Let light be a disturbance moving at c through a local space taken
as stationary.  Let A and B be two points 1 unit apart on the Y axis
of system K that is moving through this space at .6c in the x
direction. At t = 0 let a ray of light emit from A toward B and
reflect therefrom back to A.
  As plotted by a system k' at rest in this space, with its X' axis
coinciding with X of K and its vertical axes parallel to those of K,
the ray moves up Y at c' = qc, where q = sqrt of (1 - v^2/c^2), thus
takes t' = 1.25 seconds each way. In order for K to measure this as 1
secodn each way, thus to let c' = 1 as plotted by K, clocks of the
moving system have to run slow by q, wherefore t = qt = .8 x 1.2 each
way. (Note that the path of the beam is on the hypotenuse of a right
triangle, of which Y is one side and vc is the length of the other.
given that B is 1 unit from A on Y, then AB = 1 is the length of Y as
measured by both systems; and the hypotenuse is 1.2 units long as
measured by k; which is WHY ittakes a ray 1.25 seconds to get from A
to b as plotted by stationary cs k.
  HOWEVER!!  There is no reason to let moving systems clocks run slow
by q or for their vertical axes to remain undeformed while their
horizontal axis shrinks by q. Suppose, for instance, that lengths
remain constant in the direction a system is moving through the above
stationary space. If its lengths EXPAND by 1/q in the vertical axes
and its clocks run slow by q = q^2 = (c^2-v^2), then it would measure
the light's time from A to B and from B to A, thus up and then down Y
or Z as t = 1 second, and the speed of light would remain c = 1 unit/
sec as plotted by K.
  Suppose that lengths in the vertical axes SHRINK by q. then clocks
of moving systems could keep identical rates as stationary ones and it
would still take 1 second for a ray to travel up 1 unit on y and back
again. (If that happens, then lengths in the direction of motion would
have to shrink by Q in order to measure the round-trip time as 1
second per unit of length, thus for c to remain equal to 1 as plotted
by the moving systems. As to the one way times per unit length of such
deformed systems, unless clocks of each such system is set to MEASURE
c = 1 in all directions - i.e. to be esynched via Einstein's defined
method which he called "synchronized" - they won't.)

p.s.  If we let moving systems deform as per the LTE - thus let
lengths remain constant in the vertical axes and shrink by q in the
direction of motion, with clocks running q slow - and consider the
first case discused above, then even though rays would travel up and
down Y in 1 second each way as plottted by k, the ray would have
emitted from x=y=x'=y'=0 and would return to x=y=y'=0 as plotted by k
and k; but would NOT have returned to x' = 0 as plotted by the
stationary system k! It would return to x' = 0 + 2vt'; which is WHY
the moving clocks on X have to have a Voigtian local time offset of -
vx/c^2 seconds per successive clock, in which x is the distance
between two such clocks as measured by the given moving system itself,
and v - which doesn't have to be known by the esyching cs - is its
speed in the 'empty space" in which Einstein postulated that light
moves at c.