The great diversity in the weights and measures used in different parts of France, and the discordance between the series of the official system, or want of system, were inconvenient, and tended to become more so with the increasing facilities of communication between the provinces. Unification was required, and was being studied at the time when the Revolution broke out.

The obvious plan was to make such alterations in the Paris system as were strictly necessary, keeping to the main standards of length and capacity, standards not irreconcilable, and to make it obligatory throughout France. As Napoleon said, ‘It was so simple that it could have been done in twenty-four hours, and adopted throughout France in less than a year.’

Amendments such as I have sketched in the last chapter would have answered the purpose sufficiently.

The ostensible plan of the new system of weights and measures was (May 8, 1790) ‘to create them anew on invariable bases, and to establish in commercial calculations the uniformity which Reason has vainly called for during so many centuries, and which must form a new bond between men.’

Even this scientific and fraternal plan, at first on the basis of a normal pendulum-length, 3/4 inch longer than the half-toise (as proposed by James Watt in 1783), might have been carried out so as to disturb the hereditary ideas and customs of the people as little as possible. But it was resolved to take a geodesical basis. This, taken afresh and not accurately, for the metre, was already at hand in a toise equal to the Olympic fathom, 1/1000 of the meridian mile. And in the report to the Convention, it was recognised that the most ancient people had measures derived from the terrestrial meridian.

More than two centuries before the Revolution an abbÉ (Mouton) had proposed a revival of the Olympic system, decimalised from the meridian mile down to a digit, 1/100 of the fathom.

Without this decimalisation, at least in the popular series of measures, there was a geodesic basis—for this was resolved as necessary—already at hand in the Olympic system, and the Olympic foot cubed would have given a unit of capacity and the Olympic talent one of weight, all the more suitable inasmuch as 1/1000 of it would have been an ounce = 453·6 grains, closely approximating to the Cologne ounce and therefore likely to be acceptable in other countries. But the real object was to make a clean sweep of the past; and the formation of a Republican system of measures was entrusted to mathematicians and other scientists who did not consider that a system convenient to them might be very inconvenient to unscientific people. The division of all measures must be on an obligatory decimal system convenient to mathematicians and most inconvenient to nearly everyone else.

The basis of the new system was a measure considered to be one ten-millionth of the quarter-meridian, of the distance from the equator to the pole. This unit was neither original in conception nor exact in measurement. When Aristotle divided the circumference of the globe into 400,000 stadia, instead of the 240,000 stadia of 1000 Olympic fathoms, his stadion, 1/100,000 of the quarter-meridian, was equal to 100 metres. But there was no practical advantage in it, and navigators continued to use the nautical mile of 10 Olympic stadia, as they do to this day.

At least Aristotle did not seek to upset all the weights and measures of the Macedonian empire; and his stadion disappeared.

It is doubtful if absolute exactness will ever be attained in the measurement of the surface of our globe, irregularly spherical in form and of very uneven surface; but there is no doubt that the ancient ChaldÆans and Egyptians measured it sixty centuries ago quite as accurately as the astronomers of the first Republic; and the Olympic standard of the meridian mile, not the kilometre, is the unit used to this day by the navigators of France as by those of every other maritime nation.

Having determined with little exactitude the metric decimal fraction of the quarter-meridian, the astronomers and mathematicians of the Republic, les idÉologues as Napoleon called them, proceeded to evolve from it the most inconvenient possible units of length, surface, capacity, and weight. All that could be said for these units is that they were exactly and decimally derived from the metre. The metre was unacceptable to the people, as no metric unit of length corresponds even approximately to the universal limb-units of fathom, cubit, foot, span, palm, finger or thumb-breadth. The different series admit only the factors, 1, 2, 5; so each decimal unit has a half (0·5) and a double, but no quarter or third. The prefixes—in Latin for divisions, deci, centi, milli; in Greek for multiples, deca, hecto, kilo, myria—give the only names allowed.

Length

The Metre, = 39·370113 inches, is divided into 10 decimetres, 100 centimetres, 1000 millimetres.

1 yard = 0·9144 metre; 1 foot = 0·3048 metre; 1 inch = 0·0254 metre, or 2·54 centimetres.

It is multiplied by 10 for the decametre, by 100 for the hectometre, by 1000 for the kilometre, by 10,000 for the myriametre. Practically the kilometre, = 0·621 mile or 1093·6 yards, is the only larger unit used; the other units are useless. And though it be interesting to know that the kilometre is approximately 1/10,000 of the quarter-meridian, it is a useless fact.

Surface

The square metre = 1·196 square yard. The lower units are little used. For land-measurement the square decametre, 10 × 10 metres, is called an Are; 100 ares = 100 × 100 metres, make a Hectare = 2·47 acres; and the square metre is a Centiare.

Solidity

The cubic metre = 35·315 cubic feet (nearly the volume of a ton of water = 35·84 cubic feet) contains 1000 cubic decimetres, each of 1000 cubic centimetres (= 61 cubic inches).

The cubic centimetre is strictly speaking 1/1000 cubic decimetre, but as used in chemistry for fluid measure it is considered as 1/1000 of the litre, which is only approximately a cubic decimetre.

