468 
MR. BA1LY ON THE CORRECTION OF 
a review of the whole question, however, it is clear that different experiments, 
even with the same pendulum, are not strictly comparable with each other, 
unless we can either ensure the perfect accuracy of the knife edges and planes, 
or provide a method of making the vibrations, in all cases, from the same part 
of the knife edge and from the same part of the plane: or, in other words, 
that the knife edge and plane shall, in all cases, touch each other at the same 
points of contact. This, I conceive, would not be difficult; and it must be 
attended to in all future experiments. We must deal with the experiments, 
already made, in the best manner we can*. 
Correction for the Arc of Vibration. 
In a recent volume of the Transactions of this Society]* Captain Sabine has 
stated that the usual formula for the reduction of the vibrations of a pendu¬ 
lum, to indefinitely small arcs, is erroneous; inasmuch as it does not agree 
with the result of his observations, which require that the hitherto assumed 
corrections should, in the case of the convertible pendulum tried by him, when 
the heaviest end is below the axis of suspension, be multiplied by C12; and 
when it is above the axis of suspension, be multiplied by T40. As this view 
of the subject was somewhat at variance with what I had imagined to be the 
case in my own experiments, I determined on making a few trials in order to 
ascertain more minutely the difference which arises from the use of large and 
small arcs: and for this purpose I took the brass bar convertible pendulum 
No. 25 above enumerated. Two series were made (in the vacuum apparatus, 
and at about one inch pressure of the atmosphere,) on the knife edge A, and 
two on the knife edge 33 : and each of these series was divided into three por¬ 
tions ; in the first of which, the arc was taken from about 1°*Q0 to about 0°*60; 
in the second, from 0 o, 60 to about 0°*38; and in the last, from 0°*38 to about 
0 o, 20 and 0°T0. The first series on the knife edge A showed that the usual 
correction ought to be increased about xoth ; which accords very nearly with 
* Since this was written, I have caused my agate planes to he slightly rounded, so that a very line 
thread of light can he seen under the knife edge, on each side of the small line where it touches the 
curve. By this method I have got rid of the discordancy in the pendulum No. 25—26, which is the 
only one I have yet tried in this way. 
t Philosophical Transactions for 1831, page 461, &c. 
