( 219 ) 



The fundamental formula, fonnd in the above-mentioned text-books ^), 

 which represents this curve, runs : 



(Tq r da 1 ^ 



— -1 --] q = (9) 



dt^ ' m dt mc 



Here m, r and c have the same meaning as before, namely ?7i the 

 virtual mass of the image of the string, r the virtual resistance, 

 damping the motion of the string, and c the sensitiveness of the 

 galvanometer for constant currents, t means the time and q the 

 distance of the image of the string from its second position of equi- 

 librium or in other words : the distance of any point p of the curve 

 from the line CD. 



All units are expressed in the millimetre-micrampere or [?>???? — (.lA] 

 system. 



Calling Q the radius of curvature in any point of the curve, we 

 have : 



3 



'dq^^'y^ 



9=±- ~-^-^ ^ (10) 



d^q 



dt" 



dq 

 and further putting the tangent of the angle of inclination — = u, 



we may write: 



q = crv -\- cm (llj 



9 

 Here q is positive when v increases, negative when v decreases 

 with increase of t. 



For the case that we may put 9 = co formula (1 1) simplifies into : 



q = crv (12) 



This case must present itself somewhere in a point 6^ of the curve. 

 From B to s the curve is concave upward, from s to D concave 

 downward, s itself being the point of inflection. For the point s 

 Q — cp, SO that for this point formula (12) applies. We write it in 

 the form 



r = ^ (13) 



cv 



In order to determine the value of the resistance r by means of 

 this formula, the sensitiveness c of the galvanometer must be known, 



1) Vide KoHLRAuscH 1. c. p. 450 and Fleming 1. c. p. 368. 



