http://www.pitt.edu/~jdnorton/papers/companion.pdf John Norton: "Einstein could not see how to formulate a fully relativistic electrodynamics merely using his new device of field transformations. So he considered the possibility of modifying Maxwells electrodynamics in order to bring it into accord with an emission theory of light, such as Newton had originally conceived. There was some inevitability in these attempts, as long as he held to classical (Galilean) kinematics. Imagine that some emitter sends out a light beam at c. According to this kinematics, an observer who moves past at v in the opposite direction, will see the emitter moving at v and the light emitted at c+v."
Is this prediction of Newton's emission theory of light confirmed experimentally? Yes it is. If the speed of light is c'=c+v, then the frequency the observer sees (measures) is f'=(c+v)/L=f(1+v/c), where L is the wavelength and f is the frequency seen by an observer at rest relative to the emitter.
That is, the assumption c'=c+v entails the formula f'=f(1+v/c); the latter has been confirmed countless times:
http://rockpile.phys.virginia.edu/mod04/mod34.pdf Paul Fendley: "Now let's see what this does to the frequency of the light. We know that even without special relativity, observers moving at different velocities measure different frequencies. (This is the reason the pitch of an ambulance changes as it passes you it doesn't change if you're on the ambulance). This is called the Doppler shift, and for small relative velocity v it is easy to show that the frequency shifts from f to f(1+v/c) (it goes up heading toward you, down away from you). There are relativistic corrections, but these are negligible here."