47 6 Mr - Cavendish’s Experiments to determine 
point of rest found by the second, third, and 4th extremes, is 
24,7, and so on. The fifth column is the time at which the 
arm came to the middle point of the vibration, which is thus 
found: the mean between 27,2 and 22,1 is 24,65, and is the 
middle point of the first vibration; and, as the arm came to 25 
at io h 23' 4", and to 24 at io h 23' 57", we find, by proportion, 
that it came to 24,65 at io h 23' 23 // . In like manner, the arm 
came to the middle of the seventh vibration at n h 5' 22"; and, 
therefore, six vibrations were performed in 4 i' 59", or one vibra- 
tion in 7' o". 
To judge of the propriety of this method, we must consider 
in what manner the vibration is affected by the resistance of 
the air, and by the motion of the point of rest. 
Let the arm, during the first vibration, move from D to B, (Tab. 
XXIV. fig- 3.) and, during the second, from B to d; ¥>d being less 
thanDB, on account of the resistance. Bisect DB in M, and Bd in 
m, and bisect M m in n , and let x be any point in the vibration ; 
then, if the resistance is proportional to the square of the velocity, 
the whole time of a vibration is ver}^ little altered ; but, if T is 
taken to the time of one vibration, as the diameter of a circle 
to its semicircumference, the time of moving from B to n ex- 
ceeds ~ a vibration, by - - "P— nearly ; and the time of moving 
from B to m falls short of j- a vibration, by as much ; and the 
time of moving from B to x, in the second vibration, exceeds 
that of moving from x to B, in the first, by 
supposing Y)d to be bisected in T; so that, if a mean is taken, 
between the time of the first arrival of the arm at x and its re- 
turning back to the same point, this mean will be earlier than 
the true time of its coming to B, by -o^ 7 ¥Fx 7 r 
