1890.] Rapid Variations of a Difference of Potential. 5U 



Oy = axis of y, graduated in -j-gVc of a volt. 

 Ot = axis of t, and asymptote of the curve. 

 PN and PjNj = ordinates at the points P and P! respectively. 

 PT and P,^ = tangents. 

 NT and N t T, = subtangents. 

 [NT = N.T,.] 



(4.) The time required by the meniscus to traverse half the dis- 

 tance through which the sudden introduction of a permanent 

 difference of potential would cause it to move, is, within wide limits, 

 independent of the amount of that difference. This time may be 

 conveniently referred to as the " time of half-charge." It is one of 

 the constants of an instrument, and is affected only [with the excep- 

 tions indicated in (7)] by the external resistance of the circuit. 



(5.) The above conditions are fulfilled if the equation to the 



normal curve is of the form log - = ct, where y is the vertical dis- 

 ci 



tance of a point P upon the curve from its asymptote (i.e., the level 

 at which the meniscus finally comes to rest) and t is the horizontal 

 distance of P from a point O upon the asymptote, which is taken as 

 the origin of coordinates. There is a well-known characteristic ot 

 all curves having this equation, by which they can be easily re- 

 cognised, namely, that the eubtangent NT, or intercept upon the 

 asymptote between the tangent PT of any point P upon the curve 

 and its ordinate PN, is of constant length. I have accordingly 

 measured the length of the subtangent at various points upon a 

 number of normal curves, and find it to be constant for each electro- 

 meter, except so far as it is altered by the total resistance of the 

 circuit and the variations of resistance, <fec., which will be referred to 

 in (7). The normal curve is therefore approximately the logarith- 

 mic curve. 



