Mass in special relativity detail by Oliver Heaviside (1889) and George Frederick Charles Searle (1897). So the electrostatic energy behaves as having some sort of electromagnetic mass formula_25, which can increase the normal mechanical mass of the bodies. Then, it was pointed out by Thomson and Searle that this electromagnetic mass also increases with velocity. This was further elaborated by Hendrik Lorentz (1899, 1904) in the framework of Lorentz ether theory. He defined mass as the ratio of force to acceleration, not as the ratio of momentum to velocity, so he needed to distinguish between the mass formula_26 parallel to the direction of motion
Velocity-addition formula appear there must be inverted here: This matrix rotates the a pure time-axis vector to , and all its columns are relativistically orthogonal to one another, so it defines a Lorentz transformation. If a fly is moving with four-velocity in the ship frame, and it is boosted by multiplying by the matrix above, the new four-velocity in the shore frame is , Dividing by the time component and substituting for the components of the four-vectors and in terms of the components of the three-vectors and gives the relativistic composition law as The form of the relativistic composition law can be