Thus the above set of electro-magnetic experiments contradict the Hertz-Heaviside equations, and these must be abandoned. [P. C. M.] Note 2. Lorentz Transformation. Lorentz. Versuch einer theorie der elektrischen und optischen Erscheinungen im bewegten Körpern. (Leiden—1895). Lorentz. Theory of Electrons (English edition), pages 197-200, 230, also notes 73, 86, pages 318, 328. Lorentz wanted to explain the Michelson-Morley null-effect. In order to do so, it was obviously necessary to explain the Fitzgerald contraction. Lorentz worked on the hypothesis that an electron itself undergoes contraction when moving. He introduced new variables for the moving system defined by the following set of equations. _x¹_ = β(_x_ - _ut_), _y¹_ = _y_, _z¹_ = _z_, _t¹_ = β(_t_ - (_u_/_c²_)·_x_) and for velocities, used _v__{_x_}¹ = β²_v__{_x_} + _u_, _v__{_y_}¹ = β_v__{_y_}, _v__{_z_}¹ = β_v__{_z_} and ρ¹ = ρ/β. With the help of the above set of equations, which is known as the Lorentz transformation, he succeeded in showing how the Fitzgerald contraction results as a consequence of “fortuitous compensation of opposing effects.” It should be observed that the Lorentz transformation is not identical with the Einstein transformation. The Einsteinian addition of velocities is quite different as also the expression for the “relative” density of electricity. It is true that the Maxwell-Lorentz field equations remain _practically_ unchanged by the Lorentz transformation, but they _are_ changed to some slight extent. One marked advantage of the Einstein transformation consists in the fact that the field equations of a moving system preserve _exactly_ the same form as those of a stationary system. It should also be noted that the Fresnelian convection coefficient comes out in the theory of relativity as a direct consequence of Einstein’s addition of velocities and is quite independent of any electrical theory of matter. [P. C. M.] Note 3. See Lorentz, Theory of Electrons (English edition), § 181, page 213. H. Poincare, Sur la dynamique ‘electron, Rendiconti del circolo matematico di Palermo 21 (1906). [P. C. M.] Note 4. Relativity Theorem and Relativity-Principle. Lorentz showed that the Maxwell-Lorentz system of electromagnetic field-equations remained practically unchanged by the Lorentz transformation. Thus the electromagnetic laws of Maxwell and Lorentz _can be definitely proved_ “to be independent of the manner in which they are referred to two coordinate systems which have a uniform translatory motion relative to each other.” (See “Electrodynamics of Moving Bodies,” page 5.) Thus so far as the electromagnetic laws are concerned, the principle of relativity _can be proved to be true_.