Take, for instance, the application of the decimal system, which seems at first sight simple and complete. It is unquestionably an immense improvement on the old confusion; but even here we encounter a difficulty in the circumstance, long since recognized by mathematicians, that our scale of decimal arithmetic is more the child of chance than of philosophy. I know not if any better reason can be given for its adoption than because man has everywhere reckoned by his ten fingers. On this account it is often called “natural.” But, considering whether the number _ten_ possesses any intrinsic excellence, convenience, or fitness, as a ratio of progression, good authorities have answered in the negative. It is the duplication of an odd number, which can furnish neither a square nor a cube, and which cannot be halved without departure from the decimal scale. In this scale we seem to see always those early days when “wild in woods the noble savage ran,” and for arithmetic used fingers or toes. An _octaval_ system, founded on the number eight, would have been better adapted to the divisions of material things. Among us the decimal system is adopted for money; but you all know that we are not able to carry it into rigid practice. Thus convenience, if not necessity, requires the half-dollar, the quarter-dollar, the half-dime, and the three-cent piece. In fact, eight divisions to the dollar, as prevailed in Spain, are more available in the business of life than the decimal division. The number _eight_ is capable of indefinite bisection. The progression beginning with two would proceed to four, eight, sixteen, thirty-two, sixty-four, and so on. The decimal scale is made easy of use by the happy system of notation borrowed from the Hindoos, which might be applied equally well to an octaval scale; but at this time it would be vain to propose a change in the radix of the numerical scale. The number _ten_ is the recognized starting-point, and gives its name to the scale. It only remains for us at present to follow other nations in applying it to an improved system of weights and measures. * * * * * A system of weights and measures born of philosophy, rather than of chance, is what we now seek. To this end old systems must be abandoned. A chance system cannot be universal: science is universal; therefore what is produced by science may find a home everywhere. If we consider the proper elements or characteristics of such a system, we find at least three essential conditions. First, the new system must have in itself the assurance of unvarying stability, and, to this end, it should be derived from some standard in Nature by which to correct errors creeping into the weights and measures from time or imperfect manufacture. Secondly, the parts should be divided decimally, as nearly as practice will warrant, in conformity with our arithmetic. Thirdly, it should be such as to disturb national prejudices as little as possible.