The Astronomic Science of Tihuanacu. How Kalasasaya was Built to be Used as a Stone Almanac

(Plan III)

      As was pointed out in another section, in order to construct the quadrilateral of Kalasasaya of the Second Period, with the purpose of having this serve to determine the seasons of the solar year with their subdivisions, it was necessary for it to have special form and orientation, or for the east and west walls to be located exactly on the meridian and especially, that the PROPORTION BETWEEN THE LENGTH AND WIDTH OF THE BUILDING CONFORM TO THE MAXIMUM ANGLE OF SOLAR DECLINATION BETWEEN THE SOLSTICES OF THAT TIME.

The problem was not a difficult one, as the careful observers of celestial phenomena of that time, who were the priests and rulers, and who certainly constituted special castes of Kholla stock, (63) had preserved the traditions of many centuries of observation and experience.

Neither is there the least doubt that before venturing to construct the great Temple of the Sun, they had in Tihuanacu itself, or previously at some other point of one of the large islands or peninsulas of the inter-Andean lake, an adequate and prominent site with an horizon free of elevations and relatively flat to the east, (64) (or perhaps a similar building on a smaller scale), in which they obtained their great experience in making observations and determining the dates of the year. In the construction of that primitive, or let us say, trial solar temple, their knowledge was, without doubt, developed little by little. They became familiar with the celestial phenomena, until they attained the summum of learning to be able later to venture the construction of this great Temple of the Sun of the Andes.

Possibly one of these trial observatories was that of Lukurmata, which we discussed at the beginning of subchapter "B."

Let us consider now what methods they used in the acquisition of this knowledge. Since for these precise calculations they did not have at their disposal, as we do, such instruments as theodolites, sextants, astronomical almanacs, etc., but only sundials (65), plumbs, levels (66) and topos (67,67a) we are led to wonder whether with such ordinary, though at the same time such efficient means, they could carry out unquestionable celestial observations; this, of course, from their anthropocentric point of view, in which they believed the earth to be the center of the universe, around which all the celestial bodies moved, and Tihuanacu the center of the earth, taking into account the age-old observations of the atmospheric phenomena. It should not be forgotten that in very ancient times not only the residents of Tihuanacu made astronomical observations of unquestionable value.

In China, 2,700 B. C, during the reign of Wuwang in Lo Yang, they observed and determined the obliquity of the ecliptic, measuring with a sundial nine feet high the shadows in the solstices. The emperor Tschukong in the year 1100 B. C. measured the obliquity of the ecliptic (68) and Eratosthenes (born 276 B. C.) reckoned it at 23° 51' 15". (69)

Thus it is that China, Babylon and Chaldea gave to humanity the celestial circle of 360° which we still preserve in our astronomical measurements, atlantes, maps, geometry and all the calculations which have angles as their basis.

Why then could the Tihuanacuans not have determined, during the solstices, the line of the meridian on the basis of measurements of the corresponding shadows? Why could they not have determined the solstices with their famous topos, taking points of observation between marks on the horizon, which would indicate the maximum oscillation of the sun toward the north and six months later toward the south?

There are still many other primitive methods which they might have used as a basis for determining the line of the meridian, knowing the amplitude of the sun between the solstices. But there are also ordinary systems for obtaining in a single night, with the primitive resources mentioned above --- which without any doubt they had at their disposal --- the line of the meridian with considerable accuracy. I shall present here a very eloquent example to show how, through the culmination of some fixed star and with the ordinary resources we have mentioned, they could have arrived at the line of the meridian.

They would have searched in the firmament toward the South Pole for a circumpolar star; they would stretch a tape line more or less from east to west (a line familiar to them since in the equinoxes they saw the sun rise and set on that line) ; they would true the line with a level, (Fig. 15); they would string on this two small perforated discs of stone or wood; they would place a block of stone or adobe in front of the tape line and on it an observation topo (sight).

