the Pendulum vibrating Seconds in the Latitude of London. 425 
by having the bar so thin as to ensure its becoming perpendicular 
by its own weight, had the position of the knife edge been in a 
small degree erroneous ; for though the form the bar would as- 
sume is strictly speaking a curve, it may without sensible error 
be considered as a straight line. 
With regard to temperature, every precaution was taken to 
prevent error. The thermometer used was made by Mr. Trough- 
ton for the late Sir George Shuckburgh. It is divided into half 
degrees, and the height of the mercury may be estimated to one- 
tenth of adegree. It has been already observed in the preceding 
part of this paper, that the thermometer was approached only 
at the first and last coincidences. 
The experiments themselves afford, it is presumed, a sufficient 
proof of the stability of the knife edges. Every care was taken 
to form them in the first instance as perfect as possible ; and after 
four sets of experiments had been made, they were found on 
remeasurement to have suffered no perceptible alteration; and 
it is evident by the near agreement of the results, that they re- 
mained uninjured during the succeeding experiments; it is dif- 
ficult therefore to conceive that any error can have arisen from 
this source. 
I may here remark, that the method I have employed in de- 
termining the length of the pendulum, possesses other advan- 
tages besides that of superseding the errors arising from unequal 
density or figure; and one, not the least eonsiderable; i iS, that after 
a very few vibrations, the true length of the pendulum is bounded 
by certain known Linaits, Thus in the two first sets of experiments, 
after the remeasurement of the distance betwcen the knife edges, 
we may remark that when the slider was at 29 divisions, the num - 
ber of vibrations (the great weight being below) was, 86057°85 
and in defect ; and when the slider was removed to 19 divisions, 
the number of vibrations was 86059-41 and in ewcess. ‘The true 
number of vibrations then is evidently between the two, and the 
utmost extent of error in using either of these numbers must fall 
short of 1+75 their difference when reduced to the same tempera- 
ture. But if the mean be employed in the computation, the 
length of the pendulum will be found to differ only about four 
ten-thousandths of an inch from the mean result given in the 
foregoing table. 
It may not be unnecessary to add, that every experiment made 
has been retained; nor do I consider any one as less entitled to 
credit than the rest, excepting that marked A, in the table; and 
that, only because the rate of the clock was not observed on the 
day of the experiment, but was taken to be the same as the rate 
of the following day. 
The 
