After having considered these things, I wondered what would happen if the light would be sent backwards through the rainbow - that means, if light source and observer would change position.
I had simply thought that there where first the lamplight rainbow had appeared (i.e. directly in front of the eye), now the “reversed rainbow” would appear directly behind the lamp. So I imagined that in diverging light there would also a small rainbow appear around the light source. As I had never heard about this bow, I was motivated to make a new discovery, but I did not find that “reversed rainbow”.
When I made a construction later, my mistake in thinking became obvious at once. When I looked at the part of the “apple” (“Minnaert-cigar”) situated behind the lamp, I saw the same part of the “apple” from a completely different position. The addition of all possible rainbows at all angles led to the conclusion that they would extinguish each other. The lamplight rainbow would not appear at 1°, 2°, 3°, and so on and thus would not be visible for me.
Theoretically, the “reversed lamplight rainbow” existed at any point between 0° and 138° (180°-42°), but just for this reason it would not be possible to observe it. This would only be possible if one would be able to perceive such a bow only at an isolated angle. This was impossible, as it would never rain only on a narrow sectional plane.
I forgot about the “reversed lamplight rainbow”
One month later, I read Christoph Gerber's report about bows he observed at a street lamp. He described two different observations, which however were rather similar to each other.
In his first report Christoph Gerber describes a bow that had appeared behind him in the night and was at the same time situated on the other side of the lamp. The bow seemed to follow him (see fig.6).
In his second report he describes a bow that seemed to have been orientated around a lamp, getting smaller when Christoph Gerber came nearer to the lamp and bigger at a larger distance from it (see fig.7).
Both bows were no typical forms of a rainbow as they changed their size and appeared in direction towards the light source. So at first sight the possibility that Christoph had observed a rainbow here, could be excluded.
The situation is different, however, when you put the regularity of rainbows in diverging light into consideration. I already said above, that in diverging light rainbows can appear around the “antilamp” point and that they do not appear in direction towards the light source just because the “reversed lamplight rainbows” which are theoretically possible superimpose each other, so that they could only be visible at an isolated angle. The isolation of a single angle at a single point, however, cannot be observed in the atmosphere, as in such a case raindrops had to fall only at certain positions.