475 
the Density of the Earth. 
two given divisions between these extremes, taking care, as well 
as I can guess, that these divisions shall be on different sides of 
the middle point, and not very far from it. I then compute 
the middle point of the vibration, and, by proportion, find the 
time at which the arm comes to this middle point. I then, after 
a number of vibrations, repeat this operation, and divide the 
interval of time, between the coming of the arm to these two 
middle points, by the number of vibrations, which gives the 
time of one vibration. The following example will explain 
what is here said more clearly. 
Extreme 
Points. 
Division. 
27,2 
2 5 
24 
22,1 
- 
27 
22,6 
- 
26,8 
- 
23 
2 6,6 
25 
, 24 
2 3>4 
Time. 
Point of 
rest. 
Time of middle 
of vibration. 
h. 
/ V 
10 2 3 41 
h - / 
57 J 
10 23 23 
- 
24,6 
- ~ 
24,7 
- 
24-75 
- 
24*8 
ecu 09 
24,85 
— - 
2 4>9 
11 5 221 
6’ 48} 
! 
11 5 22 
The first column contains the extreme points of the vibra- 
tions. The second, the intermediate divisions. The third, the 
time at which the arm came to these divisions ; and the fourth, 
the point of rest, which is thus found : the mean between the 
first and third extreme points is 27,1, and the mean between 
this and the second extreme point is 24,6, which is the point of 
rest, as found by the three first extremes. In like manner, the 
3 P 2 
