  An in-depth and mathematically-detailed analysis of Langevin's popular 1911
article on the special theory of relativity is presented. For the reader's
convenience, English translations of large parts of the original French text
are given. The self-contradictory nature of many of Langevin's assertions is
pointed out. Of special interest is the analysis of the exchange of light
signals between the travelling and stay-at-home twins in Langevin's thought
experiment, in which antinomies are found in the conventional relativistic
treatment. Their resolution shows that the physical basis of the differential
aging effect in the experiment is not `length contraction', as in the
conventional interpretation, but instead the application of the correct
relative velocity transformation formula. The spurious nature of the correlated
`length contraction' and `relativity of simultaneity' effects of conventional
special relativity is also demonstrated. In consequence, an argument given,
claiming to demonstrate that an upper limit of $c$ on the speed of any physical
signal is required by causality, is invalid. Its conclusion is also in
contradiction with astronomical observations and the results of a recent
experiment.
