equal to that which it covered in the first second of its flight. Second, if it were not moving
horizontally, but merely falling, it would fall vertically with a velocity proportional to the time
since the flight began. In fact, its change of place is what it would be if it first moved horizontally
for a second with the initial velocity, and then fell vertically for a second with a velocity
proportional to the time during which it has been in flight. A simple calculation shows that its
consequent course is a parabola, and this is confirmed by observation except in so far as the
resistance of the air interferes.
The above gives a simple instance of a principle which proved immensely fruitful in dynamics,
the principle that, when several forces act simultaneously, the effect is as if each acted in turn.
This is part of a more general principle called the parallelogram law. Suppose, for example, that
you are on the deck of a moving ship, and you walk across the deck. While you are walking the
ship has moved on, so that, in relation to the water, you have moved both forward and across the
direction of the ship's motion. If you want to know where you will have got to in relation to the
water, you may suppose that first you stood still while the ship moved, and then, for an equal time,
the ship stood still while you walked across it. The same principle applies to forces. This makes it
possible to work out the total effect of a number of forces, and makes it feasible to analyse
physical phenomena, discovering the separate laws of the several forces to which moving bodies
are subject. It was Galileo who introduced this immensely fruitful method.
In what I have been saying, I have tried to speak, as nearly as possible, in the language of the
seventeenth century. Modern language is different in important respects, but to explain what the
seventeenth century achieved it is desirable to adopt its modes of expression for the time being.
The law of inertia explained a puzzle which, before Galileo, the Copernican system had been
unable to explain. As observed above, if you drop a stone from the top of a tower, it will fall at the
foot of the tower, not somewhat to the west of it; yet, if the earth is rotating, it ought to have
slipped away a certain distance during the fall of the stone. The reason this does not happen is that
the stone retains the velocity of rotation which, before being dropped, it shared with everything
else on the earth's surface. In fact, if the tower were high