My mother has spent the past year reading a wonderful book entitled, "1000 Years of Annoying the French", Stephen Clarke, 2010 ISBN9780593062722 Bantem Press

This is an extract from pp293-5 headed "A day for parsnips"

Napoléon was obsessed by the decimal system. Not only did he force through a metric system of weights and measures, he instigated a decimalised day with 100 seconds in a minute, 100 minutes in an hour and 10 hours in a day. As Stephen Clarke remarks you don't need to be an expert mathematician to realise that there is a fundamental flaw in the system. The Earth rotates once on its axis each day. If you divide the day up into 24 hours, each hour the Earth rotates 15° with respect to the Sun. Each minute it rotates 1/60th of 15° or 1/4°, and each second 1/4'arc. There is a linkage between our sexagesimal time and angle measuring systems. Napoléon in his typically bombastic French manner, overlooked this fact.

At the same time Napoléon was abolishing the ludicrous Revolutionary Calendar he was having to deal with sometimes violent peasant resistance to the acceptance of the metric system introduced under the reign of Louis XVI in 1791. Beyond Paris people still thought in terms of Pouces (inch), Pied (feet) and the Toise (fathom or double yard), 12 Pouce = 1 Pied, 6 Pied = 1 Toise. The Pouce was divided into 12 Lignes. Weight was measured in Livres or "pound" and subdivided into Onces (ounces), 16 Onces = 1 Livre, and further subdivided into Gros, 8 Gros = 1 Once, each Gros being 72 grains (the same as the English Grain). Capacity or volumes of liquids was measured in Litres, a litre being subdivided like an English Quart into Demis (literally "halves") equivalent to a Pint of about 16 fluid ounces. Quarts were literally "fourths". Grain capacity was measured in Boisseau, or Bushels.

Napoléon despised the flexible factorability of traditional measures in favour of decimalisation. He considered decimal counting superior and would not countenance what he regarded as the "inconvenience" of surrendering to fractional arithmetic. But he recognised the difficulty of educating a largely illiterate and enumerate peasantry. In 1812 he introduced "Systém Usuel" which maintained the old measures, but in terms of the newly defined metric measures for weight, length and volume. The transitional period ended by decree in 1837, to take effect from 1st. January 1840.

The unit of length, recommended by the French revolutionary Assemblée Constituante, based on a paper to the Royal Society by its first secretary John Wilkins in 1668, and a subsequent suggestion by Gabriel Mouton in 1670, was based on a subdivision of the Paris meridian from the equator to the pole. A fundamental unit of length, to be known as the Metre, was adopted based on 1/10,000,000 the quadrated Paris meridian. Unfortunately the precise Great Circle distance could not be measured with anything like adequate accuracy. The ten millionth subdivision was quite arbitrary, but based on decimal fractions, and the desire to adopt a standard length similar to the existing Yard. The fundamental unit of mass was the Gram, and of capacity, the Litre. A Kilogram (1000 Grams) was the mass of 1 Litre of pure water at its melting point. A Litre was the volume of 1000 cubic centimetres of pure melting water.

So far, so good. But a complete system of weights and measures must also include time. The French metric system could not decimalise time or the equivalent measure of arc (angle), so the ancient Babylonian Sexagesimal system remained. But not for want of trying as already pointed out.

I have heard it argued ad nauseum by physicists that the French metric system, as modified into System International (SI), is a "rational" and "coherent" measurement system. BOLLOX!!!!!!!!



The SI system is based on the earlier MKS system (Metre-Kilogram-Second). The second is defined in terms of the speed of light (a frequency subdivision) as is the Metre. The Kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK), which is almost exactly equal to the mass of one litre of water. It is the only SI base unit with an SI prefix as part of its name. It is also the only SI unit that is still defined by an artefact rather than a fundamental physical property that can be reproduced in different laboratories.

So, in other words, the K in the MKS (SI) system is arbitrary and cannot be absolutely defined or even absolutely reproduced.

However the general public are not concerned with Mass but Weight, and herein lies a fundamental problem for the SI system. Since weight is a force due to gravitational acceleration, and since the acceleration at the Earth's surface due to gravity is not exactly 10 (Oh dear it is 9.80665 m/sec/sec), the SI unit for weight, Newton = 1/9.80665 Kilograms force, or ~ 102 grams force.

We are now beginning to enter the same messy world as the much, and unjustifiably, derided British Imperial System.

In the SI system, any calculation that involves either time or weight, ends up dealing unavoidably with factors that are not decimal. Any Imperial System calculation involving weight and time ends up with precisely the same difficulties, except being based on even number fractions, the mental arithmetic is a lot easier.