The priest-observer, would kneel in front of the topo and wait until the star passed the line on the left "toward the top" and he would instruct his assistant to move the small disc of wood to the spot where the star passed through the line; they would then have waited some hours until the star had culminated and again passed through the line "downward" so that the assistant could place the second disc in the corresponding location.

They would wait until daytime and then would divide the space between the two discs in half, from which they dropped a plumb to the ground. Then they would take another line with which they could obtain a straight line from the hole of the observation topo to the plumb and would prolong the line. THIS STRAIGHT LINE WAS THE LINE OF THE MERIDIAN. At a great distance from the line thus obtained, they marked their "sight", which at the present time is visible on the hill Quimzachata, in the form of a white circle which can be distinguished perfectly from the balcony wall of the Third Period.

In order to determine what degree of accuracy could be obtained in the determination of the meridian with this ordinary method of observation, we made, in the year 1928, and in company with one of the astronomers who had come to Bolivia with the German mission, a similar calculation. We used nothing more than a tape line, a level and a plumb; for discs we used two empty spools which we strung on the line and not having a topo de observación at hand, we improvised one from an empty sardine can, perforating it in the center and fastening to the side a stick sharpened to a point on the end which we stuck in the ground.

My companion, stretched on the ground, observed the culmination of the star and I, following the directions of the improvised "observer", moved the spools along the line; then we divided in half the distance between the two spools and from this point (one half of the line) we stretched a straight line to the center of the improvised topo de observación (the hole in the tin can); simultaneously with this empirical operation and in order to test its relative accuracy, we made that same night and on the same spot a calculation with a theodolite, based on the same star. Comparing both operations, a slight difference was apparent. (70)  

By repeating these ordinary observations and striking an average for all of them, one would get an exact calculation. There is not the least doubt that the priest-astronomers of Tihuanacu, in order to determine their "sight", made not only one observation, but perhaps hundreds of them. This probably went on over a long period of years until they were in a position to establish the "definitive line of the meridian" on a building of the magnitude and importance of that of Kalasasaya, the stone calendar of the most civilized inhabitants of the America of that time.

Also, without the direct establishment of the meridian, with which they would not have obtained the proportion of width and length of the building, the plan and subsequent construction of the cardinal walls could have been effected much more advantageously, exclusively on the basis of careful observations, at each six months of the solstices, or in the following manner.

For an exact observation of the solstices there could have been built on the site where today the center of the primitive west wall of Kalasasaya of the Second Period is found, a platform (71) of relative height, on which they would have erected the "observation pedestal", (Pl. XV). In order to determine the solstices from this point they could have made a simple apparatus more or less in the following form and using only the primitive materials which they had at hand.

Since they were clever forgers and smelters of bronze they could have prepared a simple apparatus in the form of a box or cover the size of the last step of the aforementioned pedestal, over which it would be fastened. Then almost on the edge of the cover near the observer, there would be bored a central hole. (Cf. the reconstructed drawing, Fig. 16).

Next on this bronze cover set on top of the "observation block" with the hole as we have indicated, they would place a strip of bronze, silver or gold, let us say some 10 cm. wide and 1 cm. thick. This was something less than 73.4 cm. in length, the diameter of the platform of the pedestal, and both of its ends were pointed, (Fig. 17). Each end of the strip would be drilled so that there could be placed in them the observation "topos" in a stationary manner. This would be done in such a way that the one near the observer would pass through the strip about a centimeter like a spike. The latter would be introduced in the upper hole, or the hole in the bronze cover, and in this way the strip with its two "topos" would be free to swing freely on the cover.

In this very simple manner they could have made an apparatus which today we would call a sight or a diopter. (72) Its manipulation was extremely simple as can be seen in Fig. 18 and looking through the two holes of the "topos" they would have observed not only the rising of the sun in the solstices, but also daily and during many years, marking carefully the maximum oscillation of the sun toward the north and to the south. Thus they would obtain, easily and simply, an angle which would constitute the total amplitude of the sun between the two solstices, the vertex of which would be the spike of the first observation "topo."