Capacity

The Litre was originally a cubic decimetre, but this definition has been abandoned. It is now defined as the volume of a kilogramme of pure water in air at 4 degrees Centigrade = 39·2° Fahrenheit.

At ordinary temperatures a litre of water weighs about 998·8 grammes or 0·9988 kilogramme (see Table at end of Chap. X).

The only minor unit practically used (and only in scientific work) is the millilitre, under the name of cubic centimetre, = 15·432 grains of water.

1 Litre = 2·204 lb. water, or 1·76 pint.

1 Pint = 0·568 litre; 1 gallon = 4·546 litres.

The principal larger unit is the Hectolitre = 22·04 gallons or 2·75 bushels. The Decalitre = 2·2 gallons.

1 Bushel = 36·37 litres; 1 Quarter 291 litres or nearly 3 hectolitres.

1 Bushel to the acre = 0·9 hectolitre to the hectare. (Deduct 1/10 on English.)

1 Hectolitre to the hectare = 1·11 bushel to the acre. (Add 1/10 to French.)

Weight

The original unit was the Gramme, defined as the weight of a cubic centimetre of water at 4° Centigrade = 15·432 grains. It is divided into 10 decigrammes, 100 centigrammes, 1000 milligrammes. Of its multiples the decagramme is useless; the hectogramme is merely the name inscribed on a 100-gramme weight; the kilogramme of 1000 grammes is used when its use cannot be avoided.

But the present legal unit is not the gramme but the kilogramme = 2·2046 lb. or 15,432 grains.^[51]

Intended to be the weight of a cubic decimetre of water at 4° C. (as the gramme was that of a cubic centimetre), this definition has been abandoned as inexact; it is now, like our pound, the mass of a certain platinum standard, in a vacuum.^[52]

Practically, the unit of weight in the ordinary transactions of life is the ‘half-kilo’ of 500 grammes, more usually known as a livre or pound, though the use of this word in trade is punishable.

The livre or half-kilo = 1·1 lb. or 7716 grains.

1 kilo = 2·2046 lb. or 15,432 grains.

100 kilos or Quintal metrique = 220·46 lb.

1000 kilos or Tonne 2204·6 lb. = 0·984 ton.

1 ton = 1016 kilos; 1 cwt. = 50·8 kilos; 1 lb. = 0·4536 kilo or 453·6 grammes.

1 ounce = 28·35 grammes; 1 grain = 6·48 centigrammes.

100 kilos of wheat = 3·53 bushels, at 62-1/2 lb.

100 litres (1 hectolitre) of wheat = 2·75 bushels.

7 fr. duty on 100 kilos wheat = 2 fr. a bushel or 12s. 4d. a quarter.

1 bushel = 36·4 litres.

Money

The monetary unit is the Franc, practically the same as the old livre, somewhat less. According to the original plan, the Republican franc was to be 10 grammes weight, so that the decimal harmony of the system should not be disturbed. But financial expediency required it to be of about the same weight as before, so 80 old livres were recoined as 81 francs at 5 grammes weight and 0·900 fineness. The franc was to be of 100 centimes instead of 20 sous of 4 liards.

The copper coins, changed to bronze in about 1854, are pieces of 10 and 5 centimes, the latter equivalent to the old sou, so that the franc is commonly called a 20-sou piece, and the other silver coins, nominally of 5, 2, and 1/2 franc, are called in the same way piÈces de cent sous, quarante sous and dix sous. The centime is so rarely seen as to be practically non-existent, and the decimal system not allowing the half or quarter of the 5-centime piece or sou, great inconvenience is felt by the poor,^[53] yet the symmetry of the system has been marred by the issue of nickel quarter-francs, of a size which makes them often undistinguishable from francs. But this is 25 centimes, while the half-sou would be written 2·5 centimes, marring the symmetry of the centime column in accounts—where practically it would never appear.

Since the adoption of a gold standard under the second Empire, the gold 20-franc piece is the standard of exchange, and of payments in trade. It weighs 6·451 grammes = 99·5635 grains; it is of 0·900 fineness (= 22-1/5 carats) and thus contains 86·6071 grains of pure gold. Its exchange value is usually 15s. 10-1/2d., our sovereign being equal to 25 francs 20 centimes.

The system of international currency has led to the French currency containing coins, both gold and silver, of strange devices, and the necessity of placards in shops showing figures of the numerous coins which should not be accepted. Considerable vigilance is necessary to avoid taking coins not current, or taking for francs the nickel five-sou pieces scarcely distinguishable from them except in a good light.

The French thermometer, called Centigrade (the proper term would have been centesimal), is on Celsius’s scale, of 100 degrees between the freezing and boiling points of water, under the normal atmospheric pressure, which for France is 760 millimetres = 29·92 inches.

Metric Measures of Time

These are dropped, officially, at present; but they may be re-established, for they were the essential part of the Republican system. Ardent republicans constantly claim their re-establishment, and sound republican newspapers, dated according to the republican calendar, take care that this shall not be forgotten. Scientific journals demand the re-establishment of decimal time and decimal degrees; for even to sell eggs or handkerchiefs by the dozen is a sin, and ought to be made a crime, against the decimal system.

