It, has been suggested that the distortion of the revolving mirror, either by twisting or by the effect of centrifugal force, might cause an error in the deflection.
The only plane in which the deflection might be affected is the plane of rotation. Distortions in a vertical plane would have simply the effect of raising, lowering, or extending the slit.
Again, if the mean surface is plane there will be no effect on the deflection, but simply a blurring of the image.
Even if there be a distortion of any kind, there would be no effect on the deflection if the rays returned to the same portion whence they were reflected.
The only case which remains to be considered, then, is that given in Fig. 15, where the light from the slit a, falls upon a distorted mirror, and the return light upon a different portion of the same.
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.