follow precisely the method indicated by progress thus far, we would put a dot inside of this for forty-one, but the Maya does not seem to have done this, but made a slight change, perhaps to avoid confusion, and he put the dot outside and to the left, [symbol]. Four of these dots make forty-four, and then forty-five is represented by a straight line vertically within. Dots now outside as before carry to forty-nine, when a vertical line replacing the dots gives fifty. Adding dots again as before leads to fifty-four, while doubling the lines with the dots produces all figures up to fifty-nine, [symbol]. Then once more a new character is needed to go on, and one is chosen that is very common in the Dresden Codex, occurring in a number of different forms. It is this [symbol] in its simple form. Thomas takes it in this form [symbol] for naught, and Försteman for the same numeral in this form [symbol]. The difference between these two is immediately apparent, and it seems that both these able investigators have made a mistake in this respect. It is as if some future investigator should give as our naught the figure 6 and the figure 9. The simple form is possibly one of the chief Maya numerals and the enclosed lines give it the necessary differentiation. Some change occurs again here, in the system I have attempted to outline. There are used lines instead of dots, though dots also were used, and the horizontal line does not appear to have been doubled; at least I have been unable to find an example of it, though, as the number of manuscripts is limited, I could hardly expect to find examples of all the figures in them. The carved inscriptions being, as is believed, older than the manuscripts, there would be a difference between the numerals in them and in the books. But we will take the simple character [symbol] for, say, sixty. It may be mentioned again that these selections and their order are merely tentative. Only by long study might the matter be determined. Adding lines transversely as found in the Dresden Codex, we arrive easily at sixty-four. Following the previous system, a horizontal line with an upward curve then gives [symbol] sixty-five, and transverse lines again take us to sixty-nine. A horizontal line with a down curve produces seventy [symbol]. Seventy-four would then be [symbol], and as the horizontal line seems not to have been doubled we are forced to choose another character for seventy-five [symbol]. A down curved horizontal line then gives seventy-six [symbol], while for seventy-seven an entirely new form is used. The reversal of seventy-five and seventy-six carries to seventy-nine. The cross lines in some cases appear to have been used up to sixty-seven. There are so many different figures of this kind that it is possible they were used interchangeably in some cases. For eighty a new figure is required, and I have selected one that occurs frequently in the Dresden book, in shape something like a bow, [symbol].