The Michelson-Morley experiment, compared the longitudinal and transverse cases of reflected light, expecting to detect an ether wind (*Figure 1*).

Figure 1. Michelson-Morley apparatus

They explain: “Let *sa* … be a ray of light which is partly reflected in *ab*, and partly transmitted in *ac*, being returned by the mirrors *b* and *c*, along *ba* and *ca*. [Then] *ba* is partly transmitted along *ad*, and *ca* is partly reflected along *ad*. If then the paths *ab* and *ac* are equal [lengths *L*], the two rays interfere along *ad*.”

By rotating the apparatus they expected to detect an ether wind parallel to *ba* or *ca*. They calculated the round-trip duration (in the notation here) as

But since the independent variable is the distance traversed, duration is a *dependent* variable, and the experiment is in the distance domain. Speeds are distance rate speeds, which add by harmonic addition. So the denominators should be:

and

The period of a round trip is then:

As with a light clock, the round-trip periods would be equal whether or not there was an ether wind, so their null result should have been expected.

*The Lorentz Adjustment*

Expand the mistaken Equation (1) to get

Move one *γ* factor under *T* to get

Equation (3) is still mistaken but suggests an adjustment by defining variables *T′* and *L′* such that

in which time is ‘dilated’ and length is ‘contracted’. Then substitute *T′* and *L′* into Equation (3):

That is,

which is correct. The Lorentz transformation compensates for the mistake in Equation (1) but doesn’t fix it.