the Density of the Earth. 481 
It must be observed, that in this experiment, the attraction 
of the weights drew the arm from 1 1,5 to 25,8, so that, if no 
contrivance had been used to prevent it, the momentum ac- 
quired thereby would have carried it to near 40, and would, 
therefore, have made the balls to strike against the case. To 
prevent this, after the arm had moved near 15 divisions, I re- 
turned the weights to the midway position, and let them remain 
there, till the arm came nearly to the extent of its vibration, and 
then again moved them to the positive position, whereby the 
vibrations were so much diminished, that the balls did not 
touch the sides ; and it was this which prevented my obser- 
ving the first extremity of the vibration. A like method was 
used, when the weights were returned to the midway position, 
and in the two following experiments. 
The vibrations, in moving the weights from the midway to 
the positive position, were so small, that it was thought not 
worth while to observe the time of the vibration. When the 
weights were returned to the midway position, I determined 
the time of the arm's coming to the middle point of each vibra- 
tion, in order to see how nearly the times of the different vi- 
brations agreed together. In great part of the following expe- 
riments, I contented myself with observing the time of its 
coming to the middle point of only the first and last vibration. 
MDCCXCVIIL 
