Whitworths micrometer and the length of a metre

• I have just finished reading Simon Winchester’s excellent book, “ Exactly” the story of how precision engineering created the modern world, but for me two questions have arisen
• 1 about Whitworths micrometer
• 2 The length of a meter

1. Whitworth’s micrometer made in 1859 has a 250 division on the hand wheel, which when turned will move the anvils 1/4,000 of an inch thus one division is 1 millionth of an inch. Presumably this was via a differential screw with pitches sleightly different. The closest i have got is 0.95 millionth using a 40 and 41 tpi.

Does anybody know the exact numbers? In addition how was he able to cut threads with the extreme accuracy needed for this device which he produced in serious numbers.

2 ) The standard meter was required and the French parliament commisioned a survey to find the exact length.. This was to be defined as 40 millionth of a global meridian It was decided to work on a 1/4 meridian from the North Pole to the equator, about 1000 klm long running from Dunkirk to Barcelona which would be surveyed using the French Toise( about 6 ft long). The survey was carried out over 6 years ( during the Terror). By Merchain and Delambre and the results were announced in April 1799 it came out as 5,130,704 Toise which divided to 0.5130740 Toise, for a metre. A platinum bar was cast ( 25mm x 4 mm section ) to this length and became the standard metre and it still exists . It was later re surveyed and found to be out by 0.2 mm all an epic task.

In modern terms the metre is defined in terms of the wavelength of krypton radiation ( 1,650,763.73 wavelengths in a vacuum) making the closely guarded platinum bar a historical relic.

The question here is exactly what was the standard which the new 1799 1 metre standard created against and how was this exacting length measured?????

I read the book a while ago, really good read.

Can Anyone confirm that Winchester's "Exactly" and "The Perfectionists" are actually the same book under alternative titles?

Full title of each is:

The Perfectionists: How Precision Engineers Created the Modern World

Exactly: How Precision Engineers Created the Modern World

It looks like it's the same book, and like someone in the editorial team wanted to avoid the negative connotations [in some people's eyes] of the word "perfectionist".

I cannot an swer the first question but, as I understand it, the new metre was 'defined' against the length of the meridian from north pole to equator running through Paris, The radius of the earth, was a measure already in use for astronomical measurements at the time. It was calculated, as, you said, by measuring the meridian arc, or part of it.

I hesitate to ask this as the measuring of the earth and the establishment of the metre was done by people a lot brighter than me. My question is this: does it matter that the standard metre is some proportion of a measurement of the earth ? In my mind, as long as we have a stable standard length that can be accessed for comparison the job is done.

The goal was to define length in a way that could be recreated by anyone who had the specification. Assuming that the earth was a perfect sphere, this was done by measuring a quadrant and dividing it by 10 million. The quadrant can be measured in any local unit, foot, yard, toise, mile, or handy length of chain. The local unit, whatever it is, doesn't have to be accurately defined: that comes from the big divide.

The earth's circumference is 24,859.734miles or 40075.017km or 22263898 duffers laid end to end. Any of these divided by 40,000,000 is a metre (roughly)

Unfortunately, the 'anyone can create a metre' idea failed. They soon found that the earth isn't a perfect sphere, so the metre had to be redefined as a carefully made platinum bar and copied. Then started a long difficult search for way of defining the metre that could be recreated by anybody, anywhere, which it now is - just count wavelengths of a particular type of light source. Another failed proposal was to define the metre (and yard) from the length of a pendulum beating at a certain rate; no good - turns out gravity varies with location.

The kilogram was the last international standard to be defined physically. Now all standards are defined in ways hat any suitably equipped laboratory can generate.

Dave

Edited By SillyOldDuffer on 10/02/2023 20:38:31

Now known to be a fairly variable entity, depending on where you stand.

As always, they used the best value they could get. That it was wrong is neither here nor there. It was something that could be measured again.

That it changed, over time, is not really surprising. Plate tectonics had not been invented back then?

A bit like the Fahrenheit temperature scale - using a particular reproducible freezing mixture - was chosen as zero and the boiling point of water was chosen as 212 degrees - using the same change, per degree, as another scale (in use at the time), I believe.

A bit like the railway tracks being related to the width of two horse’s hind quarters, or the ’furrowlong’ (furlong) etc, etc. All old arbitrary standards of the time. Thankfully, the world has not just about settled on the SI System of measurements. At least for the time being….

Zan

May I suggest you read this: **LINK**

https://archive.org/details/whitworthmeasur00whitgoog

MichaelG.

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Meanwhile … this illustration from it should help with your question:

Presumably this was via a differential screw

Edited By Michael Gilligan on 10/02/2023 21:21:32

Edited By Michael Gilligan on 10/02/2023 21:23:07

I Know I've posted this link before, but it seems an appropriate time to give it another airing.

Which Inch, does mention the 1795 brass standard length of 1m, and the later platinum one in 1799
http://metricationmatters.com/docs/WhichInch.pdf

It's a pdf download, but I've used it many times and it appears to be safe.

Bill

The link between railways and the widths of 'osses' botts is probably just legend though Standard Gauge is certainly an odd value. Really though any system of measurement is arbitrary.

