Then show that a weight may be replaced, not only by another weight, but by force of a different nature; for instance, Prony's brake permits replacing weight by friction.
From all this arises the notion of the equivalence of two forces.
The direction of a force must be defined. If a force F is equivalent to another force F´ applied to the body considered by means of a stretched string, so that F may be replaced by F´ without affecting the equilibrium, then the point of attachment of the string will be by definition the point of application of the force F´, and that of the equivalent force F; the direction of the string will be the direction of the force F´ and that of the equivalent force F.
From that, pass to the comparison of the magnitude of forces. If a force can replace two others with the same direction, it equals their sum; show for example that a weight of 20 grams may replace two 10-gram weights.
Is this enough? Not yet. We now know how to compare the intensity of two forces which have the same direction and same point of application; we must learn to do it when the directions are different. For that, imagine a string stretched by a weight and passing over a pulley; we shall say that the tensor of the two legs of the string is the same and equal to the tension weight.
This definition of ours enables us to compare the tensions of the two pieces of our string, and, using the preceding definitions, to compare any two forces having the same direction as these two pieces. It should be justified by showing that the tension of the last piece of the string remains the same for the same tensor weight, whatever be the number and the disposition of the reflecting pulleys. It has still to be completed by showing this is only true if the pulleys are frictionless.
Once master of these