.
When this experiment was made, the possibility of doubling, by means of a reflecting telescope, the value of the displacement, and at the same time of completely compensating any effects due to accidental differences of temperature or pressure in the two tubes, had not suggested itself; but I employed a sure method of distinguishing between the effects due to motion, and those resulting from accidental circumstances.
This method consisted in making two successive observations, by causing the rays to traverse the apparatus in opposite directions. For this purpose the source of light was placed at the point where the central band had previously been, when the new bands formed themselves where the source of light had previously been placed.
The direction of the motion of the air in the tubes remaining the same in both cases, it is easy to see that the accidental effects would in both observations give rise to a displacement towards the same tube, whilst the displacement due solely to motion would first be on the side of one tube and then on the side of the other. In this manner a displacement due to motion would have been detected with certainty, even if it had been accompanied by an accidental displacement due, for instance, to some defect of symmetry in the diameters or orifices of the tubes, whence would result an unequal resistance to the passage of air, and consequently a difference of density.
But the symmetry given to the apparatus was so perfect that no sensible difference of density existed in the two tubes during the motion of the air. The double observation was consequently unnecessary; nevertheless it was made for the sake of greater security, and in order to be sure that the sought displacement was not accidentally compensated by a difference of density, which, though small, might be sufficient totally to mask such displacement.
Notwithstanding these precautions, however, no displacement of the bands occurred in consequence of the motion of the air; and according to an estimate I have made, a displacement equal to one-tenth of the breadth of a band would have been detected had it occurred.
The calculations with respect to this experiment are as follows. Under the hypothesis that the air, when moving, carries with it all the æther, we have
