of Edinburgh, Session 1877-78. 
639 
Fig. 2. 
N 
i 
9 
,5 
1,0 
1,0 
fore, is to reach a definite terminal velocity, and the stone ultimately 
moves almost uniformly. If it had been 
thrown downwards at a rate greater than this 
terminal velocity, its motion would have been 
retarded, but less and less so as it approximated 
to the same limit of uniform motion. 
We may study the ascent by tracing it back- 
wards from the highest point, fancying the air 
to have then the quality of hastening the 
motion. In this case the velocity would in- 
crease to become infinite ; but this infinite 
velocity would be acquired in a finite time. 
In fact, the time being represented by a cir- 
cular arc, the velocity would be proportional 
to the tangent of that arc, so that in the time 
corresponding to a whole quadrant, the velocity 
would become infinite. Thus it seems that, 
however rapidly a stone may be thrown up- 
wards, its motion is extinguished within a 
finite time determined by the coefficient of 
resistance. 
Each particular body has its own terminal 
velocity depending on the weight and on the 
extent and peculiarities of the surface exposed 
to resistance ; but the motions of all follow 
exactly the same law, so that one diagram may 
serve for all, the units of comparison alone 
needing to be changed. 
Also, one table of the positions and velocities 
may be made to do for all cases. In the 
arrangement of such a table we have to seek 
for the most convenient system of units; now, 
on contemplating the motion of a projectile 
independently of our measures of time and 
distance, we perceive that the terminal speed 
is the only standard with which we can com- 
pare the velocities at the various parts of the path, wherefore we 
adopt this terminal velocity as the tabular unit of speed. 
1,5 
A 
2,0 
Z 
