I think the best to do is calling the maker and asking for a new headjoint. There is probably a problem with yours. I had a problem quite similar and the maker suggested himself a new headjoint should be necessary.
Best regards.
When I first moved to the Seery Pratten I had almost exactly the same problem you describe–the second octave seemed very sharp to me; if I tuned to the second octave the bottom end of the first octave was very flat.
The problem was not the flute but rather the player. I was not adequately supporting the lowest notes on that flute.
Regarding the intonation on the Hamilton flute, I find mine to be well in tune. I doubt Hammy would have obtained the reputation his work has if he was in the habit of letting grossly out of tune flutes leave his workshop.
I would suggest moving the stopper back to the normal setting for a Hamilton, around 19 mm from the center of the embouchure hole, and work on supporting the lower octave.
If possible, you might have a more experienced player try your flute and see if they experience the tuning problem.
–James
Stop p***ing around with the cork. Thats not a great thing to do at all atall. Why dont you just e-mail Hammy and ask him for a measuring stick with the depth the cork needs to be, marked on it? I distinctly remember Breandan O`Hare having one with which to adjust his cork. Since he worked for Sam Murray a long time, I dont believe its not something that Hammy would be able to do, for you.
My Hamilton came with a cleaning rod that has the cork distance marked on it.
I’d never heard that Hammy Hamilton worked for Sam Murray, though. Curiosity: what years?
–James
Not Hammy, silly,Breandan OHare worked for Sam. Hammy and Sam in the same workstuio. Now thats something Id pay good money to see. Sam once told me if I adjusted the cork myself again, he would beat me with my flute. Is it possible there could be a good reson for this?
This is not that complicated really. Think about what you do when you tune your flute. If you tune it flat you pull out the tuningslide to increase the lenght of the vibrating air column. Since the tuningslide is just below the headjoint, above the first fingerhole it is always going to affect internal tuning to some extent, since the slide is closer to the top holes, they will be affected more becauce the difference will be larger. Think about the lenght of the air column when you blow a D, pull the tuningslide out and it will be slightly longer, but the difference will be greater on the B since the aircolumn is shorter to begin with, and the difference will be greater when you pull the slide out the same distance as you did with the D.
This effect becomes more and more noticeable the more you pull the slide out. If you just have it pulled out a little, you’ll hardly notice it, but pull it out a full inch and the effects will become very noticeable.
Leonard, messing around with the cork is probably the only answer if you don’t want to adjust your approach on blowing and embouchure, or get a new head from Hammy, tuned to your demands.
Well, like I said yesterday, I pulled out the cork even more then it was. Now it’s quite far away from the embouchure, and the cap is not close tight on the head since the screw is quite long.
But … I have quite no problem anymore! 
First, the two octaves are now in tune. Second, my low D has never been this strong.
So I will let it like that, and ask Hammy to cut a bit of the screw when I send the flute back next year for having keys added…
But I would really like to know what is wrong with my blowing (except that it’s strong) and/or my embouchure …
Now, I want to say I’m always be delighted with this flute, and I know the problem is me … not the flute!
Leo
Having (somewhat foolishly) messed around with the stopper on my flute, I’ve found that pulling the stopper past 20 or 21mm results in a muddy sounding instrument. One has the illusion of having a stronger low register, but it’s much blander sounding. At 19mm (or wherever the maker set it in the first place), the harmonics are in tune, resulting a more vibrant, responsive instrument, and a more colorful sound. I’ll add my vote to those who recommend finding out from Hammy where he intended the stopper to be in the first place.
Leo- how would you estimate the relative volume of your 1st & 2nd octaves? my impression is that many flutes are designed for the 2nd octave to be played more softly to compensate for the fact that higher notes are more penetrating. blowing the higher notes more gently makes them flatter. typical cork positions are intended to compensate for this. it is possible you are playing the 2nd octave louder, hence sharper, and need the cork pushed out further.
otoh, there’s nothing wrong if you are happy w/ the tone & tuning you are getting. some flutes are meant to be played full bore. (e.g. Skip Healy’s “Super-Pratten” has a fixed position cork at ~22m and seems to want to be played very hard.)
there’s a great electronic tuner program available for PCs & Macs here. it shows not only the pitch, but also a scrolling display of volume, and of the harmonic structure of the tone, in real time. it is a great way to see the relative volumes at different pitches as you play them.
enjoy! /dan
edited to fix typos
My understanding is that the cork is pretty much guaranteed to leak if you move it around too much – that’s why it’s in there so nice and tight to start with. So no, you shouldn’t move it around. That being said, tho’ – my other understanding is that if you sound like ca-ca, it’s not out of the realm for the cork to be loose, leaky, or somehow shifted (they do shrink with age & drying out).
I always find it funny that even thos emost student-y Boehm flutes come with a marked tuning slide like maire mentions, altho’ the first thing your 4th grade teacher tells you is DON’T MOVE THAT CORK!
xo,
cat.
I’ve never seen a Hamilton flute with a screw-cap arrangement, though I’ll admit I’ve not had a chance to view many up close except my own.
When was your flute made?
–James
PeeblJ: I received it last july and gonna have it upgraded to 6 keys just like yours (but post mounted) next march…06… how did you bare the wait yourself?
Bang, thanks very much for this super tuner! I’ll try it tonight!
Leo
The wait was hard…but the end result was worth it! 
Give yourself some time to get used to that flute–you’ll wind up loving it.
–James
Ah. Thanks, Henke! I never really thought much beyond the old “if it’s flat push it in; if it’s sharp pull it out” adage, so was mystified when the flute would suddenly seem sharper when I pulled the head out past a certain point. (interestingly, things seemed most pronounced on my Hammy – maybe they’re just sensitive that way?).
Again, thanks!