148 ON MR. EWART’S PAPER ON THE 
v=velocity which would be generated in a body 
p, during its fall through a distance s, and g= the 
force of gravity (=32}) feet); then, by the laws 
of falling bodies, =F and 
ps=piv . 
Here ao is called the vis viva of the body p, 
whose velocity is v, and the quotient “ represents 
the mass of the body. 
If ps be represented by w we have 
w= Hiv’ 
whence the vis viva is equal to double the work 
done. 
It appears that the quantity of work done by 
gravity, to impress a certain velocity v upon a 
falling body p, is equal to the half of re the vis 
viva generated in it. And, for the same reason, 
the quantity of work done by gravity in the 
taking away of a velocity v from a body p, thrown 
upwards, will be measured by half the vis viva, 
as before. 
