94 
MR G. J. BURCH OH THE TIME-RELATIONS OF THE 
estimated with the aid of a lens. As a check, three different reference lines were 
taken on successive days, and the results so obtained were found to be identical. 
The next stage of the operation consisted in the determination of the asymptotic 
circle. In so short a period as that comprised between the passage across the slit 
of an eight-inch plate, the mercury has not time to reach its final position, which must 
therefore be found by calculation. Assuming for the time-relations of the excursion 
the simplest formula, given in my preliminary note, viz.:— 
y — ae~ d , 
we may write for the distances from any reference circle of three points corresponding 
to equal intervals of time, 
A = n + y, 
B = n + Ty, 
C = n + T 2 y, 
where n = the distance of the reference circle from the asymptotic circle, and T is 
some function of t. 
Whence 
C-B 
B - A 
B - A 
t — i y ’ 
A — y — n. 
Selecting three points as far apart as possible, I found the position of the 
asymptotic circle and reduced the observed readings of the ordinates to the values of 
y measured from it, which were as follows :— 
