Your correspondent DX. is mistaken in supposing that "foreigners
ordinarily commence the astronomical day at midnight."
With respect to France, in the _Explication et Usage des Articles de la
Connaissance des Temps_ it is expressly stated: "Le jour astronomique
_commence a midi_."
And in the explanation appended to the _Berlin Jahrbuch_, it is in like
manner distinctly laid down:
"The time which must be always understood, unless it is otherwise
particularly expressed, is the mean time of the meridian of the
New Berlin Observatory, which is taken to be 44m 14.0s eastward of
Paris, and 53m 35.5s eastward of Greenwich. _The beginning of the
day is at noon._"
The _civil_ day always commences at the midnight preceding this
_astronomical_ day.
It follows that Sept. 17, 3h 40m 30s Greenwich mean time, is simply
Sept. 17, 4h 34m 5.5s Berlin mean time.