The one pencil takes the course _a b c d e f a′_, while the other follows
the path _a f g h i b a′_.

In other words, besides the image coinciding with _a_, there would be two
images, one on either side of _a_, and in case there were more than two
portions having different inclinations there would be formed as many
images to correspond. If the surfaces are not plane, the only effect is to
produce a distortion of the image.

As no multiplication of images was observed, and no distortion of the one
image, it follows that the distortion of the mirror was too small to be
noticed, and that even if it were larger it could not affect the
deflection.

The figure represents the distorted mirror at rest, but the reasoning is
the same when it is in motion, save that all the images will be deflected
in the direction of rotation.



Imperfection of the Lens.


It has also been suggested that, as the pencil goes through one-half of
the lens and returns through the opposite half, if these two halves were
not exactly similar, the return image would not coincide with the slit
when the mirror was at rest. This would undoubtedly be true if we consider
but one-half of the original pencil. It is evident, however, that the
other half would pursue the contrary course, forming another image which