McCullough wrote:

As for deriving the Lorentz tranformations, here's a derivation, going
back to Sam and Joe. Let's introduce two new characters, Sally and Jane.

Sam and Joe are at rest relative to frame B (for Boys).
Sally and Jane are at rest relative to frame G (for Girls).
Let the speed of frame B as measured in frame G be v.

Androcles:
_______________________________  --> v
_|_|_|_|_|_|_|B|_|_|_|_|_|_|_|_

_______________________________
_|_|_|_|_|_|_|G|_|_|_|_|_|_|_|_


McCullough:
Also, by symmetry let the speed of frame G as measured in frame B also
be v.

Androcles:
_______________________________
_|_|_|_|_|_|_|B|_|_|_|_|_|_|_|_

_______________________________ --> v
_|_|_|_|_|_|_|G|_|_|_|_|_|_|_|_

v = 0