34 Capt. Kater’s experiments for determining the 
arise from a want of uniformity in density or figure. After 
numerous trials however, and as frequent disappointments, 
I was at length convinced of the impracticability of obtaining 
a rod sufficiently uniform, and I was besides aware, that 
under certain circumstances errors might arise from this 
cause which it would be impossible by any method to 
detect. 
Not feeling at all satisfied with the prospect which the use 
of a rod presented, I endeavoured to discover some pro- 
perty of the pendulum of which I might avail myself with 
greater probability of success ; and I was so fortunate as to 
perceive one, which promised an unexceptionable result. It is 
known that the centres of suspension and oscillation are reci- 
procal ; or in other words, that if a body be suspended by its 
centre of oscillation, its former point of suspension becomes 
the centre of oscillation, and the vibrations in both positions will 
be performed in equal times. Now the distance of the centre 
of oscillation from the point of suspension, depending on the 
figure of the body employed, if the arrangement of its parti- 
cles be changed, the place of the centre of oscillation will 
also suffer a change. Suppose then a body to be furnished 
with a point of suspension, and another point on which it 
may vibrate, to be fixed as nearly as can be estimated in the 
centre of oscillation, and in a line with the point of suspension 
and centre of gravity. If the vibrations in each position 
should not be equal in equal times, they may readily be made 
so, by shifting a moveable weight, with which the body is to 
be furnished, in a line between the centres of suspension and 
oscillation ; when the distance between the two points about 
which the vibrations were performed being measured, the 
