of Edinburgh, Session 1877 - 78 . 
641 
velocity 3 -60210, as at A in fig. 2, it will reach its highest point 
in the time 1*3, the height to which it will rise being 1 ‘31864, as 
shown in the third column. The subsequent fall is shown in the 
fourth column, and there we find that the same level is reached just 
before the time 2*0; the whole time of flight being somewhat less 
than 3 3. 
To translate this into ordinary measures, let us suppose a body 
whose terminal velocity is 320 feet per second ; the time in which 
this velocity is acquired in free fall is 10 seconds, and therefore all 
the tabular times must be multiplied by 10, the tabular velocities 
by 320, and the linear distances by 3200. Hence if such a body 
were thrown upwards with a velocity of 1152 feet per second, it 
would rise in 13 seconds to a height of 4230 feet, and would thence 
descend in 19 ‘9 3 seconds, striking the ground with the velocity of 
308 feet per second. 
This table enables us to interpret easily the results of experiments 
made on falling bodies. Thus, if the height and the time of descent 
be accurately observed, we may thence deduce the terminal velocity; 
from which, again, knowing the weight and the extent of surface, 
we may discover the constant of the coefficient of resistance. In 
order to facilitate the computations for this class of experiments, we 
may annex another column to our table, namely, one containing the 
ratio of the time of free fall to the actual time of fall. Thus the 
fall through the distance 1*32500, which is done in the time 2*0 
with resistance, would be accomplished in 1*62788 if there were no 
resistance due to velocity, and the ratio, as shown in the annexed 
column, is *81394. 
Suppose now that a body has been dropped from a height of 400 
feet, and that the observed time of the fall is 6 seconds ; the time 
of falling freely from this height is known to be 5 seconds, and 
therefore the ratio is *83333. The table shows that this ratio be- 
longs to the tabular time 1*8271, and that, consequently, 3*284 
seconds is the time in which the terminal velocity is acquired in 
falling freely ; that terminal velocity, therefore, must be 105 feet 
per second. 
In experiments of this kind, the disengagement at the beginning 
and the stroke at the end of the fall may be made, by help of the 
