go Capt. Kater’s experiments for determining the 
during a certain number of seconds and parts of a second which 
constitute the interval. The disappearance of the disk can how- 
ever be noted only to a single second, and the brass pendulum 
may arrive at the lowest part of the arc either precisely at this 
second, or at any portion of a second preceding it. An error 
might possibly arise from this circumstance amounting to 
nine tenths of a second, by which the interval deduced from 
observation would be less than the truth, and as an error of 
one second in the interval, occasions a difference of 0,63 in 
the number of vibrations in 24 hours, if 0,55 ( the proportional 
part of 0,63) be divided by 4 (the number of intervals form- 
ing each set of experiments) we have 0,14 for the greatest 
error in defect in the number of vibrations in 24 hours which 
can arise from this cause. 
On the contrary, if the second coincidence or return of the 
brass pendulum to the lowest point of the arc, should have 
taken place nine tenths of a second before the second at 
which the disappearance of the disk was noted, the error in 
the number of vibrations in 24 hours would amount to the 
same quantity, and would now be in excess. 
If the first and third coincidences take place accurately at 
the time of the observed disappearance of the disk, and the 
observation of the second coincidence should differ nine tenths 
of a second from the truth, it is obvious that the number of 
vibrations in 24 hours deduced from each interval will be 
erroneous about 0,56 the one being in excess, the other in 
defect : The mean of both will be the truth, though the ob- 
served difference between the two amounts to so considerable 
a quantity as 1,2. 
The last coincidence of each set, takes place when the arc 
