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Rh composition of velocities we find for these velocities the relations $$u_{1}=\tfrac{u-v}{1-uv/c^{2}}$$ and $$u_{2}=\tfrac{-u-v}{1+uv/c^{2}}$$. Since these velocities are not of the same magnitude, the two bodies which have the same mass when at rest do not now have the same mass to this observer. Let us call these masses before collision $$m_1$$ and $$m_2$$. During collision, the velocities of the bodies will all the time be changing; from the principle of the conservat1on of mass, however, the sum of the two masses will always equal $$m_{1}+m_{2}$$. When in the course of the collision the bodies have come to relative rest and are both moving past our observer with the velocity -$$v$$, their momentum will be $$-\left(m_{1}+m_{2}\right)v$$, and from the principle of the conservation of momentum this must be equal to the original momentum before collision, giving us the equation,-

Simplifying, we have,-

which by direct algebraic transformations may be shown to be identical with