laborious, unscientific, stupid system on the I., II., Ill VII., VIII., IX. plan? Nevertheless, sensible people long continued sturdily to resist the innovation. Moreover, it is stated that the change was frequently particularly resisted by the professional arithmetical experts.
The above presentations, while surprising at first apprehension, may claim perhaps a greater admiration and regard for our beautiful, and now universal, arabic arithmetic, which has asserted its supremacy by the laws of evolution and the long struggle for existence from which the fittest and the locally best emerge.
Even after our modern arabic arithmetical system prevailed, it was long before its decimal refinements were reached. According to Ball's history, decimal fractions were only invented about the year 1617, and it was not until the beginning of the eighteenth century that the decimal point came into use. In fact, an examination of eighteenth-century literature seems to indicate that fractions were more generally expressed as vulgar fractions in the earlier part of the eighteenth century, and it was not until the latter part that decimal fractions became customary.
A simple, practical and scientific system of units requires to be a decimal system, in order to transfer from a larger to a smaller denomination, or vice versa, by a mere change of the decimal point. This generally acknowledged fact is instanced by our American currency, which has three decimal units—the dollar, cent and mill. In effect, however, there is but one unit, the dollar; because a sum of money expressed in dollars is instantly converted into cents, or into mills, by a shift of the decimal point, without any appreciable mental effort. In Great Britain, however, the currency not being decimal, but divided into guineas, pounds, crowns, florins, shillings, pence and farthings, there are seven different units. Pencil and paper will generally be required by any but skilled mental arithmeticians to transfer a sum of money from one expression to another.
To an American, the superiority of the decimal currency over the non-decimal currency of his British cousin is generally so self-evident as to require no emphasis. But it is notorious that many intelligent and cultivated Englishmen do not recognize this superiority. They are so familiar by habit with their own currency, that they have forgotten their early schoolboy efforts in mastering it. Nevertheless, it is easily shown that the British system, as above enumerated, includes no less than 17 connecting ratios; namely, 1.05, 2, 2.5, 4, 4.2, 10, 10.5, 12, 20, 21, 24, 48, 60, 240, 252, 960, 1,008. The American decimal currency has only three connecting ratios, 10, 100 and 1,000; while these are effected without calculation, by merely shifting the decimal point.
The advantage of the decimal currency could not, however, have been realized before decimal arithmetic became generally known; or, say, prior to the eighteenth century.