Then they would have only to prolong each side of the maximum angle with lines or sights and on the prolongation of  each side of the angle measure a fixed distance, let us say, eighty "lokas" (the normal unit of measure of Tihuanacu in the First Period). (73)

Next connecting the ends of these two points they would have a line corresponding to the EXACT MERIDIAN AND AT THE SAME TIME THE PERFECT LINE OR DIRECTION OF THE EAST WALL FOR THE SUN TEMPLE, their stone calendar, which served to furnish the exact dates of the year to the dense population of farmers and graziers of Cameloidea who were their subjects.

Later, to obtain the exact directions of the other three walls, they had only to strike a right angle at each end of the direction of the east wall already determined, which in their turn would constitute the lines for the south and north walls. The west wall was the parallel of the east wall and naturally intersected mathematically the primitive observation point of the solstices which was the opening for the first "topo."

This system which we have just described was, in our opinion, the one which the priest-astronomers of Tihuanacu could logically have used, and preferably to construct the Temple of the Sun, Kalasasaya, in the Second Period. Naturally, this system could be used only in the event that to the east there existed a true horizon and not one similar to that of the present time which is located some 15 kilometers away, (Cf. profile of levels, Vol. I. Pl. I) covering the true horizon and giving rise to a false horizon.

Thus it is that looking today from the observation point toward the northeast corner of Kalasasaya, there is an elevation of 2° 47' and toward the southeast corner one of 0° 16'. In the long space which separates us from the construction of the Second Period of Tihuanacu, which is presumed to be, as will be shown later, from ten to fourteen thousand years, there were, in our opinion, definite tectonic movements and alluvial accumulations which undoubtedly could have changed the topography of the high plateau. On the subject of tectonic changes, we presented a paper in 1931 before the Twenty-third International Congress of Americanists meeting in New York City entitled "La remoción del cíngulo climatérico como factor del despueble del Altiplano y la decadencia de su alta cultura".

On the basis of the explanations set down in that work, we presume that when they planned to construct Kalasasaya, there was perhaps an almost free horizon to the east. But in the case that the present hills extended toward the east at the time of the Second Period, they still could have constructed the temple in the same place in an exact mathematical manner, in the following way. With a sight similar to the one described above --- in a temporary observatory near Tihuanacu --- (for example the already mentioned one of Lukurmata or one on an island in the lake where to the east there would have existed an apparently free horizon) they would make note of the solar amplitude and mark the angle on the metallic plate underneath the sight.

Later, on the spot where they wished to construct the "east wall", they would determine the line of the meridian and from the middle of this line they would strike a perpendicular. At the distance that they believed fitting for the size of the building they would set on the perpendicular line the observation point, and on it the sight with the angle of amplitude brought from the temporary observatory, and they would prolong the sides of the angle until they struck the line of the meridian. Of course, previously they would have divided the angle of solar amplitude in the middle and then would proceed in the manner described above for the plan of Kalasasaya.

Carrying out this operation, as without doubt they must have done, the people of Tihuanacu were the first to observe the obliquity of the ecliptic. Thus, without question, Kalasasaya must have been constructed, using one or the other of the systems which we have studied and described. Kalasasaya being divided longitudinally into equal parts and, of course, also the angle of solar amplitude, they believed likewise that they had divided the year into four equal parts. This belief proved to be erroneous and later they had to rectify it, as we shall see subsequently when we consider the great monolithic perron which, in the east wall, gives access to the Temple of the Sun.

Another problem presents itself: after various careful triangulations carried out in the interior of the great enclosure of Kalasasaya, we discovered that the angles of its four corners were not completely right at the present time. Those of the southeast and northwest are somewhat acute while those of the northeast and southwest are slightly obtuse. We transcribe herewith the measurements of these angles made by Professor Arnold Kohlschütter, Dr. Rolf Müller and the author.

