FOR DETERMINING THE MEAN DENSITY OF THE EARTH. 
313 
Section III. — General System of observing the Pendulums and of reducing the 
Observations. 
29. Before describing the obsei-vations, &c., I will remai-k that the pendulums 
above and below wei’e mounted in exactl}’^ the same manner. Each angle of the 
iron stand, in each station, rested on a single brick ; and gi-eat cai’e was taken by 
Mr. Dunkin that the bearing of these bricks should he perfectly solid. It was also 
a subject of Mr. Dunkin’s special attention to make the supplementary hexagonal 
iron fi’ame (which I have described in article 15) quite firm ; and, above all, to fix 
firmly at the beginning of each series and to examine cai-efully at the end of each 
series the frame carrying the agate-planes. In every instance these were found per- 
fectly firm in their attachment. At every interchange of pendulums, Mr. Dunkin 
carefully oiled and wiped the knife-edges and their agate-planes. At the beginning 
of every swing, the observer raised the knife-edge from contact with the agate-plane, 
by the screw-lifting apparatus, and then lowered it gently to a definite line of bearing. 
30. The pendulum being observed in Rater’s manner, by using the concealment 
of the bright disk on the clock-pendulum-bob behind the tail of the detached pen- 
dulum, when passing the aperture through which alone the disk can be seen, as indica- 
tion of the Coincidence of the two pendulums in the times of passing their respective 
quiescent points; and supposing that there are trifling errors in the adjustments 
of position ; it is seen in practice, or is shown by a very simple investigation, that the 
disk will first disappear in passing from one side (suppose the right side) towards 
the centre, then will disappear in passing from the left side (after which, if the errors 
of adjustment are in the proper direction, it will be invisible during several vibra- 
tions), then it will reappear on the left side, and will finally reappear on the right 
side. Either the mean of the times of the first and fourth phenomenon, or the mean 
of the second and third, or the mean of all four, may be used as the true time of 
Coincidence; and it was left to the discretion of the observers to adopt which they 
preferred. They chose, in every case, to observe the first and fourth only. This 
amounts in fact to using only one side of the aperture. 
It is necessary for the success of this observation that the arc of the detached 
pendulum be less than that of the clock pendulum ; in fact it was always much less. 
It is indifferent whether the detached pendulum vibrate quicker or slower than the 
clock pendulum ; in fact it always vibrated slower. 
31. Several Coincidences were always observed at the beginning- of a Swing, and 
several at the end. These gave the Interval of Coincidences nearly enough to enable 
me to fix upon the number of intervening Coincidences. In general, some of the 
observed Coincidences were rejected, so that from two to five Coincidences were 
retained at the beginning, and a number at the end so corresponding that the differ- 
ence of their means would represent an integral number of Intervals (thus there 
might be 3 at the beginning and 5 at the end, or 4 at the beginning and 2 at the 
2 T 
MDCCCLVI. 
