Page:Poincare Goettingen En.djvu/2

 In the new mechanics, on the contrary, we assume it to be impossible to communicate to a body starting from rest a velocity beyond that of light. What happens? Consider the same body at rest; give it a first impulse, the same as before, it will take the same velocity; repeat this impulse a second time, the velocity again augments, but it no longer will be doubled; a third impulse will produce an analogous effect, the velocity increases but less and less, the body opposing a resistance which becomes greater and greater. This resistance is inertia, it is what is commonly called mass; all this happens then in this new mechanics as if the mass was not constant, but increased with the velocity.

We can represent the phenomenon graphically: In the old mechanics the body after the first impulse takes a velocity represented by the sect $$\mathrm{O}n_{1}$$; after the second impulse $$\mathrm{O}n_{1}$$ increases by a sect $$n_{1}n_{2}$$ equal to it; at each new



impulse the velocity increases by the same quantity, the sect representing it increasing by a constant length. In the new mechanics, the velocity sect increases by sects $$n'_{1}n'_{2},\ n'_{2}n'_{3},\dots$$ which become smaller and smaller so that we cannot pass beyond a certain limit, the velocity of light.

How have we been led to such conclusions? Have we made direct experiments? The divergences only come out for bodies impelled by great velocities; only then do the indicated differences become perceptible. But what is a very great velocity? Is it that of an automobile making 100 kilometers an hour? We would go wild with excitement over such a speed in the street. But from our