Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/140

 and therefore (neglecting second-order terms in w/c)

Denoting by δ the value of δ1, when w is zero, we have

Subtracting this equation from the preceding, we have

Now the telescope by which the emergent wave-front B1D is received is itself being carried forward by the earth's motion; and we must therefore apply the usual correction for aberration in order to find the apparent direction of the emergent ray. But this correction is w sin δ/c, and precisely counteracts the effect which has been calculated as due to the motion of the prison. So finally we see that the motion of the earth has no first-order influence on the refraction of light from the stars.

Fresnel inferred from his formula that if observations were made with a telescope filled with water, the aberration would be unaffected by the presence of the water—a result which was verified by Airy in 1871. He showed, moreover, that the apparent positions of terrestrial objects, carried along with the observer, are not displaced by the earth's motion; that experiments in refraction and interference are not influenced by any motion which is common to the source, apparatus, and observer; and that light travels between given points of a moving material system by the path of least time. These predictions have also been confirmed by observation: Respighi in 1861, and Hoek in 1868, experimenting with a telescope filled with water and a terrestrial source of light, found that no effect was produced on the phenomena of reflexion and refraction by altering the orienta-