78 
Proceedings of Royal Society of Edinburgh. [sess. 
weight of the body has over the resistance of the air, after any 
interval of falling. Thus the downward acceleration 
GA 2 
7?^ 
a GA „ 
W 
W 
9 
= 3 - W*' 
or 
du GA „ j 7, 
-n = 9 — ww and dt = 
dt '' W 
dv 
GA . 
As can never actually become equal to the expression 
GA 
GA 
g--^v^ will never become zero ; thus the left-hand side of the 
last equation is continuous, and can be integrated in all cases. 
or 
whence 
and 
therefore 
IH; 
dv 
-w^ 
t= 
/GA, 
V w 
. lot 
- /GA 
j9 + \J YU ^ 
V 
GA 
1 1 ^ ^ GA 
t; ; where ^ ^ 
^Jkg Jg-vJk’ W 
1 -1 — s/g + ^ 
log 2 t - 1 ^ 
\og-'^2t ^ g 
~ 2 
i Q^W^g + 1 j 
Whence it will be seen after the first second, the falling body 
will have attained a velocity of only i= short of its 
log ~^^J' 
GA 
AY 
^7+1 
