In these cases the digit itself, or decimal multiples, seem to have been used.
The first national coinage was begun in 1822, and the decimal system was adopted in 1863.
According to Krummel the following relations hold, good at 18° C. for the monochromatic light of the D line of the sodium spectrum in units of the fifth decimal place.
It originated in Babylonia as the foot of that system (24), in accordance with the sexary system applied to the early decimal division of the cubit.
To Napier seems to be due the first use of the decimal point in arithmetic. Decimal fractions were first introduced by Stevinus in his tract La Disme, published in 1585, but he used cumbrous exponents (numbers enclosed in circles) to distinguish the different denominations, primes, seconds, thirds, &c. Thus, for example, he would have written 123.456 as 123@4050603.
The Greek system, however, adopted this foot as a basis for decimal multiplication, forming --
Seeing the good reasons for this digit having been exported to the West from Egypt--from the presence of the 18.23 cubit in Egypt, and from the 0.729 digit being the decimal base of the Greek long measures--it is not surprising to find it in use in Italy as a digit, and multiplied by 16 as a foot.
It is remarkable how near this early decimal system of Germany and Britain is the double of the modern decimal metric system.
The fact that when the base is io the mantissa of the logarithm is independent of the position of the decimal point in the number affords the chief reason for the choice of io as base.
In tables of logarithms of numbers to base io the mantissa only is in general tabulated, as the characteristic of the logarithm of a number can always be written down at sight, the rule being that, if the number is greater than unity, the characteristic is less by unity than the number of digits in the integral portion of it, and that if the number is less than unity the characteristic is negative, and is greater by unity than the number of ciphers between the decimal point and the first significant figure.
In the Swedish House of Nobles his contributions to political discussion had great influence, and he dealt with such subjects as the currency, the decimal system, the balance of trade and the liquor laws (where he was the pioneer of the Gothenburg system) with marked ability.
The accuracy of a meter is tested by drawing calibration curves showing the percentage departure from absolute accuracy in its reading for various decimal fractions of full load.
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.
3 Besides his connexion with logarithms and improvements in the method of prosthaphaeresis, Byrgius has a share in the invention of decimal fractions.
In 1782 he prepared an elaborate report on the coinage, suggesting the use of the decimal system and of the terms dollar and cent.
Briggs appreciated clearly the advantages of a centesimal division of the quadrant, and by dividing the degree into hundredth parts instead of into minutes, made a step towards a reformation in this respect, and but for the appearance of Vlacq's work the decimal division of the degree might have become recognized.
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.
Since 1871 the decimal system of coinage, corresponding to that of the United States, has been the only one employed.
The Sum Will Be The Year Of The Christian Era, And The Day Of The Year Will Be Found By Multiplying The Decimal Figures By 365.
The decimal point is, however, used systematically in the Constructio (1619), there being perhaps two hundred decimal points altogether in the book.
(1) he saw that a point or separatrix was quite enough to separate integers from decimals, and that no signs to indicate primes, seconds, &c., were required; (2) he used ciphers after the decimal point and preceding the first significant figure; and (3) he had no objection to a decimal standing by itself without any integer.
Napier thus had complete command over decimal fractions and the use of the decimal point.
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.
To him are due the introduction of the decimal system of currency and the adoption of a system of protection to Canadian manufactures.
4d.) is the standard coin, with a subsidiary decimal coinage.
The Egyptians report the weight of a measure of various articles, amongst others water (6), but lay no special stress on it; and the fact that there is no measure of water equal to a direct decimal multiple of the weight-unit, except very high in the scale, does not seem as if the volume was directly based upon weight.
This is also evidently the Olympic cubit; and, in pursuance of the decimal multiple of the digit found in Egypt and Persia, the cubit of 25 digits was (1/4)th of the orguia of 100 digits, the series being --
-- The ounce (480 gr.) and multiples and decimal parts of the ounce troy from 500 ounces to 0.001 oz.
When the base is to, the logarithms of all numbers in which the digits are the same, no matter where the decimal point may be, have the same mantissa; thus, for example, log 2.5613 =0-4084604, log 25.613 =1.4084604, log 2561300 = 6.4084604, &c.
These extracts contain all the original statements made by Napier, Robert Napier and Briggs which have reference to the origin of decimal logarithms. It will be seen that they are all in perfect agreement.
Decimal or Briggian Antilogarithms. - In the ordinary tables of logarithms the natural numbers are all integers, while the logarithms tabulated are incommensurable.