( 261 ) 



that the inniiciice of Ihe mass of the siring- on its velocity of motion 

 can only then he neglected, if a strong damping is present. 



If hy (liniinisiiing the intensity of the tield one goes on reducing 

 the damping, and yet wishes to retain the aperiodicity of the deflect- 

 ion, one will be at last obliged to make the quartz thread, the 

 ohmic resistance remaining the same, still lighler than it is already. 



We can generalise these considerations, and at the same time 

 calculate the obtainable maximum of sensitiveness for thermo-currents 

 in absolute measure, if we proceed as follows. 



We put the condition that the deflection of the thread shall be 

 aperiodic and that the duration of a deflection shall not exceed a 

 pre-determined amount, e.g. 10 seconds. The most favourable conditions 

 are then obtained if the movement of the thread is just brought at 

 the limit of aperiodicity. 



We further assume that of damping influences only the electro- 

 magnetic damping has lo be reckoned, either because the thread is 

 in a vacuum, or because the electromagnetic damping has so increased 

 that relatively to it the air-damping may be neglected. 



At the limit of aperiodicity the formula, mentioned at the close 

 of chapter lY, holds : 



4m 

 ^ = -;;7 (26) 



and besides 



2m 

 T = — , 



?■ 



in wiiich T I'cpresents the time constant ^). 



Both formulae I'efer to the [mm — nA] system. Expressing )\ in 

 dynes, rn^ in grammes and Tj in seconds, we get 



I'H' 2 

 r, = X - X 10-^ dynes (46) 



mJfJ 32 



X — \ 10-^ b millimetres per micrampere. . (47) 



i\ Jt' 



and 



_ w, 16 



T, = — X — seconds (48) 



From formulae (46), (47) and (48) we deri\e that 



c = ^X IO'.tX^'Tj ...... (49) 



1) See Fleming, J. c. p. p. 377 seq. 



