A theory of optics without the speed of light postulate:
http://www.ruhr-uni-bochum.de/wtundwg/Forschung/tagungen/OWR_2006_10.pdf
Jean Eisenstaedt: "At the end of the 18th century, a natural extension of Newton's dynamics to light was developed but immediately forgotten. A body of works completed the Principia with a relativistic optics of moving bodies, the discovery of the Doppler-Fizeau effect some sixty years before Doppler, and many other effects and ideas which represent a fascinating preamble to Einstein relativities. It was simply supposed that 'a body-light', as Newton named it, was subject to the whole dynamics of the Principia in much the same way as were material particles; thus it was subject to the Galilean relativity and its velocity was supposed to be variable. Of course it was subject to the short range 'refringent' force of the corpuscular theory of light --which is part of the Principia-- but also to the long range force of gravitation which induces Newton's theory of gravitation. The fact that the 'mass' of a corpuscle of light was not known did not constitute a problem since it does not appear in the Newtonian (or Einsteinian) equations of motion. It was precisely what John Michell (1724-1793), Robert Blair (1748-1828), Johann G. von Soldner (1776-1833) and François Arago (1786-1853) were to do at the end of the 18th century and the beginning the 19th century in the context of Newton's dynamics. Actually this 'completed' Newtonian theory of light and material corpuscle seems to have been implicitly accepted at the time. In such a Newtonian context, not only Soldner's calculation of the deviation of light in a gravitational field was understood, but also dark bodies (cousins of black holes). A natural (Galilean and thus relativistic) optics of moving bodies was also developed which easily explained aberration and implied as well the essence of what we call today the Doppler effect. Moreover, at the same time the structure of -- but also the questions raised by-- the Michelson experiment was understood. Most of this corpus has long been forgotten. The Michell-Blair-Arago effect, prior to Doppler's effect, is entirely unknown to physicists and historians. As to the influence of gravitation on light, the story was very superficially known but had never been studied in any detail. Moreover, the existence of a theory dealing with light, relativity and gravitation, embedded in Newton's Principia was completely ignored by physicists and by historians as well. But it was a simple and natural way to deal with the question of light, relativity (and gravitation) in a Newtonian context."
Pentcho Valev