Now let us see what follows. There is at the base of classical mechanics, as it was founded by Galileo, Huyghens, and Newton, and as it is taught everywhere, a principle which is in the long run, like all the principles of mechanics, grounded upon experience. It is the principle of the composition of velocities. If a boat, which makes ten miles an hour in smooth water, sails down a river which flows at five miles an hour, the speed of the boat in relation to the bank will be, as we may find by actual measuring, equal to the sum of the two speeds, or fifteen miles an hour. This is the rule of the addition of velocities. In a more general way, if a body starts from a state of rest, and under the action of some force takes on in a second the velocity =V=, what will it do if the action of the force is prolonged for another second? According to classical mechanics it will take on the velocity =2V=.[7] Let us imagine an observer who is travelling at the velocity =V=, yet thinks he is at rest. It will seem to him, at the end of the first second, that the body is at rest (because it has the same velocity as the observer). In virtue of the Classical Principle of Relativity, the apparent movement of the body must be the same for our observer as if the rest were real. This means that at the end of the second second the relative velocity of the body in reference to the observer will be =V=, and, as the observer already has the velocity =V=, the absolute velocity of the body will be =2V=. In the same way it will be =3V= at the end of three seconds, =4V= at the end of four seconds, and so on. Could it increase indefinitely if the force continues to act long enough? Classical mechanics says “yes.” Einstein says “no,” because there cannot be a greater velocity than that of light. [7] As an example of an identical force acting during periods of time successively equal to 1, 2, or 3, we may take three guns of the same calibre, but of lengths equal to 1, 2, and 3, and of which the charges, or rather, their propulsive forces, are identical and constant. It is found that the initial velocities of the shells are, in relation to each other, 1, 2, and 3. We have imagined an observer who has the velocity V relatively to us, and who believes that he is at rest. For him the body observed was likewise at rest at the beginning of the second second, because its velocity was the same as that of the observer. From the fact that the apparent movement of the body is for the observer, during the second second, the same as it was for us during the first, classical mechanics concluded that its velocity doubles during the second second. It did not know what Einstein has now taught us: that the time and space of this observer are different from ours.