ORIENTATIONS AND DIMENSIONS OF ARCHAIC AND CLASSICAL GREEK TEMPLES By Erin Ann Nell

ORIENTATIONS AND DIMENSIONS OF ARCHAIC AND CLASSICAL GREEK TEMPLES By Erin Ann Nell
ASTEONOMICAL ORIENTATIONS AND DIMENSIONS OF
ARCHAIC AND CLASSICAL GREEK TEMPLES
By
Erin Ann Nell
Copyright © Erin Arm Nell 2003. All rights reserved.
A Thesis Submitted to the Faculty of the
DEPARTMENT OF CLASSICS
,
In Partial Fulfillment of the Requirements
For the Degree of
MASTER OF ARTS IN CLASSICS
WITH AN EMPHASIS IN CLASSICAL ARCHAEOLOGY
In the Graduate College
UNIVERSITY OF ARIZONA
October 15, 2003
1
UMI Number: 1418602
Copyright 2003 by
Nell, Erin Ann
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C
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APPROVAL BY THESIS DIRECTOR
This thesi^has been approved on the date shown below:
y#
Albert Leonid, Jr.
Professor of Classics
Date
2
Aclinowleigements
This project would not have become a reality without the support of many scholars with
interests in both ancient astronomy and Classical archaeology. I am indebted to the
American School of Classical Studies in Athens (ASCSA), especially to James Muhly for the
survey permits, Bob Bridges for his support and suggestions, and to Maria Pilali for her help
and infinite patience. My deepest appreciation for the help and contributions of the
excavators at the following Greek archaeological sites: Dr. Roland Etienne and Litsa Trouki
at Delphi, Dr. Guy Sanders at Corinth, Dr. Elizabeth Gebhard and Dr. Fritz Hemans at
Isthmia; Dr. Stephen Miller at Nemea, Dr. K. Fittschen at Olympia, and Dr. Eric 0stby and
Dr. Mary Voyatzis at Tegea. Sincere thanks to Dr. Cynthia White for her assistance with
Latin translations.
Deepest gratitude to my Master's thesis advisors from the University of Arizona;
Professor Albert Leonard, Jr. (Department of Classics), who directed my committee and gave
me invaluable counsel regarding Greek and Egyptian archaeology, and thesis structure and
organization; to Professor Mary Voyatzis (Department of Classics) for her significant
contributions regarding temple evolution from the Late Bronze Age to the Classical period,
and for her enthusiasm and total support regarding my success as a graduate student; and
special thanks to Distinguished Professor Emeritus, Raymond E. White (Department of
Astronomy). Without Professor White's willingness not only to share his GPS collection
techniques and statistical processing procedures but also his infinite patience in guiding me
through the various mathematical and statistical procedures required, this Master's thesis
would not have been realized.
3
TABLE OF CONTENTS
t HISTOMY OF SCHOLARSHIP.....................................................3
A. JosephN.
B. Frances C. PenTose..................................................................... 10
C. WilliamB. Dinsmoor.................................................................. 12
D. Vincent J. Scully
16
E. Marj^ Blomberg and Goran Henrikssoa..................................................18
F. Alexander Mazarakis-Ainiaii and Bogdan Rutkowski.............................22
G. Conclusion............................................................................... 23
IL GREEK TEMPLE ORIENTATION PROJECT: Part I.
A. Temple Alignments
1. GTOP survey parameters
a. temples
1) Corinth, temple of Apollo
2) Delphi, temple of Apollo
3) Isthmia, 7^ century temple of Poseidon.
4) Isthmia, 5*'' century temple of Poseidon
5) Nemea, temple of Zeus.
6) Olympia, temple of Hera.
7) Olympia, temple of Zeus
8) Tegea, temple of Athena Alea.
b. survey instruments
c. observing technique
d. reduction form'ula............................................
1) determining the quality of the quantity of waypoints
2) determining the precise coordinates of each station.
3) determining the specific orientation of each temple
2. Survey results: the precision of Greek temple alignments.
a. lunar alignment issues.
b. stellar alignment issues
B. Geographical Parameters
1. Location
a. masks
b. solar altitudes and azimuths
c. the effect of a mask on solar altitude.
2. Sighting time.
a. sunset
b. sunrise vs. sunset
3. Survey results: western orientations
C. Conclusion.
25
25
25
25
27
28
29
30
30
32
34
34
36
37
40
40
43
44
46
50
50
52
52
53
54
56
59
61
61
62
63
4
TABLE OF COMTENTS ™ Cmtinmi
III. ANCIENT ARCHITECTS AND ALIGNMENT TECHNIQUES
65
A. Architects
65
1. Vitruvius.
65
a. astronomical education of architects.
66
b. gnomons
67
c. street alignments
69
2. Temple alignment techniques........................................................69
a. western temple orientations
70
b. measuring cords
.74
B. Conclusion.
74
IV. GREEK TEMPLE ORIENTATION PROJECT: Part11.......................76
A. Gnomon Shadows and Temple Dimensions.
76
1. Measuring shadows at sunrise and sunset.
76
2. Temple lengths and widths.
80
3. Gnomon heights.
82
4. Gnomon heights and mask heights.
..84
a. sunrise
85
b. sunset
86
5. Gnomons, masks and foundation heights.
87
B. Application of Theory.
90
1. The 7* century temple of Poseidon at Isthmia.
90
a. western exposure: equinox sunrise
90
b. eastern exposure: equinox sunset......................................................91
2. The temple of Apollo at Delphi.
92
a. northeastern exposure; summer solstice sumise................................... 92
b. southwestern exposure: winter solstice sunset.
94
C. Conclusion
95
V. FINAL CONCLUSION.................................................................96
VI. LIST OF WORKS CITED...........................................................102
5
LIST OF ILLUSTEATIOMS
FIGURE 1.1
FIGURE 2.1
FIGURE 3.1
FIGURE 4.1
FIGURE 5.1
FIGURE 6.1
FIGURE 7.1
FIGURE 8.1
FIGURE 9.1
FIGURE 9.2
FIGURE 9.3
FIGURE 10.1
FIGURE 10.2
FIGURE 11.1
FIGURE 12.1
FIGURE 13.1
FIGURE 13.2
FIGURE 14.1
FIGURE 15.1
FIGURE 16.1
FIGURE 16.2
FIGURE 17.1
FIGURE 17.2
FIGURE 17.3
FIGURE 18.1
FIGURE 18.2
FIGURE 19.1
FIGURE 20.1
FIGURE 20.2
FIGURE 20.3
FIGURE 21.1
FIGURE 21.2
FIGURE 22.1
FIGURE 22.2
Temple of Apollo at Corinth
27
Temple of Apollo at Delphi.
28
Archaic Temple of Poseidon at Isthmia..................................29
Classical Temple of Poseidon at Istlimia.................................30
Temple of Zeus at Nemea.................................................. 31
Temple of Hera at Olympia..................................33
Temple of Zeus at Olympia
34
Temple of Athena Alea at Tegea
35
GPS Temple Collection: Stations
38
GPS Temple Collection: Station Offsets
38
GPS Temple Collection: Virtual Walls
38
Solstitial Temple Orientations
48
Equinoctial Temple Orientations
49
Landscape: Temple of Apollo, Delphi
53
Solar Positions at the Solstices and Equinoxes..........................55
Northeastern Horizon at Corinth
57
Corinth: Northeastern Azimuth, Mask, and Orientation
57
Orientation Differences: Athena Alea at Tegea.
60
Sundial with Gnomon Attached: Delos, 5"^ century BC
67
Vitruvius: Western Architectural Orientations
....71
Vitruvius: Eastern Cult Statue Exposures.
71
Cactus/gnomon: Sunrise Shadow
76
Cactus/gnomon: First Shadow Length.
77
Cactus/gnomon: Second Shadow Length.
77
Sunrise Shadow of a 12 ft. Gnomon
83
Zenith Shadow of a 12 ft. Gnomon
83
Temple Foundation Levels
87
Archaic Isthmia: Western Azimuth, Mask and Orientation
91
Archaic Isthmia: Eastern Azimuth. Mask and Orientation.
92
Eastern Horizon of Archaic Isthmia.
92
Northeastern Horizon of Apollo at Delphi.
93
Apollo, Delphi: Northeastern Azimuth, Mask and Orientation.
93
Apollo, Delphi: Southeastern Azimuth, Mask and Orientation.
94
Southwestern Horizon of Apollo at Delphi.
94
6
LIST OF TABLES
TABLE 1.1
TABLE 2.1
TABLE 3.1
TABLE 4.1
TABLE 4.2
TABLE 5.1
TABLE 5.2
TABLE 5.3
TABLE 6.1
TABLE 7.1
TABLE 7.2
TABLE 8.1
TABLE 8.2
Tempie Dating Discrepancies.............................................. 13
Dates and Sequences of GTOP Temples..................................26
Temple Aligmnents......................................................... 46
Mask Heights................................................................ 54
GTOP Solar Arc Azimuths...................................................56
Simrise Temple Orientations.,...
................58
Sunset Temple Orientations.................................................61
Sittirise/Sunset Comparison Table.........................................62
Temple Ratios............................................................... 81
Sunrise: Shadow and Temple Length Comparisons.................... 85
Sunset: Shadow and Temple Length Comparisons.
86
Adjusted Gnomon Shadows at Sunrise................................... 88
Adjusted Gnomon Shadows at Sunset
89
APPENDICES
APPENDIX A: GPS Reduction Graph: Temple of Apollo at Corinth.
By Erin Ann Nell and Raymond E. White, Ph.D..
110
APPENDIX B: Computing the Slope and Zeropoint of a Straight Line.
By Raymond E. White, Ph.D...............................................................121
APPENDIX C: Accounting for the Change in Rising Azimuth of a Celestial
Object due to an Opaque Mask.
By Raymond E. White, Ph.D.......................................
124
APPENDIX D: The Length of a Shadow Cast by a Solid Object.
By Raymond E. White, Ph.D......................................................127
7
ASTRONOMICAL ORIENTATIONS AND DIMENSIONS OF
AMCHAIC AND CLASSICAL GREEK TEMPLES
Abstract
Previously it has been assumed tliat the majority of Greek temples were oriented
towards the eastern horizon, in the direction of sunrise. The author of this thesis
conducted a GPS temple orientation survey of eight Greek Doric temples and concluded
that these structures were actually oriented to the western, not eastern, horizon, in the
direction of sunset. The following facts support this hypothesis: 1) of the eight temples
surveyed, the western orientations of six were more precise than their eastern
orientations, 2) in the Archaic and Classical periods of ancient Greece, architecturally
aligning structures to the western horizon could have been accomplished with far greater
ease and higher precision than to the eastern horizon, 3) literary evidence by Vitruvius
supports this claim of western temple alignments, and 4) the lengths of each temple
surveyed appear to have been determined via the same technique which oriented them to
the sun on the western horizon.
Introduction
Greek Doric temples were meticulously-constructed edifices dedicated to
specific gods and goddesses who, for the most part, were considered to reside in the
cosmos. As such, these temples served as terrestrial liaisons to many celestial deities.
Since the ancient Greeks made such reverent associations, we should expect that some
architectural components of their temples would embody direct connections to the
celestial sphere. As the entrances and cult statues of the majority of Greek Doric
temples face the east or northeast, it has been assumed by some scholars that the
astronomical connections would be between the temples' eas-tem orientations and
sunrise at either summer solstice or vernal equinox.
8
After conducting a comparative analysis of eight Greek Doric temples utilizing
orientation data from a Global Positioning System (GPS)' survey, I would like to present
a new two-fold hypothesis: first, although the cult statues and entrances of Doric temples
face towards the east, the structures themselves appear to be architecturally aligned to the
west, specifically to sunset at winter solstice or either of the equinoxes. Second, there is
a strong probability that the length of each temple was determined by the same
astronomical procedure that precisely aligned it.
I. HISTORY OF SCHOLARSHIP
The issue of Greek temple orientation has, for the most part, been avoided by
the majority of scholars. Of the few researchers who have offered a temple alignment
hypothesis, most agree that temples were either oriented, to celestial asterisms, terrestrial
landscape features, cultural objects, or a combination of the three. Of those scholars
supporting celestial alignments, they agree that Greek temples were oriented to the
solstices or equinoxes, but they disagree as to which astronomical body those alignments
were based: the sun, the moon, or certain stars. An overview of the most prominent
alignment theories will be presented in the following section.
' GPS: Global Positioning System. This is a hand held device that sends signals to satellites which in turn,
transmit to the GPS unit the correct terrestrial coordinates of loagitude and latitade.
9
A. J. Norman Lockyer
J. Norman Lockyer, a British astronomer, wrote several articles in the 1§90s
•J
regarding celestial alignments of ancient structures and subsequent dating techniques.
He believed that Egyptian temples, on their day of foundation, were aligned to equinox
or either of the solstices based on stellar observations. His theory was supported by
research he conducted on several Egyptian temples, including the Great Temple of
Amon-Re at Kaxnak, in which Lockyer determined that that temple's main axis also
corresponded with sunset at summer solstice? He then hypothesized that since many
Greek temples were also aligned along similar axes, they most likely utilized the same
formula as Egyptian temples.
B. Francis C. Penrose
Francis C. Penrose, an elder contemporary of Lockyer, was a scholar who
obtained measurements of at least thirt>' Greek temples.'^ In the 1890s, he and Lockyer
began collaborating their information in an attempt to establish Lockyer's hypothesis;
that the axes of certain Greek temples were aligned to specific stellar risings in such a
way that the great annual festival of each temple could be foretold by observing heliacal
^ Lockyer, J. Norman, "On Some Points in the Early History of Astronomy," Nature. London: Macmillan
Joumais, Ltd. Multiple articles of CQntinued research were published in issues dating: April 16, May 7, May
21, June 4, Jaiy 2,1891; Januaiy 28, February 18,1892.
^ Lockyer, J. Norman, (1894), The Dawn of Astronomy. London. Lockyer's sunset orientation theory was later
challenged by many scholars inclnding: G.S. Hawkins (1973), Paul Bargaet (1962), and Ed Kmpp (1988), all
who provided evidence that Kamak was aligned to winter solstice sunrise instead of sunset. These challenges
are collectively introduced in the following publication; Kmpp, E.C. (1988), "Light in the Temples," Records in
Stone, ed, Clive Ruggles. Cambridge; Cambridge University Press: 479-483.
* Penrose, F.C. (1893-1901), "On the Orientation of Certain Greek Temples and the Dates of their Foundation."
Proceedings of the Royal Society, LIl, LXL, LXV, LXVIII (multiple articles of continued research). London:
10
risings or settings® of asterisms which occurred on either of the solstices or equinoxes.®
As stellar heliacal risings and settings occur simultaneously with the solstices or
eqainoxes only at great time intervals, Penrose and Lockyer hypothesized that (once a
particular constellation or star could be associated with a particular temple) when a
certain asterism rose heiiacally in coiijunctioa with equinox or either of the solstices, the
foundation date of the temple could be established.
The most notable problem associated with this dating hypothesis is the broad
temporal difference between the proposed astronomical temple foundation date and the
foundation date based on archaeological evidence: if one were to follow this
astronomical dating formula, many Egyptian and Greek temples would have been
constructed several centuries earlier than the evidence indicates. For example, Lockyer
dated the founding of the Egyptian temple of Amon-Re at Kamak to 3700 BC when the
earliest date that archaeological evidence will support is 1900 BC:^ Penrose dated the
Greek temple of Hera at Olympia to 1445 BC, a date almost 850 years earlier than its
material remains suggests.''
Another problem associated with Penrose's theory regards his temple orientation
data. Penrose had an opportunity to re-measure some of his previous temple alignments
The Society.
' "^Heliacalty ( rising or setting) refers to a star that either first appears low on the eastern horizon just before the
sun rises or low on the western horizon just after the sun sets.
* Penrose, 1893: 808.
^ Ibid (Penrose, 1893); 806.
® Krapp, Ed, 19§8. "Light in the Temples," Records in Stone: Clive Ruggles, editor. Cambridge University'
Press; Cambridge; 477.
' Penrose, 1893: Proceedings of the Royal Society, vol 184: 827.
II
and associated horizon heights and he found several discrepancies in his earlier
measurements: the orientation of the temple of Juno at Girgenti had to be adjusted by
2°
and its horizon elevated by 1°.^^ Sach differences in orientations and horizon elevations
couid alter the celestial focus significantly, especially if the alignment was focused OH a
small object (such as a star) as opposed to a larger object (such as the sun). Additionally,
Penrose's orientation me^urements for the temple of Apollo at Delphi" differed from
19
the measurements published by the French excavators in 1915. Because Penrose's
entire hypothesis was based on stellar observations and precise orientation
measurements, alignment and elevation discrepancies have the potential to invalidate it.
C. William B. Dinsmoor
In 1939 William B. Dinsmoor revisited the previous research done by Penrose
and Lockyer. He applauded most of their data collecting techniques but he disagreed
with their "dating formula" because, as previously mentioned, it ignored the historical
and archaeological evidence. The following table (Table 1.1) illustrates some of the
dating discrepancies noted by Dinsmoor:
t "2
Penrose, 1899: ""Proceeding of the Royal Society, vol 65: 370. The original orientation was 264° as opposed
to the new measurement of 262° 36'; the original eastern horizon elevation was !°45' while his second
measurement was 0" 35'.
" Penrose's orientation measurement for the "Ancient"' temple of Apoilo was 231° 17' W (51°17' E) md for
the "Later" temple of Apollo
227°53' W (47°23' E). Penrose, F.C. (1897). "On the Orientation of Certain
Greek Temples....." Transactions of (he Royal Society qfLondon, Vol. 190: Series A: 51.
