The BA (British Association) series of screw threads is a strange hybrid. Based upon a Swiss standard they are metric sizes, with the largest, 0BA, having the same nominal diameter of 6.0mm and pitch of 1.0mm as the standard M6 metric coarse thread. The main difference is that the BA thread form uses an unusual 47-degree angle, so it is slightly deeper and sharper than both the ISO metric threads (which use 60 degrees) and Whitworth (at 55 degrees). The threads sizes are, however, defined in inches in the British Standard.
So, why does this thread form continue, and why is it so popular with model engineers? Two good reasons - the first is it has the wonderfully useful property of having sizes in closely spaced, geometrically regular sizes. 1BA is 0.9 times the size of 0BA, 2BA is 0.9 times the size of 1BA and so on. The differences are small enough that there is always an ideal BA size when you need a small thread, with no awkward gaps - such as the big step between M3 and M4. This is good for scale modellers as with 10% change between each size, you can always find a thread within 5% of scale size, and such a small difference is negligible for most purposes. Larger BA nuts and screws (often down to 8BA) can also supplied with 'one size smaller' hexagons, so 2BA may be made from 3BA hexagon stock, for example. These fixings generally have a better scale appearance - but check, some very old machines used much larger hex nuts in proportion to the thread!
It also means that some BA sizes conveniently fit on some stock material sizes - very handy! 0BA on 6mm, 2BA on 3/16", 5BA on 1/8 and 7BA on 3/32" or 2.5mm, for example.
Finally, the BA fixings generally have a finer thread pitch than similar metric threads, another factor that makes them look better on models.
<Homer Simpson>"Is there nothing BA can't screw?"</Homer Simpson>
Here's a handy chart with all the really important figures for BA fixings. Enjoy!