Angles of the Corners of Kalasasaya

Southwest Southeast Northeast Northwest Observer
90° 19' ------- ------- ------- Müller
90° 29' 89° 29' 90° 27' 89° 36' Kohlschütter
90° 19' 89° 37' 13" 90° 20' 41" 89° 43' 5" Posnansky

The lack of rectitude in these angles causes the east wall not to be orientated on the meridian at the present time and gives it a deviation of 1° 1' 30"; that of the west shows a deviation of 1° 6' 30". The north and south walls, instead of being orientated mathematically in a north-south direction, show deviations. The north wall shows a deviation of 40' and the south 42'. The verification of the German Mission is as follows:

South Wall West Wall North Wall East Wall Observer
89° 24' 358° 55' 89° 20' 358° 53' Kohlschütter-Becker
89° 12' 358° 52' ------- 359° 4' Müller-Posnansky
89° 18' 358° 53' 30" 89° 20' 358° 58' 30" AVERAGE

Dr. Müller believes that this small deviation with the resultant lack of absolute rectitude in the angles was intentional and he gives the basis for his opinion in his aforementioned work (Baesler-Archiv).
As far as we are concerned, we believe that Kalasasaya in its time was correctly and mathematically orientated, not only with relation to the meridian but in the angles of the corners of the building and that it is not a question of any error on the part of those conscientious, prehistoric architects and astronomers.

This seems logical, for a native mason draws right angles today using the systems employed by architects and builders with a maximum margin of personal error of 6'. As the basis for this opinion which we have just set down, the following should be stated. All of the valley of Tihuanacu including the site where the ruins are located, is composed of sandy clay and represents an ancient glacial lake bed on the edge of which, without any doubt, Tihuanacu of the Second and Third Periods was located. (Cf. levels toward Lake Titicaca, Vol. I, Pl. I).

The builders of Tihuanacu set out to construct that great work without possessing the knowledge of architecture which man had in later periods, a knowledge which could be acquired only through the experience of thousands of years. The architects of those times were as yet unfamiliar with the system of putting foundations under the buildings and especially under the megalithic blocks or the lower structure, "the groundwork".

That is to say, to prepare first a base in the subsoil, rather wide and composed of a compact concrete of stone or masonry so that the foundations of the building --- which support all of the weight --- would not sink or get out of level when the subsoil became damp or moved. Megalithic Tihuanacu has no foundations and if it did have, its buildings, as solid as any in the history of architecture, would still be standing today perfectly intact. (74) 

It is a recognized fact that clay soil moves when the humidity penetrates to some depth in periods of intense and prolonged rain, and especially when steps are not taken to prevent this by means of paving or some other form of protection of the soil which will prevent the penetration of water. Naturally, in locations having but slight declivity, the slipping is scarcely measurable even after several centuries. If the studious reader will consult the general map (Vol. I, Pl. III) with its curves of level, he will note that the part of Kalasasaya which is resting on the hill of Akapana, almost forming a block with it, is the south wall of this temple, where on this account the slipping, if such there were, must have been negligible.

Thus, this wall shows a deviation of only 42' from the cardinal east-west line. The same is true of its parallel which to the north has a deviation of only 40'. As for the east and west walls, they have deviations of 1° 1' 30" and 1° 6' 30", respectively. This data could not be more eloquent. The south wall has remained, being connected to the hill Akapana, almost in its original position. With regard to the north wall, it has slipped toward the west, or rather toward the lake, pulling with it the east and west walls.

Also, some 150 m. to the north of the temple, there extended an arm of the lake and this in the same way was one of the causes for the slipping of the land in that direction. But the most obvious proof of the movement which took place in the subsoil is to be seen in an indisputable manner in the excavation carried out on the floor of the small semi-subterranean temple of the First Period (Cf. Vol. I, Pl. VII). Here can be seen a drainage canal which has lost its lineal form through the movement of the subsoil, and is laterally entirely twisted, and curving.

This temple with its drainage canal (Cf. infra its reconstruction) is built in the subsoil. After the destruction of the metropolis it was filled with alluvium and shows perfectly the tectonic disturbances of the lower ground. In that period the aforementioned canal was straight, well-lined and leveled, with a small declivity toward the north branch of the lake, so that the rain waters which fell within the enclosure of the roofless building would run toward it.

