We frequently fail to notice that every action of a force is accompanied by a reaction. If a valise is placed on a bed with a spring mattress, the bed will sag. The fact that the weight of the valise acts on the bed is obvious to everyone. Sometimes, however, we forget that the bed also exerts a force on the valise. As a matter of fact, the valise lying on the bed does not fall; this means that there is a force acting on it equal to the weight of the valise and directed upwards.

Forces which are opposite in direction to gravity are often called reactions of the support. The word “reaction” means “counteraction”. The action of a table on a book which is lying on it and the action of a bed on a valise which has been placed upon it are reactions of the support.

As we have just said, the weight of a body can be determined with the aid of a spring balance. The pressure of the body on the spring which has been placed under it, or the force stretching the spring on which the load has been suspended, is equal to the weight of the body. It is obvious, however, that the contraction or tension of the spring can just as well be used to obtain the value of the reaction of the support.

Thus, measuring the magnitude of some force by means of a spring, we measure the value of not one but of two forces opposite in direction. Spring balances measure the pressure exerted by the load on the pan, and also the reaction of the support—the action of the pan on the load. Fastening a spring to a wall and pulling it by hand, we can measure the force with which our hand pulls the spring and, simultaneously, the force with which the spring pulls our hand.

Therefore, forces possess a remarkable property: they are always found in pairs and are, moreover, equal in magnitude and opposite in direction. It is these two forces which are usually called action and reaction.

“Single” forces do not exist in nature—only mutual reactions between bodies have a real existence; moreover, the forces of action and reaction are invariably equal—they are related to each other as an object is related to its mirror image.

One should not confuse balancing forces with forces of action and reaction. We say that forces are balanced if they are applied to a single body; thus, the weight of a book lying on a table (the action of the Earth on the book) is balanced by the reaction of the table (the action of the table on the book).

In contrast to the forces which arise in balancing two interactions, the forces of action and reaction characterize one interaction, for example, of a table with a book. The action is “table-book” and the reaction is “book-table”. These forces, of course, are applied to different bodies.

Let us try to clear up the following traditional misunderstanding: “The horse is pulling the waggon, but the waggon is also pulling the horse; why then do they move?” First of all, we must recall that the horse will not move the waggon if the road is slippery. Hence, in order to explain the motion, we must take into account not one but two interactions-not only “waggon-horse” but also “horse-road”. The motion will begin when the force of the interaction “horse-road” (the force with which the horse pushes off from the road) exceeds that of the interaction “waggon-horse” (the force with which the waggon pulls the horse). As for the forces “waggon nulls horse” and “horse pulls waggon”, they characterize one and the same interaction, and will therefore be identical in magnitude when at rest and at any instant during the course of the motion.