There is another point in regard to these series which may as well be illustrated by means of the example given as any other. What is the signification of the red numerals of the series? They are unnecessary if the only object in view was to indicate the intervals between the days of the column. Nor will the supposition that the Mayas had not discovered a means of representing higher numbers than 20 suffice, as the introduction of 13 would have lessened the labor and shortened the calculation. But one answer to this inquiry appears possible, viz, that these numbers are intended to denote certain intermediate days to which importance was for some reason attached. These intermediate days can readily be determined from the data given, and in the present example are as follows: (1) Between 1 Caban and 1 Muluc they are 12 Lamat, 5 Ix, 1 Akbal, 5 Manik, 12 Ix, and 8 Akbal. (2) Between 1 Muluc and 1 Ymix they are 12 Ahau, 5 Cimi, 1 Men, 5 Cauac, 12 Cimi, and 8 Men. (3) Between 1 Ymix and 1 Been they are 12 Eb, 5 Ezanab, 1 Manik, 5 Chuen, 12 Ezanab, and 8 Manik. (4) Between 1 Been and 1 Chicchan they are 12 Kan, 5 Oc, 1 Cauac, 5 Akbal, 12 Oc, and 8 Cauac. These, as will be readily perceived, are found by counting on the calendar from 1 Caban, 1 Muluc, &c., as heretofore explained.[283-1] Our interpretation of the series of this particular class is now complete, except as to their application or the object in view in forming them and the determination of the particular years to which they apply. Possibly they may be of general application, so far as consistent with the calendar system. The conclusion on this point depends largely upon the conclusion as regards the system, as it is evident their location in time--if the year of 365 days and the four series of years formed the basis of the system--would not correspond with their position in a system based upon the year of 360 days, in which the four year series does not play any necessary part. Dr. Förstemann calls attention to the fact that the pairs of numerals representing the intermediate days are usually placed in separate compartments, each containing a figure or a picture generally symbolic or of a priest dressed to indicate some particular god. It is therefore very probable that these intermediate days are to be devoted to ceremonies relating to the divinities or subjects indicated by these figures. In order to confirm the theory we are now discussing and at the same time show some of the different varieties of the series of the type now under consideration, the following additional examples are given. In the middle division of Plate 5 is a day column and a numeral series, as follows: I. Manik } Cauac } 16, IV; 9, XIII; S + 5, XII; 2, I. Chuen } Akbal Men