On the other hand, the four numbers of the second row from the top are more difficult. They are, it is true, all divisible without remainder by 260, but otherwise they seem to be without rule, and they give one somewhat the impression of a subsidiary computation such as one might jot down on a slip of paper in the course of some important mathematical work. Nevertheless, the following remarkable results are obtained when the first and third and the second and fourth numbers are combined by addition or subtraction:-- 1) 185,120 + 33,280 = 218,400, which is just 600 years of 13 × 28 = 364 days, 280 Mars years of 780 days, 840 Tonalamatls of 260 days or 7800 months of 28 days. 2) 185,120 - 33,280 = 151,840, _i.e._, precisely the highest number of the top row, = 416 solar years of 365 days each or 260 Venus years of 584 days each, _i.e._, the product of the days of the Tonalamatl multiplied by the Venus years. We shall again find the 151,840 on page 51, and Seler ("Quetzalcoatl and Kukulcan," p. 400) finds this same period on a relief of Chichen Itza. 3) 68,900 + 9100 = 78,000, _i.e._, 100 Mars years or 300 Tonalamatls. The half of this number, or 39,000, we shall find again on pages 69-73 by computation; also the whole 78,000. 4) 68,900 - 9100 = 59,800, _i.e._, 520 Mercury years of 115 days, or 230 Tonalamatls, or five times the period of 11,960 days, in which these two periods are united. By computation again we find the 59,800 on page 58. This period of 11,960 days is, however, to the period of 37,960 in the proportion of 23:73, _i.e._, 23 × 520:73 × 520. 23 is the fifth part of the apparent Mercury year, as 73 is of the solar year. Let us now turn to the numbers, which form the bottom of my transcription, but only the left hand lower corner in the Manuscript. Here, in the latter, we find the following (with the correction already mentioned of the second to the third month):-- 2200 1,366,560 1,364,360 IV Ahau I Ahau I Ahau 8 Cumhu 18 Kayab 18 Zip. The first thing to be done is to arrange and fill out these numbers to suit our purpose. The 2200 is clearly nothing more than the difference between the two high numbers. We can therefore dispense with it. Further, we find by the usual computation, that the second number belongs to the first date and the third to the second. Hence the number corresponding to the third date is wanting from lack of space. This number can be calculated from that date; it is 1,352,400. It would suit this date equally well if the number were higher or lower by 18,980 or a multiple of 18,980; but it will be seen directly that it agrees with the other two numbers only at the value given above. Now, if we add to this passage the years in which the dates must lie, they are in the case of the date on the left, the year 9 Ix, in the case of the middle date, the year 3 Kan, and of that on the right hand, the year 10 Kan.