The constant $c^{2}$ in~\Eq{(7.1)} is positive according to experiments made in regions of the world accessible to us. The $3$~minus signs with $1$~plus sign particularise the world in a way which we could scarcely have predicted from first principles. H.~Weyl expresses this specialisation by saying that the world is $3 + 1$ dimensional. Some entertainment may be derived by considering the properties of a $2 + 2$ or a $4 + 0$ dimensional world. A more serious question is, Can the world change its type? Is it possible that in making the reduction of~\Eq{(2.1)} to the sum or difference of squares for some region remote in space or time, we might have $4$~minus signs? I think not; because if the region exists it must be separated from our $3 + 1$ dimensional region by some boundary. On one side of the boundary we have \[ ds^{2} = -dx^{2} - dy^{2} - dz^{2} + c_{1}^{2}\, dt^{2}, \] and on the other side \[ ds^{2} = -dx^{2} - dy^{2} - dz^{2} - c_{2}^{2}\, dt^{2}. \] The transition can only occur through a boundary where \[ ds^{2} = -dx^{2} - dy^{2} - dz^{2} + 0\, dt^{2}, \] so that the fundamental velocity is zero. Nothing can move at the boundary, and no influence can pass from one side to another. The supposed region beyond is thus not in any spatio-temporal relation to our own universe---which is a somewhat pedantic way of saying that it does not exist. This barrier is more formidable than that which stops the passage of light round the world in de~Sitter's spherical space-time (\Title{Space, Time and Gravitation}, p.~160). The latter stoppage was relative to the space and time of a distant observer; but everything went on normally with respect to the space and time of an observer at the region itself. But here we are contemplating a barrier which does not recede as it is approached. The passage to a $2 + 2$ dimensional world would occur through a transition region where \[ ds^{2} = -dx^{2} - dy^{2} + 0\, dz^{2} + c^{2}\, dt^{2}. \] Space here reduces to two dimensions, but there does not appear to be any \index{Dimensions, world of $3 + 1$}% barrier. The conditions on the far side, where time becomes two-dimensional, defy imagination. \Section{10.}{The FitzGerald contraction} \index{Contraction, FitzGerald}% \index{FitzGerald contraction}% We shall now consider some of the consequences deducible from the Lorentz transformation. \index{Lorentz transformation}%