i'2 On Rapid Variations of a Difference of Potential. [May 22, 



II. Curves produced by Rapid Variations, of Unknown Amount, of the 

 Difference of Potential between the Terminals. 



(6.) From (1), (2), and (3) it follows that in all cases the velocity 

 with which the meniscus is moving at any instant is that with 

 which it would start if the zero line were moved to the level then 

 occupied by the meniscus, and the difference of potential existing at 

 the time between the terminals of the electrometer were suddenly 

 introduced and made permanent. Thus the total indicated difference 

 f potential is made up of two parts, viz., the difference represented 

 by the distance through which the meniscus has already moved, and 

 that indicated by the velocity with which it is still moving. 



This being so, there are two ways in which the actual difference of 

 potential at the moment corresponding to any point upon the pho- 

 tographed curve may be estimated. The first is to compare it with 

 a normal curve, on which a point must be found of which the tangent 

 coincides in direction with the tangent at the required point of the 

 curve under examination. The vertical distance of this point upon 

 the normal curve from its asymptote will express the remainder of 

 the difference of potential, provided that the resistance in circuit was in 

 both cases the same. 



The second method depends upon the property of the logarithmic 

 curve mentioned above. Upon an enlarged copy of the curve to be 

 investigated, points are taken corresponding to equal intervals of 

 time (e.g., O'OOL sec.). Through each of these points a tangent and 

 an ordinate are drawn, and produced, upwards if the curve is rising, 

 or downwards if it is falling, until the horizontal distance between 

 the tangent and the corresponding ordinate is equal to the length of 

 the subtangeut of the normal curve. The level at which this is the 

 case is that to which the meniscus would have risen or fallen, had 

 the difference of potential between the terminals at that instant been 

 made permanent, and is in fact the position of the asymptote of the 

 corresponding normal excursion. Consequently, a line touching the 

 ends of all the ordinates so produced will represent the variations of 

 difference of potential during the experiment, upon the same scale as 

 the normal curve. 



(7.) This result is only an approximation ; to make it accurate 

 three kinds of corrections have to be made, as follows : 



(a.) Calibration Errors. The capillary may not be of equal sensi- 

 tiveness throughout the part employed. In this case the electrical 

 capacity of the electrometer viewed as a condenser will also vary 

 with the position of the meniscus in the tube, so that the correction 

 is difficult to make, and should be avoided by selecting a suitable 

 instrument. 



(b.) Overshooting. In instruments with small internal resistance, 