Another factor which might have contributed to the loss of rectitude in the angles of Kalasasaya, could have been the process of shrinking of the strongly soaked clay soils which contract more where they receive the sun and winds on one side. In short "to err is human". We shall not be the last to study the astronomical, geodetical, topographical, geological and stratigraphic phenomena and problems which today present themselves as indecipherable enigmas in Kalasasaya. Others will follow, perhaps with more preparation, with more patience and especially with better instruments, greater time and means, and they will check our studies and give a definitive verdict in this difficult material.

Now we shall consider another point of great importance with respect to Kalasasaya: that of the massive perron which gives access to this significant and useful monument of American man.

This staircase is not in the center of the east wall of the building as would be demanded by symmetry and all architectonic standards. Not the slightest architectural consideration caused the massive staircase to be 1m. 116 mm. to the north.

Interested for a long time in this problem, the author advanced various vague opinions and hypotheses in former publications, which of course are superseded by the present publication. Discussing this knotty problem on various occasions with Dr. Müller, the opinion of the author of the present work was always that expressed by Dr. Müller on p. 8 of his study "El Concepto Astronomico", or in other words that the perron had to mark a main calendarian point for the time of the equinoxes. Already at that time the author pointed out that the deviation of the staircase from the intermediate line of the building of Kalasasaya must have some relation with the perihelion and the aphelion of the terrestrial orbit. And thus is the case. (75)

The sun not being in the center of the orbit but in a center of the eclipse in which the earth turns about the sun (Fig. 19) the earth needs a greater length of time to go from the autumnal equinox to the winter solstice and return to the vernal equinox than to go from the vernal equinox to the summer solstice and return to the autumnal equinox. (76) That is to say, that for the moving of the earth from the twenty-first of March (autumnal equinox) to the twenty-third of September (vernal equinox) it needs 186 days, 11 hours (winter) while to travel from the vernal equinox to the autumnal equinox it needs only 178 days, 19 hours (summer). Thus there is a difference of 7 days and 16 hours between the winter and summer semesters. This is the crux of the problem as to why the perron of Tihuanacu is not in the center of Kalasasaya but is located 1 m. 116 mm. to the north. Let us explain this in simpler form.

After the priest-astronomers of Tihuanacu had established --- we may presume with the system of the "topo" sight --- the northeast and southeast corners (the solstices) of Kalasasaya, and after having logically divided the angle in half, they thought that they had also divided the year into four parts. However, in practice they noted the aforementioned fact that the sun needed more time to go from the north to the center of the building than from the south to the same place.

Thus, since they wished to divide the year into four equal parts, they made further observations in order to determine where the sun would rise at the exact middle of the year, on the twenty-fourth of March and the twenty-first of September, and they then noted --- surely with no little surprise --- that the sun did not rise in the center of the temple but 1 m. 116 mm. to the north. With this observation they were perhaps the first men in the world to note the perihelion and the aphelion, or the eccentricity of the terrestrial orbit. This difference corresponds for the 21st of September to 1° 0' 56.3" toward the north and for the 24th of March to 1° 6' 45.3" toward the south. (77)

This is the way in which they established the point which marked the rising of the sun at the exact middle of the year as the center of the massive perron. This, the principal access to the palace, was at the same time a calendarian point for the determination of the great solar festivals: in Aymara probably Kjapak-Tokori and in Quechua, Citua-Raymi (for them the twenty-first of September) (according to Felipe Guaman Poma de Ayala: Koya-Raymi).

The twenty-first of September was the beginning of spring for them, the beginning of the year, and six months later came the "Willka-Tokori" (in Aymara) or the Inti-Raymi (in Quechua), the beginning of the autumn, the festival of the harvest (according to Guaman Porna: Inca-Raymi; making a mistake of a few days he designates it as "April").

