£>4 Capt. Kater's experiments for determining the 
by the specific gravity of the pendulum, the ratio of the weight 
of the pendulum compared with that of air will be obtained. 
This ratio will express the diminution of the force of gra- 
vity arising from the buoyancy of the atmosphere ; and in 
order that the number of vibrations may be the same in 
vacuo as in air, the length of the pendulum must be increased 
in the proportion of this ratio to 1, the lengths of pendulums 
vibrating in the same time, varying directly as the force of 
gravity. 
Detail of the experiments. 
In the first experiments which were made with the pen- 
dulum, it has been already observed that the knife edges 
rested on plates of hard steel, but as these at the conclusion 
were found to have suffered penetration in no slight degree, 
planes of agate were substituted for them, and the results 
having thus been rendered doubtful, were deemed inadmissi- 
ble. It may not however be irrelevant to remark, that the 
distances of the knife edges obtained by the two methods 
which have been before described, did not differ quite one ten 
thousandth of an inch ; and, that on re-measurement after the 
knife edges had been used a very considerable time, their 
distance was found to be increased by wear, four divisions 
only of the micrometer, or not quite two ten thousandths of 
an inch. The length of the seconds pendulum deduced from 
these first experiments, differed from the result of the obser- 
vations about to be detailed, only two ten thousandths of an 
inch in defect. I nevertheless think it useless to insert these 
first experiments, as the near approximation of the result 
cannot but be deemed to have been in some degree acci- 
dental. 
