By November 1880, the Le Plongeons were back in Yucatan.  No longer in pursuit of the Chacmool, they resumed their research.   They went to the site of Mayapan, 30 miles from Merida, looking for keys to the undeciphered Maya hiero-glyphic writing.  It was their first visit to the site, and they enjoyed the monetary assistance of Pierre Lorillard and the hospitality of Don Vicente Solis de Leon, one of the owners of the Hacienda X-canchacan where Mayapan was located.
 As one of his primary purposes at Mayapan, Augustus wanted to present the facts about Maya inscriptions.  Several essays had appeared, including one by Professor Philipp J.J. Valentini, that seemed to dismiss a Maya alphabet, recorded in the sixteenth century, just after the Conquest, as a mere invention of the Bishop of Yucatan, Diego de Landa.  Le Plongeon hoped to prove that the alphabet was authentic.  His strategy was to straight-forwardly report on the monuments and the knowledge of living Maya.  "My knowledge of them must, of necessity, be greater than that of gentlemen, who write from behind their desks, ignorant of the true facts" (1881b:249-50).

Using his knowledge of spoken Maya, Augustus intended to strengthen his argument that Landa's Maya alphabet was of some use in understanding Maya hieroglyphics.  His premise was that the letters recorded by Landa's scribes were still in use then and probably corresponded to the glyphs carved in stone.  Le Plongeon reasoned that Landa must have believed the only way to disengage the Maya from old beliefs was to take away all the books that were the key to their religious beliefs and translatable only by those who understood the glyphs.  Citing the Bishop's fervor in destroying all Maya books that fell into his hands, Le Plongeon argued, "For I ask how can a reasonable and honest man deny that the prob-abilities are in favor of Landa?"

Augustus also hoped that he might find an inscription written in two or three languages, a sort of Rosetta Stone of the Maya.  This was his first thought when he saw Stela One, called the Stela of Mayapan.   As he studied the incised slab, he soon realized that even if it had once been a trans-latable text, they could no longer decipher its weathered carvings.  "Alas! had our hopes been gratified, of what earthly use would it have been to us in the present instance, these carvings being so obliterated by the hand of time and the action of water."  He could make out enough details to write some comments about the iconography on the lower section of the stela.  The floral design on the headdress reminded him of similar reliefs on the northeast end of the portico of the Castillo, and on the Lower Temple of the Jaguars at Chichen Itza.  He believed it to be the Cocom flower, "a peculiar yellow flower, well known in the eastern and southern portions of the Peninsula."

In the Maya dictionary of Don Pio Perez, compiled earlier in the nineteenth century, he found the definitions of Cocom: "Cocom is a sarmentous plant, with yellow flowers. ...Cocom was the name of an ancient Maya dynasty, and is still preserved as an Indian family name among the natives of Yucatan."

Le Plongeon found a passage in Landa's Relaciones de las Cosas de Yucatan, a book in which Landa recorded Maya stories about the gods and ancient ruling families, that seemed to suggest the name of the individual on the stela.  In one section of his Relaciones he wrote, "That after the departure of Kukulcan, the lords agreed in order to make their republic stable, to give the principal command of it to the house of the Cocomes, either because it was the most ancient, or perhaps the richest, or may be that the man then at its head, was the one of most worth among them." Augustus concluded that the personage depicted on the stone monument was of great authority because of his height on the stela relative to the other figure.  The lower figure was "but on a low stool (a proof of his inferiority) in order to reach, somewhat, to the exalted position of his lord, who is pictured condescending to stoop toward his subordinate, clearly indicates that Cocom is the King."

In addition to analyzing the carving at Mayapan, Le Plongeon surveyed some structures and determined the latitude of the site.  Using this, he hypothesized that a large mound with two upright columns on top was used as an astro-nomical gnomon, or time indicator.  The two columns provided a fixed point for gauging the sun's position.

In his report to the American Antiquarian Society, "Mayapan and Maya Inscriptions," Augustus used elaborate calculations based on his measurements of the gnomon mound to support the notion that it was used by Maya priests to keep track of time.  He felt that the mound was built to keep track of the ritual 260 day, and the solar 365 day calenders.

He stopped short of trying to explain why they had adopted two modes of computing time.

"Whatever be the theories presented to the world by others, my duty toward you, and towards
the students of American Archaeology, is to present, on what I see; because I do not believe
that we possess, as yet, sufficient positive and incontro-vertible data for any one to form a true
and correct opinion on the subject, free from hypothesis."

After surveying the pyramid of Kukulcan, the great plumed serpent, and other structures at Mayapan, Augustus designated them as "belonging to the latter period, in order to distinguish them from the most ancient, (which are built of solid stone masonry from their foundations to their summits, as those of Khorsabad)" (1881b:275).  He observed the later buildings to be "made of loose unhewn stones and rubbish, piled up so as to form the interior mass, which was then encased by a facing of care-fully hewn stones."  Noting that they were not constructed with the care and precision of earlier Maya buildings, he assumed that the difference carried through to the core.  Not having excavated the finely built structures of the classic Maya period, he did not realize they were also rubble filled.

At the close of his report to the American Antiquarian Society, Augustus cited Lorillard and Fred P. Barlee for their "moral and material support" of his and Alice's work in Yucatan.  He thanked Senator George F. Hoar, Vice President of the Society and Stephen Salisbury for their attempts "to induce the American Government to protect me as an American citizen abroad, and a scientist whose explorations were interrupted."  He noted also the indiffer-ence of the American scientific societies, which were unwilling to support him through purchase of his photographs and tracings.  Yet they " wanted to procure from me GRATIS what had cost me so much time, labor and money to acquire."

Le Plongeon was fed up by what he considered to be gross indifference by the scientific community. He hardened his resolve.  " I made up my mind to keep my knowledge, so dearly purchased, to destroy some day or other my collections, and to let those who wish to know about the ancient cities of Yucatan, do what I have done."

This was not necessarily the case in other countries, he noted, citing entreaties by Barlee and various acquaintances in England that led the Le Plongeons to publish more of their research, despite the unfavorable notice it often received.

"The main cause of my un-willingness to say more on the subject is, that my former writings,
when published, have been so curtailed and clipped, to make them conform with certain opinions
and ideas of others, that my own have altogether disappeared, or have been so disfigured as to
cause me to be taken for what I am not--an enthusiastic theorist following in the wake of Brasseur de Bourbourg."

The Le Plongeons then returned to Uxmal for a few more weeks of research.