It is interesting to note that not only is a yard defined as 0.9144 m but
the inch is not defined as 1/36 of a yard but as 25.4 mm (exactly).
Therefore, customary measures are all defined by metric ones and not in
relation to each other.
If you do the arithmetic you will find that:
0.0254 * 12 = 0.3048,
36 * 0.0254 = 3 * 0.3048 = 0.9144
0.9144 * 1760 = 1 609.344
all being exact with no rounding.
Hence:
(a) 1 in = 0.0254 m, 1 ft = 12 in
(b) 1 ft = 0.3048 m, 1 in = 1/12 ft
Are equivalent statements, as are
(c) 1 ft = 0.3048 m, 1 yd = 3 ft
(d) 1 yd = 0.9144 m, 1 ft = 1/3 yd
and so on.
Hence to define linear imperial measures all that is requires is the
absolute size of one of them (e.g. 1 yd = 0.9144 m) , and then state the
ratios between all the others. True enough we usually do see the absolute
sizes tabulated rather than the ratios but it doesn't alter anything.
The real bombshell (if they only but knew it) is the use of that word
"exact" in relation to the figures 0.0254, 0.3048, ...
When it comes to the real world there is no such thing as "exact". All
measurements have a tolerance however small it may be. Hence imperial
measures are *tied* to metric by an abstract idealised relationship.
Imperial can have no independent physical definition of its own on that
basis.
Phil Hall
