As just another application of the midframe lemma, we end this section with a proof of the obvious-seeming 'reciprocity theorem' which asserts of any pair $S$ and $S'$ of inertial frames, using standard identical standards of length and time, that each ascribes the same velocity to the other. For the manipulation performed in $S$ to determine the velocity of $S'$ can be regarded as an experiment in the midframe $S''$. By a suitable 180- rotation in $S''$ this experiment is transformed into a manipulation in $S'$ for determining the velocity of $S$. And by the assumed isotropy of $S''$ , the two outcomes must be the same.
Why does Rindler differentiate between 'experiment' and 'manipulation' in the above?