The solstices, the "Willka-kuti" (78) were festivals of prayer in which the sun was implored not to go farther away but to return and favor man with its light and benign heat. These principal agricultural periods and astronomical seasons gave rise to great festivals and the determination of their dates was the motive for the construction of the great Temple of the Sun in the Andes.

Other important dates connected with agriculture or the raising of cattle were certainly determined by the rising of the sun over this or that column and were accompanied by their respective celebrations. Thus, there is almost no doubt that the rising of the sun in the center of each pillar of the east wall, and later the setting of the sun on the pillars of the balcony wall to the west, signified important dates in the life of man of that time.

The west balcony wall which belonged to the SECOND PERIOD, is not in existence at the present time and we have found only remains of the short corner wall of the south side. On June 18, 1939, we discovered remains of the north side. (79)

At the present time, these connect the west wall with the balcony wall of the Third Period, or they may be the structural prolongations which connect it with the northwest and southwest pillars of the wall of the Second Period. As we shall see farther on, only the balcony wall was completely replaced in the Third Period. Its principal object was to guard the tabernacle of solar observation and its mysteries from profane eyes.

At about two meters from the center of the west wall of the Second Period and on the dividing line of the temple a great slab 2 m. 5 cm. wide, 2 m. 75 cm. long and 25 cm. thick (Fig. 20) was found. In our opinion this slab has no connection at all with the observation point or with its base; it belongs to the Third Period and later on we shall consider its object. Some 8 m. from the slab and also on the dividing line of the temple, in the course of the excavations in 1903, the piece which we have called the "observation pedestal", was found. In Fig. 20 it can be seen at the moment of the excavation, still in its original place, of in the fifth test pit counting from the great slab. (80)

On the basis of the material and the technique, it belongs without question to the Third Period. At the time of the construction of the modern church of Tihuanacu, it was covered with earth. It was therefore saved from destruction and only similar blocks of red sandstone found on the surface and supposedly from the Second Period were used. At the present time they are enchased in the balustrade of the atrium of the church, (Vol. I, Plate IV a and Plate XIV a). We judge that these pedestals may have served a purpose similar to that indicated by the drawing of the sight.

The north and south cardinal walls of Kalasasaya, as can be seen in the illustrations of Vol. I, Plate XVII a and b, are of red sandstone and at the present time consist only of a few pilasters --- today showing a very rustic appearance owing to erosion --- and remains of the same.

Their object at the time of the construction of the temple was to support the intermediary walls, as can still be seen perfectly on the south corner of the west wall of the Third Period (Plate XV a) and on the walls of the temple of the First Period (Vol. I, Pls. VI and VII) as well as in the remains of the west wall of the Second Period which were recently excavated. This technique, which we have called "Kalasasaya", is still in use in rural constructions, especially in fences, throughout Bolivia and Peru. It is not unusual to see this very old system in all parts.

The columns today have the appearance of crude stones planted in the ground. However, in their time they were not only carefully aligned and carved but on the sides facing the interior of the building were magnificent symbolical inscriptions as can be seen on a piece that has fallen from one of them and on which a part of these drawings has been miraculously saved, (Figs. 21 and 21a). Because of the enormous age of these great pilasters which were the support of the walls, some of them have fallen down and others are so thin in certain parts that they threaten to fall over from one moment to the next.

At the present time nothing is being done to preserve this precious monument which still serves, as it has for centuries, as a quarry for the inhabitants of the region. Possibly they were also enchased with carved human heads, as in the walls of the temple of the First Period, (Cf. aforementioned figures). This idea is supported by the discovery --- from the Third Period --- of intermediary blocks which show such carved heads and in the most perfect technique of that period, (Fig. 22).

(63) Cf. Posnansky, Antropología y sociología, Figs. 8 up to 30.

(64) There exist various "Kalasasayas" on the Altiplano as, for example, in Chiripa, Cumana, Lukurmata, Khonto, Kaskachi, Merkhetihuanacu and other places.

(65) Jean Baptiste Biot, Recherches sur I'ancienne astronomic chinoise Paris, 1840.

