pepe PROCEEDINGS OF SECTION E. 
(b) The knife-edges are exchangeable, so that the oscillations 
may also be made independent of their cylindrical shape and 
of the influence of the planes of agate, upon which the knife- 
edges rest when the pendulum oscillates. 
(c) There is no adjustable weight attached to the pendulum 
bar, as in former constructions, by which the main conditions 
of the correctness of the instrument may be fulfilled, namely, 
that the duration. of an oscillation in the air is the same, 
round whichever of the two knife-edges the pendulum oscillates. 
The manner in which this is effected, according to Bessel’s sug- 
gestion, is very simple. The slips of brass, in which the pendu- 
lum ends, are in the beginning left too long, and are by degrees 
cut off until the oscillations in both positions are alike ; So 
for instance, in the instrument in question, the duration of an 
oscillation was originally with the light weight above 1.00654 
sec.,and thesame quantity with the light weight below 1.00764 sec. 
From this difference in duration “of 0.00110 sec. I computed 
the piece, which was to be cut off from both ends, as being 
35mm. long. I preferred, however, not to shorten the slips of 
the whole amount, for some reason which will presently appear 
obvious, and consequently only 25 mm. were taken off ; and after 
this correction the duration of an oscillation with the light 
weight above was 1.00470 sec., while the duration of an oscil- 
Jation with the hght weight below was 1.00494 sec., which 
leaves a difference of only 0.00024 sec., a degree of accuracy 
quite sufficient for the object in view (Bessel’s determination of 
Leta. Su) 
The theory of this instrument requires the centre of gravity 
of the pendulum to be known. I adopted two methods for 
accomplishing this—-an experimental one, and one based on 
calculation. : 
In carrying out the former, a strong copper wire was fixed to 
the ceiling of the room, nearly touching a table underneath ; by 
this wire the pendulum was suspended in such a manner as to 
admit of being moved to and fro in a loop of the wire of sus- 
pension until equilibrium was established. Attention had to be 
paid, however, to keep the pendulum, when suspended, on its 
edge, and to effect this I placed two glass tubes, distant from 
each other by the thickness of the bar of the pendulum, and 
fixed perpendicularly to a piece of wood, which could be moved 
on the table below, until the instrument was kept free and on its 
edge. By this arrangement the friction was very small, and the 
nicety with which the various sets of observations tallied proved 
its efficiency. The weights were exchanged after the first 
expernnent and the same repeated, whereby | a determination of 
the centre of gravity on the other side of the central weight was 
obtained. 
