IN THE OBSERVATORY OF GREENWICH. 
461 
as the compensation for the arcs is obtained. During the progress of the ex- 
periments, however, I had occasion to suspect that, particularly when the pen- 
dulum was vibrated with the weight above, the retardation of the vibrations, in 
consequence of their being performed in circular arcs, was greater than the com- 
pensations computed by the customary formula N • ^ ^ ; ■ 4^ —y 
To examine this more closely, and to obtain practically a just compensation 
for the arcs in which the pendulum had been vibrated in the course of its em- 
ployment, I made several series of experiments distinct from those made to 
determine the rate, and which I shall proceed to describe in the first instance, 
though they were not the first in the order of time. 
Correction for the Arcs of Vibration. 
§ 1 . Weight above. 
On the 2/th of January 1830, I made the following observations, purposing 
to compare, under circumstances otherwise similar, the rate of the pendulum 
in different arcs ; 1st, commencing with 1°.32 and ending with 0°.73 ; 2nd, 
commencing with 0°.70 and ending with 0°.42 ; and 3rd, commencing with 0°.42 
and ending with 0°.19. Having withdrawn the air from the apparatus, the re- 
sistance to the vibration was so far diminished, that the time which the pendu- 
lum took to reduce its arc from 1°.32 to 0°.73, from 0°.70 to 0°.42, and from 
0°.42 to 0°.19, was in each case sufficient to give the rate of the pendulum within 
the respective arcs with tolerable exactness. 
The rate of the clock on this day was taken from its average rate in several 
days, viz. from the 24th to the 30th of January ; exactness in the daily gain 
or loss of the clock was not required, as the observations were only to be used 
in their relation to each other. 
