Produced by Joshua Hutchinson, Josephine Paolucci and the Online Distributed Proofreading Team at http://www.pgdp.net. (This file was produced from images generously made available by Cornell University Digital Collections). THE ATLANTIC MONTHLY. A MAGAZINE OF LITERATURE, ART, AND POLITICS. VOL. V.--FEBRUARY, 1860.--NO. XXVIII. Transcriber's Note: Minor typos have been corrected. Footnotes have been moved to the end of the article. COUNTING AND MEASURING. Though, from the rapid action of the eye and the mind, grouping and counting by groups appear to be a single operation, yet, as things can be seen in succession only, however rapidly, the counting of things, whether ideal or real, is necessarily one by one. This is the first step of the art. The second step is grouping. The use of grouping is to economize speech in numeration, and writing in notation, by the exercise of the memory. The memorizing of groups is, therefore, a part of the primary education of every individual. Until this art is attained, to a certain extent, it is very convenient to use the fingers as representatives of the individuals of which the groups are composed. This practice led to the general adoption of a group derived from the fingers of the left hand. The adoption of this group was the first distinct step toward mental arithmetic. Previous groupings were for particular numerations; this for numeration in general; being, in fact, the first numeric base,--the quinary. As men advanced in the use of numbers, they adopted a group derived from the fingers of both hands; thus ten became the base of numeration. Notation, like numeration, began with ones, advanced to fives, then to tens, etc. Roman notation consisted of a series of signs signifying 1, 5, 10, 50, 100, 500, 1000, etc.,--a series evidently the result of counting by the five fingers and the two hands, the numbers signified being the products of continued multiplication by five and by two alternately. The Romans adhered to their mode, nor is it entirely out of use at the present day, being revered for its antiquity, admired for its beauty, and practised for its convenience. The ancient Greek series corresponded to that of the Romans, though primarily the signs for 50, 500 and 5000 had no place. Ultimately, however, those places were supplied by means of compound signs. The Greeks abandoned their ancient mode in favor of the alphabetic, which, as it signified by a single letter each number of the arithmetical series from one to nine separately, and also in union by multiplication with the successive powers of the base of numeration, was a decided improvement; yet, as it consisted of signs which by their number were difficult to remember, and by their resemblance easy to mistake, it was far from being perfect.