May 9, 1907] 



NA TURE 



45 



represents the actual succession of temperatures, we may 

 modify our diagram of the annual wave by substituting 

 for it a circle (Fig. 4), on which time and temperature 

 may be read together. The centre of the circle is at a 

 height above the base-line proportionate to the mean 

 temperature, the radius is proportionate to the half-range, 

 and when we shall have marked upon the circle a date- 



mark having reference to the phase, the temperature at 

 a given date will be proportional to the perpendicular that 

 falls on the base from a corresponding point of the circle. 

 By superposing a number of such circles, or, better still 

 perhaps, by combining them at proportionate distances in 

 a solid model, we may represent all the various changes 

 from point to point. 



D'Arcy W. Thompson. 



MAY A HIEROGLYPHS.'^ 

 TDY way of encouraging the study of ancient documents 

 having reference to the early history of the Mayas, 

 the museum committee on Centrr.1 .American research pur- 

 pose publishing translations of the more important papers 

 that have appeared in connection with the deciphering of 

 the Maya hieroglyphs. The most recent issue of this series 

 is a translation of Dr. Forstemann's commentary on the 

 Maya .M.S. in the Royal Library of Dresden, generally 

 known as the Dresden Codex. The figures of the original 

 manuscript may be known to students from the admirable 

 reproductions due to Lord Kingsborough (London, 183 1), 

 and for the proper appreciation of the value of Forste- 

 mann's commentary, these plates or some other facsimile 

 should be consulted. Without such assistance Dr. Fbrste- 

 mann admits that his description is of little value, and 

 even with this aid, the book will scarcely be intelligible 

 without some previous knowledge. 



It is very much to be regretted that the committee has 

 not seen its way to give some indication of the process 

 by which the figures have been conjecturally deciphered, 

 and to enable us to assign the degree of trustworthiness 

 that can be placed on the suggested readings. This in- 

 formation is the more necessary, because research on Maya 

 hieroglyphs is confined to a few experts, and the explan- 

 ations that are now accepted cannot be regarded as final. 

 We may confidently assert that these MSS. to some extent 

 represent encyclopaedias of astronomical or astrological 

 lore, but, at the same time, it must be admitted that they 

 include subjects of very diverse origin, the meaning of 

 which is still obscure. 



1 Papeisofthe Peabody Museum of American Archeology and Ethno- 

 logy, Harvard University. Commentary on the Maya Manuscript in the 

 Royal Public Library of Dresden, by Dr. Ernst Forstemann. Translated 

 by Miss Selma Wesselhoeft ant* MI'S A. M. Parker.' (Cambridge, Mass.: 

 Published by the Museum, 1906.) 



The key of the whole is the Tonalamatl. This is a 

 period of time, determined by the combination of the 

 numerals 1-13, with twenty different signs indicating as 

 many days, consequently giving rise to a period of 

 20x13 = 260 days. The number 20 was the base of the 

 ancient Mexican numerical system, and it was natural that 

 for the measurement of time a count of twenty davs should 

 form the first unit of a higher order. The 13 is not so 

 easily explained. Apparently it may be compared with a 

 period analogous to our week. Such a period wa> but 

 little suited for chronological purposes, since it was neither 

 directly based on astronomical observation nor was it the 

 expression of any uniform recurring motion in time. Yet, 

 by its divisions and references to natural objects, such a 

 calendric system was destined to become a useful artifice 

 in the^ hands of the priestly caste for supporting forecasts 

 and giving force to divination. Consequently, the chrono- 

 logical importance of the MS. merges into the astro- 

 logical, and we find mixed up with the pictures figures 

 representing gods, one of whom is delineated no less than 

 141 times, and several others who recur with greater or 

 less frequency. It seems not impossible, therefore, that 

 hidden under these symbols we have the essential part 

 of the religious conception of the Maya peoples in a 

 tolerably complete forin ; but, unfortunately, anv connec- 

 tion between the figure of the god and the principle it 

 represents remains vague and undetermined. The accounts 

 of the Spanish authors regarding the mythology of the 

 Mayas correspond very slightly with these figures of gods, 

 and since all other conjectures respecting their significance 

 are very dubious, the deities can only be safely and 

 temporarily defined by alphabetical designations. Dr. Paul 

 Schellas suggested this method of distinguishing, without 

 describing, any particular deity, and this plan has been 

 wisely followed by Dr. Forstemann in his commentary. 



We may now ask whether the planets have been 

 identified with greater certainty? The first reference 

 to a planet is made in connection with " an inverted 

 figure of a person in a squatting attitude, the head 

 surrounded by stars, and a sign on the back, which 

 may be a suggestion of the Sun glyph. In this figure I 

 see the planet Mercury, and I believe that the planet's 

 retrogression (which lasts 17-18 days) or disappearance 

 into the light of the Sun during this week is the subject 

 of this passage." The evidence, to those unused in the 

 exercise of a vivid imagination in such matters, does not 

 seem overpoweringly strong. The retrograde motion of 

 Mercury, though variable in length, has a longer duration 

 than seventeen to eighteen days. There is the suggestion 

 of forced agreement here, but if we are to understand the 

 time during which the planet remained invisible between 

 the evening and the morning appearance, the construction 

 is not impossible. But if it were the intention of the 

 scribe to record such phenomena, it is difficult to under- 

 stand why such symbols do not occur with some approach 

 to regularity. 



The references seem to be a little less obscure in the 

 case of Venus. The author exhibits a series of numbers 

 the law of formation of which, unfortunately, is not given 

 in this treatise, which indicate that the Mavas were 

 aware of the approximate equality of five synodic periods 

 of Venus to eight solar years. Assuming the length of 

 the solar year as 365 days, and the synodic period of 

 Venus 584 days, 2920 days include both periods. This 

 number occurs repeatedly. The author takes a further 

 step, which also seems w;irranted. In 3 rn<ir>nf.r com- 

 parable with that by which the cycle of 7980 Julian years 

 is determined, he proposes to bring in the Tonalamatl of 

 260 days by connecting it with the number 37,960 da\"s. 

 This number occurs in various combinations, and is equal 

 to 146x260 (Tonalamatl), 104x365 (solar year). 65x584 

 (Venus, synodical period). This combination is sufficiently 

 remarkable, and still more noticeable is the recurrence 

 of higher numbers running into millions, in which it seems 

 possible to trace this factor. But a very rigorous ex- 

 amination of the manner in which these numbers are 

 formed is necessary before it can be concluded that they 

 bear but one interpretation. It must also be remembered 

 that the synodic period of Mars, taken at 780 days, is 

 equal to precisely three Tonalamatls. 



But if the instances of allusion to planetary periods are 



NO. 1958, VOL 76] 



