The methods usually adopted for demonstrating the Lorentz Transformation are algebraic. Algebra is a powerful means of arriving at results, but does not in itself explain those results. In the present matter, the average reader is left with a sense of puzzledom, baffled by the paradoxes evolved by the algebra ; the results are demonstrated, but he is unsatisfied. The following paper is an attempt to treat the matter from first principles, avoiding algebra and getting down to the plain common sense. The results are obtained quite simply ; paradox is avoided. Some observations are hazarded at the end on the questions of simultaneity, “before” and “after,” in which the view taken differs somewhat radically from that ordinarily adopted.