The French team in 1915, only published measurements of the 4*' century temple of Apollo, which were
47°8' (227°8'). Courby, Fouilks de Delpkes, vol II: La Terrmse du Temple, 4
I -2
Dinsmoor, W.B. (1939) 'Archaeology and Astronomy,' Proceedings of the American Philosophical Society,
12
Table 1.1: Temple Dating Discrepancies
Teiaple
fPeni'ttsc)
\
'i
CHjTOpia; Hera
1445 EiC
610-600 BC
50 vr$
Olympic: Zeas
790 BC
472-460 BC
ilijiiii
2020 BC
535-525 BC
ISfKI yrs
1130 BC
429 BC
71)4) yrs
.thens: Old AthenaTemple
Athens: Nike
Such large temporal discrepancies of foundation dates (from 320 to 1500 years)
strongly suggest that the astronomical dating technique used by Penrose (and Lockyer)
was incorrect.
Dinsmoor had another reason for disagreeing with Penrose's dating formula; the
Greeks and the Egyptians used different celestial bodies as the basis for their calendars.
The Egyptian civil calendar was based on solar and stellar observations whereas the
early Greek calendar was based on lunar observations.''* How could this affect temple
orientation? When the motion of the moon is compared to that of the sun or stars, the
lunar path appears erratic. Greek temples have inconsistent, or erratic, orientations,
especially when comparing their alignments to solar and stellar motions associated wi th
the solstices and equinoxes. Dinsmoor believed that those inconsistent temple
orientations could be attributed to the complicated nature of lunar motion relative to the
sun. He hypothesized that a combination of Greek lunar calendars and religious
vol. 80. Philadelphia: The American Philosophical Society. 104.
Greek lunar calendars were numerous, very erratic and not standardized between city-states. Lunar
intercalations were made on arbitrar)' bases and were not based on mathematical calculations.
13
observations associated with each temple, were the real basis for temple orientations.
To be more specific, Dinsmoor proposed that Greek temples were aligned in such a
manner that not only on the date of their foundatioiis would a Mi moon appear
simultaneously with either of the solstices or equinoxes, but also that this particular
celestial event should correspond with an important feast day associated with each
temple in question.^®
This alignment scheme introduced by Dinsmoor is very complicated and
nowhere in his article did Dinsmoor propose how the ancient Greeks would execute it.
The design for these temples, specifically Doric,'' was introduced in the 7"^ century
BC'^ and not fully developed until the early 6^'' century
This Doric design was
unique: it was considerably larger, and employed vastly different construction
technologies and building materials than did the Greek temples which were erected in
previous centuries. Therefore, the 7^ and 6® century BC architects would not only be
required to learn the new Doric design and associated, complex construction technology,
but also they would need to obtain a sophisticated understanding of astronomy and the
Greek lunar calendar system for each potis in order to align their temples in the manner
that Dinsmoor had suggested.
" Dinsmoor, 1939: 105, 118, 120-132.
'"'Ibid-. 118-119, 133.
" Aithough Dinsmoor was studying several Greek temple styles, the Doric design was the earliest.
" One example is the temple of Apollo at Thermon: Lamence, 66.
" Artemis at Coreyra: Lawrence. 77.
As 7* and 6"' century BC lunar calendars differed greatly from poUs to poUs, the ancient architect may not
have been sufficiently educated in astronomy to predict a liinar period occurring sinailtaneously at equinox or
solstice from one poUs to another. Additionally that same ancient architect may not have been able to determine
14
The final problem associated with Dinsmoor's hypothesis is that he did not
collect Ms own temple orientation data: Ms projections were based entirely on temple
alignment and liorizoii elevation measuremeats gathered by Penrose, almost 50 years
earlier?' Some inconsistencies in Penrose's data were previously mentioned.
Diiismoor, however, found additional discrepancies in Penrose's horizon elevation
(altitude) measurements:
"Penrose, to whom we owe the orientations, had likewise observed these
altitude angles on the spot but for the reason that he frequently altered his observations
to accord with the calculated path of the sun on a morning indicated by the heliacal
rising (or setting) of an arbitrarily selected star, I (Dinsmoor) have checked his results
wherever possible by means of maps. These horizon altitudes become the apparent
altitudes of the sun as it rises in the lines of the temple axes. These altitudes, however,
are subject to various corrections."^^
So now Dinsmoor's theory becomes questionable not only because 7til and 6th
century BC Greek architects may not have been capable of correctly interpreting the
complicated lunar alignment scheme and incorporating it into the innovative, complex
temple design, but also because the data on which Dinsmoor based his hypothesis is now
suspect.
the date to lay the temple foundation by correctly predicting either solstice or equinox to coincide with the
temple deity's feast day. And finally, even if the architect was successful in these predictions-'caiculations,
would he have agreed to delay laying the temple foundation for an indeterminate number of years until the
precise celestial alignments occurred? This author thinks that such a scenario would be improbable, that the
ancient architects more likely aligned their temples to the solstices or equinoxes by basing their observations on
a celestial body that more consistently appeared in association with the equinoxes and solstices, such as the SUE.
Dinsmoor, 1939:145.
15
D. Vincent J. Scully
In 1969, Vincent Sculiy introduced a different approach to Greek temple
alignments in Ms work. The Earth, The Temple, and The Gods. He hypothesized that
certain Minoan and Mycenaean structures as well as later Greek temples were aligned
with a primar}' regard to religious beliefs and terrestrial features rather than to celestial
bodies or events. Scully suggested that the redirection of the north-south structural
orientations of the Minoan and Mycenaean buildings in the Middle and Late Bronze
Ages to the east-west alignments which occurred after the fall of the Bronze Age in the
"post-Dorian" era, resulted from a change in religious beliefs. Scully stated that the
Minoan/Mycenaean earth-based goddess preferred north-south alignments, whereas the
"Dorian" sky-based god preferred east-west alignments.
One example of Scully's theory of Minoan orientation would be that their major
palace, Knossos, was north-south oriented towards Mount Jouctas and many of the
goddess' sanctuaries, which were located on top of that mountain.^'* According to
Scully, the later Mycenaeans purportedly inherited this general north-south orientation
out of respect for the mother goddess. Then, in approximately 1200 BC, these previous
cultures were destroyed, some believe by the conquering Dorian people, who didn't
accept the pre-established earth goddess: they supplanted her with the sky-based male
^ Dinsmoor, 1939: 145-148.
^ The Dorians were thought to have invaded Greece ca. 12"' and 11"" centuries, BC, and effectively brought
about lie demise of the Mycenaean culture. However, from an archE^ological poiot of view, this theory has not
been proven (Bury and Meiggs: 48).
^ Scully: 12
16
god Zeus?^ Scully suspected that this direct conflict between the previous earth-based
goddess and the new sky-based god was responsible for the change ia the alignmeiit of
important architectural structures from north-south to east-west.
Additionally, Scully
strongly believed that other landscape features, such as moimtain ranges, valleys, rivers,
aad oceans, played a more important role for Minoans, Mycenaeam, and later Greeks, in
aligning temples than did orientation to celestial objects.
On one hand, the landscape aspect of Scully's hypothesis bears merit because
many Minoan, Mycenaean and later Greek structures appear to be either generally or
specifically aligned to various landscape features such as mountain peaks, depressions
between two mountains, or bodies of water. This author (herinafter, "EAN") however,
believes that these landscape alignments were done in conjunction with but secondary
to, astronomical orientations. On the other hand, Scully's hypothesis of the earth
goddess's substitution by the sky god in regard to the celestial orientation of architecture
is too generalized and problematic: Scully believed that the Dorian invasion was
responsible for the fall of the Mycenaean civilization and that their arrival introduced the
new sky-based god, Zeus. However, Zeus, along with Hera, Poseidon, Athena (and
others), were referred to in Mycenaean Linear B texts?^ and Plato tells us that legendaiy
Minoan kings received their laws from ZeiK.^® Both of these sources indicate that the
Scully: 36,41.
^llbid:44.
Ventris, Michael, and John Chadwick (1956), Documents in Mycenaean Greek Cambridge: University
Press; 125-127.
^ Biomberg and Henriksson, 1998; 87. Plato (1942) laifs.London: Heinemann Loeb Classical Library;
translation by R.G.Bury,
17
Mycenaeans and Minoans were familiar with Zeus long before the Dorians arrived, so
the sky-god Zeus could not have been introduced by the Dorians.
Finally, Scully credits the Dorians for being responsible for the change in
architectural orientations from north-south to east-west. The Dorian's were believed to
have invaded Greece around 1200 BC but consistent east-west architectural orientations
did not begin until the late 8* century BC,^^ almost 500 years after the Dorian invasion
purportedly occurred.
E. Mary Blombcrg and Goran Henriksson
Mary Blomberg and Goran Henriksson. began conducting orientation surveys of
Minoan and Mycenaean structures and peak sanctuaries in the 1990s. Most important to
this research project are Blomberg's and Henriksson's orientations "and other
relationships'" of fifteen Minoan structures including: four palaces, five villas, and six
peak sanctuaries. Their term "other relationships" refers to orientations of Minoan sites
in which there are "/jo orientations of architectural features,^^" only observations of
celestial events occurring in the vicinity of buildings.
Blomberg and Henriksson claim that ten of the fifteen structures surveyed were
oriented to major celestial events including: sunrise or sunset at summer solstice, sunrise
at winter solstice, sunrise or sunset at equinox, moonrise of the southern major standstill,
and the heliacal rising and setting of Arcturus.^' Blomberg and Henriksson state that the
^ Mazarakis-Ainian (1997), From Rulers' Dwellings to Temples: 283.
Blomberg and Henriksson: 2003; 131.
Ibid: 131-2.
18
Minoan peak sanctuary of Pyrgos was built ca. 2000 BC and aligned to sunrise at
summer solstice. They hypothesize that this alignment was not primarily based on
sunrise at SBmmer solstice, but to the heliacal setting of Arctiirus with the mountain
peak of Kako Kefali in the foreground?^ Then, they infer that there is a connection
'X'X
e
.
e
«
between Minoan circumpolar stellar observations and later Greek navigation by citing
a passage in Book V of the Odyssey, in which Kalypso refers to the circumpolar
asterism, the Bear.^^ Finally, Blomberg and Henriksson project that the alignments of
Archaic Greek temples were directly influenced by earlier Minoan structures.
There are several problematic issues with the hypotheses of Blomberg and
Henriksson, the first being that some of their Minoan orientations were not based on
architectural features. If there were no building entrances or even walls on which to
measure an alignment, it would be difficult to state, for certain, that the sanctuary in
question was architecturally and/or celestially oriented in any manner.
The second issue is that out of the fifteen Minoan locations surveyed, Blomberg
and Henriksson claim that only ten were celestially oriented and, out of those ten
locations, there were no celestial alignment consistencies. These ten sites vary from
being aligned to the solstices or equinoxes by means of the sun, moon, or stars, in either
their rising or setting positions. Such alignment inconsistencies would suggest that,
® They base this alignment on computed measurements which they gathered with a theodolite: the weighted
mean value of the minor axis of the building at Pyrgos was computed as: 325.2° ±0.2°. Blomberg and
Henriksson (2003): 129,130.
A returns is very close to the limits of circumpolar stars when viewed from Pyrgos (N 35° 19"). Blomberg and
Henriksson (2003): 129.
Blomberg and Henriksson (2003): 129.
19
either the Minoans had no favorite orientation asterism, or that Biomberg and
Henriksson (in some of their structures) were searching for a more specific celestial
connection (lunar or stellar). No evidence, including Minoan astronomical records,
celestial sighting devices, or terrestrial survey instruments, has been discovered which
would support specific lunar or stellar architectural alignments of Minoan structures.
The only evidence that Biomberg and Henriksson offer to support their stellar
alignment hypothesis was between the alignment of the Minoan peak sanctuary Pyrgos
with the heliacal setting of Arcturus, and Book V of the Odyssey,where Kalypso
referred to Bootes, Pleiades, Orion, and the circumpolar constellation, the Bear, but
never to Arcturus. The Odyssey was written approximately 1,200 years after the
sanctuary at Pyrgos was constructed: to assume there is a connection between Pyrgos
and the Odyssey is tenuous, at best. A slightly better reference that Biomberg and
Henriksson should have used would have been. Works and Days, written in the 7'^
century BC by Hesiod; it specifically mentioned that the spring equinox could be
predicted by the evening rising of the star Arcturus.'^ The wide temporal gap would still
exist but at least Biomberg and Henriksson would be referencing the same asterism,
Arcturus.
The final problem of Biomberg and Henriksson's hypotheses is their claim that
the Archaic Greeks used the same architectural alignment principles as the Minoans.
Biomberg and Henriksson (1998): 87.
Homer, Odyxsey. 5:270.
Hesiod, Worh and Days: 564-569.
20
Blomberg and Henriksson state that certain Late Bronze Age Minoan shrines at Mallia
and A via Triada were the prototypes of later Archaic Greek temples. While there may
be some architectural similarities between these structures,^® this orientation hypothesis
of Blomberg and Henriksson is fragile. First, they claim that these Late Bronze Age
Minoan shrines and Archaic Greek tempies^^ have similar eastern alignments.'*® Then,
they attempt to fill the 600 year gap between the end of the Late Bronze Age (ca. 1200
BC) and the beginning of the Archaic period (600 BC), with the orientation of only one
temple, that of Magna Mater at Phaistos. which they claim was founded no later than
900 BC."*' Although this temple (or shrine) does have an eastern orientation (sunrise at
winter solstice),'^" the latest date for its foundation was 900 BC. Between 1200 BC and
800 BC, structures in Greece were oriented in many directions."*^ It was not until the late
8*'' centuiy BC that Greek temples began to be consistently oriented in one direction."^
To use the orientation of a single temple built between 1200 and 800 BC as the
"alignment connection" between the Late Bronze Age and Archaic periods, is
unconvincing.
For more information regarding architectural connections between the Late Bronze Age and the Archaic
Period, please refer to: Coldstream (1977), Fagerstrom (1988). and Mazarakis (1997).
They quote Dinsmoor (1939) as saying that 73% of temples were oriented to sunrise (1998); 87.
Blomberg and Henriksson (1998); 84-87.
Myers, Myers and Cadogon (1992): Blomberg and Henriksson (1998): 86.
Blomberg and Henriksson (1998); 86.
'"Riitkowski(1986): 197-8.
Mazarakis-Ainian (1997); 283.
21
F. Alexander Mazarakis-Ainian, and Bogdan Rutkowski
Mazarakis-Ainian"*^ and Rutkowski'*^ have done extensive research regarding
cult places, domestic structures, and temples dating from the Late Bronze Age to the
Geometric Period. Their general consensus was that the factors determining the
orientation of stnictures built within those periods is unclear; they could have been
cultural, terrestrial, or celestial. A good example of cultural orientation was mentioned
by Rutkowski who suggested that certain temples at Mycenae were aligned to cult
objects, in this case a sacred stone, where the natural rock was shielded by the temple's
main room.'*' Regarding terrestrial alignments, Mazarakis-Ainian theorized that climatic
conditions could have been important factors. For instance, structures with north-south
alignments may have been oriented so that their main entrances would face the south
and thus avoid the north wind."*^ Additionally, many early Greek Arcadian temples had
approximate north to south orientations."^^
Finally, Rutkowski cites several examples of general celestial alignments,
including structures at Goumia, Ayia Triada, and Myrtos which, because their front
doors face the setting sun at equinox, have general west-east orientations; the only
temple with an eastern-facing front door was located at Tiryns.'® Additionally, structures
at Mallia, Eleusis, Pseira Mycenae, Philakopi and Keos, have entrances facing the north-
From Rulers' Dwellings to Temples (1997), Sweden: Paul AstrSms F6rlag.
The Cult Places of the Aegean (1986). New Haven and London: Yale Universit}' Press.
'•Rutkowski (1986): 197.
Mazarakis-Ainian (1997): 283,
Voyateis, Maiy (1990), Early Sanctuary of Athena Alea at Tegea. Goteborg, Sweden: Paul AnstrSms fSrIag:
258.
'"Rutkowski (1986): 197-8.
22
west, which would indicate a general orientation to sunset at suinmer solstice.^^ Only
towards the end of the 8tli century BC did temples gain any contiauity in alignment:
Mazarakis-Ainian believes they all started aligning towards the east/"
The studies done by Mazarakis-Ainian and Rutkowski support this research
project wth the exception that Mazarakis-Ainian believes that temples constructed from
the late 8^^ century BC onwards were oriented to the east-west. Certainly Doric temples
had their entrances facing east, but, based on information presented later in this research
project, Doric temple architectural orientations appear to have been based on west-east,
not east-west alignments.
G. Conclusion
Greek Doric temples are geometrically-balanced, imposing stone monuments
that required a high degree of technical precision to complete. Every aspect of their
construction, including laying their foundations, suggests that an inordinate amount of
precision was applied to each structural component. Unfortunately, some of the most
important construction criteria, including the focus of temple alignments and the
technological methods by which Doric temple foundations and orientations were
executed, has eluded scholars for quite some time.
While many researchers believe that Greek temple alignments were celestially
based, none have offered alignment hypotheses which take into account not only the
survey tools available to 6* century BC Greek architects, but also the intellectual level
" Rutkowski (1986): 197-8.
" Mazarakii (1997): 283.
23
of architectural engiBeering and astronomy necessary to execute such gi'and architectural
orientations. Some hj^otheses involve unrealistic dating methods or alignments
schemes that were far beyond the skill of the 7'"^ or 6^ century BC Greek architect.
Although ancient Greeks may have been able to navigate by the stars'^ or harvest and
plant by observing heliacal risings of celestial asterisms^"* that does not mean that ancient
Greeks coBid accurately lay the foundation of a massive, stone stracture to a small
asterism or to the erratic motion of the moon.
This research project. Astronomical Orientations and Dimensions of Archaic
and Classical Greek Temples, introduces scientific information which not only offers a
reasonable method by which ancient Greeks could celestially align megalithic temples,
but also suggests strongly that Greek temples were aligned to, and their dimensions were
derived from, the most easily traceable and obvious celestial object of all - the sun.
" Reference to Kalypso in the Odyssey: Book V.
