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XIV. On the pendulum. By J. W. Lubbock, Esq. F.R.S. 
Read March 11, 1830. 
Captain kater was the first who made use of PIuygens’s theorem with 
respect to the convertibility of the centres of suspension and oscillation to 
eliminate the moment of inertia, and to obtain the length of the simple 
pendulum by measuring the distance between the knife edges or axes of sus- 
pension. But this very ingenious method of determining the length of the 
simple pendulum must be considered as a first approximation, which is 
true only when many circumstances which might affect the truth of the result 
are not taken into account, but of which the following investigation shows 
that when the experiments are conducted with care, the effect is insensible. 
It is, however, desirable to ascertain carefully the limits of the errors which 
may rise from the circumstances to which I have alluded, and to render the 
theory of Captain Rater’s pendulum as perfect as the method of observa- 
tion. Laplace has given a complete theoiy of the apparatus used by Borda 
in the Connaissance des Temps ; and he has shown that in the apparatus of 
Captain Rater, the distance between the knife edges is equal to the length of 
the simple pendulum, when they are considered as cylinders of small curvature, 
provided their radii of curvature are equal ; which theorem is also proved in 
Professor Whewell’s Dynamics. But no one I believe has yet discussed all 
the circumstances which affect the accuracy of Captain Rater’s method ; and 
I have therefore attempted to do this in the following paper, in which I have 
treated the question with the utmost generality, taking the case of all possible 
deviations and of axes any how placed, provided only that they are synchro- 
nous. 
I have taken the pendulum used by Mr. Baily, and described by him in the 
Philosophical Magazine of last February, to afford a numerical example, and I 
2 D 
MDCCCXXX. 
