S25 
Pape7' on the Length of the Pendulum. 
may arrive at the lowest point of the arc of vibration, either 
precisely at the second when the disappearance of the disk was 
observed, or at any part of a second either before or after this 
observation ; so that an error might possibly arise, amounting to 
9|10ths of a second, by which the interval deduced from ob- 
servation would be either less or greater than the truth, and 
thus an error of one second in the duration of the interval, would 
occasion a difference of 0,63 in the number of vibrations made 
by the pendulum in twenty-four hours. 
But, I beg leave to ask, why cannot the disappearance of the 
disk be noted to a quarter of a second, as readily as an entire 
second ? Is the thing impracticable ? By no means ; for I ima- 
gine that it might be easily effected by means of a stop-watch, 
with a quarter second-hand, such, for example, as Litherland’s 
patent watch, and regulated, like the clock, according to mean 
solar time If this can be done, and I entertain no doubt of 
its practicability, then in this case the greatest error in the num- 
ber of vibrations performed in twenty-four hours may be redu- 
ced to a fourth part of what it is in Captain Kater’s experiments. 
It appears, moreover, that the law of the diminution of the arc 
of vibration, does not proceed exactly in geometrical progres- 
sion, as we might naturally expect it would; and the discre- 
pancy is very apparent throughout the whole set of experi- 
ments ; but more particularly when the great weight is upper- 
most, in which case, the decrease of the arcs of vibration is 
much more rapid and irregular than when it is below. 
What are the causes of these irregularities ? I imagine, in 
the first place, that a very considerable portion of these irregu- 
larities is due to errors of observation, by not determining the 
amplitudes of the arcs of vibration with the requisite degree of 
exactness ; and the apparent inconsistencies in the law of de- 
crease of the arcs of vibration, confirm me in this opinion. 
Secondly, A part of these irregularities might possibly be 
occasioned by the great inequality of the weights applied to 
the brass pendulum, and to the mode of their arrangement ; 
because, when the great weight is above, the reciprocation of the 
* M. Breguet’s ingenious invention, which we have already described in p. 323. 
will, we have no doubt, be found applicable to this class of experiments. — En. 
Z S 
