10 FR A OMENTS OF SCIENCE. 
upward, it moves in opposition to gravity, which inces- 
santly retards its motion, and finally brings it to rest at an 
elevation of sixteen feet. If not here caught by the brick- 
layer, it would return to the hodman with an accelerated 
motion, and reach his hand with the precise velocity it 
possessed on quitting it. 
An important relation between velocity and work is here 
to be pointed out. Supposing the hodman competent to 
impart to the brick, at starting, a velocity of sixty-four 
feet a second, or twice its former velocity, would the 
amount of work performed be twice what it was in the 
first instance? No; it would be four times that quantity; 
for a body starting with twice the velocity of another, will 
rise to four times the height. In like manner, a three- 
fold velocity will give a ninefold elevation, a fourfold 
velocity will give a sixteenfold elevation, and so on. The 
height attained, then, is not proportional to the initial 
velocity, but to the square of the velocity. As before, 
the work is also proportional to the weight elevated. 
Hence the work which any moving mass whatever is com- 
petent to perform, in virtue of the motion which it at any 
moment possesses, is jointly proportional to its weight and 
the square of its velocity. Here, then, we have a second 
measure of work, in which we simply translate the idea of 
height into its equivalent idea of motion. 
In mechanics, the product of the mass of a moving body 
into the square of its velocity, expresses what is called 
the vis viva, or living force. It is also sometimes called 
the "mechanical effect." If, for example, a cannon 
pointed to the zenith urge a ball upward with twice the 
velocity imparted to a second ball, the former will rise to 
four times the height attained by the latter. If directed 
against a target, it will also do four times the execution. 
Hence the importance of imparting a high velocity to 
projectiles in war. Having thus cleared our way to a per- 
fectly definite conception of the vis viva of moving masses, 
we are prepared for the announcement that the heat 
generated by the shock of a falling. body against the 
earth is proportional to the vis viva annihilated. The 
heat is proportional to the square of the velocity. In the 
case, therefore, of two cannon-balls of equal weight, if 
one strike a target with twice the velocity of the other, 
it will generate four times the heat, if with three times 