24
II. GREEK TEMPLE ORIENTATION PROJECT: Part I
A. 2001 GPS Survey: Temple Alignments
In the summer of 2001, a GPS Survey of select Archaic and Classical Greek
religious structures was conducted in order to determine their accurate alignments with
regard to solar, lunar, and/or stellar movements. This survey will hence forth be referred
to as, "The Greek Temple Orientation Project," or "GTOP."
1. The Greek Temple Orientation Project (GTOP): survey parameters
Eight Greek temples built between the 7th and 4th centuries BC were included
in GTOP: the temples and their foundation dates are listed below in Table 2. These
eight temples were selected for this survey because they collectively represent
approximately 400 years of Greek temple construction and design evolution.
Additionally, they are distributed over the Peloponnese and Greek mainland in an area
of approximately 75 km north to south, and 200 km east to west. These wide ranges of
physical and temporal dispersions allow these temples, which were constructed on
similar axes, to be compared with each other over large land areas and extended time
periods.
a. temples
Table 2.1 lists the temples surveyed in GTOP. their foundation dates, and the
earlier temples and foundation dates on which the GTOP temples were aligned.
Hesiod, Works and Days.
25
TABLE 2.1: Dates and Sequences of GTOP Temples
illM
iIM
I) Corinth: Apollo Temple
540 BC:
Temple
liliB
m
v-a' tsanple
IlililBiililMllllillliMill
Pates and $eflieiim
ca675BC?^^n*temple''
3) Isthmia: Poseidon Temple '»i25
ca 650-600
I^HempIe
59
2°^
temple
ca. 545 BC
WTET
No previous temples
4) Isthmia: Poseidon Temple
7" c. BC:
2) Delphi: Apollo Temple
5) Nemea: Zeus Temple
6) Olympia; Hera Temple
330 BC?""
3'" temple
temple
temple
7) Olympia: Zeus Temple
47M57 BC^ r' i«,mp!e
8) Tegea: Athena Alea
Temple
345"335"icF'""''4®tiBpfc'
1 temple
1 temple
No previous temples.
c, BC temple of Hera at
Olympia was originally
70
dedicated to Hera and Zeus.
' c. BC:
c. BC:
2"*^ temple
3^ temple
7*^ c. BC:^
Lawrence: 79. Stillwell, R. (1941). Corinth, I, ii. Architecture. Cambridge, Mass.
'^Morgao: 133.
57
Borguet, Emile {1914). Les Ruins de Deiphes, Paris: Fontemoing Et Cie, Editeurs; 253.
58
Morgan: 133.
" Petsas, Photios (1981). Delphi: Monuments and Museum. Athens; Krene Editions: 48.
Gebard, Elizabeth md Fredrick Hemaas (1992). "Univereity of Chicago Excavations at Isthmia: 1."
Hesperia, vol. 61: no. I. American School of Classical Studies at Athens: 35.
" Morgan: 133.
Broneer, Oscar (1971). "Temple of Poseidon, vol.,!," Isthmia: Excavations by the University of Chicago
under the Auspices of the American School of Classical Studies at Athens. Princeton, New Jereey: ASCSA: 3.
Gebbaxd, Elizabeth and Fredrick Hemans (1992): 23-25.
Gebhard and Hemans (1992): 36. Gebhard and Hemans (1998): 5.
''^Miller, Stephen, ed. (1990). Nemea: Site and Museum Guide. Berkeley: UC Press: 130.
Md: 58.
Morgan: 42.
Pausanius (5.14.9-10); Morgan: 28-29,42.
^ Coulton, J.J. (1977). Ancient Greek Architects at Work New York: Cornell University Press, 114; Gottfried
Gruben, (1966). Die Tempel der Griechen. Munich: Hirmer Verlag: 53.
™Dinsmoor(1928):53.
Norman, Naomi (1984). "The Temple of Athena Alea at Tegea," American Journal of Archaeology, vol 88;
no. 1: 193.
" 0stby, Eric (1994). "Recent Excavations in the Sanctuary of Athena Alea at Tegea," Archaeology in the
Peloponnese: 58-59.
26
A more complete description of the dating process and other important features
of each temple in Table 2.1 will now be presented:
1) The 6*^ century' BC temple of Apollo at Corinth (Fig. 1.1) was dated by
pottery found in mason's chippings. It was one of the early Doric temples built on the
foundations of ari earlier 7* c BC temple to Apollo; the later may not have been of the
Doric order. This earlier 7*** century Apollo temple, due to its unusual, innovate roof
design and use of heavy roof tiles^^ indicates that, while it was being buiit (ca. 675 BC),
significant changes were occurring within Greek temple design. GTOP surveyed the
visible remains of this 2"^ temple of Apollo at Corinth.
Fig. 1.1: Temple of Apollo at Corinth. Photograph by Erin A. Nell.
" Lawrence: 66.
27
2) The 4 century BC temple of Apolio at Delphi (Fig. 2.1) was built on the
foimdations of two earlier temples dating to the 7**^ and 6^ centuries BC. The earliest
Apolio temple was dated by comparing its roof tiles with 'those belonging to temples at
Corinth and Isthmia. As the first temple to Apollo at Delphi had a hipped roof, 600 BC
is the latest date that can be assigned.'^'^ Herodotus recorded not only the destruction of
this
century BC temple,'® but also the building of the second Apollo temple at Delphi
in the 6* century BC.^^ This second Apollo temple was subsequently destroyed by an
earthquake in 373 BC. The third Apollo temple, which was built in the 4'^ century BC,
still exists today. It is this third temple of Apollo at Delphi, which was surveyed and
included in the GTOP.^^
Fig. 2.1: Temple of Apollo at Delphi. Photograph by Erin A. Nell (2001).
Morgan: 133.
"'^Herodotus: 1.50.
Herodotus: 5.62.
Borguet: 253.
28
3) The first temple of Poseidon at Isthmia (Fig. 3.1) was built sometime in the
7^^ ceHtury BC; a specific foimdation date has not been agreed on. The current
excavators, Elizabeth Gebhard and Fredrick Hemans, believe this temple was
constructed between 690 and 650 BC: their e\ddeiice is based on Middle Protocorinthian
pottery which they believe gives a terminus post quern for the first temple to Poseidon at
'70
Isthmia.
•
However, Catherine Morgan assigns a foundation date of 625 BC: Morgan's
later date was based on comparisons of construction aspects between this temple to
7Q
Poseidon and the early temple of Apollo at Corinth.
The 7® century Poseidon temple may have been of the Doric design. Its
alignment was inconsistent with either the geological formations or other 7® century
structures in its close proximity: this means that the orientation of the
century temple
to Poseidon at Isthmia was very significant.
Fig. 3.1: Temple of Poseidon at Isthmia. Photograph by Erin A. Nell.
Gebhard and Hemans (1992): 35.
" Morgan: 133.
Gebhard and Hemans (1992): 23-25.
29
4) The 7*^ century Poseidon temple at Isthmia was destroyed by fire in 470 BC
and another Poseidon temple (the 5® century Classic temple)
erected in its place.*^
This second temple to Poseidon (Fig. 4.1) was of the much larger, all stone, Doric design
and it was very closely aligned along the foundations of the earlier, 7*^ century temple.
This 5®* century Doric temple was damaged by fire in 390 BC.®^ Because the temple had
been ftmctioning for a time previous to the fire, we can assume that it was constructed
sometime between 470 and 400 BC.
_ .g
-
.
. .J. ,
•
-
-
-
-
' " • • • • • •
r.
Fig. 4.1; Fifth cent my temple of Poseidon at Isthmia: restored illustration
by William B. Dinsmoor, Jr.®^
5) The first temple of Zeus at Nemea was constructed in the 6'^ century BC,
possibly in the first quarter as this date would coincide with the Nemean festival held in
573 BC.^ This 6® century temple did not belong to the Doric order as it had neither
Gebhai-d and Hemans (1992): 35-36.
® Gebhard and Hemans (1998): 5.
Broneer, Oscar (1971), Isthmia: vol. I: cover page.
Miller (1990), Nemea: Site and Museum Guide: 58.
30
iQS
pediments nor gables and its western side was enclosed by a hipped roof. " Paiisanias
noted that the roof of this temple had collapsed and its cult statue was missing by the
middle of the 5*^ century BC.®^
Fig. 5.1: Temple of Zeus at Nemea. Photograph by Erin A. Nell (2001).
A new temple to Zeus was constructed at Nemea in 330 BC; the foundations of
this 4^ century temple were surveyed for GTOP (Fig. 5.1). Although the 4*'' century
temple was oriented on a slightly different longitudinal axis than the 6^ century temple,
the latitudinal axes of both temples remained the same. Other buildings on this site
(including the Oikoi and Heroori) were oriented along different axes than the two
temples of Zeus.®'^
Additionally, the design of the 4® century BC Zeus temple differed greatly from
the earlier temple; it was of the Doric order (based on the columnar design of its
peristyle), but had Ionic columns on the second floor and Corinthian columns on the
' Miller (1990). Nemea: Site and Museum Guide: 59.
' Pausanias; 2.15.2.
31
inner coioonade aiid, instead of an opisthodomos, it had an adyton.
6 ) The accepted fouBdation date for the first (and only) temple of Hera at
Oljmpia is 600 BC (Fig. 6.1). This date is based on pottery and Hera figurines which
began appearing on the site late in the 7® century BC.^^ Pausanias^® assigned an earlier
date of 1096 BC to this temple of Hera. Catherine Morgan stated that Pausanias' 11®
century BC date cannot be correct because it was not supported by archaeological
evidence; pottery was absent from the site until the 7^ century BC.^^ However, based on
more recent excavations under the direction of Helmut Kyrieleis,®^ a black stratum layer
from the Pelopion area was more fully explored. The earliest pottery contained in this
black stratum layer dated to the second half of the 11^ century BC. Other drinking and
pouring vessels were found in this stratum, which suggest a continuous use from the
Submycenaean/early Protogeometric to the late Geometric and the early Archaic
period.^^ Therefore, because the dating of Hera's temple at Olympia is no longer
restricted by 6^*"' century BC pottery, this temple may be older than previously assumed.
Certainly the technique and building materials used for Hera's temple more closely
represent 7'^ century BC building styles rather than 6*^ century BC.^
Miller (1990), Nernea: Site and Museum Guide: 34.
Ibid: 130,132. Opisthodomos is the "back room" and adyton refers to the "holy of holies." Miller
(1990):133.
® Morgan: 42.
^ Pausanias:5.14.9-10.
" Morgan: 28-29,42.
^ Kyrieleis, H. (1990). "Neue Ausgrabungen in Ofympia,".4«ft"fe fFelt 21.3: 177-188. "Neue Ausgrabungen in
Olympia," In Proceedings of m International Symposium on the Olympic Games (1992): 19-24.
Eder, Birgitta (2001), "Continuity of Bronze Age Cult at Olympia?" Potnia: Deities and Religion in the
Aegean Bronze Age. Proceedings of the 8"* International Aegean Conference, Gdteborg University, 12-15 April
2000. Austin, Texas: Univereity of Texas at Austin: 2001: 202-204.
^ Lawrence: 77.
32
Fig. 6.1: Temple of Hera at Olympia. Photograph by Erin A. Nell.
The temple to Hera at Olympia would be considered the first complete Doric
temple except that only the first three feet of its cella walls were built of limestone; the
rest of the temple originally consisted of wood, mud brick, and roof tiles.^ Although the
temple of Artemis at Corfu (580 BC) was built ca. 20 years after the temple of Hera at
Olympia (600 BC), the Artemission was awarded the distinction of being the earliest
known complete Doric temple built entirely out of stone.^ The deities Hera and Zeus
originally shared this "temple of Hera" at Olympia: after the construction of the 5*^
century temple of Zeus at Olympia, this earlier temple of Zeus and Hera was assigned to
Hera alone.
Lawrence: 77. For more information regarding the 6* century temple to Hera at Olympia, refer to: Maliwitz,
A. (1972). Olympia undseine Bauten. Munich; Prestel-Verlag.
Lawrence; 77. For further information on Artemis at Corfu, see: Rodenwaidt, G., and others (1939-40).
Korkyra. Archaische Bauten und BUtM'erk, I and II. Berlin.
Dinsmoor, W.B. (1928). The Architecture of Ancient Greece, New York: Biblo and Tannen: 53.
33
7) This new 5* century BC temple to Zeus was built between 470-457 BC.^ It
is located jiist south of, but parallel to, the original Zeus and Hera temple (which will
now be referred to as the temple of Hera). The temple of Zeus at Olympia (Fig. 7.1)
was much larger than the temple of Hera and completely Doric in design:^® Pausanias
describes the temple in great detail.^®®
Fig. 7.1; Temple of Zeus at Olympia. Photograph by Erin A. Nell (2001)
8) Finally, the 4*^ century BC temple of Athena Alea at Tegea (built ca. 340 BC)
was surveyed for GTOP. Existing beneath this 4^'* century Doric temple are the
foundations of three earlier temples dating from the 8*^ and 7^ centuries BC.'®' The first
two temples, built in the Geometric period, were small, simple buildings.'®^ The third
Couitoti, J.J; 114.
Lawrence: 104,105. For more information, refer to "Rodenwaldt;" see footnote 88.
Pausanias: 5.14.
0stby: 58, 59.
51,58-59.
34
temple to Athena Alea at Tegea dates to the late 7^ century BC (based on comparison to
the temple of Hera at Olympia) and it was much larger than the earlier Geometric
temples.^®^ According to Pausanias*®^ the third temple to Athena Alea was destroyed by
til
fire in 395 BC and then replaced with the more impressive, 4 century Doric temple
(Fig. 8.1). The construction date of this 4^ temple to Athena Alea has been determined
to be somewhere between 345-335
Fig. 8: Temple of Athena Alea at Tegea. Photograph by Erin A. Neil.
Although all four temples to Athena Alea at Tegea differ in design, they
represent 400+ years of continued cultural activity on one specific location, and share
the same east-west
axial orientation. This continuation of orientation suggests that
0stby: 44.
Pausanias: 1.433-435.
'"'Norman: 193.
Later, this research project will argue for a west-east, instead of as east-west orientation.
35
alignment was an important feature of religious architecture, even though the structui'al
size and design of each of the four temples was significantly different/®'
In concliisioB, the eight Doric temples selected for GTOP are prime examples of
Doric architecture that represent 350 years of that particular monumental building
tradition. The temples included in this survey not only embodied the Doric architectural
tradition from its inception to its standardized form, but also are physical examples of
the importance that ancient Greeks placed on the continuance of specific orientation
principles: many temples were built on earlier foundations and utilized previouslyestablished structural orientations. Unfortunately, we do not yet know for certain to
what these temples were oriented, how precisely they were aligned, nor how their
structural dimensions were determined. These are some of the issues this research
project will attempt to address through analysis of the GPS data collected in GTOP.
b. survey instruments
The primary instruments used for the GTOP survey were a Garmin® 12cx
Global Positioning System (GPS) instrument, and a Suunto® inclinometer. The GPS
unit is a hand-held, three-dimensional recording device which determines its terrestrial
t rtO
position by receiving radio signals from a series of satellites.
The geographical
coordinates then appear on the GPS screen in longitude, latitude, and altitude above a
reference geoid. The GPS unit was instrumental in determining the orientation of each
temple in GTOP.
0stby: 58.
Ferguson: 5-7.
The Suunto inciinometer PM-5 is a hand-held optical reading clinometer with a
level bubble, which, among other things,'®^ measures slope angle in degrees."® This
instrument ifldicates the inclination of an object to the horizontal of an axis. The Suunto
inclinometer was used to measure the angular heights of the horizons (usually mountain
ranges) which were aligned to the axial orientations of each temple.
An observing technique and reduction formula was developed by Professor
Raymond E. White from the University of Arizona,"^ which would not only determine
the orientation of each temple, but also preserve the precision of the GPS data to ±0.01
arc-minutes. With statistical reductions the measurements obtained from these GPS
•
110
units may achieve higher degrees of accuracy than engineers' transits and stadia rods.
c. observing technique
Prior to the GPS data collection process, consistent and specific areas of the
peripteral pteron, pronaos, naos/cella, and opisthodomos of each temple were marked
with surv ey tape (Fig. 9.1); each area is designated with a large "X". When the
geological parameters of each temple site permitted, additional offset points were
marked from five to ten meters outside of the
" such as giving the height of the point of sight and expressing it in percent of the horizontal distance."
Suunto manual-PM-S: Finland.
Suunto Instruments. Clinometer manual for the PM-5/360 PC. Finland.
RaymoBd E. White, University Distinguisiied Professor and Professor of Astronomy: Department of
Astronomy, University of Arizona, USA.
37
FiGURE 9.1: GPSTenipleCo!!«tion Stations
s
i #1fe
^ *|i a
m~¥W^
9= lil^ J-
•booBQS o f r as e s a ^
FIGURE 9.2; GPSColbction Station Offsas
I •'QWWW'W"S'W'W"¥~®^''
I® pp^S^
w
I © &« B
» ® lla I®
r- L ^ ' iJfii.lj,'^
l'@ fS|1 3 9 e &
\)»
rTS•fc^a^'
FKURE 9,3: GPS Cofetion:Virtie! Watis
V
Q
e
e
^1
il
If
Ji
peripteral pteron area (Fig. 9.2)."^ The precision of the individual GPS readings were
within four seconds of arc or 0.06 arc minutes which is 3 meters (9.14 feet) in terms of
ground distance.
Therefore, the "offsets" of between five to ten meters per site helped to
overcome the confusion error on the ground due to the finite resolution of the
equipment Additionally, the intersections of the offset lines at the temple comers
created "virtual" walls which directly overlapped the actual parameters of the peripteral
pteron of each temple (Fig. 9.3). The comparison of the "virtual" walls with the actual
walls was instrumental in reaffirming the accuracy of the GPS readings.
