The law of parallelogram of velocities hold up to the first order of approximation. We can put
,
and
i.e., is put equal to the angle between the velocities v, and w. Then we have—
It should be noticed that v and w enter into the expression for velocity symmetrically. If w has the direction of the ξ-axis of the moving system,
From this equation, we see that by combining two velocities, each of which is smaller than c, we obtain a velocity which is always smaller than c. If we put , and where and are each smaller than c,
.
It is also clear that the velocity of light c cannot be altered by adding to it a velocity smaller than c. For this case,