One who tries to perform with Roman numerals a simple problem in addition or subtraction--or better yet, in multiplication or division--will have no difficulty in understanding why people unacquainted with the Arabic system of notation have had recourse to a counting-machine or abacus. The difficulty, of course, lies not so much in the clumsy form of the individual Roman numbers as in the absence of the zero and the reckoning by position which it makes possible. This defect the abacus supplied. By means of a sanded board or a cloth-covered table or a string of counters it provided a row of columns each of which represented a decimal group--units, tens, hundreds, etc.--by which numerical operations could be rapidly and accurately performed. Employed by the ancient Romans, as by the modern Chinese, the arithmetic of the abacus became a regular subject of instruction in the schools of the Middle Ages, whence its reckoning was introduced into the operations of the Anglo-Norman treasury. The most recent student of the subject, Reginald Lane Poole, connects the change with the Englishmen who studied at the cathedral school of Laon early in the twelfth century. To me it seems somewhat earlier, brought by abacists who came to England in the eleventh century from the schools of Lorraine.[36] In either case its introduction was much more than a change of bookkeeping. Convenient as such reckoning was in general, it was the only possible method for men who could neither read nor write, like the Anglo-Norman sheriffs and many of the royal officers, and its use made it possible to carry on the fiscal business of the state on a large scale, in an open and public fashion, with full justice to all parties, and with accuracy, certainty, and dispatch. It was a businesslike system for busy and businesslike men. * * * * *