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If, however, the younger forms of the stomata are examined, it is perceived at once, that what were taken as guard-cells are not really such, but are cells corresponding to the accessory cells described in Tradescantia. In the mature leaf the epidermal cells are long and narrow, and have a very marked sinuous outline; but in the young leaf they are proportionately much shorter, and have a nearly straight outline. The formation of a stoma is as follows:

A vertical septum is formed across the end of a cell, shutting off a cell, which is very short (Plate 11, Fig. 1). This cell, however, lengthens rapidly, and soon is nearly square in shape. The stomata are at first formed in rows, but when mature this regularity is not very obvious. Almost as soon as the mother-cell of the stoma is formed, two small cells, at the sides, are cut out from the adjoining epidermal cells, much as in Tradescantia (Fig. 11). These at the outset scarcely keep pace with the development of the mother-cell; but finally grow much faster, and in the end so crowd it as to completely change its shape. The mother-cell rounds off and divides, developing for some time very much as any ordinary stoma (Figs. 111-VIII); but when it is about half grown there is a marked change. The stoma gradually begins to lengthen (Fig. 1x), and the accessory cells which have hitherto been small and unimportant, begin to grow more rapidly, beginning also to show their triangular form. The stoma becomes more and more elongated, and at this stage is nearly rectangular (x), and two or three times as long as broad. Distinct vacuoles are usually present and situated at the ends, but these soon disappear, and their position marks the place of greatest condensation. From this time, the accessory cells form the most conspicuous part of the stoma. They grow toward the center of the stoma, and in consequence the guard-cells become more and more contracted, until the stoma itself, instead of being oval, as it was when half grown, has becoine somewhat dumb-bell shaped, and to a casual observer, the accessory cells, which are no part of the stoma proper, might easily seem to be the guard-cells, while the real guard-cells are so altered that they look like mere thickenings around the pore.

The shape of the accessory cells varies somewhat, but is, in general, approximately triangular, or, rather, three-lobed; but sometimes the lobes are so indistinct, that the cells are nearly

semicircular, while at others the lobes are so strongly marked as to make the cell approach a trefoil. Occasionally, as in Trades

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cantia, the ordinary number of these cells is increased, and an additional one is present; but this is apparently formed by the division of one of the others. Occasionally stomata are also found on the underground stems for some distance below ground. In all such cases they are without the accessory cells, and the guard-cells are of the ordinary shape, and not compressed.

As far as I have been able to ascertain, the form of stomata found in Indian corn is general among the grasses, but usually the stoma proper is neither so narrow nor so much constricted; this is, however, not so in all cases.

In the examination of both these plants, it is necessary to examine the youngest attainable growth, as the stomata are fully formed very early. In Tradescantia, I took the bases of the youngest leaves that I could procure, those that scarcely showed at all without removing the outer leaves, and taking the youngest parts of this, placed it under the microscope without attempting to remove the epidermis. The leaf at this stage of its growth is so thin as to be almost transparent, and by careful focussing, I was able, with little difficulty, to get the youngest forms. In corn I made an oblique section of the stem quite low down, and taking out the bundle of young leaves from within the stem, treated them the same way as in Tradescantia. Only by doing this is it possible to get at the young forms, since any leaf which is firm enough to allow the epidermis to be removed, would show only forms complete, or nearly so.

In the Tradescantia the stomata are confined to the lower surface of the leaves, the upper surface being absolutely without them, while in Indian corn, although they are much more numerous on the lower than on the upper side, they are still found to some extent on the latter.

On first examining the younger forms of the Indian corn stomata, I thought that the accessory cells were formed from the mother-cell by internal division; but after having examined the formation of the accessory cells of Tradescantia, I was struck by the similarity of the two, and on reëxamination of the Indian corn, I was convinced that they were cut out of the adjoining epidermal cells, and were in all respects identical with those around the stomata of Tradescantia.




In my former paper (AMERICAN NATURALIST for August, 1881),



First.-That the Ahau or Katun consisted of twenty-four years.

Second.---That but twenty of these years were usually counted. Third.—That the grand cycle consisted of 312 years.

Fourth.—That the cycles began with the year i Cauac, or in other words that the Cauac column in the table of years should stand at the left.

Two important points yet remain to be determined before we are in a condition to compare Maya dates with those of the Christian era :

First.The position of the different Katunes according to their numbers in the grand cycle.

Second.Some one year of the Christian era that corresponds with some one year of a given Katun, or, in other words, to determine one more contemporaneous dates of the two systems.

Before entering upon the discussion of the topic mentioned in the title to this paper, I wish to present the following additional proof that the year series commenced with a Cauac year, as this is a point which must be settled before we can feel certain in regard to any comparison made between dates of the two systems.

In the manuscript discovered by Perez and translated into English by Stephens, we find the following statement :

“In the 13th Ahau, Chief Ajpula died. Six years were wanting to complete the 13th Ahau. This year was counted towards the east of the wheel and began on the 4th Kan. Ajpula died on the 18th day of the month Zip, on 9 Ymix; and that it may be known in numbers, it was the year 1536, sixty years after the demolition of the fortress."

As the years could only begin with one of the four days, Cauac, Kan, Muluc, 1x, which followed each other in the order here given, it is evident this Ahau must have ended on 10 Ix, and must have commenced with 13 Cauac, if we count 24 years to the Ahau. As I have shown in the previous paper that this period consisted of 24 years, I shall assume that point as settled, and will give, opposite, a table of years sufficiently extended to cover one entire grand cycle, also the closing cycle of the preceding, and the first of the following grand cycles, showing the position of the Ahaues.

As the grand cycle includes just 13 Katunes—312 years—I take for granted that the first year of this period coincides with the first year of a Katun, and consequently the close of the former coincides with the close of a Katun. By dividing the former into periods of twenty-four years, we will obtain the positions of the Katunes, and our next step will be to find their respective numbers.

The commencement and ending of the great cycle are marked thus —... ; the divisions between the Ahaues with single transverse solid black lines. According to the quotation just made from the Perez manuscript, the 13th Ahau was one that required six years to complete it after the year 4 Kan. This can only be found in the one I have numbered xui (the Roman numerals indicate the numbers of the Ahaues or Katunes). If we take for granted that the periods were numbered thus, I3, II, 9, 7, 5, 3, I, 12, 10, 8, 6, 4, 2—a point in reference to which all the authorities agree—having determined the number of one in the grand cycle, it is an easy matter to number the rest.

I call special attention to the fact that the one numbered XIII, found as above stated, begins with the year 13 Cauac ; also that the first years of the others correspond with numbers and order as given in the above series. The selection of xil as the one with which to begin the series, was, as Dr. Valentini has given good reasons for believing, an arbitrary proceeding on the part of the Maya priests.

This numbering, as any one can see, agrees precisely with the position and numbers of the periods marked in table xi of my previous article (p. 639). The position and numbers of these periods, as I have given them here (Table xii) agree exactly with the dates in the Manuscript Troano and the Perez manuscript.

As 4 Kan of the 13th Ahau coincides with the year 1536 of

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