HOWEVER that might be, there was no question that he had been the official keeper of the Mayan records, the astronomer, the soothsayer, the sage, the historian of the people of Mictolan for innumerable years. He had explained his method of making astronomical observations through the carefully calculated and accurately placed slits in his tower, and I had been astounded at his deep knowledge of the planets, the constellations and the celestial universe. Though, as I have said, he had adapted his green sphere apparatus to serve as a working model of the earth and its rotation, orbit and relation to the planets, and from this was able to work out problems by which he checked up on the Mayan calendar, yet he verified his calculations by observations of the heavenly bodies, and by the crudest and simplest of instruments. And he proved conclusively to me, that the results were amazingly accurate. The Mayan calendrical system, as I already knew, was perhaps one of the greatest achievements of any race, and was considered superior to anything of the sort previous to that in use by ourselves at the present time. But I had never before fully realized how truly astonishing it was, the more especially in view of the manner in which it was worked out and checked for errors. To read of a thing, to see characters, dates and figures cut in cold stone, is one thing; but to stand beside a living man of a supposedly-vanished race, and have him explain and demonstrate the same facts, is quite another. As old Nohul Voh patiently explained the meaning and the calculations of the twenty Mayan days and their names, the solar year of 360 days, with the addition of the five “unlucky days” or _Uayeb_, and the relationship of the divine year or Tonalmatl with the civic year, matters that had been confused and hazy before became clear and simple. It was the same with the Calendar-Round and the Initial Days of the years, the Tuns, Katuns and Baktuns, the Long Count and the system of numerical glyphs. And his method of using the planet Venus for checking up on his observations was astounding and intensely interesting. By observing the periods elapsing between the appearances of this planet as the morning star, Star-periods of almost precisely 584 days--he knew that when the planet had appeared five times its appearance should tally with the eight years of 365 days each of his calendar. His arithmetical method of working out the Venus and calendrical coincidences was truly remarkable, both for its accuracy and its simplicity, and as I watched him, I began to appreciate the superiority of the Mayan vigesimal system over our decimal system, and realized how non-essential were the complicated higher mathematics employed by our scientists and astronomers.