Well… playing on my Hammy, I realise my second octave is too sharp. And after asking questions to Hammy himself … I’m still confused… 
The second octave (the upper one) is too sharp, so I want to flatten it. So I have to pull the stopper out (away from the embouchure) … no?
Is’nt that sentence right? … or my brain is upside down in my head?
Leo
Yes.
Pulling the stopper out effectively increases the length of the vibrating air column.
Longer vibrating medium (air column, string) = lower pitch.
Thanks guys!
But now, I can’t pull the stopper using the screwing cap because the screw is at the really bottom of the cap. I measured it, and it is at 21 millimeters form the middle of the embouchure, witch is not enormously far away, and I really need to pull it further out …
Now, the only way I can pull it further out is buy pushing it out, using my cleaning stick like I would do with a non-screwing cap. But doing that, since the screw is too long (or the hole in the cap not deep enough), the cap is not “closed” against the head anymore…
Do you think it’s bad if the cap is not closed tight on the head? Or do you think it’s bad if the cap is not there at all?
But wouldn’t that affect both octaves, not just the upper one?
Max
The location of the cap is basically irrelevant as far as the physics of the instrument goes. However, with the cap “sticking out”, and you being unable to change the stopper depth further, if you bump the cap, the cork will end up reseating itself back where it was before, thus undoing your adjustment. Do you have the option to replace the screw? Or can you possibly take it out completely, and perhaps hacksaw a couple of millimeters off?
Yes, both octaves are affected by moving the cork, but not by the same amount. The changes with stopper placement are subtle, but I believe more prominent in the upper register.
Max - moving the cork back won’t change the lower octave much if at all (unless you really move it back).
Leonard - what notes up top are sharp? Is it just A and B, or is it anything above a certain note? Is it just something you can roll in a tad or decrease breath pressure to adjust to?
As for the cap not being closed, are you saying it’s simply not flush with the headjoint but it’s still closed and not hanging open, right? I can’t imagine you’d need to move the whole thing so far back that the tennonish part of the cap doesn’t still seal. If the cap is still partly in the headjoint, I don’t think it would make any difference.
Eric
Thanks guys for answers!
I’m used to hear that the average is about 19 millimeters back from the middle of the embouchure. Mine is at 21 millimeters, and it won’t go further unless I push it with my cleaning stick.
Now, I want to push it further out because if I tune my first octave properly, the upper G, A, B, C and D are too sharp. And if I tune them first, then the first octave’s G, F sharp, E and D become flat. So, in other words, both octaves are too far away from each other!
I can bring the upper octave down a bit by changing the embouchure angle, but it affect the tone too much and it’s still not perfectly in tune.
Fyffer- yes actually, the best thing would be to cut a few millimeters off the screw that’s a precision job since the screw thread must fit back in the cap!!
Ouch!!
My Hammy doesn’t have a screw cap. It is just a cork lapped plug, cosmetic. The cork has to be moved by manually pushing it.
Why do you feel it needs adjustment, was it not tuned correctly or did it move? Perhaps your playing is sharp? Just asking because I’d be hesitant to mess with it, heeding Vallely’s warning in “Timber”, which says basically ‘don’t mess with it’.
Stoppers are very easy to move manually. Rather than trying to use your cleaning rod, which may have a small, rounded end, I recommend using a wooden dowel that is just a wee bit smaller than the ID of the headjoint. The flat end of the dowel will push the cork without damaging it, as could happen with using your cleaning rod.
You may try playing octaves in D as a test for intonation. Play the fundamental, first octave D, and second octave D. If they are all in tune, then the stopper is in the correct position. Then you will know that any intonation problems of the other notes will have nothing to do with the placement of the stopper.
D’s a dangerous note to tune on when the lowest D is often flat by design so you can blow a hard D…I think G is a good tuning note.
Leonard - Since you have spare flutes, I’d probably send it back across the pond and have the maestro look at it himself…or, can you unscrew the screw from both the headjoint and the cork and just move it manually?
Eric
Doug Tipple:
Well what I find a bit weard is that the three D are quit in tune … the difference between octaves is a lot easier to hear on the G and A and B then on D …
Father Emmet:
Actually, I’m pretty sure I play sharp cause my tuning slide is often pulled out by an inch. I’ve playing trombone before flute so that might explain why I have this much air to give.
Actually, is there anything bad about hard blowing (if the flute is tuned to suit this)?
Alleluia
Wow, I think a full inch would definitely cause intonation problems. I’m not sure how you can blow flatter, maybe more ‘down’ into the emboucher hole, rather than across?
What model Hamilton do you have, or how old is it, that you have a screw type cork adjuster?
Are you sure you don’t have an Eb flute?</wiseass comment>
The fact that you play with the tuning slide pulled out so far is probably the reason for your intonation problems.
Leonard – is that a keyed or keyless Hamilton? (I’ll explain later)
Also, I’ve run into the same phenomenon Henke mentions. Sometimes having the slide pulled way out can indeed throw your upper register off completely, almost sending the tuning into a “flattish C#” mode. Alas, I don’t know why…
And, blowing too hard can also send you sharp, as can aiming your airstream too high. Hammys tend to be bright anyway, so maybe try blowing down into the flute more. ?
Finally, could your cork be leaky? If it’s that easy to move around, that might be part of your problem.
Just a few thoughts off the top of my head…
cat.
First thanks everybody for answers!
I checked my flute instructions and … no it’s not a Eb flute! 
Funny Fyffer!
Father : I received my Hamilton brand new last july.
Cathy: No I don’t have keys yet … they’ll come next march …
Henke: I think your right. The problem is for sure the fact that I play with the tuning pulled that far.
Cause I just discovered something this morning: I pulled out the cork 5 millimeters out. It’s now at about 25-26 or maybe even 27 millimeters out… pretty far out no? And actually, the cap is not tight anymore on the head of the flute but … Wow! I think I just discovered the reel sound of my Hammy… First, the tuning problem seems to be over … and I always had problems with the low D and now it booms like crazy.
So … I would be happy to know why I have the tendency to play with the tuning slide this far out but it’s not the flute cause when I play on others flute, I have to pull it out to be in tune. Hope I’m not doing anything completly wrong. But I still have quit a good sound though …
Leo
If you think the cork is the wrong length change it !
Are Hamilton flutes known for being in tune anyway as opposed to just being loud ?
Leo - have you tried watching yourself play in the mirror to see if you’re blowing much more across the embouchure instead of down into it? The other likely issue with being sharp may be that you’re simply blowing exceptionally hard since you’re an ex-trombone player.
Regardless, if with the cork out you’re sounding great - who cares?
Eric