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.British Association or BA screw threads are a largely obsolete set of small screw threads, the largest being 0BA at 6 mm diameter. They were, and to some extent still are, used for miniature instruments and modelling.
They are unusual in that they were probably the most "scientific" design of screw, with a basis in metric size (the 1 mm pitch and 6 mm diameter of 0BA) and with a mathematical relationship between the 'number' (e.g. 2BA with K=2) and the corresponding pitch, major diameter, and then spanner size. Though originally defined in terms of the imperial units then in use in the United Kingdom, this was deliberately set to be exact multiples of the metric system units, rounded to the nearest thousandth of an inch. This anticipated worldwide metrication by about a century. The design was first formulated in 1884, following a study of Swiss practice and was standardised in 1903.
The British Standards Institution recommended the use of BA sizes in place of the smaller BSW and BSF screws (those below 1/4"). Generally, the 0BA size was dropped in place of 7/32" BSF in assemblies that included larger fasteners, however, in smaller equipment that was primarily electronic/electrical the 0BA size would typically be used in place of the BSF or BSW screw where it was the largest size required.
BA threads are still used in some precision instruments, such as optics and moving-coil meters, relays etc. A 2BA thread is used to connect the head of a dart to its shaft — as such, it is one of the few common uses of this thread in North America.
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