A series of 12 GPS waypoints (position measurements)''" were collected from
the previously marked areas of each temple. The breakdown of waypoint collections is
as follows: there were four sets of three waypoints for each marked area (for a total of up
to 12 waypoints for each marked area). The three waypoints in each set (of four) were
collected at intervals of 30 seconds of time. Two of the four sets of waypoints were
collected within one hour of each other and the remaining two sets were collected at
intervals greater than three hours. This minimum three-hour time gap allowed available
satellites (averaging from seven to eleven) to move to different locations in the sky thus
marking the same terrestrial location from a set of different satellite positions. This
observing method not only preserved consistency within each waypoint set, but it also
The "peripteral pteron" refers to the exterior rows of temple columns. In Figures 9.1,9.2, and 9.3, the
peripteral pteron includes 6 columns (including comers) on each of the smaller sides and 15 columns (including
comers) on the longer sides.
39
allowed the satellites to relocate, sending the GPS unit the same coordiHates from
di fferent celestial locations thus establishing an independent set of GPS values to "blend
in" with the other data. In this way, meaningfii! statistical results may be obtained.
d. reduction formalae
Between 108 to 408 waypoints were recorded for each temple using the Garmin
GPS unit. A grand total of 1716 separate observations of geographic positions were
collected for all eight temples. After all of the waypoints and associated data had been
collected in the field, this information was downloaded into EAN's IBM Thinkpad and
processed by means of Microsoft Excel spreadsheets through a series of reduction
formulae (see Appendix A; page 109: GPS Reduction Graph: Temple of Apollo at
Corinth. These formulae had three general goals: 1) to determine the internal quality, or
self-consistency, of the quantity of waypoints gathered (the accuracy of EAN's field
work), 2) to determine the precise coordinates of each station and plot them onto a
graph, and 3) to determine the specific orientation of each temple.
1) determining the quality of the quantity of waypoints
In order to determine the accurate orientation of each temple based on the
collected GPS information, each waypoint that was gathered in the field had to be
processed through "quality control" to assure that it was collected and recorded in an
accurate and precise manner. Quality control was determined via the following
Ferguson; 8-14,15.
40
mathematical applications contained in the spreadsheet of the temple of Apollo at
Corinth which can be found In Appendix A. All eight temples in GTOP have similar
Excel spreadsheets.
Ail of the waypoints gathered for each temple were collectively processed via
the residuals method on a temple to temple basis.
In the residuals method the "most
likely estimator" or arithmetic mean needed to be determined. In GTOP, the average of
the sum of all the waypoints (per temple) was used for the arithmetic mean (Q), where
"Q" represents the set of all waypoint measures in a given set. In GTOP, "Q" represents
the set of all waypoint measures in a given set for one temple; therefore, <Q> represents
the arithmetic mean of the set Q. The arithmetic mean was then subtracted from each
individual waypoint to determine the residual value (v) for each waypoint. If these
values were plotted in a graph, they would be distributed more-or-less equally on either
side (positive and negative) of the error distribution's "zero." Therefore, if the residuals
were summed in this state, they would equal "0.00" identically so the arithmetic mean
would be useless if it were to be applied in this manner. However, if the residuals (v)
were individually squared (v^) and then summed, a positive value would result. This
positive value was then divided by the number of waypoints (n(Q)) minus unity to
determine the variance; the square root of the variance is the sample standard deviation,
s. The standard error of the mean (sem) is calculated by dividing s by the square root of
the number of data point, n:
Each waypoint marks the geographical measurement of that particular area in terms of longitude and latitude.
Appendix A of this report: pgs. 111-113.
41
sei]i= ±sxll'''^^
The standard deviation (or "root mean square" value) is the smallest value for
the sum of the squared residuals of this collective GPS waypoint sample: it gives a good,
objective estimate for determining tlie quality of EAN's data set without personally
being there. For example, if all of the squared residuals of the Corinth graph were
plotted in a histogram, the standard deviation would locate the "inflection points" which
occur on either side of the arithmetic mean of this normal distribution. If the result
numerical value of the standard deviation was small, the internal consistency of the
waypoint collection method would be high: if the standard deviation was large, the
consistency of the gathered data would be considered low or marginal. The standard
deviations for the collective GPS gathered waypoints for the temple of Apollo at Corinth
were very small: ± 0.007591" (North Latitude); ± 0.015836" (East Longitude)
(Appendix A, pg. 112)."^
From the standard deviation, the standard error of the mean (sem) can be
determined. As the sem will be located closer to the mean than the standard deviation it
will give us not only an even better idea regarding not only the precision of the mean
value's placement, but also the quality of EAN's gathered GPS waypoints. The sem
values of the temple of Apollo at Corinth were: ± 0.000693" (North Longitude) or an
error of 0.02%, and ± 0.001446" (East Latitude), or an error of 0.03%. This incredibly
low sem value is reflected in all of the other spreadsheets for all of the temples surveyed
N.B: 1° = 3600 arc seconds, denoted 3600".
42
in GTOP: this strongly indicates that the data collection strategy and implementation
process was done with great consistency.
2) determining the precise coordinates of each station
Now that the accuracy of the waypoints has been determined each waypoint
must be grouped by "station" to determine the precise orientation of each station. The
values for North Longitude and East Latitude were determined separately in the
following manner;''®
The arithmetic mean (Q) and the value of the Range (R(Q)) from the maximum
(max(Q)) and minimum (min(Q)) values of the collective waypoints in each station were
determined (R = max - minX> Because each station had from 6 to 12 waypoints, the
Keeping's small sample method was used to determine the standard deviation (s) and the
standard error of the mean (sem) for the position of each station, instead of the method
of residuals, which requires 30 or more independent measures to form a reliable
estimate. The sem of each station was very small (for example, the sem for station E-NE
was ±0.00032219", which represents an error of O.I 14% [or approxirately one-tenth of
one percent]), which once again, reaffirmed the self consistency of the collected data.
The residuals (v) and standard errors of the mean (sem) were then processed to
determine the weighted means (Wi*<Q>) and the standard errors of the weighted means
(sewm) in the coordinates of each station."® From this process, the final, global.
The worksheets for the precise station coordinates of North Latitude and East Longitude are on
page 114 in Appendix A of this report.
Refer to Appendix A; pg. 116.
43
weighted meaB (Q*) and global standard error of the weighted mean (semw) of the
entire series were calculated. The sem of the global weighted mean was minlsciile (±
0.00177679" [North Latitude]; ± 0.00322052" [East Longitude]), again indicating that
the internal consistency of the data (and by extension, arithmetic mean) was very high.
Finally, the arithmetic mean (Q) of each station's position^ coordinates and its
global average, were plotted in a graph;
the key to this graph is located at its left hand
side. Numbers were assigned to the collective North Latitude (y-axis) and East
Longitude (x-axis) points which gave additional numerical labels to each station. For
example, station "E-NE" now became, #1 E-NE, station E-SE was labeled, #2 E-SE, and
so forth. The final graph, which represents all of the GPS coordinates gathered in the
field, can be compared to a previously illustrated plan of the temple of Apollo at Corinth
(Figures: 9.1, 9.2, 9.3). This comparison gives the reader a visual representation of how
the plotted GPS stations compare to the floor plan of the temple.
3) determining the specific orientation of each temple
At this point, specific stations were gathered together with regard to the axial
orientation of each temple. With regard to the temple of Apollo at Corinth, all six
stations associated with the central southwest-northeast axis of the temple were grouped
together.'^' These stations included: the central northeast offset (#12: NE); the temple
entrance on the northeast (#13: EntNE): the center of the rear of the first cella on the
northeast side (#14: CellaBack); the center of the rear of the second cella on the
This graph is located in Appendix A; pg. 117.
44
southwest side (#15: OpisBack); the southwest entrance to the temple (#16: EntSW);
and the central southwest offset (#6:
This particular grouping of specific stations
is called the "Central Sequence."
The stations in the Central Sequence were then plotted onto a Cartesian plane
and foniied a slightly scattered iiiie. Because the x- and y-values of these six stations
were seen to fall raggedly along an unknown line, it was necessary to use the Least
Squares Fitting technique to determine their final "straight-line fit." The following
equation was used:
y = mi + zi,
with nil being equal to the slope (mi = tan Oi) of the line, and zi being equal to the zeropoint, or the intercept of the line with the y-axis.
Through this technique, the angles of the slopes of y with respect to x were
determined. From this information, the accurate slope of the linear fit through the six
stations of the Central Sequence was determined with precision. For a more detailed
explanation, refer to Appendix B, Computing the Slope and Zeropoint of a Straight Line
between Two Known Points, by Raymond E. White, Ph.D.
Then, this same method was applied to two other southwest-northeast axes of
the temple of Apollo at Corinth: the South Line'^^ and North Line'"^ sequences. The
axis of the South Line of this temple included stations #2 (E-SE), #3 (SE), and #4 (S-
Refer to Appendix A; page 118.
Ibid; page 119.
Ibid; page 120.
45
SE); the North Line axis included stations #8 (W-NW), #9 (MW), #10 (N-NW); Finally,
the slopes for these three sequences (Centra! SequeHce [72.2751744° E], North Line
[71.4831682° E], and South Line [7L828§444° E]) were averaged to find the arithmetic
mean and its standard error which would represent the precise northeast-southwest
orientation for the temple of Apollo at Corinth, i.e: 71.8623957°.'^"* The sem for this
value is ±0.270152137°, which represents an error of only 0.375929767% or less than
four-tenths of one percent.
2. Survey results: the precision of Greek temple alignments
The orientation results for the alignment of each temple (in decimal degrees) are
listed in Table 3.1 below:
Table 3.1: Temple Alignments
/Vligiumenf
Gmeral afigoment
..
1% . ..J.-"-J
Solstice; smnmeravinief
Delphi: 4® century Apollo
N 54.76° E
j Solstice; sanimermittter
Isthmia: 7® century Poseidon
N 87.40° E
Eqiiisox
Isthmia; 5® century Poseidon
N 87.90° E
Eqiiiiiox
Nemea: 4^ century Zeus
N 73.41° E
Solstice: SiiHaaef/winter
Olympia: 6 century Hera
N 89.26° E
Eqaifiox
Olympia: 5^ century Zeus
N 83.54° E
Eqaiaox
Tegea: 4'" century Athena Alea
N 85.53° E
tk|iiiaox
•.
..
_
-
"Note: Regarding the temples which are "generally aligned" to the solstices, the specification is
summer solstice sunrise/winter solstice sunset, not winter solstice sunrise/summer solstice
sunset.
Refer to Appendix A; page 120.
46
Although these initial survey results indicate a generalized alignment of three
teinples to sunrise at summer solstice and sunset at winter solstice, and five temples to
sunrise and sunset at either of the equinoxes, each temple has a slightly different
alignment (Fig. 10.1, 10.2).
Initially, it was assumed that these erratic orientations would reflect temple
alignments to either lunar motions (such as in Dinsmoor's hypothesis) or to heliacal
risings of specific stars or constellations which occurred simultaneously with either the
solstices or the equinoxes such as in the Lockyer/Penrose or Blomberg/Henriksson
hypotheses.
47
Figure 10.1
SOLSTICIAL TEMPLE ORIENTATIONS
1 oo
S-
EquincK
^.00
:^ijinc8c
' 27aoo"'
\
4^yf?^
\
%
SUNRISE
SUNSET
Ma^:smmBi at fcift sd^as wm few# sn
Mfa& ^ fc
a/ 4?i5fe st Sri A
48
Figure 10.2
EQUINOCTIAL TEMPLE ORIENTATIONS
* ^
Egukios
Egumos
'""'27"aoo"'~
4#^ #'"
SUNRISE
mmET
MB^:stmvistbs&tMAB9mlmeim§ts Mft»&
^
Ttgsa.
49
a. lunar alignment issues
The lunar alignments were eiiminated early, mainly due to the generally
confused nature of 6*^ century BC lunar calendars; they varied greatly from poUs to polls
and there were no formulae for lunar intercalation.
In fact, Greek lunar calendars
were so disorganized that the 5'^ century Athenians joked about this problem in
theatrical performances. In The Clouds, by Aristophanes, the Moon complains that the
Athenians do not reckon their days correctly on her behalf and so their calendars are
constantly out of sync. As a result, the Moon grumbles when the other ,gods chastise
her because, since the Athenians do not hold their sacrifices on the correct days, they
e ®
1 "yft
continuously cheat the gods out of their dinner.
This remark tells us that the Greeks (specifically the Athenians) knew that their
lunar calendars were disorganized. Therefore, to expect an architect to be capable of
calculating the lunar periods, then synchronizing those periods with the solstices and
equinoxes, and finally, incorporating those calculations into the proposed temple
orientations, might have been calculationally unrealistic for 6® century BC architects,
b. stellar alignment issues
Aligning Greek temples to heliacal risings of specific stars and constellations
were also discarded: there were no consistent connections between the deity of each of
Every year has approximately 12.33 lunar cycles. Therefore, approximately every three years an additional
month must be added to the lunar calendar to keep it accurate. Intercalation refers to the periodic insertion of
the extra month. A correct and standardized iiiteFcalation formula was introduced by Meton in ca. 430 BC. He
suggested that a period of 19 years (approximately 235 months) could be usefijl to correlate the solar and lunar
calendars (Geminus: Isagoge, Chapter VIII). However, before 430 BC, intercalation was done haphazardly and
differed from one citj' state to another: Samual, Alan, Greek and Roman Chronology. C.H. Miinchen;
Beck'sche Verlagsl>uchhandlung.pgs; 58,67, 74, S3, 86,91,92,94,97,99.
Aristophanes, The Clouds. Liaes; 615-626; Evans: 183; Henderson: 50-51.
50
the temples and the asterisms that heliacaliy rose during the general time period of the
actual foiHidation dates of the temples. Although 6'*^ century BC Greeks were able to
detetmine the onset of either of the solstices or equinoxes by means stellar
observations,
1 'J'l
the relationship between the sun and the various asterisms on those
specific days is not fixed. Due to precession, the tropical year'^® is 1224 seconds (which
equals 20 minutes, 24 seconds) shorter than the sidereal
1"JQ
year, and so the same
constellations do not always rise with the sun on solstice or equinox. Because EAN
(unlike Penrose) was unwilling to arbitrarily select an asterism to "fit" the theorized
alignment parameters, attempts to fix temple orientations to specific stars or
constellations were discarded.
And finally, Greek astronomy and architecture in the early 6'^ century BC were
evolving rapidly; the ancient architects may not have had a chance to incorporate new,
precise astronomical developments into the survey formula of the innovative Doric
architectural forms.
I
Therefore, a less complicated formula for aligning these
monolithic temples was considered by EAN, one which would involve the most obvious
and predictable celestial body of all — the sun.
At this juncture, three other considerations must be introduced to the temple
alignment formalism: the geological location of each temple, how the local horizon
Hesiod, Works and Days: 564.
The amount of time needed for the Sun to return to vernal equinox. Calendars are based on the Tropica!
year; Kaufmann: 32.
A Sidereal (star) day is approximately 4 minutes shorter than a solar day (23h; 56m; 4.091s).
Please refer to Chapters IV and V in this thesis for complete historical reviews of the development of Greek
astronomy and architecture, respectively.
51
irreguiaiities change the altitudes and azimiilhs^^^ of rising celestial objects, and the time
of day in which the ancient architect may have based Ms origiml alignments (spnrise or
sunset).
B. Geographical Parameters
1. Location
The geological location of each temple is important for both aesthetic and
geographical purposes. Aesthetically, Greek temples are visually pleasing not only due
to their large sizes, elegant designs and high quality of building materials, but also
because of their geological locations (Fig. 11.1). The landscape setting of each temple,
whether adjacent to a towering mountain peak, situated in a serene valley setting, or
residing over a harbor or bay, further enhanced its monumental yet graceful, structural
design. Although landscape features were important elements of temple orientation,
EAN does not agree with Scully's hypothesis that Greek landscape issues were the most
important aspects of alignment.
Aesthetics are not the only reason that landscape is important: the actual heights
of mountain ranges, thick groves of trees, or other terrestrial obstacles that are located
along a temples' orientation horizon, are very important to structural alignment
principles. By their different terrestrial elevations, these mountains and trees can
determine the rising azimuths of all celestial objects.
Altitude: the angular elevation of a celestial body above the astronomical horizon. Azimuth: horizontal
direction expressed as the angular distance between the direction of a fixed point (such as true north) and the
direction of an object (in this case, a celestial body).
52
Fig. 11.1; Landscape: Temple of Apollo, Delphi. Photograph by Erin A. Nell (2001).
A mountain range located between a temple and the point of sunrise would
visually conceal the sun until it rose above the height of the mountain range: the same
principle is true for sunset. Any terrestrial element that conceals the sun as it moves
close to the horizon is referred to as a "mask." In terms of this survey, a "mask" will
refer to a mountain range, sometimes with trees, along the horizon which "conceals" the
sun when it first appears at sunrise, or when it disappears at sunset.
a. masks
The heights of the eastern and western masks of the eight temples in GTOP
were measured with a Suunto inclinometer.'"^ The mask height of each temple varied
greatly: the highest was the northeastern mask at the temple of Apollo at Delphi which
53
me^ured approximately 32.0°; the lowest was the eastern exposure at Istlimia on the
Saronic Gulf
measured 0.5°, The heights of the eastern and western masks to
which each temple is axiaily aligned are listed in the following Table, 4.1:
Table 4.1: Mask Heights
Temple
Eastern Mask
Western Mask
Corinth, temple of Apollo
3.8°
4.0°
Delphi, temple of Apollo
32.0°
6.5°
Isthmia, temples of Poseidon
0_5O133
5.0°
Nemea, temple of Zeus
8.0°
8.5°
Ol>Tnpia, temple of Hera
4.5°
6.0°
Olympia, temple of Zeus
2.5°
6.0°
Tegea, temple of Athena Alea
5.0°
5.0°
The heights of the eastern and western masks differ from each other, sometimes
greatly such as at Delphi, where the eastern mask is 25.5° higher than the westem mask,
b. solar altitudes and azimuths
Now that the heights of the masks have been determined, the correct location
and altitude of the sun at sunrise or sunset can be plotted. The sun travels in a diurnal
path across the celestial sphere: once it rises it moves across the sky at a southward
angle, constantly 'arcing' to the right. Once it passes the zenith, it still 'arcs' to the right
An inclinometer indicates the inclination to the horizontal of an axis. In the case of a mountain range, it
determines the height of its mask in degrees
The eastern mask of Isthmia varied slightly, making allowances to the view for fog obstructions and
refraction. Refraction is the change in the apparent position of a celestial body due to the bending of light rays
emanating from it as they pass through the atmosphere.