(66) We have seen a level of Tihuanacu, taken to London by one Mr. Thomas Richards. (Cf. the corresponding figure, infra. (Fig. 15.))

(67) Bronze, silver or gold sights in the form of a flat spoon with a hole in the spoon-shaped part.

(67a) In the Museum of the American Indian (Haye Foundation), New York City, there are "observation topos" of silver, the largest of which is 46 cm. long. (Cf Fig. 16a in Vol. III).

(68) R. Müller, op. cit., gives (according to Wolf) 2100 years B. C. instead of 1100.

(69) Id., gives (according to Wolf) 23° 45' 1" instead of 23° 51' 15".

(70) Dr. Müller in his work "El Concepto Astronómico del Gran Observatorio Solar Kalasasaya" (Anales de la Sociedad Científica de Bolivia, Vol. I, p. 6) says: "Out of curiosity and in company with Prof. Posnansky, we carried out, without using any instrument, a determination of the meridian based on the culmination of stars and as a result of that test it was seen that it is possible to obtain good results by ordinary means by making a number of observations".

(71) Recently, upon building a road in this locality, remains of foundations were found, possibly from a building used for observations.

(72) That in the Third Period and perhaps also in the Second they used and worked bronze perfectly, is obvious from the large metal bolts with which they joined the gigantic stone blocks in Puma-Punku and from a great variety of bronze objects found in the excavations. This apparatus itself might have been made of wood in the beginning, but naturally this would not have the lasting qualities of bronze for extended observations.

(73) The "loka" of the First Period of Tihuanacu was 174 cm. as can be seen clearly in the preglacial building on the island of Simillake in the Desaguadero River (Cf. Posnansky: Antropología y sociología andina, 1937). For example the semisubterranean building of the First Period of Tihuanacu is 2890 cm. wide (16 lokas) and 2600 cm. long (15 "lokas"). Each "loka" of the First Period measures 175 cm. The building of Simillake has thirty "lokas" of the First Period. With regard to the "loka" of the Third Period of Tihuanacu it is only 161.51 cm. refer to the balcony wall of Kalasasaya. But in the Second Period, which has more connection with the First than with the Third, it seems that the "loka" had the same size of 175 cm. as in the First Period. For example, the width of the perron of Kalasasaya is 4 "lokas" and that of the sides of the CONSTITUENT ANGLE of the Kalasasaya of the Second Period has 80 "lokas" of 175 cm. The change in the size of the "loka" of the First Period of Tihuanacu is due, in our opinion, to anthropological reasons. The difference in the arm span (basis of the "loka") of the primitive men of the First Period, or a length of 13.49 cm., corresponds to the greater physical development of the man of this period as compared to the man of the Third Period, more developed intellectually but with a correspondingly reduced physical development.

(74) Last but not least, if the later destruction caused by man had not taken place.

(75) Cf. Müller: "Der Sonnentempel in den Ruinen von Tihuanacu", Baesler Archiv, pp. 132-133.

(76) We are, of course, referring to the southern hemisphere in which is situated Kalasasaya.

(77) Data for the year 1919.

(78) Cf. Vocabulario of Bertonio, Spanish-Aymara Volume, p. 436. 
Guaman Poma in his Crónica calls the solstice of June "Huaucay quisqui" and that of December "Inti Raymi." In support of the supposition that in Cuzco in very ancient times there were also "sign posts" which marked the sunrise, we note what Polo de Ondegardo said in his book Los errores y supersticiones de las Indios, 1571 (that is to say, a few years before Guaman Poma began to write his Crónica). In Ch. 7 he says: "They divided the year into twelve months by the moons. Already, each moon or month had its marker or pillar around Cuzco, where the sun arrived that month."

(79) We should point out that this communication between the balcony wall of the north side of the Third Period with the west wall of the Second Period was effected in the Third Period as we proved personally in our excavation carried out the 18th of June, 1939. In this operation this wall replaced, without any doubt, a previous sandstone wall of the Second Period.

(80) Test pit of the Crequis de Montfort Mission, 1903-1904.