the reflection would take place in the direction _a″_, making the angles
_c′ o p_, and _p′ o a″_ equal. But the angle _c o c′_ must be added to _p
o a″_, in consequence of the motion of the mirror, or the angle of
deviation will be _a o a″ + c o c′_; or _a o a″ + c o c′ = d_. (1)

By construction--

c o p′ = p′ o a′ (2)
c′ o p′ = p′ o a″ (3)

Subtracting (3) from (2) we have--

c o p′ - c′ o p′ = p′ o a′ - p′ o a″_, or
c o c′ = a′ o a″_

Substituting _a′ o a″_ for _c o c′_ in (1) we have--
_a o a″ + a′ o a″ = a o a′ = d_.

Or the deflection has remained unaltered.



Retardation Caused by Reflection.


Cornu, in answering the objection that there may be an unknown retardation
by reflection from the distant mirror, says that if such existed the error
it would introduce in his own work would be only 1/7000 that of Foucault,
on account of the great distance used, and on account of there being in
his own experiments but one reflection instead of twelve.