54
but at a northward angle until it falls below the earth's western horizon, or sets. In the
northem hemisphere, this degree of arc is least severe at summer solstice and most
severe at winter solstice (Fig. 12.1: Solar Positions at the Solstices and Equinoxes).
»Visa.
^
^
A*
ioBwa fL',4
w
Saiat
Fig. 12.1: "Solar positions at the Solstices and Equinoxes." Hahn, Robert (2001).
Anaxitnander and the Architects. New York: State University Press: 207.
Next, the sun's azimuth relevant to the latitude of the site and the height of the
mask had to be determined. The hour angle, tg and the azimuth of the sun at the top of
the mask. Zo, were calculated by way of spherical trigonometry using the latitude of the
site, (p, the angular height of the mask, 0, and accounting for the obliquity of the ecliptic
The western mask heights of the temples of Hera and Zeus at Olympia, due to tree obstructions, were
estimated based on photographs. Because trees may have obscured the skyline in ancient times as well as
modem, western mask heights st Olympia inciBcled trees.
55
in aatiquity.^^^ The actual soiar azimuths were calculated by Raymond E. %Tiite using
the follomdng formula:
cos Zo - cosZeCOsd = tmf sinO
For a more detailed explanation, please refer to Appendix C; pages 124-126:
Accounting for the Change in Rising Azimuth of a Celestial Ohject due to an Opaque
Mask in the Direction of View, by Raymond E. White, Ph.D.
The solar arc azimuths and mask heights pertaining to both sunrise and sunset of
each temple in GTOP are listed in the following table, 4.2;
Table 4.2: GTOP Solar Arc Azimuths
Stinrtee: Solar
West MfOTz;
Mmk Iff.
4.0°
Simsets S«Iar
Arc AMinatli
235,85^ W
Masfe Ht
Corinth; Apollo
Delphi; Apollo
32.0°
83.7r E
6,5®
231.77® W
Isthmia: Poseidon
(both temples)
Nemea: Zeus
0.5''
91)39° E
5.0^
266.48® W
8.0°
66.09° E
8.5®
232„28^ W
Olympia: Hera
4.5°
93.48° E
6.0^'
265.35® W
Olympia: Zeus
2.5°
91.93® E-
6.0^
26535'^ W
Tegea: Athena
5.r
93.84° E
5.fF
266J 6" W
c. the effect of a mask on solar altitude
For an illustrated example of how masks affect the geographical location of
sunrise or sunset, refer to Figs. 13.1. 13.2 below, a picture and sketch of the northeastern
The obliquity of the ecliptic is the internal angle at the vernal (and autumnal) equinox between the Celestial
Equator and the Ecliptic (also, the angle separating the North Celestial and North Ecliptic Poles).
56
mask as seen from the entrance of the temple of Apollo at Corinth; the height of this
mask measures 3.8° up from the horizon (a).
Figure 13.1: Northeastern Horizon at Corinth: PhotoIjy Erin Nell.
CX
Figure 13.2: Corinth: Northeastern Azimuth, Mask, and Orientation: Illustration by
John Papageorgiou: a = 3.8° mask height; P= N 62.65° E solar arc azimuth; y = N
71.K7° E temple orientation; 8 = location of san at 0° (sea level) altitude: N 59.34° E.
When the sun rises at summer .solstice at Corinth, its location at zero (0.00 )
altitude is N 59.34°E (5). As the sun ascends it moves across the sky along its diurnal
path, appearing to arc towards the right, or southwards. By the time the sun finally
57
appears over Corintli's 3.8° mask it will have subtly ^'arceil" to the right southwards
across the sky by 3.31°. Therefore, when the sun visibly rises over the eastern mask at
Corinth on summer solstice its location is actually at an azimuth N 62.65°E (P). As the
GPS orientation of the temple of Apollo at Corinth is N 71.87°E (y), the orientation of
this temple deviates by 9.22° from the point where the snn first appears over the mask. A
deviation this great suggests that this temple is not specifically aligned towards sunrise
at summer solstice. Similar situations at sunrise exist for the other seven temples; their
measurements are listed in the following table, 5,1:
Table 5.1: Sunrise Temple Orientations
Temple
;.
...
.....
Solar are
azimtttfc
leiBpfe
Differeiicej
3.8°
62.65° E
¥S, aziBiHti
9.22"
Delphi: Apollo
54.76° E
32.0°
83.71° E
28.95^
Isthmia: 7* Poseidon
87.40° E
0.5°
90.39° E
238"
Isthmia: 5® Poseidon
87.90° E
Nemea: Zeus
73.41° E
Olympia: Hera
89.26° E
Olympia: Zeiis
Tegea; Athena Alea
90.39° E
o
p
nortli/nortbeast
71.87°E
0
o
Corinth: Apollo
66.09° E
7.31^
4.5°
93.48° E
4.22^
83.55° E
2.5°
91.93° E
8.39'-^
85.53° E
5.0°
93.84° E
8.3P
i
t
The differences in temple orientations and solar arc azimuth vary greatly from
2.5° to 29.00°. Such large deviations imply that none of the temples in GTOP were
aligned to the sunrise positions at equinox or either of the solstices.
58
2. Sighting time; sunrise or sunset
The other eiemeiit affecting the architectural orientation of a temple is the time
of day at which the alignment was obtained. The best time for orientation purposes
would be at sunrise or sunset. These times most accurately depict the celestial positions
of solstice and equinox, and, if a gnomon were used for alignment purposes, it would
cast its longest shadow at sumise or sunset. A longer shadow would facilitate the
alignment of these very long buildings.
Regarding temple alignment, sunrise and sunset at equinox do not always
transpire at a geographical position 180° from each other.To illustrate better the
orientation differences between sunrise and sunset, refer to (Fig. 14.1), which features
the orientation of the temple of Athena Alea at Tegea. This temple is aligned at
approximately 85.53°E; it deviates 4.47° from sunrise at equinox (90.0°E) at sea level
(0° altitude). However, because this temple has an eastern mask of 5.0°, visual sunrise
would not occur until approximately 93.84°E, or 8.31° southward from the temple's
orientation (85.53°E). The western alignment of the temple of Athena Alea at Tegea is
265.53° W (85.5°Eplus 180.0°). Taking into account Tegea's 5.0° western mask, visual
sunset transpires at an arc azimuth of 266.16°W, which represents a miniscule deviation
of only 0.63° from the orientation of this temple.
Because a deviation of 4.47° exists between the eastern orientation of Athena
Alea's temple and visual sunrise, and a deviation of only 0.63° exists between the
59
temple's western orieatation and visual sunset, the temple of Athena Alea at Tegea
appears to be aligned to sunset rather than to sunrise. This means that visual simrise and
sunset at equinox mil not occur at the exact opposite ends of the horizon. Therefore,
unless conditions are highly coincidental, alignment of temples to celestial events must
be specified as occtming at either sunrise or sunset.
Figure 14.1
ORIENTATION DIFFERENCES: Athena Aim at Tegeg
i!O
I^O
•;g
A
\
\! „\fc!
/
i'lgaiax
,,.. -
/:
•&fts
{»i®
SUNSET
SUNRISE
An exception to this would be if both sunrise and sunset locations were directed at the ocean and therefore,
without masks.
60
a. sunset
Table 5.2 provides orientations, related mask heights, and solar arc azimuths,
regarding western (sunset) horizons of all GTOP temples:
Table 5.2: Sunset Temple Orientations
Tciii.pie
Corinth: Apoiio
Orieatati0ii; | Mask
west to sdetevest •Heiglit
4.0=
251.87" W
Solar Arc i Difference: teaiple
tsrieatatleB vs azimiifh
Aafimth
16.02=
235.85° W
Delphi: Apollo
234.76° W
8.5=
231.77° W
Tsthmia: 7*^ Poseidon
267.40° W
5.0°
266.48° W
Isthmia: 5' Poseidon
267.90° W
5.0^
266.09° W
Nemea: Zeus
253.41° W
8.5=
232.28° W
Olympia: Hera
269.26° W
6.0°
265.35° W
3.90"^
Olyrapia; Zeus
263.55° W
6.0°
265.35° W
1.90'^
Tegea: Athena Alea
265.53° W
5.0°
266.16° W
0.63'^
Tjr
IMf
OI
1 ao
2. « ^
With the exception of Corinth and Nemea, the orientations of the remaining six
temples deviate from visual sunset by only 0.63° to 3.90°. These deviations are very
small and well within typical errors of naked eye observing of that era.'^'
b. sunrise vs. sunset
Since all of the temples in this survey have their front entrances and cult statues
facing in an easterly direction, sunrise would have been the most likely recording
location. However, after computing the alignment of each temple at both sunrise and
sunset, six of the eight temples surveyed paralleled the example of Athena Alea at
Schaefer: 121-126.
61
Tegea; i.e. they were more closely aligned tom^ards sunset rather than sunrise! Table 5.3
more closely compares the sunrise and sunset orientations of each temple:
Table 5.3: Sunrise/Sunset Comparison Table
Temple
fleiiatlois; siiftrise
Deviation: sonsef
16.02°
Cori.nth: 6"' c. Apollo
fj.2*
Delphi: 4'" c. Apollo
28.95"
Isthmia: 7^' c. Poseidon
2.98°
mz"
Isthmia: 5^ c. Poseidon
2.4r
ur
Nemea: r c. Zeus
7ji«
21.13°
Olympia: 6* c. Hera
4.22°
3.90"
Olympia: 5'" c. Zeus
8.39°
1.90^
Tegea: 4^' c. Athena Alea
8.31°
The two anomalies would be the temples of Apollo at Corinth and Zeus at
Nemea. Although these two temples appear to be more closely aligned to sunrise rather
than sunset, their deviations (9.22° and 7.31° respectively) are too great to assume an
accurate sunrise alignment. These temples could either, a) be aligned to a different
asterism, or b) they could be examples of attempts (and subsequent failures) to precisely
align structures to sunrise. More discussion regarding the technical difficulties of
eastern vs. western alignments can be found on pages 70-73 of this report.
3. Survey results: western orientations
Previously, most Greek temples were believed to be oriented towards the east.
However, GTOP indicates that, with the exception of Apollo at Corinth and Zeus at
Nemea, all of the temples were aligned toward the west and sunset rather than the east
62
and sunrise. Additionally, these temples were not just generally aligned IE these
western directions, but they were done so with a high degree of accuracy; their
orientations deviate only 0.63° to 3.90° from the sun's azimutlial arc at sunset on either
winter solstice or equinox.
This predominant western orientation of Greek temples is undeniable, and in
direct contradiction to most previous scholarship regarding temple alignments. Lockyer
believed Kamak was aligned to the west but his theory was later disproved by several
scholars. Penrose's proposed temple orientations were overwhelmingly eastern as were
EHnsmoor's, Blomberg/Henriksson's, and Mazarakis-Ainian. Rutkowski was the only
scholar to record that the majority of his Late Bronze Age/Dark Age structures were
oriented to the west: his only exception was the eastern alignment of the front door at
Tiryns.
C. Conclusion
In the past, the eastern alignment assumption seemed obvious: the main temple
entrance practically always faced the eastern horizon as did the naos and the cult statue.
Additionally, the sanctuar>' altar was located on the eastern side of the temple inside the
temenos. So why does the data collected from GTOP suggest that the ancient Greek
architects oriented their Doric temples to the west? Was there an elusive spiritual
stipulation for such orientations, or were Doric temples easier to align (in terms of
available technology) to the western horizon?
EAN hypothesizes that Doric temples were oriented to the west because (in
terms of structural mechanics) it was easier by far to achieve precise astronomical
63
alignments to cdestial objects which were located low on the western, rather than the
eastern, horizon. BAN also believes that this western orientation alignment procedure
determined the lengths of each temple. However, before these alignment and dimension
issues are further discussed, the techniques and toois available to 6^ century BC Greek
architects will be reviewed. TMs review will have two objectives: to present literary
evidence documenting the western orientation of Doric temples and, to reconstruct the
methods by which these ancient architects may have aligned and determined the
dimensions of these monumental structures.
64
III. ANCIENT ARCHITECTS AND ALIGNMENT TECHNIQUES
A. Architects
Although
have knowledge of over 100 Greek architects from 650 BC to 50
BC, we know very little about these individuals.
Even though the first architectural
treatises were written in the 6th century BC, the earliest one recovered was a partial
treatise from the 4^ century BC.' "''^ The first form of literary evidence regarding ancient
Greek architects and general construction is in the form of 5® century Greek building
codes and repairs which can be found inscribed on the structures themselves.'"^"
Unfortunately, these inscriptions make no references whatsoever regarding how Greek
temples were aligned, nor by what procedure they used to determine the dimensions of
those sacred structures.
1. Vitruvius
The most complete manual of architectural engineering that has survived, De
Architeciura by Vitruvius, was not written until ca.25 BC,'"^' almost 600 years after the
first Greek Doric temple was completed. Vitruvius attempted to make meticulous
records of every aspect of building design, material, and associated technology of both
Greek and Roman architecture of which he was aware. U nfortunately, due in part to the
sheer volume of information connected with this subject and the 600 year time lapse
between the first Doric temple and De Architeciura, many areas of structural
Couiton: 15.
Couiton: 24.
An early 5"' century building code is in the Athenian decree which states that no altars could be constructed
or stones quarried in the area of the pelargikon (JG, I: 767, lines 55-58). in reference to the Propylaea please
refer to: IG, I: 92; Hesperia, XIV (1945): 87-92 [no.6]).
65
engineering and survey techniques were either only cursorily examined, or lost, or
excluded altogether.'"'' Specific information regarding Greek temple alignments and
dimensions were among the building information not included in Vitruvius' work.
However, we can glean tantalizing pieces of information from De Architectura which
may help us to reconstruct the original orientation and dimension formula.
In his manual Vitruvius made several references to architecture and alignment
techniques and tools such as: the astronomical education of an architect, use of sundials
and gnomons, specific directions for street alignments, and general directions for temple
orientations.
a. astronomical education of architects
Vitruvius noted that an architect must be skilled in the craft of construction and
be knowledgeable regarding many sciences including astronomy.He claimed that
astronomy was important because an architect must determine the directions of the
cardinal points, the order of the heavens, and the locations of the equinoxes and the
solstices. It is generally assumed that the ancient architects oriented structures to these
celestial points.
In Book IX of De Architectura, Vitruvius explained the motions of the sun, the
moon, the planets, and the constellations with an accuracy that seems limited or basic if
one were to compare him to an astronomer.
Therefore, we can assume that an
elementary, not an advanced, level of astronomy was required of
century BC Roman
"" Coulton: 15.
Ibid: 15.
Vitruvius: I; 1:1-3.
66
architects. Accordingly, if we apply this assumption to previous architects, we must
assume that the celestial alignment formula used by 6*"' centurj' BC Greek architects
needed to be astronomically straightforward and uncomplicated. Aligning monumental
structures by means of sophisticated lunar or stellar calculations may not have been
within the realm of the ancient architects' astronomical knowledge or mathematical
abilities. Orienting buildings to the sun, however, is still a possibility.
b. gnomons
Vitruvius also tells us that unless architects were familiar with the locations of
the equinoxes and solstices that they would not be able to understand the construction of
clocks or sundials.
Fig. 15.1; Sundial with Gnomon Attached: Delos, 5* century BC.
Gibbs, Sharon, Greek and Roman Sundials.
Vitruvius; IX: I-VI; Evans 132-3.
Vitruvius, I; c.1.10.
67
This implies that architecture, the location of the equinoxes and the solstices,
and time-keeping devices, were interrelated. The solstices and equinoxes are determined
by solar observations, and the sun is used in connection wth a sundial. Therefore, it
appears that Vitruwis was telling us that architecture, the sun, and the solstices and the
equinoxes, are closely linked. The Romans inherited much of their astronomical
information from the Greeks who were aware of solstices and equinoxes from at least
the 8*^ century BC. However, the earliest record of Greeks using time keeping devices,
such as the gnomon,
dated to the 6^ century
Sixth century Greek astronomers used the gnomon to mark celestial events (Fig.
15.1).^'^® By the
century BC, the Greeks had perfected their techniques so well that
the Greek scientist Erastosthenes^'^^ conducted a brilliant and far reaching experiment.
He used both a gnomon and a deep well in two different locations in Egypt to make a
successful and accurate determination of the circumference of the Earth.
Obviously the gnomon was of great interest to the Greeks and not just for
marking the solstices or equinoxes or telling daily time, but for grand scientific
experimentations. It is very likely that the gnomon had many other applications in
ancient Greece such as orienting Greek temples to the solstices or equinoxes. Although
The most important component of a sundial, also called "the style."
Diogenes Laertius; II.I. l .
Thales used an anthropomorphic gnomon to help determine the height of the Giza pyramids: Anaximander
used a gnomon to mark the solstices and equinoxes (Diogenes Laertius: 1.1.27; II.I.l).
Cleomcdes, On the Elementary Theory of the Heavenly Bodies 1,10, 3-4.
''°Kaufinan:40.
68
Vitruviiis does not associate building orientatioii with the gnomon, he does use the
gnomon to align streets.
c. street alignmeuts
Vitruvius placed great emphasis on the cardinal orientation of city streets. He
said that streets should be aligned to the eight 'winds' or directions, which equate with
the eight compass points.*^' Vitruvuis wrote that compass points were determined by
the following method. A 'shadow tracker' or gnomon was first placed on a marble slab
or dial. Then, at specific times of the day, the end of the shadow cast by the gnomon was
marked. These shadows were then used in a geometric procedure to deteraiine the
directions of the eight points of the compass.'^" Although Vitruvius only applied this
geometrical scheme to aligning streets, it could have been used to orient other city
features such as public buildings or even temples.
