Einstein's derivation of stellar aberration formula: replacing the direction of the ray with a difference in angles justified?

Question

I was going through the translation of Einstein's 1905 paper "On the Electrodynamics of Moving Bodies"(See https://einsteinpapers.press.princeton.edu/vol2-trans/175). In deriving the stellar aberration formula, the text says "If we call the angle between the wave-normal (direction of the ray) in the moving system and the connecting line “source-observer” $\phi '$, the equation for $\phi '$ assumes the form: $$cos\phi'=\frac{cos\phi-v/c}{1-cos\phi .v/c}$$ However, if we look at the original German version (https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.19053221004), it says, "Nennt man $\phi'$ den Winkel zwischen Wellennormale (Strahlrichtung) im bewegten System und der Verbindungslinie ,,Lichtquelle-Beobachter", so nimmt die Gleichung fur $a'$ die Form an:" $$cos\phi'=\frac{cos\phi-\frac{v}{V}}{1-\frac{v}{V} cos\phi}$$ Here Einstein has replaced $a'$, his original direction cosine with $cos\phi'$ (See Annalen der Physik, Volume 322, Issue 10, Page 911). (Note: $V$ is the velocity of light in old notation).

As far as my understanding goes, $a'$ or equivalently $cos\phi'$ is the cosine of the angle measured from the $X$-axis of the moving coordinate system for the ray direction and NOT "the angle between the wave normal (beam direction) in the moving system and the connecting line “light source” observer".

Can somebody please help me understand this switch?

Answer 1

In the annotated German original (see https://einsteinpapers.press.princeton.edu/vol2-doc/333) we find next to the aberration formula the note 29, which says:

In a reprint copy (see the preceding note), Einstein canceled the phrase "Verbindungslinie "Lichtquelle-Beobachter" " and interlineated "Bewegungsrichtung."

The interlineated expression "Bewegungsrichtung" means "direction of motion". Thus Einstein himself corrected his original text by replacing the phrase "connecting line 'source-observer'" by the expression "direction of motion".