( 233 ) 



plane only to take into aecounl tlie velocity of the motion of the 

 menisens. When analysing' a eiir\e, iiowever, recorded by the string 

 galvanometer, tlie analogous data are not snfticient in general. It 

 will often be necessary to take into acconnt not only the velocity 

 bnt also the acceleration presejited by the image of the string. 



This mnst be ascribed to the fact that in the capillary electi'ometer 

 the resistance to the motion of the menisens is very great ^) compared 

 with the mass of the mercni-y thread, so that this mass may be 

 neglected, when it is desired to calcnlate the existing potential ditfer- 

 ence from the velocity of motion, whereas with the string galvano- 

 meter the resistance to the motion of the quartz-thread is very small, 

 and hence the mass of the thread in many cases has a distinct 

 ijitluence on the \elocity of its detlections. 



These considerations may be succinctly rendered by formula (11), 

 already developed in the preceding chapter: 



(1 + ^r .... 



q =z crv -\- cm — (ii) 



9 



If r is very great compared with ;?? the second term behind the 

 = sign may be dropped and the formula becomes 



q = crr (12) 



This formula (12) can be applied as well for the analysis of 

 capillary electrometric curves as for curves of the string galvanometer 

 for which ?' is small and q large. 



On the other hand, for moderate A-alues of v and ^ the mass m 

 may no longer be neglected, so that then analysis of the curve will 

 only be possible if besides tlie velocity also the acceleration can be 

 measured. This acceleration, expressed as virtual acceleration of the 

 image of the string in millimetres distance per millimetre of time, is 



nothing else but . 



Q 

 Assuming as known the general conditions under which a curve 



is written bv the string galvanometer, and also the distance from anv 



point of the cui-ve to the zero line, one will have to measure the 



tangent v of the angle of inclination and also 9 the radius of curvature, 



in order to calculate the potential ditlerence which existed between 



the ends of the quarlz-thread at the moment, that the arbitrary i)oiut 



mentioned Avas recorded. Under unchanged general conditions each 



1) On the influence of friclional resistance on the movement of the meniscus in 

 Lippmann's capillary electrometer, see these "Proceedings" II, p. 108, 1899. 



