EXCURSIONS OF THE CAPILLARY ELECTROMETER. 
85 
so that 
Integrating 
or, 
= — whence — celt = —. 
dt’ y 
ff* =1 ° Si = - Ct ’ 
y = ae d . 
It is obvious that any curve having this equation can easily be recognised in either 
of two ways. The tabular logarithms of a series of ordinates corresponding to equal 
time-intervals, are in arithmetical progression. This method was used in verifying 
the hypothesis as to the time-relations of the normal excursion. The second is a 
graphic method depending on the fact that the subtangent NT (fig. 1) of a logarith¬ 
mic curve, or intercept, upon the asymptote between the tangent and ordinate to any 
point upon the curve, is of constant length. This property affords a means of finding 
the position of the asymptote when only a portion of the excursion has been included 
in the photograph. Two points are chosen some distance apart, and the tangent and 
ordinate drawn to each. The level is then found by trial, at which the horizontal 
distance between the one tangent and its ordinate is equal to that between the other 
and its ordinate, or, in other words, the level is found at which the subtangents are 
constant. 
The possibility of doing this in the case of the normal curve suggested the method 
of analyzing other curves propounded in my preliminary note. If, as my experiments 
have indicated, the velocity of the meniscus at any moment is due solely to the 
difference of potential between the terminals of the electrometer at that moment, and 
is not influenced in any way by its motion at any previous time, and adds nothing to 
its velocity at any subsequent time—in other words, if the electrometer is perfectly 
dead-beat—then the rate of movement at any given instant, during an irregular 
change of electromotive force, must be exactly the same as would be communicated to 
the meniscus by a permanent difference of potential equal to the electromotive force 
acting at that instant. That is to say, the tangent to a given point on the curve pro¬ 
duced by any excursion must coincide in direction with that of the commencement of 
the normal curve given by the difference of potentied still existing between the terminals 
of the electrometer. If, therefore, the length of the constant subtangent to the normal 
curve is known, the length of the ordinate for that particular inclination of the tan¬ 
gent can be determined, and it will show how far the meniscus has still to move 
before reaching the position in the capillary corresponding to the difference of 
potential to which its velocity is due at the time in question. If the mercury is at 
zero, the length of the ordinate thus determined will represent the actual electro¬ 
motive force at that instant. If it is not at zero, the distance it has already travelled 