Republican zeal, unable to reform the solar system, had to content itself with reviving the ancient Egyptian year of twelve equal months followed by five extra days, to be called Jours Sansculottides, and with instituting a new era. The extra day of leap-years made a sixth sansculottide; these years were therefore sextile, and the period of four years ending with leap-year was to be called a Franciade.

In justice to the authors of the Metric system, it must be said that they were not responsible for the Republican calendar; this was the work of a separate Committee, to whom the Convention handed over the work carried out by the Weights and Measures Committee of the AcadÉmie des Sciences. On August 1, 1793, it thanked the W. and M. Committee for their work, on the 6th it closed all the Academies, and soon after sent the great chemist Lavoisier, the principal member of the Committee, to prison and ultimately to the scaffold. Among the small number of real republicans who ruled France from Paris, there was much less enthusiasm for the metric system, intended to sweep away the memory of the old customs of weights and measures, than for the calendar, the essential part of which was a new era and the sweeping away of past superstitions, whether Pagan or Christian. In both cases one can see the power of a very small but enthusiastic, well-organised and violent minority of Jacobins against the large, but unorganised and terrorised, majority of the French people. In both cases we see the truth of Guizot’s saying: ‘Blind aversion for the past is full of falsehood and of ignorance.’^[54]

The decree instituting the complete Republican system began by these words, characteristic of the times:

The French era begins with the foundation of the Republic, which was on 22nd September 1792 of the vulgar era, the day when the sun arrived at the true autumnal equinox, entering the sign of the Balance, at 9h. 18m. 30s. a.m., Paris Observatory time.

Thus (it continued) the heavens marked the equality of days and nights at the same moment that civil and moral equality was proclaimed by the representatives of the French people as the sacred foundation of its new government.

The month was divided into three decades and the days of the decimal week were numbered from one to ten.

The saints whose names had been attached to the days were abolished. They were replaced by objects of republican veneration, animals, vegetables, minerals, tools, &c. Each Decadi was consecrated to an agricultural implement, the plough, the watering-pot, the pitchfork, &c.

Each Quintidi was consecrated to a useful animal, the horse, the ass, the pig, the trout, &c.

The eight other days of the decade were consecrated to plants, &c. It was difficult to find 288 useful plants, but by bringing in such as the nettle, the dandelion (under its vulgar French name), strange plants discovered in a herbal dictionary, together with the manure heap and a few useful minerals, the saints were entirely replaced. To popularise these substitutes for the ci-devant saints an appendix to the Decadaire or Annuaire (for the term Calendar was abolished as savouring of superstition) gave popular information, in the crudest terms, on the diseases for which the vegetables and herbs were recommended by the scientific advisers of the Republic.

To complete this system, the circles of the globe, and all other circles, were divided into 400 degrees, divided decimally. The day was divided into 10 hours, of 100 decimal minutes, each of 100 decimal seconds.

The republican division of the day was not generally put into practice except in official documents, probably because the Jacobin leaders found it personally inconvenient. Decreed as obligatory in Frimaire, an II, it was suspended in Germinal, an III, yet that it was extant, if not in force, up to 1800 is shown by a police-report of an occurrence on ‘21 Brumaire an VIII À 2 heures 10 minutes dÉcimales,’ i.e. at 5 A.M.

The story of the means by which the unpopular republican measures were enforced has not yet been told. Some idea of it may be guessed from a remark of de Bonald (1817):

I believe that the same firmness, rigour, and lavish expenditure, used to establish, or rather to try and establish, uniformity of weights and measures, would have been sufficient to establish uniformity of religion.

If in a country which had experienced Louis XIV’s system for establishing uniformity of religion, this could be said of the means by which the republican weights and measures were enforced, it is evident that the new system met with anything but the welcome usually supposed.

But a man had arisen who delivered France, for a time at least, from the more objectionable parts of the republican measures, and the good he effected in this way had doubtless much to do with his popularity. From the time of his Consulate, at the end of 1799, the rigour of the system was gradually relaxed. His contempt for the mathematician-advisers of the Republic, whom he had found to be incapable in public business, was probably brought to a climax by the following event.

The ordnance survey-maps of France were on Cassini’s scale of 1/86,400, i.e. 1 line to 100 toises (which is the proportion of the second to the mean day). A new map having been made on the metric scale of 1/100,000, Napoleon soon found this out, and ordered the map to be restored to the old scale.

‘Je la veux sur l’Échelle de Cassini, et je me moque des divisions dÉcimales’ (letter to the Minister of War, 1809).

The republican calendar and era were used until the end of 1805, when Napoleon restored the Gregorian calendar and its era; thus 11 Nivose, an XIV, was the last day of the republican system.

But the republican idea of a new calendar and a new era is not dead; it has so little died out that a calendar and era devised by a French mathematician and sociologist in 1852 is now actually used, not only in France, but in England, and also in Brazil, by the followers of this reformer.^[55]