[USMA:35748] Re: decimal time

[Pat Naughtin]

Title: Re: [USMA:35747] Re: decimal time

Dear Phil,

Thanks for your analysis, below.

This is why I refer to the post-1959 measures as:

the metric inch = 25.4 millimetres exactly,

the metric foot = 304.8 millimetres exactly,

the metric yard = 914.4 millimetres exactly,

the metric chain = 20.116 8 metres exactly,

the metric furlong = 201.16 8 metres exactly, and

the metric mile = 1 609.344 metres exactly.

I do this because I find that their descriptively accurate title, 'post-1959 measures with quaint old pre-metric names' too cumbersome.

Cheers,

Pat Naughtin
PO Box 305 Belmont 3216
Geelong, Australia
61 3 5241 2008
[EMAIL PROTECTED]
http://www.metricationmatters.com

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On 20/01/06 10:13 AM, "Philip S Hall" <[EMAIL PROTECTED]> wrote:

>> 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
>
>
>