2. Temple alignment techniques
After presenting the various attributes of Doric, Ionic, and Corinthian temples,
Vitruvius then maintained that these temples should be oriented to the west, when the
geological parameters of the area permit.'"'^ However, as previously mentioned, the
archaeological remains of most Doric temples have their entrances and cult statues
facing towards the east Based on this information, why would Vitruvius write that
temples should be oriented toward the west and not the east? Although it is possible that
he either inaccurately recorded his cardinal directions, or he was not aware that the cult
The eastern wind was named 'Soumus,' the southern 'Ausier,' the western 'Fmonim,' and the northern
'Spetentno." Northeast, northwest, southeast, and southwest also had specific names (Vit. I.VI.4).
" Vitruvius: I.VI.6.
69
statues and entrances of Doric temples usually faced the east, these alternatives are
unlikely because Vitruvius was well informed regarding floor plans of religious
structures and he certainly knew the directions of the cardinal points. Therefore, the only
remaining alternative is that Vitruvius was Mly aware of what he wote. Vitruvius'
western temple orientations are reinforced with the results of GTOP, which determined
that six of the eight Doric temples in that survey were aligned to the west and not the
east.
a. western temple orientation
Vitruvius was quite specific regarding this western orientation. He said that,
unless there were extenuating circumstances, the temple and the "marker"in the
sanctuary,
should face the west so the worshipers (when facing the marker) would be
looking towards the altar and the east;
Moreover the quarters which the sacred sanctuaries of the immortal
gods ought to look to will have to he established in such a manner that, if no
reason hinders and the opportunity is presented, the sanctuary and the marker,
which is in the cella, look towards the western quarter of the sky, so that those
performing vows may contemplate the sanctuary and the eastern sky, and the
statues themselves (which) seem to he rising up, and so look over those
supplicating and sacrificing, because it seems necessary that all altars of the
gods look t o the east (IV.V I).
Vitruvius: IV.V.l
Sigmm: marker or token.
Aedis: sanctuary, dwelling of the gods. Templum is a larger structure.
Regioms autem, quas debent spectare aedes sacrae deorum inmortalium, sic erunt comtituendae, uti, si
nulla ratio inpedierit liberaqm fuerii potestas, aedis signumque quod erit in cella conlocatum, spectet ad
vespertinam caeli regionem, uti, qui adierint ad aram immolantes out sacrificia facientes, spectent ad partem
caeli orientis et simulacrum, quod erit in aede, et ita vota suscipientes contuentur aedem et orientem caelum
70
When Vitravittis wrote that the marker should "face the west," this implied that
this marker (signmum) should be erected on the far western side of the sanctuary space,
in an area that would place the marker closest to the western horizon (Fig. 16.1).
Hffire Ml
VITRUl'TC'S: Western Architeawai Orimt&iims
Hi
wgrf
emi
Figure 16.2
VITRUVIUS: Eastern Cult Statue
J'^8
wat
ipsaque simulacra videantur exorientia contueri suppticantes et scarificantes, quod aras omnes deorum necesse
esse videatur ad orientem spectare.
71
If a gnomon ("marker") was thiisly erected then, when the sun rose oa the
eastern horizon and its light hit the gnomon, a shadow would be cast which would fall to
the west and outside of the temenos space. However, when the sun set oa the western
horizon the shadow from that same gnomon would be cast to the east and Inside the
temenos space (Fig. 16.1). Now, GTOP has previously introduced evidence which
strongly suggested that the Doric temples included in the GPS survey were precisely
aligned to the western, rather than eastern, horizon. Because these temples are so
aligned, then the sunset shadow of the aforementioned gnomon would not only fall
inside the temenos space, but also it would precisely parallel the alignment of the temple
located within (Fig. 16.1). Therefore, it is the hypothesis of EAN that a gnomon was
used to align Doric temples directly to the setting sun at either winter solstice or
equinox.
Although these Doric temples were aligned with greater precision to the west,
their entrances, altars and cult statues still faced the eastern horizon (Fig. 16.2).
Viturvius stated that when worshipers approached,
...they may contemplate the sanctuary and the eastern sky, and the
statues (simulacrum) themselves (which) seem to he rising up (IV.V.I).
This implies that the worshipers approached from the west and looked towards
the east, and that the temple statues, as well as the altars, were in front of them. This
description makes sense as temple statues are located in the naos (the center of the
temple [Fig. 16.2]). Therefore, if a suppliant approached the temple from the west,
when the sun rose on the eastern horizon, the cult statue would appear to loom up in
front of him. However, the shadows cast from those statues would begin in the center of
72
the temple (Eot the eastern parameter) and they would not be as precisely aligned to the
solstice or equinox as the western, gnomon shadows. Nevertheless, the spiritual
elements of the temple and temenos complex would be complied with by this
generalized alignment to the east on solstice or equinox. At the same time, the
technological requirements of the temple's alignment would also be fulfilled: the
structure would be precisely aligned to the equinoxes or either of the solstices by means
of the western (rather than eastern) horizon. Therefore, EAN suggests that this
alignment scheme fulfilled two requirements: 1) specific architectural orientation was
satisfied by means of precise alignments to the western horizon, and 2) spiritual
requirements were complied with by a generalized orientation to the east.
Vitruvius was not the only Roman author to comment on this "strange" western
alignment of religious structures. Clement of Alexandria'also claimed that temples
should face westward.
However, other Roman contemporary authors, including
Plutarch,said that temples should be aligned to the east because when the suppliant
enters the temple his back should be towards the rising sun.'^
As this discrepancy regarding the eastern or western alignments of Greek
temples encompasses not only Roman authors but also the archaeological evidence, one
must conclude that either the particulars of the alignment issue were not well researched
by Vitruvius, or that Vitruvius, as a qualified architect, was aware of the fact that
Bom ca. 150 AD: OCD; 249.
Clement of Alexandria: Sir ornateis.. VII: 724; Dinsmoor (1939): 100.
Bom ca. 50 AD: OCD: 849.
14,4; Dinsmoor (1939): 100.
73
temples actually were aligned to the west and not to the east. It is suggested here by
BAN that Vitruvus was not negligent, that he puiposely commented on the western
orientation of Greek religions structures.
b. measuring cords
Long cords may have been used to mark the location and length of each
gnomon shadow. One person could stand at the base of the gnomon shadow while the
other person stood at the other end of the shadow. A cord then would be stretched
between these two people; this cord could be used to record the length and alignment of
the gnomon shadow. This technique was used by the Egyptians for at least 2000 years
previous to the construction of Greek Doric temples.'^' Clement of Alexandria quoted
Democritus
as referring to the skill of these Egyptian harpendonaptae (rope-
stretchers) and claimed that he (Democritus) could perform this task better than the
Egyptians could.
This indicates that the Greeks were aware of this particular aspect of
foundation-laying as early as the 5^ centur>' BC. This measuring technique, combined
with the gnomon, would have been a simple formula to execute and could only be used
in tandem with one celestial object - the sun.
B. Conclusion
Based on the results of GTOP and the words of Vitruvius, we are able to
reasonably assume that Greek temples were specifically oriented to either the solstices
Wilkinson, Richard (2000), The Complete Temples of Ancient Egypt. New York: Thames and Hudson: 38.
The Egyptians also referred to this "stretching-of-the-cord" ceremony as, thepedj shes ceremony.
Democritus (ca. 470 BC) was knowledgeable in theology and astrology; he claims that he learned geometry
in Egypt (OCD: 327, 328)
Clement of Alexandria, Strom., i: 304 A.
74
or to the equiBoxes, and that the commoii direction of Doric stmctuial alignment was
west, towards sunset, rather than east toward suiirise, ^ previously thought. We can also
hypothesize, based on Vitmvius' astronomical accounts, that 6® century Greek architects
did not know the minute specifics of astronomy such as the 19-year lunar cycle
developed by Meton in the 5^ century,or the precession of the equinoxes^^^
developed by Hipparchus^®® in the 2"*^ century BC. Although the education of the 6*^*
century BC Greek architect was most likely far above that of an ordinary citizen, it was
not of the same caliber as an astronomer of that time period. Therefore, whatever
techniques ancient architects used to orient temples, those methods needed to be rather
straightforward and uncomplicated. The gnomon technique that Vitruvius used to align
streets was direct and easy to follow; its application could very well have been used to
orient monolithic structures, especially in conjunction with measuring cords.
Why would the Greeks orient their Doric temples to the west when the main
entrances, altars and cult statues faced the east? The answer, developed below, is
intimately connected with determining the length of each temple.
Thurston, Hugh (1994), Early Astronomy. New York: Springer Verlag; 111. The first mention of Melon's
19-year (235 month) lunar cycle was found on early parapegmata. References to this 19-year period were also
found in: Geminus, Isagoge, chapter VIII.
Ptolemy. Syntaxis, VII, I, vol. II: 2, 22-3, 11. Heib. Found in Sir Thomas Heath's, Greek Astronomy: 142.
Greek astronomer; ca. 190-126 BC.
75
IV. GREEK TEiMPLE ORIENTATION PROJECT: Part II
A. Gnomon Shadows and Temple Dimensions
1. Measuring shadows at sunrise and sunset
In the search for a practical reason as to why Greek temples were oriented to the
west rather than the east, EAN conducted an experiment which was based on the
assumption that the Greeks used gnomons and measuring cords to align their temples. A
12 ft. tall gnomon was first selected. This gnomon, a saguaro cactus, was located in a
valley; its eastern mask was 6.5° (Fig. 17.2) and its western mask was 2.5° (Fig. 17.1).
Two separate observations regarding the lengths of the gnomon's shadows were made:
one at sunrise and the other at sunset.
Fig. 17.1: Tucson, Arizona: 12 ft. tall cactus/gnomon.
Height of western horizon (mask): 2.5°.
76
When the shadow of the cactus iirst appeared at sunrise its shadow tip was
marked and a picture was taken (Fig. 17.2); the length of the shadow (from cactus base
to tip) measured 102.75 ft.
Fig. 17.2:
Same cactus as Fig. 17.1, 3; eastern mask height: 6.5°.
Length of cactus shadow at sunrise: 102.75 ft.
Fig. 17.3: Length j.':,;
• 8.25 ft.
77
However, after mathematically calculating the length of the shadow, its actual
length at sunrise should have measured 105.32 ft. So there was a discrepaacy of 2.57 ft.
between the measured length of the shadow and the calculated projected lengfli.
Approximately 45 seconds after the sunrise shadow length was marked, the
shadow had moved a significant distance so a third picture was taken (Fig. 17.3). The
length of the second shadow in Fig. 17.3 measured 98.25 ft. and it appeared to angle
towards the north when compared to the shadow in Fig. 17.2. These alignment
differences become more apparent if one compares the location of both shadows relative
to the hole in the grass next to the sidewalk. These two photographs illustrate that, in a
matter of only 45 seconds, the shadow not only shorted by 4.50 ft., but it also had a
significantly different alignment angle.
These three measurements, the calculated length of the sunrise shadow (105.32
ft.), the observed length of the sunrise shadow (102.75 ft.), and the length of the shadow
45 seconds after sunrise (98.25 ft.), illustrate the difficulties one would encounter when
using the sunrise shadow of a gnomon for orientation and measurement purposes. For
example, at sunrise, the shadow appears suddenly, and immediately begins to recede and
move toward the north (the first shadow in Fig. 17.2 falls to the south of the hole in the
ground, while the second shadow in Fig. 17.3 is more northerly and is in the hole in the
ground). In order to obtain the correct orientation of the sun and the shadow length, the
end of the shadow must be immediately located and marked at the moment of sunrise.
Because the shadow appears suddenly at sunrise, one must move quickly to find its tip:
the longer the shadow, the more difficulty one will encounter in finding the end of the
78
shadow. Therefore, the true orientation of the sun and the length of the shadow at
sunrise are difficult to obtain with any precision. Additionally, due to the phenomena of
diffraction,
the gnomon shadow tip is fuzzy: it would be difficult to determine within
the first few seconds of sunrise, precisely where the end of the gnomon shadow fell.
The sunset observation was easier to measure by far. The end of the gnomon
shadow was marked 15 minutes before sunset so there was plenty of time to make an
accurate determination of the location of the indistinct end of the gnomon shadow.
Then, as the sun descended towards the horizon and the shadow extended, EAN simply
kept pace with it. When the sun actually set, the length of the sunset shadow was
measured with a cord and marked; its length was 274.40 ft. This measurement was
compared with the mathematically computed measurement which was 274.85 ft. The
discrepancy between the shadows which were physically measured and mathematically
computed was only 0.45 feet, or about four and-a-half inches. Therefore, if one were to
use a gnomon and measuring cord to determine the orientation and length of a temple,
the measurements could be collected with a far greater degree of accuracy at sunset
rather than sunrise.
Finally, if these measurements had to be done at either equinox or solstice, one
would have a window of only a couple of days to obtain correct orientations and shadowlengths. If too many days passed, the sun's rising location would have shifted too much
to acquire a true alignment to equinox or solstice. The temple would either have to be
"Diffraction" is a disturbance of light as it passes through an opening or around an obstacle. Diffraction
limits the ability to distinguish fine details in images.
79
improperly aligned or the architect wouid have to wait at least another six months until
the next equinox or solstice.
Due to these time and distance problems in accwately measuring the sun's
orientation and the gnomon shadow length at sunrise and sunset, it is reasonable to
conclude that the ancient architects surveyed and laid the temple foundations based on
western alignments (sunset) as opposed to eastern alignments (sunrise). Supporting this
theory are not only statements made to this effect by Vitruvius and Clement of
Alexandria, but also the results of GTOP. which indicate that six of the eight temples
surveyed had western, not eastern orientations.
2. Temple lengths and widths
The final premise in this work involves determining temple dimensions,
specifically their lengths. The following table (Table 6) lists the lengths, widths, and
ratios of the GPS surveyed temples.
80
Table 6.1; Temple Ratio;
Temple
Ltagtli {flj
Wiiitli PI
laiia; L/W
Corinth: Ap»llo^®^
176.64
70.47
1;2JI
Delphi: Apollo'
197.90
78.15
iaj3
Isthmia: 7® c. Poseidon'^
128.77
47.24
l±73
fethmia; 5*' c»
175.52
78.41
Nemea: Zeus*^
139.60
65.91
1:2J:2
Otympia: Hera''^
164.00
61.52
1:2.67
Otympta: Zeus'^^
'' '
"1
Tegea: Athena Alea
210.36
90.78
!:2J2
156.00
62.96
1:224
I
i
i
.J
tij
i
The mean ratio of width to length in these eight Greek temples is; 1;2.45 (1;2.5),
or one temple length is equal to two-and-a-half times its width. This commonality of
ratios is unusual because the lengths and widths of these temples are drastically
different; they vary from 210 ft. to 128 ft. in length, and from to 91 ft. to 47 ft. in width.
What makes this similarity in ratios more interesting is the fact that these temples were
constructed in varying types of terrains including expansive areas like valleys or broad
plains, or in limited spaces, such as near mountain peaks or cliffs. Although the
geological parameters of each site probably limited or augmented the size of each
temple, those parameters still did not materially affect the general 1:2.5 dimension ratio.
Temple dimensions from: American Journal of Archaeology, vol. IX (1906): 58.
Temple dimensions from: Fouilles de Delphes, vol. II (19 ): 4.
™ Temple dimensions from: Gebhard and Hemans (1992). Hesperia: 34.
Temple dimensions from: Broneer, vol. 1: 71.
Temple dimensions from: Miller, Nemea: Guide to Site and Museum: 135.
™ Temple dimensions from: Mallowitz: 142.
™ Temple dimensions from: Mallowitz: 214.
Temple diaiensions from: Norman: 170-172.
81
These si m il ar ratios suggest some sort of commonality inherent within the
procedure by which the dimensions of all eight of the temples were determined. The
concept of a "dimension" schema grows stronger when one considers that these temples
represent 400 years of Greek building traditions and that these sacred stnictures were
constructed over a large area exceeding 15,000 square kilometers. Whatever the original
dimensioning scheme may have been, it must have been easy to follow for so many
architects to have employed it in the innovative Doric temple design over such a large
land area. Additionally, the procedure must have worked well for the Greeks to
continue using it for the next 400 years, at least. It is concluded here that this
"dimension" methodology is directly associated with the alignment procedure previously
discussed, in which gnomons and masks play a vital role.
3. Gnomon heights
We noticed previously how the heights of masks can influence the length of a
shadow cast by a gnomon. Another element that affects the length of a gnomon' shadowis the height of the gnomon itself. However, a tall gnomon will not necessarily cast a
82
Fig. 18.1: Sunrise shadow of a 12 ft. gnomon with a 6.5° mask; 105.32 ft.
Fig. 18.2: Noon shadow of a 12 ft. gnomon (sun at zenith): approximately 8 ft.
long shadow. If the mask associated with a tall gnomon is also high, then the gnomon's
cast shadow will be short (Fig. 18.2): if the mask associated with that same gnomon is
short, then the shadow being cast will be long (Fig. 18.1). So, masks and gnomons work
together to create shadows of varying lengths - it is the combination of the two that is
important. The formula used to determine the length of the gnomon's shadow is:
tan (h^) = H/S
or
S = II/tan(//|^)
where the altitude of the sun = h^, the height of the gnomon = H, and the length
of the gnomon's shadow = S. For a more complete description of this formula, please
refer to Appendix D; pages 127-129: The Length of a Shadow Cast by a Solid Object, by
R.E. White, Ph.D.
The gnomon height necessary to create shadows the length of the eight temples
in GTOP with their associated masks needs to be somewhere between 10 ft. to 35 ft.
