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.
In my own experiments the same reasoning shows that if this possible error made a difference of 1 per cent. in Foucault's work (and his result is correct within that amount), then the error would be but .00003 part.