How Ampere could have derived the Lorentz Transformations
  Lorentz Transformations of Special Relativity are derived from two postulates: the first is the Principle of Relativity, while the postulate of invariance of the velocity of light, used in usual derivations, is replaced by a law of lectro-magneto-statics and invariance of electrical charge. Our derivation does not require the assumption of regularity conditions of the Transformations, such as linearity and continuity required by other derivations. The level of the needed mathematics and physical concepts makes the proposed derivation suitable for Secondary School. 
Gemma Faraco, Giuseppe A. Nistico'