These examples show that Napier was in possession of all the conventions and attributes that enable the decimal point to complete so symmetrically our system of notation, viz.
A decimal system of numeration was used, with numbers going up to io,000.
To 175° F., corresponding to decimal parts of an inch of mercury of the vacuum gauge.
The first national coinage was begun in 1822, and the decimal system was adopted in 1863.
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.
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.
In 1782 he prepared an elaborate report on the coinage, suggesting the use of the decimal system and of the terms dollar and cent.
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.
During the Revolution, he was one of the three members of the council established to introduce the decimal system, and he was also a member of the commission appointed to determine the length of the metre, for which purpose the calculations, &c., connected with the arc of the meridian from Barcelona to Dunkirk were revised.
The great spread of the Phoenician weight on the Mediterranean, of the Persian in Asia Minor and of the Assyrian in Egypt are evident cases; and that the decimal weights of the laws of Manu (43) are decidedly not Assyrian or Persian, but on exactly the Phoenician standard, is a curious evidence of trade by water and not overland.
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.
In these cases the digit itself, or decimal multiples, seem to have been used.
Which stand as (1/6)th of the other decimal series based on the digit.
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.
8), the continual mention of large decimal numbers of shekels in the earlier books, and the certain fact of 100 shekels being = mina.
And a strange division of the shekel in 10 (probably therefore connected with this decimal mina) is shown by a series of bronze weights (44) with four curved sides and marked with circles (British Museum, place unknown), which may be Romano-Gallic, averaging 125/10.
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.
The explanation of this property of the base io is evident, for a change in the position of the decimal points amounts to multiplication or division by some power of 10, and this corresponds to the addition or subtraction of some integer in the case of the logarithm, the mantissa therefore remaining intact.
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.
The former translated the work into English; the latter was concerned with Napier in the change of the logarithms from those originally invented to decimal or common logarithms, and it is to him that the original calculation of the logarithmic tables now in use is mainly due.
The power of io, which occurs as a factor in the tables of both Napier and Byrgius, was rendered necessary by the fact that the decimal point was not yet in use.
The next great advance on the Trigonometria artificialis took place more than a century and a half afterwards, when Michael Taylor published in 1792 his seven-decimal table of log sines and tangents to every second of the quadrant; it was calculated by interpolation from the Trigonometria to 10 places and then contracted to 7.
As has been stated, Abraham Sharp's table contains 61-decimal 10 b= log 24 = - log (1-160) d =10g 49 = - log (1-160) 17253 8 35 62 21868 Briggian logarithms of primes up to I ioo, so that the logarithms of all composite numbers whose greatest prime factor does not exceed this number may be found by simple addition; and Wolfram's table gives 48-decimal hyperbolic logarithms of primes up to 10,009.
He also reduced the solar parallax to 14" (less than a quarter of Kepler's estimate), corrected the sun's semi-diameter to 15' 45", recommended decimal notation, and was the first to make tidal observations.
In 1400, M?dhava of Sañgam?grama calculated pi to thirteen decimal places, that is, 3.1415926535897.