Since these measurements correspond somewhat to the heights of the columns of each
83
temple, a new suspicion developed: were the colimms of each temple based upon the
heights of the gnomons used to align each of these strectures? Additionally, did the
length of the shadows cast by each respective column/gnomoE determine the length of
each temple? It is very likely that they did and hom^ it works is explained below.
4 Gnomon and mask heights
The following table (Table 7.1) is a comparison chart of each temple at sunrise
in which the height of the column (without the capital) and the height of the sunrise
mask are first computed and then compared to the length of the temple. Please note that
the mask heights and column heights vary.
84
Table 7.1: SUNSET: Shadow and Temple Length Comparisons
S
ti
DelpbiTA^lo^"
32.78
32.0°
197.90
52.46
im
Isthmia:
7'^c. Poseidon'^
Isthmia:
5*^ c. Poseidon' ''
Olympia: Hera^"
12.47
0
J-
o
All's / ^
128.77
1428.92
IL!»
20.77
0.5°
175.52
2380.01
1356
17.09
4.5°
164.00
217.15
L32
Olympia: Zeus'*'
32.28
2.5°
210.36
73933
3.51
Nemea: Zeus^®
33.89
8.0°
139.60
241.14
1.69
Tegea;
29.15
5.0°
156.00
333.19
2.14
Athena Alea""
a. sunrise
The last column marked "Comparison" is the comparison ratio of the length of
the shadow cast by the column, compared to the length of the temple. For example, at
Corinth, the length of the shadow of the column at sunrise (312.56 ft.) was 1.77 times
Column height without capital: 20.77 ft: American Journal of Archaeology, vol. IX (1906): 58.
Column height of column with capital: 34.75 ft. Dinsmoor (1928). Projected capital height: 1.97 ft.
Projected column height without capital: 32.78 ft.
Because original columns of this temple were made of wood, column height was estimated by Broneer at
13.78 ft. (vol. I: 54). Broneer did not specify whether this height was with or without a capital. Column height
without capitals was estimated by EAN to be 13.26 ft.
™ Broneer (1:71) based the height of these columns on the height of the colunms of the temple of Apollo at
Corinth {AJA (1906), pg. 58) which was 20.77 ft. without capita!.
Mallowitz said these columns were 17.10 ft. tall: he did not specify if this included the capital: 142.
Mallowitz did not specify the height of these columns. The height (32.28 ft.) was obtained from Dinsmoor
(1928) who estimated that these columns were 34.25 ft tall. Deducting an estimated 1.97 ft for the columns
gives an estimated height of 32.38 ft. for the columns without the capital.
Miller said that the height of the column was based on 13 drums (without capitals) which measured 33.89 ft
(1990): 142.
Naomi Nonmn said the columns (without capitals?) were 29.15 ft: 172,179.
85
the length of the temple; at Delphi, the length of the shadow (52.46 ft) at suniise was
less than 1/4®*' the length of the temple (0.22 times the length), and so forth,,
b. sunset
The next table (table 7.2) is similar to table 7.1 except that it compares the
heights of the columns (without the capitals) and temple lengths with the western or
simset masks.
ons
f £i¥ir«j£.
20.76 ft.
4.0"
• L •; • ;
Delphi: Apollo
32.78 ft
6.5°
197.90 ft
287.71 ft.
1.45
Isthmia:
7* c. Poseidon
Isthmia:
S**" c. Poseidon
Olympia: Hera
12.47 ft.
128.77 ft.
142.53 ft.
1.11
20.77 ft.
5.0°
175.52 ft
237.40 ft.
135
17.09 ft.
6.0°
164.00 ft.
162.60 ft. i
0,99
Olympia: Zeus
33.89 ft.
0
o
21036 ft
307.12 ft. i
IM
Nemea: Zeus
33.89 ft.
8.5°
139.60 ft.
226.76 ft. !j
s
1.62
Tegea;
29.15 ft.
5.0°
156.00 ft.
333.19 ft.
2.14
a
Corinth: Apollo
b0
Tftai|»lc 1 Sliatlow i ConaparisoJt
Leoglfe 1 Length [
1.70
Athena Alea
A ver}' interesting correlation begins to develop: the shadows created by the
columns of each temple at sunset are becoming closer to the same lengths as each
temple; they average about one and-one-half times the length of their respective temples.
This is more than an unusual coincidence, especially if one were to contrast these
numbers with the sunrise temple and shadow length comparisons, which varied between
1/4® the length of the temple to almost 14 times the length of the temple. This
remarkable and consistent similarity of the sunset column shadow length and the temple
86
length should not be ignored. However, another interesting feature must now be added to
the alignment "equation": if a gnomon the height of the temple column was used to align
the temple, it must have been done before the temple foundations were laid.
5. Gnomon, mask and foundation heights
Doric temple foundations are massive architectural components that have
considerable depth. They consist of three steps from top to bottom: one in the
stylobate, two in the stereobate, and a narrow euthynteria, which is located under the
stereobate (Fig. 19.1).
Figure 19.1:
Temple Foundation Levels.
<=Stylobate (top step)
<=^tereohate (middle 2 steps)
<='Euthynteria (bottom step)
Because these four courses have considerable depth, that depth must be
subtracted from the column height in order to determine the height of the gnomon
possibly used to lay each temple's foundation. The next two tables (Table 8.1 and 8.2)
first subtract the foundation height from the height of each column, and then compare
these numbers with the lengths of the associated temples. Table 8.1 pertains to sunrise
and table 8.2 to sunset.
Vision S.R.L. (©1997). Ancient Greece: the famous monuments. Athens; The Muses Publishers.
Reconstruction of Aphai at Aegina: 33.
87
Table 8.1: Adjusted Gnomon Shadows at Sunrise
i .• ipiiipic
licjehl
20.76
3.8
8.2
12.57
176.67
189.25
32.78
32.0
4.92
27.85
197.9
44.57
j
ismrnm^
frnmml'f'
Poseidoi/Sth
Olympia:
OlyaiMa:
Zeas''®®
Hfiiaea:
Zeus'"'
Tegeat
Athena'®^
]
lA'fl
0.23
•
iiiiiiiiiiiiiiiiiiiliiiiiiiiiiiliil
I
ill•a •'•••
i i
i
i!
:•
Coriath:
Lmonwn i lempjei ij 5n«uow(;s| vmipanson i
heighl-ft j ienglb'ft.i leBgtlJ-ft.j Ratio: 'I7S j
tieigM-ft.
12.47
0.5
2.1
9.84
128.77
1127.55
8,76
20.77
0.5
10.16
10.64
175.52
1215.10
6.#
17.09
4.5
5.05
17.17
164.00
280.67
1.71
32.28
2.5
8.2
24.08
210.36
551.52
33.89
8.0
4.46
29.43
139.6
209.41
1.47
29.15
5.0
15.42""
13.73
156.00
156.93
i.OI
The eastern and western foundations were taken from AJA, vol. IX (1906): 55-56.
Foundation heights of the eastern side were based on the eastern ramp height of 4.92 fit or i.5 meters. Pouilles
de Delphes: II; 15. The western foundation heights were calculated at 9.88 ft. or 3.01 meters. Fouilles de
Delphes: II: 11.
Foundation heights for the eastern side were composed of 2 steps of 0.40 meters each (0.80 meters); the
western foundation was only one step of 0.40 meters. Broneer: I: 64.
Foundation heights for both the eastern and western sides were 3.098 meters each. Broneer: I: 71.
Foundation heights for both eastern and western sides were 1.54 meters or 5.05 ft. Mallowitz: 88.
™ Foundation heights for both eastern and western sides were 2.50 meters or 8.20 ft according to Mallowitz:
213-214.
Nemea east was i .36 meters based on..Nemea west was 2.83 meters based on the depth of the crypt (2.50
meters) and the estimated height of the euthynteria (0.33 meters).
Foundation heights of both the east and west sides of Tegea were 2.70 meters or 8.86 feet (Norman: pgs 171,
172). The entire temple of Athena Alea sits in a seemingly man-made depression which, (based on photographs)
was estimated to be an additional 2 meters to the foundation height.
The height of the foundation of the temple of Athena Alea at Tegea is 2.70 m or 8.86 ft. However, the
depression that the temple sits in has been estimated to be ca. 2 meters or 6.56 ft. This estimate was based on
photographs and a persona! acquaintance with the site. This figure was not found in any excavation reports and
therefore, had to be estimated.
88
;
Table 8.2: Adjusted Gnomon Shadows at Sunset
leiiiple
llliiiMlilll iiiiilliiliiiii rouactatioB
height-feet.
heigfit:
feet
20.76
4.0
8.2
•
Corinth:
•'
ijiiomor! iiiiiiiliiiiii llllHiliiilllll i.oinpanson ^
(S)
(T)
iiiiiiiiiiBiiii iengtli tl.
r,f)2
•!
12.57 r 176.67
179.76
32.78
6.5
4.92
22.90'^''^
197.9
200.99
12.47
5.0
2.1
11.15'""=
128.77
127.45
20.77
5.0
10.16
10.64
175.52
121.20
0.69
17.09
6.0
5.05
17.17
164.00
163.33
&.995
32.28
6.0
8.2
24.08
210.36
229.11
1.09
33.89
8.5
4.46
24.6'''"
139.6
164.60
lis
29.15
5.0
15.42''''
13.73
156.00
156.93
i.oi
Apollo
. f oseiioa
IsftfjiaTs®™
foseMoii ;
Oiympia:
^ lifllS
Neiaea:
• &0S
Tegea:
Athena
^
b.#
After accounting for the heights of the foundations of each temple, this "dimension"
criterion becomes even more apparent. The lengths of each temple and the lengths of
1 05?
their respective gnomons' shadows at sunset are very, very close: in fact, the
comparison range every gnomon shadow, it can be assumed that the lengths of the
temples and the gnomon shadows were equal. Additionally, when the shadow/temple
ratios of sunset vs. sunrise are compared, the only logical conclusion one can make is to
Foundations on the western slope were thicker than eastern. The eastern foundation was based on the height
of the ramp.
The western foundation was not as thick as the eastern.
This takes into account the 2.5m adyton and .33 euthnyteria.
The height of the foundation of the temple of Athena A lea at Tegea is 2.70 m or 8.86 ft. However, the
depression that the temple sits in has been estimated to be ca. 2 meters or 6.56 ft. Tnis estimate was based on
photographs and a personal acquaintance with the site. This figure was not found in any excavation reports and
therefore, had to be estimated.
With the exception of the S"" century temple of Poseidon at Isthmia.
89
assume that the length of each temple was determined by a gnomon the height of each
temple's column minus the foundation height. This confirms that not only were these
temples celestialiy aligned to the sun at sunset at winter solstice or equinox, but it also
tells us that the length of each temple was determined via astronomical observations.
The only anomaly would be the 5^*^ century temple of Poseidon at Isthmia and
there could be a simple explanation. Both the 1^ and the 5^ century Poseidon temples
were built in the same 'sacred' place. The 7* ccntury temple was smaller and possibly
of an early Doric design. When, in the 5* century, the Greeks decided to re-bulM their
temple using the larger, matured Doric style, they had to make a decision: either find a
new sacred space that would conform to the larger temple design, or use the original
space and sacrifice the gnomon orientation scheme. I am suggesting that the Greeks
kept the sacred space and sacrificed the orientation 'scheme.'
B. Application of Theory
By referring to the following diagrams, the way in which the dimension
criterion is worked may be demonstrated.
1. The 7® century temple of Poseidon at Isthmia
a. western exposure: equinox sunset
Figure 20.1 is an illustrated example of the western horizon of the 7* century
temple of Poseidon at Isthmia: this temple is oriented at 267.40° W (87.40° E) and the
temple's western mask is about 5.0°. When the sun sets its arc azimuth is 266.48° W, so
With the exception of the 5"' century temple of Poseidon at Isthmia.
90
this temple orientation only deviates from the sun's arc azimutli by a mere 0.92°.
Additionally, when the swi sets at this particular angle (5.0°), and casts its light agaiast
the temple's 11.15 ft. gnomon, it will create a shadow that is 127.45 ft. iong. As the
length of the temple is 128.77 ft., the shadow is 0.99 times the length of the temple: the
gnomon shadow and archaic temple lengths are equal.
Figure 20.1: Archaic Isthmia: Western Azimuth, Mask and Orientation. Illustrated
example of the western horizon of the Archaic temple of Poseidon at
Isthmia: a = mask; P = solar arc azimuth; y = temple orientation.
b. eastern exposure: equinox sunrise
The eastern horizon of this temple to Poseidon (Figs. 20.2; 20.3) has a much
lower angular height: it is at sea level and its mask, at the most, measures 0.5°: this mask
is almost non-existent. When the sun appears at sunrise, its angle is so low that when its
light hits the gnomon of the archaic temple, it will cast a shadow of 1127.56 ft., about
8.76 times the length of the temple. Additionally, because the mask is lower on the
eastern horizon, the orientation of this temple (N 87.40° E) has a greater deviation to
sunrise at equinox (2.98°) than it does to sunset (0.92°) at equinox. Therefore, taking
91
into consideration the smaller orientation deviation at sunset and the gnomon shadow
and temple lengths being equal, it is safe to assume that this temple had a western, not
eastern orientation to equinox.
P
Fig. 20.2: Archaic Isthmia: Eastern Azimuth, Mask and Orientation. Illustration by John
Papageorgiou: eastern horizon of the temple of Poseidon at Isthmia: a = mask
height; P = solar arc azimuth; y = temple orientation.
Fig. 203: Eastern Horizon of Archaic Isthmia: Photograph by Erin A. Nell (2001).
2. The temple of Apollo at Delphi
a. northeastern exposure: summer solstice sunrise
Figure 21.1 is the northeastern horizon of the temple of Apollo at Delphi.
Whereas Isthmia's eastern mask was almost non-existent, Delphi's is huge, almost
92
32.0'^. The temple of Apollo at Delphi has an orientation of N 54.76" E. By the time the
SUB finally crests Delphi's huge eastern mask at summer solstice, its arc azimuth will be
87.71°, almost 33° north of this temple's orientation.
•••
i Northeastern Horizon of the temple of Apollo at Delphi.
Photograph by Erin A. Neil.
Fig. 21.2 : Apollo, Delphi: Northeastern Azimuth, Mask and Orientation. Illustration
by John Papageorgiou: a = mask height; p = solar arc azimuth; y = temple orientation.
Additionally, by the time the sun rises over Delphi's tall eastern mask, its angle
will be very high. When the sun's light strikes the temple gnomon, the shadow it will
93
cast will measure only 44.57 ft. - less than a 1/4 the length of the temple, which
measures 197.90 ft.
b. southwestern exposure: winter solstice sunset
Figure 22.1 is the southwestern exposure of the same temple; the mask on this
side is only 6.5°. As the sun sets at winter solstice, it not only appears to do so right
between the center columns (there is only a 1.35° difference between visual sunset at
winter solstice and the temple's orientation), but the shadow cast by the temple's
gnomon (200.99 ft.), will virtually equal the length of the temple (197.90 ft.).
Fig. 22.1: Apollo, Delphi: Southeastern Azimuth, Mask and Orientation. Illustration by John
Papageorgiou: a = mask height; p = solar arc azimuth; y = temple orientation.
Fig. 22.2: Southwestern Horizon of the temple of Apollo at Delphi.
Photograph by Erin A. Nell'®®
199 The differences in mask heights between the illustration (Fig. 22.1) vs. the picture (Fig. 22.2) are due
to the angle at which the photographer took the picture. If taken from the correct angle (on top of the
ramp [on the stylobate]), the "illustrated" mask height wouM be correctly reflected.
94
Based on the huge differences not only between tMs temple of Apollo's sunrise
and sunset orientations, but also betmwn the comparisons of the gnomon shadow/tempie
lengtli at sunrise and sunset, it is certain that tills temple of Apollo at Delphi was
oriented to winter solstice sunset.
C. Conclosion
The similar comparison ratios of length to width (1:2 V2) shared by these eight
Doric temples are too consistent to be ignored, especially when one considers that these
temples were dispersed in an area of 15,000 square kilometers. However, because each
temple's actual measurements of; length, width, column height, and foundation depth
were not similar, there had to be another alignment component which would give each
temple its similar comparison ratio. That component happened to be an unchangeable
element of the landscape: the horizon elevation, or, mask. In a way Vincent Scully was
correct, the landscape surrounding each temple is vastly important - to the celestial, not
terrestrial, alignment of each temple. Additionally, there is only one celestial body that
can make this formula work - the sun. This combination of celestial and terrestrial
elements is greatly significant and should not be ignored - it is no mere coincidence.
95
¥. FINAL CONCLUSION
In the
centuiy BC Greek temples underwent radical revisions: their sizes,
floor plans, and construction technologies drastically changed. The orientations of these
temples appeared to standardize with the infusion of the new Doric order; entrances
consistently began facing to the east or northeast. If Greek temples had remained small
in size and continued to use ephemeral building materials (such as wood, thatch, and
mudbrick) consistent orientations would have been relatively easy to achieve. However,
with the dramatic size increase and i ntroduction of large, cut, stones as the primary
building material, temple alignment schema became far more complex and difficult to
execute. How did the Greeks correctly, and so precisely, align their new temples?
Current research has not revealed a de facto plan because neither building plans, nor
treatises, nor drawing implements, nor survey instruments have survived from that early
period of Greek history, except for one - the gnomon.
Many complicated theories have been introduced previously regarding Greek
temple alignment issues. Some scholars hypothesized that Doric temples were oriented
to the stars because the Greeks, as early as the 1^ century BC, planted and harvested
')f\n
their crops according to .stellar observations relative to the equinoxes and solstices.
However, astronomically predicting when to reap and sow did not automatically qualify
those same 7* century Greeks to celestially align their innovative, stone structures to
specific stars. For agricultural purposes only one stellar measurement was required: for
aligning large temples at least two measurements should have been collected (one from
96
either end of the projected temple) that would botii depict accurately the exact position
of one star. If either of those measurements were imprecise, the orientation paradigm
would be inaccurate as well.