Lets consider a typical mechanical engineering calculation. I want to know the force exerted by a body due to gravity. Suppose the body has a mass of 1000kg (a metric Tonne) and is cuboidal and made of steel. The density of steel is 7.8g/cubic centimetre, or 7800kg/cubic metre. The volume of steel will be 1000/7800 = 0.128205128 cubic metres, and it will measure 0.50423749m per side. The area of the base will be 0.50423749 squared = 0.254255446 square metres. The pressure under this body due to its weight is 1000 x 9.80665/0.254255446 = 38,750.06854 Pascals = 38.75006854Kp. (1 Pascal = 1 Newton / square metre)

Lets do the equivalent calculation using Imperial units. Lets consider a steel cube that weighs 1 Ton. The weight of steel is 490 Pounds/cubic foot. There are 2,240 pounds in a ton. The volume of the steel cuboid will be 2240/490 = 4.571428571 cubic feet, and each side will measure 1.659653067 feet. The area of the base will be 1.659653067 squared = 2.754448302 square feet. The pressure it exerts will be 2240/2.754448302 = 813.2300028 pounds/square foot. Note I did not need to bring the acceleration due to gravity into the Imperial System calculation. How so? Simple, because in the British Imperial System 1 pound weight is the force exerted in 1g by a 1 pound mass. Weight and mass have the same numeric value. So if I weigh myself on weighing scales, whether they be spring balance or mass balance scales, whatever poundage is on the scale (my mass) is also my weight. (The fundamental Imperial Pound is defined by a Platinum cylinder made in 1834.)

Not so in the SI system. People talk of Kilograms as though it was weight. Kilograms is NOT weight, it is MASS. The unit of weight in the SI system is the NEWTON, and there are 9.80665 Newtons in 1 Kilogram force. You never see anybody buying weighed items in a shop in Newtons. (There are spring balance weighing scales that read Newtons but they are few and far between). I doubt if a shopper selected at random would have ever heard of a Newton.

Aficionados of the SI system point out that if you weigh yourself on the Moon using mass scales, you will weigh the same, but if you weigh yourself using spring balance scales you will weigh about a sixth what you weigh on Earth because of the lower gravitational acceleration. Well how many folk do you know who have encountered that snag?

Notice also that in either system, the arithmetic is equally awkward. The SI system offers no arithmetic advantages despite being a decimal system.

That is the first reason why the SI system is BOLLOX!!!!!


Having dealt with the impracticalities of the Kilogram and the Newton, we now come to the Metre. It is basically an arbitrarily redefined Yard, but its all dressed up in terms of wavelengths of light and atomic resonance frequencies. The man in the street couldn't care less about the fundamental definition of the Metre. What he wants to know is "How Long is it?" When you tell him its a pace of a very tall man he gets the general idea. But why is it slightly longer than the average pace? No good reason, it just worked out that way after they'd subdivided the distance from the equator to the pole through Paris, ten million fold.

The Metre is subdivided or multiplied by powers of 10 cubed in the SI system, so we have Millimetres, and Micrometers &c decreasing in length, and Kilometres increasing in length. The Kilometre is an OK unit of travelling distance, but the Millimetre is a tad small for a unit of length intended for most everyday objects. So the SI system gets corrupted and we revert back to the earlier MKS system and use Centimetres. There's no simple way round the practical problems of dividing or multiplying the standard length by thousands. The length system is far to coarse for everyday use. Area measure in square metres is OK for floor and wall areas, but way to coarse for furniture areas. Go to square millimetres and the numbers are way too big. A similar difficulty arises with land measure. Who for instance has a notion of what a Hectare looks like?

The standard unit of length in the British Imperial System is the Yard. The Yard is defined by a bronze bar, together with the Foot (1/3 Yard) and the Inch (1/36 Yard) made by Troughton & Simms and on public display at the Royal Greenwich Observatory since 1859.

If I want to measure longer distances I use the Mile, being 1,760 Yards. The reason there are 1,760 Yards in a Mile is because of the Surveyor's "Chain". A Chain is 22 yards, and there are 10 Chains in a Furlong, and 8 Furlongs in a Mile. Anyone who has played Cricket knows how long a Chain or 22 Yards is, its the distance between the wickets. Anyone who follows horse racing knows that a Furlong is.

If Yards are too big a unit I can use Feet, or for smaller objects, Inches. Its easy subdividing Yards, or Feet or Inches. Half a Yard is half of 36 inches, or 18 inches, or (because there are 12 inches in a Foot) 1 Foot 6 Inches. A third of a Yard is a Foot. A quarter of a Yard is 9 inches and so on. I can keep halving and in some instances thirding, &c, and still end up with whole numbers.

