470 CAPTAIN SABINE ON THE LENGTH OF THE SECONDS PENDULUM 
to infinitely small arcs ; but circumstances not permitting me to do so at pre- 
sent, I have only to state my conjecture, that it is caused by the gliding of the 
knife edges on the planes, a consequence of the elasticity of the planes. It has 
been found by M. Bessel, that small movements of this kind always took 
place in a pendulum vibrating on a knife edge, whatever might be the nature 
of the supporting planes ; that its direction was the same as the motion of the 
pendulum, — to the right when the pendulum moved to the right, and vice versa; 
and that its amount was proportioned to the arcs of vibration. Supposing 
that the cause is as I have conjectured, it would have been satisfactory to have 
measured the amount of the gliding corresponding to particular arcs, directly , 
in the manner that M. Bessel has done, and to have compared the correction 
of the length, which is the mode of compensation adopted by M. Bessel, with, 
the correction of the rate, which is the method that has been adopted here ; by 
either mode the experiments ought to give the same length for the seconds 
pendulum. 
In discussing the correction for the arcs of vibration, it has appeared the 
most satisfactory course, to introduce the detail of the experiments relating to 
that branch of the subject into the body of the discussion itself. In the re- 
mainder of the paper I shall pursue the more usual course, of placing to- 
gether, at the close, the detail of all the experiments, in the order and suc- 
cession in which they were made ; introducing into the discussion, abstracts 
and results, with proper references to the part of the paper containing the 
details. 
Before we enter on the examination of the rate of the pendulum, it is neces- 
sary to ascertain the reduction to a vacuum for the small residue of air which 
cannot be pumped out of the apparatus, as well as for the small additional 
quantity which occasionally leaks in. I proceed to collect in one view the re- 
sults of the experiments which were made at suitable opportunities to deter- 
mine the amount of this reduction. 
Reduction to a Vacuum. 
^ 1. Weight above. 
'Hie plan of experiment was to compare the vibrations made in full atmo- 
spheric pressure, with those in the exhausted apparatus, in circumstances in 
