834 Mr Watts’ Remarks on Captain Rater's 
Here the two first arcs of vibration measured in degrees, 
are and 1°,09, so that wg shall have, 
o + 6 = 2,30, its log 0,36172784 
and a — 6 = 0,12, its log 1,07918125 
«=: 86056,47, its Jog 4,93478550 
4,37569459 
241886,08 its log 5,38361095 
log I its log 2,65666225 
4,04027320 
Log S = 0,SS54i^lS9) the logarithm of the 
correction due to the arc of vibration, and whose number is 
2,1648; consequently 
n'z=:n + 2,1648 = 86058,6348. 
Captain Kater makes it 86058,63, being a small fraction too 
little ; and as this is the case with the remaining arcs, it follows 
that his determination of the length of the simple pendulum 
in vacuo, vibrating seconds at the level of the sea, and measur- 
ed at the temperature of 62° of Fahrenheit’s thermometer, is 
also a small fraction of an inch too short. 
There is another minute error in the correction due to buoy- 
ancy of the atmosphere, amounting to about 0,00002 inch in 
excess: Captain Kater makes it 0,00544; but it is only 0,00542. 
I remark, in the last place, that notwithstanding all the 
precautions adopted by Captain Kater in the determination of 
the number of vibrations performed by the brass pendulum 
during a certain number of seconds, I cannot help thinking, 
that the different periods of coincidence have not been assigned 
with the requisite degree of precision, by establishing the limits 
between which they v/ere found to be comprised, that is to say, 
by noting when the coincidence did not exist; when it was exact ; 
and, lastly, when it had elapsed, so as to be enabled to reckon 
with a greater degree of certainty with regard to the instant in 
which it should be fixed. 
Captain Kater asserts, that the disappearance of the disk can 
be noted only to a single second, so that the brass pendulum 
