With a
seven-fold velocity at starting, the weight would rise to 49 times the
height, or to an elevation of 784 feet.

Now the work done--or, as it is sometimes called, the _mechanical
effect_--other things being constant, is, as before explained,
proportional to the height, and as a double velocity gives four times
the height, a treble velocity nine times the height, and so on, it is
perfectly plain that the mechanical effect increases as the square of
the velocity. If the mass of the body be represented by the letter m,
and its velocity by v, the mechanical effect would be proportional to
or represented by m v2. In the case considered, I have supposed the
weight to be cast upward, being opposed in its flight by the
resistance of gravity; but the same holds true if the projectile be
sent into water, mud, earth, timber, or other resisting material. If,
for example, we double the velocity of a cannon-ball, we quadruple its
mechanical effect. Hence the importance of augmenting the velocity of
a projectile, and hence the philosophy of Sir William Armstrong in
using a large charge of powder in his recent striking experiments.

The measure then of mechanical effect is the mass of the body
multiplied by the square of its velocity.

Now in firing a ball against a target the projectile, after collision,
is often found hot. Mr. Fairbairn informs me that in the experiments
at Shoeburyness it is a common thing to see a flash, even in broad
daylight, when the ball strikes the target. And if our lead weight be
examined after it has fallen from a height it is also found heated.
Now here experiment and reasoning lead us to the remarkable law that,
like the mechanical effect, the amount of heat generated is
proportional to the product of the mass into the square of the
velocity. Double your mass, other things being equal, and you double
your amount of heat; double your velocity, other things remaining
equal, and you quadruple your amount of heat. Here then we have
common mechanical motion destroyed and heat produced. When a violin
bow is drawn across a string, the sound produced is due to motion
imparted to the air, and to produce that motion muscular force has
been expended. We may here correctly say, that the mechanical force
of the arm is converted into music. In a similar way we say that the
arrested motion of our descending weight, or of the cannon-ball, is
converted into heat. The mode of motion changes, but moti