A PENDULUM FOR THE REDUCTION TO A VACUUM. 469 
Captain Sabine’s determination: but the second series on the same knife edge 
indicated that it ought to be diminished by nearly the same quantity. I con¬ 
sider therefore these two series as neutralizing each other; and that the dif¬ 
ferences observed come within the errors of observation. With respect to the 
knife edge B, both series showed that the correction should be increased jth: 
which is only one half the amount indicated by Captain Sabine’s experiments. 
Further inquiries therefore are requisite to clear up this point: not only as to 
the cause of the anomaly, whether it arises from a sliding of the knife edges 
on the agate planes (in which case, it may differ in different pendulums, and 
wholly vanish in M. Bessel’s mode of suspension); but also as to the accuracy 
of the assumed data on which the generally received formula is founded. 
When the arc is very large, the formula will not lead us to the true result: 
this has been already noticed by more than one author. But whether the dif¬ 
ference arises from a defect in the formula, or from a sliding of the knife edges, 
or from the variable effect of the air on the pendulum, or from all three, re¬ 
mains still to be demonstrated. Should any experiments for determining this 
point be commenced, it would perhaps be better that the vacuum apparatus 
should not be used for the purpose: but that a heavy sphere, cylinder, or lens, 
suspended by a wire, be swung in free air, first on the knife edge, and after¬ 
wards over a steel cylinder; due care being taken, in the latter case, that the 
wire be flat at that portion of it which passes over the cylinder. A body of 
this kind will continue its vibrations for a sufficient length of time for such 
experiments : which was in fact the reason for adopting the vacuum apparatus 
for this purpose ; but which may present difficulties of another kind ; since it 
is difficult to prevent a leakage in the vacuum apparatus, which has a material 
effect on the arc of vibration ; and moreover the proximity of the pendulum to 
the sides of the tube, when swinging in large arcs, may influence the results. 
But, whatever be the cause of the discordancy, it is evident that in the pre¬ 
sent state of the subject we cannot strictly compare the results of experiments, 
where the arcs employed have been widely different. The initial arc ought in 
no case to exceed one degree: in my own experiments, I have generally com¬ 
menced with an arc of about 0 o, 9 or 0 o, 8 ; but this I think is still too large, and 
were I again to undertake any delicate experiments on the pendulum, I should 
probably make the initial arc about half a degree only. In the experiments 
3 p 
MDCCCXXXII. 
