I am getting ready to re-barrel my Martini Cadet so as I normally do I made a threaded slug to make sure my setup is right. I never gave any thought to the degree of the thread assuming it was 60 as the is nothing I have read that would dispute that in fact none of my books says either way. Well 60 degree will not thread in all the way and jams up half way through. to get it to thread all the way I have to cut deeper threads. aka sloppy.
They the bulb came on "this is not an American gun its British" I re-cut with the 55 degree bit and lo and behold class 4 threads nice and smooth right to the shoulder.
Sometime I amaze myself.

They can go either way. Most of the early ones are 55 degree while most of the later ones are 60 degree. There have been arguments where people swear they are one or the other, but if you get out the Machinerys Handbook, a bit of grease and a couple small bearing balls and actually measure them, they do go either way.
Most gunsmiths simply say: "Yeah so?" and then they custom fit cut them to 60 degree. I never completely understood that because it's just as simple to grind a 55 degree tool as a 60. But whatever. That's just me being silly again.

I may not be understanding this correctly but if the barrel only turns in part way, I would think the pitch is off. Maybe a worn lead screw. If the pitch is correct it shouldn't matter if it is 60 or 55 deg. Wrong???

Jim has a valid point.

It may not be the geometry of the thread at all. The threads in the receiver are probably slightly tapered or you are simply cutting them slightly over sized. I would cut and thread a blank in the 3 jaw from a chunk of genuine, Milwaukee patent, gumball steel until it screws up to within 1-1/2 threads by hand. Then put the machine in low gear or lock the magnetic brake and put a receiver wrench on it and see if it will crush on. By doing this you can also cut and try, cut and try. That will give you an idea of what your actual thread OD should be. Threads in receivers are seldom to the advertised size. Just sayin.

Most stuff on old guns is just a little bit haphazard and a lot of parts are hand fit. Barrels and receivers are no different.

The thread cut with the 60 degree will screw in about 3/4 of the way then tighten up making it extremely hard to turn. Since this action is not that robust I don't want to force it on to the last couple of threads. With the 55 degree the thread will screw in smoothly to the shoulder by using minimum amount of force. The 55 degree tool does fit the thread on the take off barrel. altho I have not measured it other than to fit the tool to the thread. I have fit SMLE barrels and have found that either 55 or 60 degree worked, guess this is one of those hand fit problems. Just never ran into it before. But then I have not seen every thing yet

When you thread the barrel, cut the threads to a slight interference fit and make sure you use an action wrench and screw it up really tight into the receiver and take it off at least a couple of times before going any farther with your install. The Martinis can be hard to headspace correctly because of all the slop and stretch in the action. After you crush it on to the receiver several times use a small chisel or scribe to put a witness mark against the barrel and receiver so you don't over tighten it during your try and fit's. You will probably also have to try and fit a few times to install the extractor and get the extractor slot to the proper depth. You want all the burrs crushed off the threads and shoulders and a SOLID shoulder established long before you start these other operations. If the barrel threads get lose half way through these operations you will have to knock it back a turn and start all over.

You won't like that if that happens. Don't miss that step !

I shall take your advise