£8 Mr Watts o?i the Length of the Pendulum^ 
line of my paper ; and to misrepresent the facts which it con- 
tains. 
He commences with observing, that this writer (a Mr Wil- 
liam Watts of the Customhouse, Penzance,) begins by mista- 
king the length of the Seconds Pendulum for that of the Pen- 
dulum of Experiment ; and in consequence arrives at the con- 
clusion that the number by which the square of the arc of vi- 
bration is to be multiplied is mcorrect^ In reply to this, I 
candidly acknowledge that I have committed a small mistake in 
correcting an error which Captain Kater has fallen into, rela- 
tive to the correction due to the amplitude of the arc of vi- 
bration ; and 1 now find that the said error does not amount to 
more than one-third of what is stated in my former paper ; as 
the number by v/hich the square of the arc of vibration is to be 
multiplied, should have been stated at about 1,6385, instead of 
1,645: whereas the factor given by Captain Kater is 1,635; 
consequently it is incorrect^ as already asserted, although not to 
the same degree. 
This mistatement, in the magnitude of the error committed 
by Captain Kater, is of little or no consequence,— first. Because 
the formula, which he has employed for the purpose of reducing 
a finite circular arc, to the case of an infinitely small arc of vi- 
bration, is not the appropriate one ; and, secondly. Because I 
have already furnished the proper formula, —given the demon- 
stration of it, and deduced from it the correct result, due to 
the amplitude of the arc of vibration. And although the de- 
monstration of this important formula forms a prominent fea- 
ture of my paper, and is no where else to be found correct ; yet 
it did not suit the purpose of Z even to notice it in the outline 
of my paper, which, he says, he was tempted to give ! 
The next charge is, that I have “ convicted Captain Kater 
of not having expressed the number of vibrations made by the 
pendulum in twenty-four hours beyond the nearest hundredth 
of a vihrationr This is very true, and I might have stated, 
not even to the nearest hundredth of a vibration. But, perhaps, 
it may be urged that this is a trifling error, and a matter of no 
importance ; but however this may be, such was not the opi- 
nion of Biot, Mathieu, Arago, &c., for they expressed the num- 
