86 
MR, G. J. BURCH ON THE TIME-RELATIONS OF THE 
must be added to or subtracted from the ordinate, according as its sign, and that of 
the ordinate, is positive or negative. 
In this way an excursion may be analyzed. Points are taken on the curve at 
intervals of 005 or more, and the tangent and ordinate drawn to each and produced, 
upwards if the curve is rising, and downwards if it is falling, until the horizontal dis¬ 
tance between them is equal to the subtangent of the normal curve taken through 
the same resistance. The ends of all the ordinates are joined, and the curve so pro¬ 
duced represents, on the same scale as the ordinary readings of the electrometer, the 
total difference of potential during each instant of the experiment. 
It may be useful to note that the ordinates of the original curve give the integral 
of the quantity of electricity that has passed at any instant. 
Further Investigation of the Formula for the Time-Relations of the Normal Excursion. 
Having ascertained, by measuring a number of photographed excursions, that the 
formula y — ae ~ ct would hold for some instruments and not for others, I proceeded 
to investigate the causes of these divergences. 
There are two things which may modify the time-relations of the movement—the 
one accidental, and the other essential. The first is that the instrument may not be 
of equal sensitiveness throughout the part used. Obviously this difficulty may be 
got over by selecting a suitable electrometer. The second source of error cannot be 
so eliminated. It is that the internal resistance varies with the position of the 
meniscus in the capillary. 
(1.) Calibration Error. —This has a twofold effect. It alters the electrical value of 
the scale-readings, and it has also a powerful influence upon the velocity of the 
movement. The greater the range of the excursion for a given difference of potential, 
the slower is the action of the instrument—not only relatively, but absolutely. The 
relation between the sensitiveness of an electrometer, and the time of half-charge, 
could not be determined directly by experiment, owing to the difficulty of making 
two capillaries sufficiently alike in all other respects; but from a large number of 
observations it is evident that the time of half-charge increases much more rapidly 
than the sensitiveness. I found by experiment that the electrical capacities of 
electrometers, with capillaries of the same internal diameter, are in direct proportion 
to the lengths of the excursions produced in them respectively by the same small 
difference of potential, and that the capacity is within wide limits independent of the 
difference of potential. As, therefore, the same change of surface-tension has to force 
the mercury column through distances proportional to the sensitiveness, and a 
quantity of electricity has to flow which is also proportional to the same thing, 
it seems probable that the time of half-charge may vary according to the square 
of the sensitiveness. 
Further experiments will be made with regard to this. The important point, 
