Part 7 (2/2)

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?_

Subst.i.tuting _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.

r.e.t.a.r.dation Caused by Reflection.

Cornu, in answering the objection that there may be an unknown r.e.t.a.r.dation 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.

Distortion of the Revolving Mirror.

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.

[Ill.u.s.tration: FIG. 15]

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.

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