Correct interpretation of two experiments on the transverse Doppler shift

Consider a light source S, an observer O at rest with respect to S and an observer O' in motion with respect to O. Suppose that, at a given instant of time, O and O' are in the same position and a light signal produced by S strikes both of them. Two important special cases may occur: either the motion of the source is orthogonal to the straight line that interconnects source and observers, or the motion of the source is orthogonal to the direction of the light signal, as judged by O'. In the first case, the Doppler shift perceived by O' is blue; in the second it is red. In the literature, the first condition is often confused with the second; this confusion caused the misinterpretation of two important experiments (Hay et al 1960 Phys. Rev. Lett. 4 165-6; Kundig 1963 Phys. Rev. 129 2371-5), where the first configuration occurs, but the results were interpreted as evidence of a red shift. In this paper, it is proved that the Doppler shift occurring in these experiments is blue, and that only a blue shift is compatible with the outcomes of the experiment performed by Kundig.