He again sat on the commission of 1799 for the construction of the metric system, and by his zealous advocacy of the decimal principle largely contributed to its adoption.
A fraction written in this way is called a decimal fraction; or we might define a decimal fraction as a fraction having a power of To for its denominator, there being a special notation for writing such fractions.
The coinage of Mexico, now concentrated at the mint in the capital (all others having been closed) is based (since November 28, 1867) on the decimal system - the peso being divided into 100 centavos - and consists of gold, silver, nickel and bronze coins, whose weight and fineness are determined by the monetary law of 1904.
His table gives the logarithms of all numbers up to 2200, and of primes (and also of a great many composite numbers) from 2200 to 10,009, to 48 decimal places.
Focal length a discrepancy of I unit in the 3rd decimal place in the above proportional figures would cause a linear error in the focus for that colour of only about .025 in., so that the largest deviation implied by the tables would be a focus for the extreme violet H ray about 037 longer than the normal.
The point separating the integers from the decimal fractions seems to be the invention of Bartholomaeus Pitiscus, in whose trigonometrical tables (1612) it occurs and it was accepted by John Napier in his logarithmic papers (1614 and 1619).
It is remarkable how near this early decimal system of Germany and Britain is the double of the modern decimal metric system.
Division by a Mixed Number.-To divide by a mixed number, when the quotient is seen to be large, it usually saves time to express the divisor as either a simple fraction or a decimal of a unit of one of the denominations.
An account has now been given of Napier's invention and its publication, the transition to decimal logarithms, the calculation of the tables by Briggs, Vlacq and Gunter, as well as of the claims of Byrgius and the method of prosthaphaeresis.
He was one of the first members, and became president of the Bureau of Longitudes, took a prominent place at the Institute (founded in 1796), professed analysis at the Ecole Normale, and aided in the organization of the decimal system.