128 
PRESTON. 
an error of s .00000012 in the deduced time of one oscillation. 
For pendulum No. 3 
a = --00017 
and T would be changed by s * 0000007. Admit, now, that 
the distance h d — h n is obtained to the nearest millimeter 
and we have errors that are absolutely insignificant. For 
the Peirce pendulums the ratio of the distances h A and 
h a are as three to one. Measures of center of mass have 
therefore usually been made with an accuracy far beyond 
that attained in the other quantities bearing on the same 
result, and; in the writer’s opinion, the accuracy has been 
pushed to an unnecessary extent. 
The conclusions are therefore that time may be saved, 
with no sacrifice of accuracy, by correcting for arc by Borda’s 
method. Observations extending through the entire 24 
hours are always to be recommended. Forty transits at the 
beginning and end of swings and one or two intermediate 
transits at intervals of two hours suffice when the period is 
known to the nearest ten-thousandth of a second, and finally 
the determination of the position of the center of mass to 
the nearest millimeter is sufficiently accurate when the 
times of oscillation for the two positions of the pendulum do 
not differ more than about one six-thousandth part of an 
oscillation. 
The distance between the knives has usually been ascer¬ 
tained by comparing it with a known standand in a vertical 
position, the illumination being effected for a dark field by 
throwing the light downward on the edge from a right-angled 
prism, and for a bright field by letting it enter directly to¬ 
wards the microscope in the line of the axis. Measures were 
made for edge bright and edge dark, and the mean was 
taken as the true value. Owing, however, to the construc¬ 
tion of the pendulums and the comparator, measures could 
only be made at the middle of the edge, whereas its whole 
extent fixes the axis of rotation. Moreover, in order to 
admit the prism, a part of the supporting plane was cut out, 
so that however much the knives might wear by use, the 
difference of length on this account could not be detected. 
