are as I I : — : — or as I — ^1:1:2. 



We now proceed to derive the factor — in formula (29) and sup- 



o 



pose again that the string is strongly sti-etched and is placed over 

 its whole length in a homogeneous magnetic field. 



According to the laws, obeyed by the vibrations of a string, we 

 have : 



Abn, 



S = '-, 



in which Tj denotes the period in seconds if no damping were 



present, while, as was mentioned before, S represents the tension 



in dynes, / the length in centimetres and m^ the real mass of the 



string in grammes. 



I 

 Now by formula (38) we also have S=^ ■— so that we may write 



or 



32cj 



(^1) 



From formula (4) we know that r = 2jt V'mc or m = , from 



which follows, having regard to formula (41), that 



and since — =: -— we may also write 

 r I 



m,=zmX{~\ X-X — • 

 This formula is identical with formula (29) which proves that the 



factor sought by us is indeed — . 



8 



We make a short digression here about the calculation of the 

 sought factor for the case that the motion of the quartz thread 

 deviates from the vibration of a string. We shall still assume, howe- 

 ver, that the thread is over its whole length in a homogeneous 

 magnetic field. 



