4. The sixteen Venus signs also occurring below, except on page 48. This sign likewise occurs in a very similar form on Altar R of Copan.

With these omissions, the left side of these pages presents the following appearance:—

Page 46.
III Cib II Cimi V Cib XIII Kan
XI Cib X Cimi XIII Cib VIII Kan
VI Cib V Cimi VIII Cib III Kan
I Cib XIII Cimi III Cib XI Kan
IX Cib VIII Cimi XI Cib VI Kan
IV Cib III Cimi VI Cib I Kan
XII Cib XI Cimi I Cib IX Kan
VII Cib VI Cimi IX Cib IV Kan
II Cib I Cimi IV Cib XII Kan
X Cib IX Cimi XII Cib VII Kan
V Cib IV Cimi VII Cib II Kan
XIII Cib XII Cimi II Cib X Kan
VIII Cib VII Cimi X Cib V Kan
4 Yaxkin 14 Zac 19 Zec 7 Xul
North. West South East
Gods.
236 326 576 584
9[[1]] Zac 19[[1]] Muan 4 Yax 12 Yax
Gods
East North West South
19 Kayab 4 Zotz 14 Pax 2 Kayab
236 90 250 8
Page 47.
II Ahau I Oc IV Ahau XII Lamat
X Ahau IX Oc XII Ahau VII Lamat
V Ahau IV Oc VII Ahau II Lamat
XIII Ahau XII Oc II Ahau X Lamat
VIII Ahau VII Oc X Ahau V Lamat
III Ahau II Oc V Ahau XIII Lamat
XI Ahau X Oc XIII Ahau VIII Lamat
VI Ahau V Oc VIII Ahau III Lamat
I Ahau XIII Oc III Ahau XI Lamat
IX Ahau VIII Oc XI Ahau VI Lamat
IV Ahau III Oc VI Ahau I Lamat
XII Ahau XI Oc I Ahau IX Lamat
VII Ahau VI Oc IX Ahau IV Lamat
3 Cumhu 8 Zotz 18 Pax 6 Kayab
North West South East
Gods.
820 910 1160 1168
3 Zotz 13 Mol 18 Uo 6 Zip
Gods
East North West South
13 Yax 3 Pax 8 Chen 16 Chen
236 90 250 8
Page 48.
I Kan XIII Ix III Kan XI Eb
IX Kan VIII Ix XI Kan VI Eb
IV Kan III Ix VI Kan I Eb
XII Kan XI Ix I Kan IX Eb
VII Kan VI Ix IX Kan IV Eb
II Kan I Ix IV Kan XII Eb
X Kan IX Ix XII Kan VII Eb
V Kan IV Ix VII Kan II Eb
XIII Kan XII Ix II Kan X Eb
VIII Kan VII Ix X Kan V Eb
III Kan II Ix V Kan XIII Eb
XI Kan X Ix XIII Kan VIII Eb
VI Kan V Ix XIII Kan III Eb
17 Yax 7 Pax 12 Chen 0 Yax[[2]]
North West South East
Gods
1404 1494 1744 1752
2 Pax 7 Pop 17 Mac 5 Kankin
Gods
East North West South
7 Zip 17 Yaxkin 2 Uo 10 Uo
236 90 250 8
Page 49.
XIII Lamat XII Ezanab II Lamat X Cib
VIII Lamat VII Ezanab X Lamat V Cib
III Lamat II Ezanab V Lamat XIII Cib
XI Lamat X Ezanab XIII Lamat VII Cib
VI Lamat V Ezanab VIII Lamat III Cib
I Lamat XIII Ezanab III Lamat XI Cib
IX Lamat VIII Ezanab XI Lamat VI Cib
IV Lamat III Ezanab VI Lamat I Cib
XII Lamat XI Ezanab I Lamat IX Cib
VII Lamat VI Ezanab IX Lamat IV Cib
II Lamat I Ezanab IV Lamat XII Cib
X Lamat IX Ezanab XII Lamat VII Cib
V Lamat IV Ezanab VII Lamat II Cib
11 Zip 1 Mol 6 Uo 14 Uo
North West South East
Gods
1988 2078 2328 2336
16 Yaxkin 6 Ceh 11 Xul 19 Xul
Gods
East North West South
6 Kankin 16 Cumhu 1 Mac 9 Mac
236 90 250 8
Page 50.
VII Eb VI Ik IX Eb IV Ahau
II Eb I Ik IV Eb XII Ahau
X Eb IX Ik XII Eb VII Ahau
V Eb IV Ik VII Eb II Ahau
XIII Eb XII Ik II Eb X Ahau
VIII Eb VII Ik X Eb V Ahau
III Eb II Ik V Eb XIII Ahau
XI Eb X Ik XIII Eb VIII Ahau
VI Eb V Ik VIII Eb III Ahau
I Eb XIII Ik III Eb XI Ahau
IX Eb VIII Ik XI Eb VI Ahau
IV Eb III Ik VI Eb I Ahau
10 Kankin 20 Cumhu[[3]] 5 Mac 13 Mac
North West South East
Gods
2572 2662 2912 2920
15 Cumhu 0 Zec[[4]] 10 Kayab 18 Kayab
Gods
East North West South
20 Xul 10 Zac 15 Zec 3 Xul
236 90 250 8

Let us first examine the numbers which are regularly repeated

in the lowest line:—236, 90, 250, and 8, and we shall find that the 584 days of the apparent Venus revolution are divided into these four periods.

The number 236 denotes the time of the western elongation, when Venus is the morning star, 90 the time of the invisibility of the planet, during its superior conjunction, 250 that of its eastern elongation, when Venus is the evening star, and 8 the time of its invisibility during inferior conjunction. The disproportion between 236 and 250 is somewhat striking. These periods which need not of course be exactly equal are usually computed at 243 days. The short period of eight days is only calculated for very sharp eyes; we actually find in the Anales del Museo Nacional de Mexico II, 341 (Mex. 1882), that the Aztecs calculated only eight days for the invisibility of Venus, and this period is also mentioned in the Anales de Quauhtitlan. The repetition of the cardinal points in the 15th and 20th lines of the extract given above refer to these periods; in the upper line to their beginning and in the lower to their close. Hence in the lower line the cardinal points must advance one place and the gods belonging to them in the 16th and 19th lines must follow the same course.

The numbers in the 17th line indicate to which day of the period of 2920 days the position has advanced.

But now we see that the indication of days in the lines 1-13, the indication of months in lines 14, 18 and 21, and the numbers in line 17 are separated from those directly to the right of them by a number of days equal to the numbers given in the lowest line.

From this it follows that each day of the thirteen top lines is joined to each of the month dates placed just below them, forming a complete calendar date. Therefore from the III Cib on the left upper corner of page 46 a III Cib 4 Yaxkin, a III Cib 8 Zac, a III Cib 19 Kayab must be formed.

All the 4 × 13 × 5 = 260 day indications combined with three month indications each, show therefore that this whole passage is a huge abbreviation for 780 calendar dates and that the whole refers to 3 × 37,960 days = 113,880 days. But 37,960