46 SABINE’S EXPERIMENTS. 
In the observations of coincidences I had the pleasure and advantage of the 
co-operation of Mr. Renwick, professor of Natural Philosophy and Chemistry 
in Columbia College; whose interest in the subject induced him to associate 
himself with me throughout the experiments; a circumstance extremely 
agreeable to me, and advantageous to the results. 
In the following tables, which contain these observations, those of the first 
day only are given at full length; on the others, the first, and eleventh, or 
last, coincidence only are entered, as these comprise the ten intervals from 
the mean of which the rate of the pendulum is inferred: the intermediate 
coincidences were frequently unnoticed in the observations to which my own 
name is affixed, the room being left undisturbed in preference: but they 
were always observed in Mr. Renwick’s, for the advantage of practice. 
The correction for the arc of vibration in these tables is computed by multi- 
plying the square of the mean observed arc by the difference between the 
number of vibrations made by the pendulum in twenty-four hours in a cycloid 
and in a circular arc of one degree, and being added to the observed number 
of vibrations in twenty-four hours, shows what they would have been in an are 
infinitely small ; it may be remarked, of this correction, that care having been 
taken that the pendulums should vibrate as nearly as possible in the same arcs 
in London and in New-York, it is not important that the mode of computa- 
tion should be rigorously exact, 
