IF we refer several events to the same system of position and time co-ordinates, and then consider the same events referred to another system, the position co-ordinates and times in the two systems are connected by a set of algebraic relations, called the Lorentz-Einstein transformation. The FitzGerald contraction refers only to a part of these relations between the co-ordinates; an argument that assumes it and omits to consider the other relations is not dealing with the principle of relativity. If the positions and times in two systems of reference B and C are connected with those in another system A by such transformations, those in system C can be found in terms of those referred to B by algebra, and it is found that the relation between B and C is another Lorentz-Einstein transformation, and involves no mention of A whatever.