( '256 ) 



In tlie first place it is easy to tell when the sought factor must 

 be equal to uuitj'. The stretched thread ought then always to move 

 perpendicularly to its length, and ought to execute in its entirety 

 exactly the same movements which in reality are only executed by 

 the middle of the string. 



In the second place we shall make the calculation for the case 

 that the two halves of the thread after deflection, form the two sides 

 of an isosceles triangle, while we assume that the movements of 

 the middle of the thread are the same jxs those of the middle of a 

 real siring. The sought factor then gets the value 72 ^"tl is found 

 in the following manner. 



The kinetic energy of the thread is calculated while it is in the 

 phase of its quickest motion. Let the velocity of the middle of the 

 thread then be t\ and let the mass ,1'?/?^ be distributed evenly over 

 the whole length of the thread. Under these circumstances and with 

 the assumption that the two halves of tiie thread always remain 

 straight lines, the kinetic energy is 



^ = -^ (42) 



Let the first mentioned imaginary thread for which we found the 

 factor 1 have a mass jn^ and let it execute the same movements as 

 the middle of the last mentioned thread. Then its energy in the 

 same phase of motion will be 



VI, v,^ 



^1 = -^ (43) 



Call the permanent deflection 11^ and the total ponderomotive 

 force Ii, then the Avork done by the ponderomotive force when a 

 deflection has been made, is 

 in the first case E^ =z k X ?'i , 

 in the second case E = k X. \ u^, 

 so tliat E, = 2E (44) 



From formulae (42), (43) and (44) now follows that 



and consequently that x 



3 

 3 



9 



9. The practicahllUii of the strhh/ (jalcanometer for special purposes. 

 For some pui-poscs it may be desirable in order lo judge of the 



