## 20100110

### Laplace

I have read that the great French mathematician and astronomer, Pierre-Simon Laplace, was enthusiastic about decimal time, and used it in his work Traité de Mécanique Céleste. (Treatise on Celestial Mechanics)  Unfortunately, I have been unable to find all five volumes online, and reading what is available is difficult, as it is highly technical and full of math, and I don't speak French.  But according to a translation by Nathaniel Bowditch, he wrote in his preface:
I shall adopt the decimal division of the right angle, and of the day, and shall refer the linear measures to the length of the metre, determined by the arc of the terrestrial meridian comprised between Dunkirk and Barcelona.
I thought that I might find a description of decimal time, or at least examples of how decimal times were written in France during the Revolution, something like 10h98m76s.  However, the few examples I found look like this one:
... et la distance périhélie, égale à 1,053095 ; ce qui a donné pour l'instant du passage au périhélie, sept.29j,10239, temps moyen compté de minuit à Paris.

Les valeurs précédentes de a, b, h, l, relatives à trois observations, ont donné la distance périhélie égale à 1,053650; et pour l'instant du passage, sept.29j,04587; ce qui diffère peu des résultats fondés sur cinq observations.

Roughly translated, this says:
...and the perihelion distance, equal to 1.053095, which gave for the moment of perihelion passage, Sept. 29d.10239, mean time counted from midnight in Paris.

The previous values of a, b, h, l, relative to three observations, gave the perihelion distance equal to 1.053650, and for the moment of passage, Sept. 29d.04587; which differs slightly from the results based on five observations.
Note that the superscript "j" stands for jour, meaning "day", and that the French use a comma as the decimal mark.  So Laplace is expressing the decimal time as a decimal fraction of a day in Paris mean time and adding it to the date.  This is how times are given in astronomical circulars today, except that now the times are UT, and the unit symbol is omitted. So ,10239 would correspond to 1h2m39s decimal time, and ,04587 to 10h45m87s, or 1:06:03 a.m.

He also gives times without dates, such as 0j,681798, which Bowditch renders as 0day,681798.  This is essentially identical to how Herschel wrote them a half-century later, e.g. 0d·286003.

MJD 55206.55

#### 1 comment:

1. Reading further, I have found instances where Laplace gives intervals in decimal seconds in the form 151",8 (151.8 s). I have seen the same notation in old texts used with standard time, as is still commonly used for divisions of degrees of arc, i.e. ' for minute and " for second.