"We have... to speak of a celebrated experiment made by Michelson in 1881, and repeated by him on a larger scale with the cooperation of Morley in 1887. It was a very bold one, two rays of light having been made to interfere after having travelled over paths of considerable length in directions at right angles to each other. Fig 9. shows the general arrangement of the apparatus. The rays of light coming from the source L are divided by the glass plate P, which is placed at an angle of 45°, into a transmitted part PA and a reflected one PB. After having been reflected by the mirrors A and B, these beams return to the plate P, and now the part of the first that is reflected and the transmitted part of the second produce by their interference a system of bright and dark fringes that is observed in a telescope placed on the line PC. The fundamental idea... is, that, if the ether remains at rest, a translation given to the apparatus must of necessity produce a change in the differences of phase, though one of the second order. Thus, if the translation takes place in the direction of PA or AP, and if the length of PA is denoted by L [denoting speed of light c and earth's speed \left\vert w \right\vert (the absolute value of its velocity w)], a ray of light will take a time \frac{L}{c + \left\vert w \right\vert} for travelling along this path in one direction, and a time \frac{L}{c - \left\vert w \right\vert} for going in the inverse direction. The total time is\frac{2Lc}{c^2 - w^2},or up to quantities of the second order [by multiplying numerator and denominator by \frac{1}{c^2} to obtain \frac{2L}{c}\frac{1}{(1 - \frac{ w^2}{c^2})}, then multiplying this numerator and denominator by (1 + \frac{ w^2}{c^2}) and dropping the resulting denominator's negligibly small fraction \frac{ w^4}{c^4}, giving]\frac{2L}{c}(1 + \frac{ w^2}{c^2}),so that for the rays that have gone forward and back along PA there will be a retardation of phase measured by \frac{2Lw^2}{c^3}.There is a similar retardation, though of smaller amount, for the other beam. ...a ray of this beam, even if it returns, as I shall suppose..., to exactly the same point of the plate P, does not come back to the same point of the ether, the point... having moved with the velocity W of the earth's translation over a certain distance say from P to P' while the light went from P to B and back. If Q is the point in the ether where the ray reaches the mirror B, ...with sufficient approximation...the points P, Q, P' are the angles of an isoscele triangle, whose height is L (since the distances PA and PB in the apparatus were equal) and whose base [the total distance traveled by mirror B resulting from the motion of the earth] is \frac{2L\left\vert w \right\vert}{c} [where \frac{2L}{c} is the time for light to travel distance L twice]. The sum of the sides PQ and QP' is2\sqrt{L^2 + \frac{L^2w^2}{c^2}},so that we may write\frac{2L}{c}(1 + \frac{w^2}{2c^2})for the time required by the second beam. It appears from this that the motion produces a difference of phase between the two beams to the extent of\frac{Lw^2}{c^3},and this may be a sensible fraction of the period of vibration, if L has the length of some metres."