For objects that are smaller than an inch, I can use fractions of an inch. Look at any engineer's Imperial rule and there are two subdivision systems. The halving system and the decimal fraction system. So I can measure in halves, quarters, eighths, sixteenths, thirtyseconds, sixtyfourths, and even 1/128ths. Or I can measure in tenths, twentieths, fiftieths, hundredths. Below that I need a vernier calliper or micrometer, calibrated in thousandths, or "THOUS".

Its a wonderfully simple and practical system based on usage over centuries, rather than some arbitrary system dreamt up by academics based on the decimal counting system.

That is the second reason the SI system is BOLLOX!!!!!!!


The final nail in the metric system's coffin comes when we have to include time or angle in any calculation. Time and angle measure are not decimalised. So if I have to calculate the linear or angular motion or acceleration of any object in a given time, I am going to end up with awkward arithmetic. Especially angular acceleration because it involves Pi, which is an irrational number. It matters not whether such calculations are carried out in SI or British Imperial units.

That is the third reason why the SI system is BOLLOX!!!!!!


However from a machinist's perspective the metric system has its pros and cons. Imperial drill sizes come in three flavours, Fractional inch, Decimal inch, and Letter sizes. If you have ever used Zeus tables to find the tapping drill size for an imperial screw thread you'll know what I'm talking about.

Metric tapping drill sizes and metric threads are easier and simpler to work with. Unfortunately not so the screw cutting lathe with a leadscrew. The imperial lathe with either an 8tpi or 4tpi leadscrew is far simpler to use for cutting screw threads with a single point tool. The gear sets needed to convert the leadscrew pitch to the thread pitch are usually simple fractional ratios. Not so with a metric lathe where almost all the gear sets have odd numbered teeth and awkward ratios.

In Britain at present we have the worst of all possible worlds. An unhappy coexistence of the Imperial System and a dumbed down version of the old MKS system. Most goods have to be sold in metric units. But we can still buy a dozen (12) or half dozen (6) eggs. Timber is sold in metric sizes, but the sawn sizes are rounded metric conversions of the original imperial sizes. Planed sizes become less, yet are still sold by sawn size. Metal stockists use both systems. You can buy metal bar or tube in either metric or imperial sizes. Metal sheet or flat bar is sold in either SWG (Standard Wire Gauge) or imperial or metric thicknesses. Scrap metal is sold by weight (Kilograms rather than Newtons). A mechanical engineer working in an old fashioned machine shop is obliged to work in both systems.

The metric system was introduced for similar reasons to the decimal currency in this country. It was presumed that because we have a decimal counting system, a system of weights and measures based on the same decimal counting system would be more rational. But rationality has nothing to do with how people think and deal with number problems. How many folk do you know who can readily multiply or divide sets of numbers (not just a single number) in the decimal system in their head? How many folk do you know who can readily double, or halve, or double again, or quarter a number in their head, or multiply or divide even fractions? It is easier dealing with even fractions than it is dealing with decimal quantities in your head. Decimal calculations OK on a pocket calculator, OK on paper, not OK in your head.

The British Imperial System arose out of centuries of common usage, and was practical. It still is a more practical system. The fact that it isn't rational and coherent in terms of the fundamentals is irrelevant. What matters is, do common folk understand it, and can they work with it?

Consider an ATMing question. I was asked this recently by someone who was seriously considering making their own Newtonian telescope. I suggested he start by making a 6-inch f/8. He wanted to know the relative merits of an 8-inch f/6. Same tube length, more light gathering power. Would the mirror be harder to make. Slightly more difficult, but Neale Howard regarded it as a valid starting point. Its easy comparing areas isn't it? 8 squared divided by 6 squared, that's 64 divided by 36, or 32/18 or 16/9. Now lets do the same thing in SI units, so that's 200 squared divided by 150 squared, or 40,000/22,500 = 400/225 = 80/45 = 16/9. Notice how the imperial size fraction drops out quicker and easier. Its easier to halve an even number than divide it by a factor of 10.

Having a system based on factors or multiples of ten lends itself to errors involving orders of magnitude (of powers of ten). The Imperial System lends itself to self correction. If you are converting yards or feet to miles, you are not going to end up powers of ten out. Yet I have seen folk struggle to convert metres to kilometres. You'd imagine it was a simple arithmetic task because there are 1000 metres in a kilometre. But people get confused whether to multiply or divide. So 100,000 metres becomes 100,000,000 kilometres, rather than 100 km. An error of magnitude 6 or a million. You NEVER have such confusion with the British Imperial System.

That is the fourth reason why the SI system is BOLLOX!!!!!!!


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