from a change in the radix of our numerical system, and some advantages of the present might be lost. An increase in the radix has been recommended for the greater power in computation it would afford, and its decrease has been advocated, even to the extent of suggesting the use of the binary system in which there is but one significant figure, on account of the consequent great simplicity of all calculations. It seems almost certain, however, that, "dictated by Nature," as it is, it will never be changed, as the advantages on either side are small when compared with the magnitude of the problem of a new radix. There are some people who would defer any improvement in our system of weights and measures until the decimal system of notation can be wiped out and one with sixteen as radix substituted, so that if Mr. Spencer was able to bring about such a change as he suggests he would find that his favorite number, twelve, was not alone in the field of candidates for adoption as the foundation of the new notation. Indeed, it is a well-known fact that in the evolution of number systems those not decimal have had their day, but none have survived competition with the many advantages pertaining to that growing out of the "bundle of ten fingers."
In his fourth paper Mr. Spencer again resorts to quotation, and brief reference should be made to the arguments set up by some of his authorities. The letter of Sir Frederick Bramwell contains some remarkable statements. His assertion that the new system will require "more figures to perform ordinary sums than on our present system, when rightly applied," is so grossly incorrect, as may be easily proved by a few examples, that no time need be spent in controverting it. The same might be said of his further assertion that it is more likely to lead to error, and, above all, to the common error in placing the decimal point. This last statement is frequently made, and it is worth while, therefore, to call attention to the fact that in all ordinary business transactions in which the decimal system is used, and in all calculations, for that matter, the error of a misplaced decimal point is one of the rarest of all errors. This is because of the generally quick and certain detection of such a mistake. To misplace the decimal point by the smallest possible amount is to change the result tenfold, and usually so great an error is instantly detected by means of approximate knowledge or other checks. Take our own money system, for example: it is perfectly safe to say that other mistakes are a million times more frequent than a persistent, undetected misplacing of the decimal point. Yet, curiously enough, considerable weight has been given to this objection to the metric system of weights and measures, which is, on the contrary, vastly less liable to errors of computation than that now in use.