The French tried to be clever by basing the Metre on a fraction of the Earth's circumference as well as they could measure it at the time; but really it's as artificial as the Yard only about 3 inches shorter.

They invented the Metric System though to end their own country's chaotic jumble of regional and trade units, far worse than the sometimes-ridiculed Imperial system.

I don't think plate tectonics in a mere two or three hundred years would have modified the overland survey to determine the Metre. The NW European Continental Plate is drifting NE at about 25mm/y (mean speed) but despite slow crustal subsidence of the Straits of Dover region and the much slower closing of the Mediterranean Sea, I don't think it would have warping between Dunkirk and Barcelona enough to have affected the work. Measurement errors would be far more important.

I believe it has though moved the Greenwich Meridian marker-line away from the 0º noon!

I do wonder why they didn't use the Nautical Mile as the Km though, as that is circumferentially based - apart of course from being used by the Old Enemy!

SI still uses the Metric System for its basic, everyday units but then tries to be too clever in turn, inventing things that are ever so neat arithmetically but not a deal of use outside the physics laboratory. Then muddles it further by naming compound units like the Newton and Pascal after famous scientists, to shorten the text but baffle dimensional analysis.

You need a lot of Pascals in even a Roundhouse model loco boiler, or your car tyres! Daft thing is, the ISO make the Pascal far too small for engineering but Nature makes if far too big for acoustics: sound counts in µPa - millionths of 'em! Then logarithmifies a multiple of the count, to make deciBels.

Thanks Peak4 and Michael G this will provide some interesting reading. So Whitworths device was a comparator not a micrometer and used to check the size of 1 inch standards.

but I still wonder how the Tois was divided and measured to 7 decimal places at the time to produce the metre standard

I think the Republican French were looking for a unit about a yard long that didn't rely on the length of a King's arm. I wish they had chosen a length for the metre that resulted in the acceleration due to gravity as 10m/s/s rather than the generally accepted average figure of 9.81. It would have made 'O' level physics much easier (in the days before electronic calculators).

Rod

There were days before electronic calculators ?

There were days before I was allowed to use a slide rule.

Bill

I think the standard gauge tracks were 5 feet across the outside, until someone realised that with flanges on the inside that the inside measurement was the critical one that should be specified.

Unless the rules have changed since I studied them, the decibel is a measure of power ratio, so has no direct correlation to Pascals, unless you state the base for the ratio. So if you specify dBa then there would be a relationship to sound pressure level in Pascals. But if you specify the loss of an electrical attenuator in dB, then there is absolutely no relationship to sound pressure level at all. The loss through the attenuator would be the same number of decibels no matter what signal you put in, provided it is less than the maximum power the device can stand. In telephony and radio work we used to use the dBmW a lot, this is the ratio of the measured signal to 1mW, so 1 Watt would be 30dBmW. The dBa mentioned above is used for sound pressure level relative to a fixed level, but with the frequency response weighted to match that of the hypothetical average human ear.

John

While the Bel and dB are primarilly used for electrical and acoustic power it can be used to represent the ratio of any quantity to some reference value.

If you want very small and large values try electronics.Tens to millions of ohms and 10^-12 Farad (picofarads) to 0.01 Farad (capacitance) and millionths to tenths of Henries (inductance) can exist in the same circuit. It's not the exception either. I have instuments to measure from 0.000,000,000,0001 Amp to 200,000A AC and DC (three instruments to cover picoamps to 2000A with good resolution). Three Ohmmeters cover 0.0001 Ohm to 5,000,000,000,000 Ohms.
For radio frequency work it is not unusual for a single instrument (e.g. a spectrum analyser) to have a total measurement range of 200dB (20 zeros) and 120dB in a single range.

Robert.

It is rather ironic that the USA in the 1880’s I think it was, recognised and adopted the metre standard but since then have steadfastly stuck to imperial measurements in their engineering. Dave W

I too have wondered how a meter, initially proposed as a fraction of the earth's circumference, was measured to be a meter. Presumably they used other references to create it, meaning that the accuracy of those (and how they were defined) remained an issue.

But that definition based on the earth didn't last long. Soon after, a certain length was simply declared to be one, as in "behold! This fancy rod is hereby a meter!" This had the advantage of not having to be in relation to anything else, or having to be concerned with the accuracy of prior references.

With an official length defined by a physical object, there was a concern that the reference would be lost or destroyed. Therefore, they sought a definition that could be recreated from scratch, and for a time it was decided that the length of a "seconds pendulum" (about 0.994m in length) would stand in as a "meter" in case it was lost. I don't think it's an accident that this length is very close to a meter, and wonder if it was more primal in the definition of a meter than current historical beliefs. That official backup plan only lasted about a year, though.

Most recently, the definition of a meter hinges on physical properties that are presumed to be invariant (i.e., we could tell an alien in another galaxy what a meter is without having to show one). But even so, the definition has changed 5 times more, with further (impossibly slight) adjustments in length, over the last few decades. It's currently based on a quality of Cesium.

Edited By S K on 12/02/2023 02:30:05