Will you suffer me to add some further remarks on the subject of the Arabic numerals and cipher; as neither the querists nor respondents seem to have duly appreciated the immense importance of the step taken by introducing the use of a cipher. I would commence with observing, that we know of no people tolerably advanced in civilisation, whose system of notation had made such little progress, beyond that of the mere savage, as the Romans. The rudest savages could make upright scratches on the face of a rock, and set them in a row, to signify units; and as the circumstance of having ten fingers has led the people of every nation to give a distinct name to the number ten and its multiples, the savage would have taken but a little step when he invented such a mode of expressing tens as crossing his scratches, thus X. His ideas, however, enlarge, and he makes three scratches, thus [C with square sides], to express 100. Generations of such vagabonds as founded Rome pass away, and at length some one discovers that, by using but half the figure for X, the number 5 may be conjectured to be meant. Another calculator follows {434} up this discovery, and by employing [C with square sides], half the figure used for 100, he expresses 50. At length the rude man procured a better knife, with which he was enabled to give a more graceful form to his [C with square sides], by rounding it into C; then two such, turned different ways, with a distinguishing cut between them, made CD, to express a thousand; and as, by that time, the alphabet was introduced, they recognised the similarity of the form at which they had thus arrived to the first letter of _Mille_, and called it M, or 1000. The half of this DC was adopted by a ready analogy for 500. With that discovery the invention of the Romans stopped, though they had recourse to various awkward expedients for making these forms express somewhat higher numbers. On the other hand, the Hebrews seem to have been provided with an alphabet as soon as they were to constitute a nation; and they were taught to use the successive letters of that alphabet to express the first ten numerals. In this way b and c might denote 2 and 3 just as well as those figures; and numbers might thus be expressed by single letters to the end of the alphabet, but no further. They were taught, however, and the Greeks learnt from them, to use the letters which follow the ninth as indications of so many tens; and those which follow the eighteenth as indicative of hundreds. This process was exceedingly superior to the Roman; but at the end of the alphabet it required supplementary signs. In this way bdecba might have expressed 245321 as concisely as our figures; but if 320 were to be taken from this sum, the removal of the equivalent letters cb would leave bdea, or apparently no more than 2451. The invention of a cipher at once beautifully simplified the notation, and facilitated its indefinite extension.