In BANCROFT'S _Native Races_, vol. iii, chapter vii, we find that the titles of QUETZALCOATL (CUKULCAN) were the _air_, the _rattlesnake_, the _rumbler_ (in allusion to thunder), the _strong hand_, the lord of the _four winds_. The bird symbol exists in 2021, etc. Now in 2020 and its congeners we have found every one of these titles, save only that relating to the _thunder_. And we have found a meaning for every part of the hieroglyph 2020 save only one, viz, the left-hand one-third, consisting of concentric half ellipses or circles. It may be said to be quite _probable_ that the unexplained part of the sign (2020) corresponds to the unused title, "the rumbler." But it is not rigorously proved, although very probable. The thunder would be well represented by repeating the sign for sky or heaven. This much seems to me certain. The sign is but another summing up of the attributes and titles of CUKULCAN. 2021 gave his portrait, his bird symbol, made allusion to his institution of the sacrifice of wounding the tongue, and spelled out his name in rebus characters. 2020 repeats his name as a rebus and adds the titles of lord of the four winds, of the sun, of rain, of the strong hand, etc. It is his biography, as it were. In this connection, a passing reference to the characters 1810, etc., 1820, etc., 1830, etc., 1840, etc., 1850, etc., of the left-hand side of Plate LVI should be made. Among these, all the titles named above are to be found. These are suitable subjects for future study. We now see _why_ the pair 2020, 2021 occurs so many times in Plate LVI, and again as 264, 265, etc. The right-hand half of this tablet has much to say of CUKULCAN, and whenever his name is mentioned a brief list of his titles accompanies it. Although it is disappointing to find _both_ members of this well-marked pair to be proper names, yet it is gratifying to see that the theory of pairs, on which the proof of the order in which the tablets are to be read must rest, has received such unexpected confirmation. To conclude the search for the hieroglyphs of CUKULCAN'S name, it will be necessary to collect all those faces with "_round_ beards" (see BANCROFT'S _Native Races_, vol. iii, p. 250). TLALOC was also bearded, but all the historians refer to QUETZALCOATL as above cited. I refer hieroglyphs Nos. 658, 651?, 650?, and 249? to this category. Perhaps also the sign No. 153 is the sign of QUETZALCOATL, as something very similar to it is given as his sign in the _Codex Telleriano Remensis_, KINGSBOROUGH, vol. i, Plates I, II, and V (Plate I the best), where he wears it at his waist.