# History topic: Decimal time and angles

The French Revolution marked a break with the traditions of the past and many proposed new beginnings. In particular those leading the Revolution wanted to do away with the existing calendar, which was based on Christian dates, and bring in a new one based on purely secular considerations. The first problem was to choose a day on which the calendar would start - which day should be designated day 1 of year 1? Some proposed 14 July 1789, the day the Bastille fell, while another proposal was 1 January 1789. This latter idea was that the calendar should start on the first day of the year of the Revolution. Lalande, however, proposed 22 September 1792 which was the day on which the French republic was founded, and also, by coincidence, it coincided with the autumn equinox. Lalande's proposal was taken up by Gilbert Romme, a trained mathematician who had become a politician and was a friend of Lalande. Romme said:-

Thus, the sun illuminated both poles simultaneously, and in succession the entire globe, on the same day that, for the first time, in all its purity, the flame of liberty, which must one day illuminate all mankind, shone on the French nation.
Of course, nothing can change the fact that there are 365 days in a year - not even the French Revolution! So the new year still had to have 365 days (366 on leap years). It was divided into 12 months of 30 days each. Of course this left 5 days over which were declared to be holidays. On leap years there were six extra days holidays. Lalande proposed that the twelve months each be divided into three weeks of ten days each. Lalande wrote:-
No creation of the republic will do more to break the hold of the priests over their superstitious dupes.
Now Lalande realised that people may not find a ten day week pleasing so he eased the problem of getting the proposal accepted by inserting a mid-week holiday. The new calendar was accepted and came into force at the beginning of year II, in the autumn of 1793.

But a second proposal suggested changes went further still. On 1 November 1795 (11 brumaire by the new calendar) a law was passed which required the creation of clocks with ten hours in the day, 100 minutes in an hour, and 100 seconds in a minute. A metric system of angles was also brought in, with 400 degrees in a full turn (100 degrees in a right angle). Now the earth would rotate 40 degrees in an hour and, since the metre had been designed so that one quarter meridian was 10 million metres, each degree of latitude would be 100 kilometres long. It was certainly a rational system but its introduction would require all watches, all clocks, all trigonometric tables, all charts etc. to be changed. Condorcet proposed that teams of out of work wig makers should be used to recalculate new mathematical tables with the new units. Why, one might ask, were the wig makers out of work? Well they had been employed by the aristocrats who, following the Revolution, no longer required their services!

Laplace was enthusiastic and had his watch converted to the new time. His great five volume work Traité de Mécanique Céleste , the first two volumes of which appeared in 1799, was written using the new units of time and angle. However Laplace was one of the few to greet the changes in the units of time and angle with any enthusiasm. The proposals regarding the decimalisation of time and angle did not catch on at all, although the calendar continued to be used until 1 January 1806 when the French calendar reverted to the old style. This was a political move by Napoleon Bonaparte who decided that it was better to have the Church on his side. He persuaded the Senate to scrap the new calendar just before he was crowned Emperor. Of course the change had been made for scientific reasons, so scrapping the changes also required scientific backing. Laplace, now a senator, stated that the new calendar had scientific flaws and should be scrapped.

Although the old units of time and angle continued to be used in France through the 19th century, many French scientists still felt that France, and eventually the whole world, should adopt more rational units. In 1884 an international conference was held in Washington in the United States with the aim of choosing an internationally agreed line for the zero of longitude. The decision of the conference to adopt the line through Greenwich as the zero was not made for scientific, or for that matter for political, reasons. It was made purely for economic reasons, since seventy per cent of shipping throughout the world already used British charts based on the zero of longitude through Greenwich. The French, realising that any proposal giving Paris as the zero never stood a chance of being accepted, argued strongly that the zero of longitude should be a line which did not cross any country, and so would be neutral. In the end, despite a strong showing by the French delegation, the near unanimous choice was for the zero through Greenwich but, at least partly to soften the blow for the French, the Washington Conference passed a rather vague resolution which hoped that studies on the decimalisation of time and angle would be resumed.

Following the "hope" of the Washington Conference, the Bureau des Longitudes in France set up a commission in February 1897 with the remit of determining whether France should move from the traditional units of time and angle to more rational units. Poincaré was appointed as secretary to the commission. Other members were engineers, sea captains, railway representatives and astronomers, all people with serious concerns for practical units of time and angle. Bouquet de la Grye, an engineer, expressed clearly the problems encountered by the earlier attempts at decimalisation described above:-

The metric system succeeded because it was the simplest and it put an end to a veritable incoherence in local measures; the decimalisation of time and circumference failed because the whole world employed the same measures and the proposals sinned precisely because of their lack of unity.
There was heated discussion as to the best system. A fair degree of agreement was reached over units of time, where it was proposed that 24 hours should remain, but each hour should contain 100 minutes, and each minute 100 seconds. But there was far less agreement over angle. Some backed 400 grads (the new proposed name for a unit of angle) to the circumference of a circle. Others backed 240 grads since this fitted best with 24 hours in the day. Of course there is a strong connection between time and angle since the earth rotates through the circumference of a circle in a day, in fact in 10 grads per hour with these units. There was also support for dividing the circle into 360 parts (the traditional degree) but then decimalising subdivisions of a degree. Another group supported a division of the circle into 100 parts, and some supported a division into 200 parts.

Poincaré made a table which showed the factors required to convert three different quantities: angle to time; old angular measure to new angular measure; and fractions of a circle into grads. His table, put before the commission on 7 April 1897, ignored powers of 10 in the factors (since no effort was required to multiply or divide by 10). Only 400 grads per circle satisfied the criterion that conversion never required multiplication by a two digit number. This, suggested Poincaré, made it the most practical choice. The report of the commission was, however, met with strong protests from naval men. Charts, yearbooks and table for navigators would have to be changed. All instruments such as clocks, watches, theodolites, sextants would become obsolete. Physicists also objected to the report pointing out that electrical units were based on the traditional units of time so amps, volts, ohms, and watts would have to change. Physical instruments would become obsolete and enormous expense would be incurred.

In July 1900 the report was dropped. The French government saw hostility to its ideas from every country it consulted. It therefore informed the Bureau des Longitudes that the State would not back the reforms proposed in the report of the commission. The push for decimal time and angle was at an end.

Article by: J J O'Connor and E F Robertson

October 2005

MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/HistTopics/Decimal_time.html]