1. To be complete and in keeping with native modes of representation it must have originally been painted with the symbolical colors of the Four Quarters. 2. It is on a wooden club from Brazil or Guiana that, strange to say, I find a cross symbol with bifurcated branches, which most closely resembles the Copan type. Directing the readers to the illustration of this club as fig. 8, pl. XV, in Dr. Stolpe’s work already cited, I would ask them to examine also his fig. 7, with a design expressing dual and quadruple divisions; fig. 9_b_, with circles containing cross lines; 9_a_, with what resembles somewhat a Maltese cross but also conveys duality; fig. 11_b_ with a cross in a scalloped circle and a curious disc between four signs, with a band of alternate black and white squares and its reverse 11_a_, with triangles, to which I shall revert; and figs. 10_c_ and _d_, each with a mound from which a tree is growing. Though tempted to refer to many other symbols I shall limit myself to pointing out that his fig. 1, pl. XIV, exhibits a group of five circles in a circle which strikingly recall the Mexican examples and the Maya ho=5. As each of the foregoing symbols is intelligible and belongs to a group of ideas which I have shown to have been general throughout America, but to have necessarily originated in the northern hemisphere, it seems pretty clear that they must have gradually found their way to Brazil and Guiana from the north by means of coast navigation and traffic. 3. Concerning the bowl in the hand of the figure occupying the middle of the swastika a few remarks should be added to those already given on pp. 72 and 93. Formed of clay the bowl was an expressive symbol of the earth. Placed in elevated positions on the terraces of the temples, and filled by the first annual showers which fell upon the parched earth, the bowl of celestial water naturally became invested with peculiar sanctity, and was gradually regarded as containing particular life-giving qualities. One use to which bowls full of water were put, in ancient Mexico, seems to explain further the ideas associated with them. It is well known that bowls of water were used at night for divination purposes, just as were black obsidian mirrors. This seems to prove that the latter were a subsequent invention which was adopted because it permanently afforded a surface for purposes of reflection.