An interesting co-incidence of units

We all know [don't we?] that the first integer co-incidence between Imperial and Metric linear measure is 5" = 127mm.

Today I noticed another, which might be useful for calibration or setting-up in the workshop.

1 1/4" = 31.75mm [= 31 3/4 mm] ... So not only do we have a precise, and reasonably convenient, Imperial to Metric conversion, but it also works for fractions !

This means that a single block, rod, or ball can be your calibration standard for all three systens.

I commend 1 1/4" as a compact reference.

MichaelG.

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Thanks Jason ... Stupid typo corrected 

Edited By Michael Gilligan on 29/01/2017 19:32:38

I thought 5" = 127mm

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Thanks Jason ... Stupid typo corrected

No problem Michael though I'm not sure what you are getting at regarding the fractions but if it is what I'm thinking then 1 3/8" or 1 1/2" would be closer to a full mm, 1 1/2 the more practical of teh two to use in your head.

eg 1 3/8" = 34.925mm say 35mm

1 1/2" = 38.1mm say 38mm

Edited By JasonB on 29/01/2017 19:42:57

So it follows that 5/8" is 15 7/8mm and 5/16" is 7 15/16mm and so on

Mike

No, it wasn't that, Jason

My point was that it is an exact, and reasonably useable reference for all three systems.

MichaelG.

Not according to some suppliers.

When I bought my horizontal mill I did so on the understanding that it would come with 1" and 1¼" arbors. When it arrived it came with 1" and 32mm arbors. When I rang to query I was told in no uncertain terms that 32mm was 1¼" for all practical purposes and that I didn't know what I was talking about. Bit of a bummer given that I'd been busy buying 1" and 1¼" bore cutters at auction.

Half an hour later said supplier rang back and said he'd been torn off a strip by his boss, and told he didn't know what he was talking about. Vis 32mm is not the same as 1¼" when it comes to milling machine arbors. They agreed to supply a 1¼" arbor for the cost of the postage.

I've still got the 32mm arbor, unused, on the shelf.

Andrew

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Indeed it does ... The 'convenient' size depends upon the scale to which you are working.

... I did say, in the subtitle, that it was obvious.

MichaelG

No you have lost me

I'll stick with 1" = 25.4mm as I don't have anything that measures in fractions of a mm.

.

But surely you have something that measures in fractions of an inch [?]

MichaelG.

I do and I then just multiply that by 25.4 to convert it

if using 1 1/4, I would first have to divide my measurement by 1 1/4, then multiply by 31 3/4mm and then work out what the fractional part of teh mm is in decimal.

I can measure in both mm and inch fractions. Although oddly the measurements in either unit seem to have a bias; they're always a fraction too small.

Andrew

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Sorry, Jason ... I think we're at cross purposes ... I was suggesting keeping a single physical item as a calibration standard for multiple units and systems of measure.

Please ignore me if it's not to your taste.

MichaelG.

So I'll just keep my 1" block and know it is equal to 25.4mm and also if expressed as a metric fraction is 25 4/10mm.

It will also fit inside the anvils of my 1" mic when I need to callibate them

Maybe I have missed something but I can't see the advantage of using 1 1/4"

Night

As far as I can see, the fact that, say a 1" standard is exactly 1" maybe a convenient number but for the purpose of checking a micrometer its not that important. All one needs to know is the true size of the standard. I could be 0.987454" or 25.07543mm and that is the figure the instrument should read or be set to.

Ian P

-40 Celsius is the same as -40 Fahrenheit.

0mm = 0"

Micheal you have lost me on this one ??

As I have been doing PRACTICAL engineering , man and boy for 167 years [ or so it feels like on some days ] and have all sort of gear from knotted string to DRO's via digital calipers WHY would I need to know 1 1/4" equalled 31.75mm ?

Perhaps I don't study useless theory enough or the padding in my armchair is too lumpy ?

There are many other coincidences of units relating to historical connections:

I have an allotment, '5 rods' in size. A 'rod, pole, or perch' (i.e. a precision reference standard consisting of a wooden stick) is a linear measurement of distance of a quarter of a chain, so 5.5 yards. Alternatively it is also used for an area measurement of the same linear dimension squared. A chain is a historical unit of measurement, also the length between the wickets on a cricket pitch. So using a chain to outline a square yields an area of a rod, (pole, or perch). So a linear rod is only 0.584% off a measurement of 5 metres; the area measurement is just 1.17% off 25 square metres. So my allotment is very close to 1/80 hectare. See **LINK**

Home brewers will also know that 6 wine bottles is the expected yield from a demijohn: 6 bottles of 0.75l is within 1.02% of an imperial gallon.

Other old measurement units show close correspondence:

The French monetary ‘livre’ was a ‘pound’ unit equivalent to a one pound weight of silver (Latin ‘libra' ), hence also the British pound £ symbol. **LINK** .

The French weight ‘livre’ unit was 1.079 UK pounds. The use of the livre was finally revoked by the La loi du 4 juillet 1837, **LINK** but I believe the livre may be still used in French markets. I had thought change was slow enough in UK, having allegedly ditched the antiquated old Fahrenheit measurement of temperature, and inches/yards/poles/furlongs etc of length when I was a child 50 years ago, but it has taken a long time to change.

Also the old ‘French Inch’ (Pouce) is 1.066 imperial inches (or even US inches). Still used in horology, 12 lignes = 1 pouce.

US measurements of volume (US pints/ gallons) and weight ('e.g. 'short' tons) seem to show almost no closer correspondence to UK units than Metric or other European units!

I'll just get my coat...

Martin

Edited By Martin Whittle on 29/01/2017 23:08:13

Edited to remove spurious smilies!

Edited By Martin Whittle on 29/01/2017 23:09:54