84 
MR. G. J. BURCH OH THE TIME-RELATIONS OF THE 
shifted to 50 millims., when the complete excursion was found to be 42 divisions, and 
that given with the rheotome, 21 divisions. On further reducing’ the length of rheo- 
chord wire to 25 millims., the full excursion being 21 divisions, the meniscus shot up, 
when the rheotome was used, through 10'5 divisions of the eye-piece micrometer and 
there stopped. That is to say, with only one-sixth part of the original difference of 
potential, the middle point of the excursion was reached in exactly the same time, 
namely '414 sec. In other words, the mean velocity of the meniscus during the first half 
of a normal excursion was found to be proportional to the total length of it. Further 
experiments showed that the same w 7 as true of other fractions besides the half, as for 
instance, one-fifth, one-third, and three-fourths, but in these cases the measurements 
were less reliable, owing to purely instrumental difficulties. 
From these data I concluded that the velocity with which the meniscus moved at 
any instant during a normal excursion, must be proportional to its distance from the 
final position of rest at that time. 
Fig. 1. 
Fig. 1 represents the curve of a normal excursion photographed upon a plate 
moving with constant velocity horizontally from right to left. 
The asymptote AB is taken as the axis along which the time t is measured. 
Let P be a point on the curve 
y = PN — the vertical ordinate through P. 
Then, if u denote the velocity of the meniscus in the capillary 
But, according to the experimental results, 
u varies as y, 