Others scholars believed that Greek temples were most likely oriented to the
moon because that was the celestial body on which Greek calendars were based.
However, suggesting that the ancient Greeks aligned their Doric temples to the
complicated and erratic motions of the moon is not logical either, especially since the
Greeks did not standardize their lunar calendars for at least 150 years after the first
Doric temples were erected. Of paramount importance is the fact that none of these
stellar and lunar temple alignment hypotheses have offered any suggestions as to how
the Greeks could have aligned their temples: none take into consideration the types of
survey tools available to 6 century BC Greeks which would have allowed them to
perform such architectural miracles.
To some scholars, orienting Doric temples to the sun may seem too simplistic
for a culture that had achieved as many astronomical discoveries as the ancient Greeks.
However, aligning those megalithic structures to the sun may have been one of their
most brilliant accomplishments. First, any shadow cast by the sun against a straight
gnomon will always be aligned precisely to whatever time of day or year that shadow is
measured. Second, the shadows of the moon and stars would be difficult, if not
impossible, to measure: their light is not bright enough to cast a clearly defined shadow.
Additionally, such lunar and stellar shadows would have had to have been measured at
Hesiod, Works and Days: 564-569.
97
night and, mithout tlie light of day, humaas would have had a difficult time discerning
the outlines of such indistinct shadows.
If by chance the Greeks did orient their temples to the moon or stars, what types
of alignment or survey instruinents would they have used to obtain such measurements?
The only 6*^ century BC Greek astronomical tool that has been discovered was the
gnomon and this instrument required the sun, not the moon or stars, to function properly.
Finally, why should the ancient Greeks have gone to the additional trouble of collecting
orientation measurements from the moon or specific stars when the sun's shadow could
have provided them, effortlessly, with the most accurate orientation information of all?
To use a gnomon tall enough to cast a shadow long enough to align a massive
Doric temple and determine its length, is such a simple concept that it is exceptional in
itself and totally worthy of the early Greek architects and astronomers. However, the
ancient Greeks needed to determine on which horizon (eastern or western) that those
measurements should be obtained: the sun's shadow (cast against a gnomon) at sunrise
moves too quickly to secure an accurate alignment. However, at sunset, the ancient
Greek surveyor would have had plenty of time to carefully mark the shadow and thus
obtain a precise celestial alignment and corresponding temple length.
Two temples did not conform to this report's hypothesis; the temple of Apollo
at Corinth and the temple of Zeus at Nemea. However it is possible that these two
temples inadvertently supported this western alignment scheme. The closest celestial
orientation that the temple of Apollo at Corinth and the temple of Zeus at Nemea could
have obtained would have been to summer solstice sunrise - to the east. With a few
98
exceptions, all Doric temples have their entrances and cult sMues facing the east;
possibly the Greeks attempted, from time to time, to align their temples in the same
direction. However, due to the difficulty in. collecting a precise alignment at suniise as
opposed to sunset, the temples of Apollo at Corinth and Zeus at Nemea could have been
examples of attempts and failures at eastern temple orientations. Based on experiments
conducted in this report, Astronomical Orientations and Dimensions of Archaic and
Classical Greek Temples, western alignments with gnomons were more precise and
easier to collect than were similar aligiraients based on the eastern horizon.
It is not unreasonable to consider that the Greeks used this shadow-alignment
technique when one takes into consideration the discoveries that the ancient Greeks
made in the following centuries with the aid of gnomons and shadows: in the 6® century
BC gnomons were used to estimate the heights of buildings^'^' and determine the times
of the equinoxes and solstices;"®^ in the middle of the 3'"'' century BC, less than 300 years
after Doric temples were established, Eratosthenes^®^ used a gnomon to help him
estimate the circumference of the earth with surprising accuracy; in the middle of the 2"^
century BC Hipparchus'^ determined the exact time of equinox by way of a shadow
cast on a brass ring; in the middle of the
century BC Vitruvius stated that Romans
were using gnomons to successfully align their streets. If such prominent scientists and
architects used gnomons for such important experiments and projects, we should
Thales estimated the heights of the Giza pyramids with an anthropomorphic gnomon (Diogenes
Laertius: 1:27).
Diogenes Laertius claimed that Anaximander invented the gnomon and used on in Sparta to mark the
solstices and equinoxes (II: 1).
Evans: 63-64.
99
th
consider that their 6 century BC Greek ancestors may have aligned their innovative,
Doric temples with the same tools: shadows and gnomons.
The hypotheses of this report, a) Doric temples were aligned to the setting sun,
and b) that the lengths of these temples were determined by this same temple alignment
scheme, are strongly supported by the following four facts: 1) Vitruvius stated that
Greek temples were oriented to the west, 2) the only alignment instrument discovered
from the 6^^ century BC, the gnomon, required the sun (not the moon or stars) to
function, 3) when using a gnomon for orientation purposes, alignments obtained from
the western setting sun were far more precise than alignments obtained from the eastern
rising sun, and 4) the lengths of the Doric temples in GTOP are the same lengths as the
projected shadows cast at sunset from gnomons.^®®
Celestial alignments of these brilliantly constructed Doric temples were eternal
attestations of the devotion of the ancient Greeks to their divinities, gods and goddesses
who for the most part, resided in the cosmos. To align a temple not only to a celestial
event, but to do so by means of an instrument that must be powered by a cosmic body,
the sun, suggests that the ancient Greeks did not determine the dimensions of the
terrestrial houses of their deities, their gods did that for themselves. Eternally linking
the earth and the sky with a monument made out of a highly durable, eternal substance,
immemorialized the gods of the ancient Greeks. Such immortal architectural
connections achieved by means of precise celestial orientations and divinely determined
Thurston: 112.
100
dimensioHS would suggest that the atronomical compoBents of Doric moBumental
temples were more sacred than the hallowed ground on which they stood.
^ This is based on EAN's hypothesis that height of each temple's gnomon was the same as the height as
the temple columns less the temple foundation height
101
¥1: LIST OF WORKS CITED
i^ristophanes. The Clouds. Translated with Introduction and Notes by: Jeffrey
Henderson (1992). Newburyport, MA: Focus Infomiation Group, Inc. (1992).
Aristotle, On the Heavens. Loeb Classical Library (1939), translated by, Guthrie,
W.K.C.; edited by Henderson, Jeffrey, and G.P. Goold Cambridge: Harvard
University Press.
Biers, Wiiiiam R., (1996). The Archaeology of Greece, 2^^ Qd. Ithaca and
London: Cornell University Press.
Birge, Dance and Lynn Krannak and Stephen Miller, (1992). Excavations at Nemea:
Topographical and Archaeological Studies. Berkeley: University of California
Press.
Blomberg, Maxy and Goran Henriksson (2001). "Differences in Minoan and
Mycenaean orientations in Crete." Astronomy, Cosmology and Landscape:
Proceedings of the SEAC 98 Meeting, Dublin, Ireland, Sept. 1998. Editors:
Ruggles, Clive, with Frank Prendergast and Tom Ray. United Kingdom; Ocarina
Books Ltd: pgs. 72-9 L
(2003). "The Minoan Peak Sanctuary on Pyrgos
and its Context." Calendars, Symbols, and Orientations: Legacies of Astronomy in
Culture: Proceedings of the
annual meeting of the European Society for
Astronomy in Culture (SEACy. Stockholm, 27-30 August 2001. Editors: Blomberg,
Mary with Peter Blomberg and Goran Henriksson. Uppsala Astronomical
Observatory, Report No. 59. Uppsala: University Printers: pgs. 127-134.
Boardman, Jota, (2001). The History of Greek Vases. London: Thames and Hudson.
Borguet, Emile (1914). Les mines de Delphes. Paris: Fontemoing et C®, Editeurs.
Broneer, Oscar, (1971). "The Temple of Poseidon, vol. L" Isthmia: Excavations by
the University of Chicago under the Auspices of the American School of Classical
Studies at Athens: Princeton, New Jersey: The American School of Classical
Studies at Athens.
Bimdgaard, J.A., (1957). Mnesicles: A Greek Architect at Work. Copenhagen:
Scandinavian University Books.
Bury, J.B.. and Russell Mciggs, (1978). A History of Greece, 4* ed. London:
MacMillan Press, LTD.
102
Ciagett, Marshall, (1955). Greek Science in Antiquity. New York: Abeiard-Sclmiiiaii,
Inc.
Clement of Alexandria, Stromateis, VII; 724.
Cleomedes, On the Elementary Theory of the Heavenly Bodies I, 10, 3-4.
Coldstream, J.N., (1985). 'Greek temples: Why and where?' Greek Religion and
Society, edited by: Easterling, P.E., and J.V. Muir. Cambridge: Cambridge
University Press: pgs. 67-97.
Condos, Theony, (1997). Star Myths of the Greeks and Romans: A Sourcebook. Grand
Rapids, MI: Phanes Press.
Coulton, J.J., (1977). Ancient Greek Architects at Work New York: Cornell
University Press.
Courby, M. F., (1915). "La Terrasse du Temple." Fouilles de Delphes: Topographic
Et Architecture, Tome II. Fontemoing & Cie, (eds). Paris: Ecole Francaise
D'Athenes.
Dinsmoor. Wm., (1928). Architecture of Ancient Greece. New York: Biblo and
Tannen.
Dinsmoor, W.B. (1939). 'Archaeology and Astronomy.' Proceedings of the American
Philosophical Society, Vol. 80. Philadelphia: The American Philosophical Society;
pgs: 95-173.
Dinsmoor, W.B. and Helen Searles, (1945). 'The Date of the Olympia Heraeum.'
American Journal of Archaeology, Vol. XLIX, supplement. New Hampshire: The
Archaeological Institute of America; pgs: 62-80.
Dugas, Charles (1921). "Le Sanctuire D'Alea Athena a Tegee." Bulletine de
Correspondance Hellenique (BCH), vol. 45. Ecole Francaise D'Athenes. Athens:
L'Ecole Francaise d'Athenes, et Paris: Les Editions E. de Boccard. Reprint (1976):
Nendeln/TCiechtenstein: Kraus-Thomspon Organization Limited.
Drachmann, A.G. (1963). The Mechanical Technology of Greek and Roman Antiquity.
Madison: The University of Wisconsin Press.
(1954-1970). 'Hero's Dioptra and Leveling Instrument.' in Singer (1954-1970),
vol. 3: pgs. 609-612.
103
Eder, Birgitta (2001). "Continuity of Bronze Age Cult at Oiympia?" Potnia: Deities
and Religion in the Aegean Bronze Age. Proceedings of the 8^^ Memational
Aegean Conference, Goteborg University, 12-15 April 2000. Austin, Texas:
University of Texas at Austin: 2001: 202-204
Evans, James (1998). The History and Practice of Ancient Astronomy. New York,
Oxford: Oxford University Press.
Fagerstrom, Kare, (1988). Greek Iron Age Architecture: Developments Through
Changing Times. Studies in Mediterranean Archaeology. Vol. LXXXI. Goteborg:
Paul Astroms F6riag.
Fowler, Harold North and Richard Stillwell, (1932). Corinth: Results of Excavations
conducted by The American School of Classical Studies at Athens, Vol. 1.
Cambridge: Harvard University Press.
Ferguson, Michael (1997). GPS: Land Navigation. Boise, Idaho: Glassford
Publication: 5* printing, 1999.
Gardiner, E.H., (1925). Olympia: Its History and Remains. Oxford: Oxford
University Press.
Gebhard, E.R., and Frederick Hemans, (1992). 'University of Chicago Excavations at
Isthmia, 1989: II." Hesperia vol. 61: no. 1: 1-77. American School of Classical
Studies at Athens: 1-77.
(1998). 'University of Chicago Excavations at Isthmia, 1989: II.' Hesperia
vol 67, no. 1. American School of Classical Studies at Athens: 1-63.
Geminus, Isagoge, Chapter VIII. (Thurston, Hugh, Early Astronomy, pgs. Ill, 255).
Gibbs, Sharon L., (1976). Greek and Roman Sundials. New Haven and London:
Yale University Press.
Gould, Joki, (1985). 'On making sense of Greek religion.' Greek Religion and
Society, editors: Easterling, P.E., and J.V. Muir. Cambridge: Cambridge University
Press; pgs: 1-33.
Hahn, R., (2001). Anaximander and the Architects. New York: State University of
New York Press.
Hammond, N.G.L., and J.H. Scullard (eds.) (1970). Oxford Classical Dictionary,
ed. Oxford: Clarendon Press.
104
Heath, Sir Thomas L. (1932). Greek Astronomy. New York: Dover Publications.
Herodotus, Boo'm I, II. Loeb Classical Librar^^ (1920), edited by A.D. Godley.
Cambridge, London: Harvard University Press. Reprint; 1996.
Hesiod, Works and Days. Loeb Library: translated by: Evelyn-White, Hugh G.; edited
by Henderson, Jeffirey and G.P. GooM. Revised. Edition (1936). Cambridge:
Harvard LFniv. Press.
Homer, Odyssey. Translated with an Introduction by Richard Lattimore (1975). New
York: HarperCollins Publishers
Hoskin, Michael, (2001). Tombs, Temples and Their Orientations: A New Perspective
on Mediterranean Prehistory. United Kingdom: Ocarina Books.
Huffman, Carl A. (1993). PMlolaus of Croton: Pythagorean andPresocratic. Great
Britain: Cambridge University Press.
Jaschek, Carlos and Eulalia Perez Sedefto (2001), "The transmission of Graeco-Roman
astronomy," Astronomy, Cosmology and Landscape: Proceedings of the SEAC 98
Meeting, Dublin, Ireland, September 1998. Edited by Clive Ruggles with Frank
Prendergast, and Tom Ray. United Kingdom: Ocarina Books Ltd., pgs 106-111.
Kautmanru William J. Ill, (1994). Universe, 4*^ edition. New York: W.H. Freeman and
Company.
Kirk, G.S., I.E. Raven and M. Schofield (1983). The Presocratic Philosophers, 2"^*
edition Cambridge: Cambridge University Press. Reprint, 1990.
Kyrieleis, H. (1990), "Neue Ausgrabungen in Olympia," Antike Welt 21.3: 177-188.
"Neue Ausgrabungen in Olympia," Proceedings of an International
Symposium on the Olympic Games (1992): 19-24.
— "Zu den Anfangen des Heiligtums von Olympia," Olympische Forschungen.
In XVth International Congress of Classical Archaeology, Amsterdam, July 12-17,
1998: Classical A rchaeology Towards the Third Millennium. Reflections and
Perspectives. Abstracts (1988) 82-83.
Laertius, Diogenes, Lives of Eminent Philosophers. Vol. 1. Loeb Classical Library.
edited by G.P. Goold, (1972). Reprint,1995. Cambridge, London: Harvard
University Press.
105
Lattimore, Richmond, (1961). Introduction to the lUadhj Homer. Chicago and
London: The University of Chicago Press.
Lawrence, A. W. (1996). Greek Architecture, 5*^' edition. Revised by R.A.
TomlinsoB. New Haven and London: Yale University Press.
Letham, L, (2001), GPS Made Easy, 3^" edition. Seattle, Washington: The
Mountaineers Books.
Lockyer, J.N. (1891). "On some points in the early history of astronomy." Nature,
vols. 43 (559-63); 44 (8-11); 44 (107-110); 44 (199-202). London: Macmillan
Journals ltd.
(1894). The Dawn of Astronomy. London,
Mallwitz, Alfred (1972). Olympia imd seine Bauten. Miinchen: Wissenschaftlichen
Biichgesellschaft Darmstadt.
(1988), "Cult and Competition Locations at Olympia," The Archaeology of the
Olympics. The Olympics and Other Festivals in Antiquity. W.J. Raschke (ed.): 79109.
Mazarakis-Ainian, Alexander, (1997). From Rulers' Dwellings to Temples:
Architecture, Religion and Society in Early Iron Age Greece (1100-700 BC).
Studies in Mediterranean Archaeology Vol. CXII. Sweden: Paul Astroms Forlag
Miller, Stephen, (1992). Excavations at Nemea: The Sacred Square, the Xenon, and
the Bath. Berkeley: University of California Press.
Miller, Stephen (ed.) (1990). Nemea: A Guide to the Site and Museum. Berkeley and
Los Angeles: University of California Press.
Morgan, Catherine, (1990). Athletes and Oracles. Cambridge: Cambridge University
Press.
Mylonas, G. (1961). Eleusis and the Eleusinian Mysteries. Pg 33ff.
Nell, Erin (2001). GPS Surveys of Apollo at Corinth, Apollo at Delphi, Poseidon at
Isthmia, Hera at Olympia, Zeus at Olympia, Zeus at Nemea, Athena Alea at Tegea.
Neugebauer, O., (1957). The Exact Sciences in Antiquity. 2"^ ed. New York: Dover
Publications.
106
Noman, Naomi, (1984). "Temple of Athena Alea at Tegea." American Journal of
Archaeology, Vol. 88. No. 1. Archaeological Institute of America.
0stby, Eric (1994). "Recent Excavations in the Sanctuary of Athena Alea at Tegea
(1990-93). Archaeology in the Peloponmse: new Excavations and Research.
Edited by Kenneth A. Sheedy. The Australian Archaeological Institute at Athens.
Oxbow Monograph 48: pgs. 40-64
Pausanias, Guide to Greece. Volume 1: Centra! Greece. Penguin Classical Library.
Betty Radice, editor; Peter Levi, translator. Reprint with revisions (1979). England:
Clays Ltd.
Penrose, F.C. (1893-1901). "On the Orientation of Certain Greek Temples and the
Dates of their Foundation." Proc. Royal Society, LII, LXI, LXV, LXVIII. London:
The Society.
(1899). "On the Orientation of Certain Greek Temples being the Results of
some Observations taken in Greece and Sicily in the month of May, 1898."
Proceedings of the Royal Society of London, vol. 65. Royal Society, editor.
London: The Society.
(1893). 'Mr. F.C. