6 2 Capt. Kater’s experiments for determining the 
The mean, ,000009959 may be taken as the expansion of the 
pendulum in parts of its length due to a change of tempera- 
ture of one degree of the thermometer. 
Of the method of deducing the length of the pendulum vibrating 
seconds. 
The distance between the knife edges was taken when the 
standard scale and the pendulum were both of the same 
temperature; and as this temperature did not differ consider- 
ably from 62°, the difference in the rate of the expansion (if 
any) between the pendulum and the scale may be neglected 
as perfectly insensible, and 62° be considered as the tempe- 
rature of measurement. 
The number of vibrations made by the pendulum in 24 
hours, having been determined at a different temperature, 
the length of the pendulum will be greater or less as the 
temperature of observation exceeds or falls short of 62°; and 
by applying the expansion due to such difference of tempera- 
ture, derived from the experiments contained in the preceding 
article, the distance of the knife edges, or length of the pen- 
dulum will be known for the temperature at which the num- 
ber of vibrations was determined, whence the length of the 
pendulum vibrating seconds may be readily deduced, the 
lengths of pendulums being to each other inversely in the 
duplicate ratio of the number of their vibrations in 24 hours. 
Of the correction for the buoyancy of the atmosphere. 
The length of the pendulum thus found, differing from 
what it would have been had the vibrations been made in 
