In the present application 4' is not necessarily equal to; but if P correspond to a line upon the grating, the difference of retardations for consecutive positions of P, so far as expressed by the term of the first order, will be equal to mX (m integral), and therefore without influence, provided v (sin 0-sin0') = nzX (11), where a denotes the constant interval between the planes containing the lines.
He supposed that the filaments of water which graze along the sides of the pipe lose a portion of their velocity; that the contiguous filaments, having on this account a greater velocity, rub upon the former, and suffer a diminution of their celerity; and that the other filaments are affected with similar retardations proportional to their distance from the axis of the pipe.
Taking advantage of these results, Henri Pitot (1695-1771) afterwards showed that the retardations arising from friction are inversely as the diameters of the pipes in which the fluid moves.
Let somehow or other retardations be introduced so that the optical length of the successive parts increases by the same quantity nX, n being some number and X the wave-length.
Michelson produced the successive retardations by inserting step-by-step plates of glass of equal thickness so that the different portions of the beam traversed thicknesses of glass equal to nX, 2nX, 3nX, ...
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