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
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'
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
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
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
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.
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,
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
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).
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
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
Angles of the Corners of Kalasasaya
||90° 20' 41"
||89° 43' 5"
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
||358° 53' 30"
||358° 58' 30"
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
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.
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
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
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
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
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.
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.
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.
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).
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
The solstices, the "Willka-kuti"
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.
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
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.
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
However, in their time they were not only carefully aligned and carved
the sides facing the interior of the building were magnificent
inscriptions as can be seen on a piece that has fallen from one of them
which a part of these drawings has been miraculously saved, (Figs. 21
Because of the enormous age of these great pilasters which were the
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
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
discovery --- from the Third Period --- of intermediary blocks which
carved heads and in the most perfect technique of that period, (Fig.