light to reach the bottom of the tube, the tube must be inclined at an angle different from , resulting in an apparent position of the star at angle . As the Earth proceeds in its orbit it changes direction, so changes with the time of year the observation is made. The apparent angle and true angle are related using trigonometry as: . In the case of , this gives . While this is different from the more accurate relativistic result described above, in the limit of small angle and low velocity they are approximately the same, within the error of the measurements of Bradley's day. These results allowed Bradley to make one of the earliest measurements of the speed of light. Luminiferous aether In the early nineteenth century the wave theory of light was being rediscovered, and in 1804 Thomas Young adapted Bradley's explanation for corpuscular light to wavelike light traveling through a medium known as the luminiferous aether. His reasoning was the same as Bradley's, but it required that this medium be immobile in the Sun's reference frame and must pass through the earth unaffected, otherwise the medium (and therefore the light) would move along with the earth and no aberration would be observed. He wrote: However, it soon became clear Young's theory could not account for aberration when materials with a non-vacuum index of refraction were present. An important example is of a telescope filled with water. The velocity of the light in such a telescope will be slower than in vacuum, and is given by rather than where is the index of refraction of the water. Thus, by Bradley and Young's reasoning the aberration angle is given by . which predicts a medium-dependent angle of aberration. When refraction at the telescope's objective is taken into account this result deviates even more from the vacuum result. In 1810 François Arago performed a similar experiment and found that the aberration was unaffected by the medium in the telescope, providing solid evidence against Young's theory. This experiment was subsequently verified by many others in the following decades, most accurately by Airy in 1871, with the same result. Aether drag models Fresnel's aether drag In 1818, Augustin Fresnel developed a modified explanation to account for the water telescope and for other aberration phenomena. He explained that the aether is generally at rest in the Sun's frame of reference, but objects