Paul, my comments in blue.... Allen D -- I am not seeking to escape from my offer to collaborate in clarifying your illustrations but it does seem the need may have passed. What is your opinion? well if you understand the drawings then what are your arguments against the star trails proof?...i addressed all thoes issues that you keep bring up and i show that any reason against being able to see the annual motion would prevfent you from seeing the nightly motion. and Any valid reason that would allow you to see the nightly motion demands our ability to see the annual motion.....are you conceding....otherwise i missing something.....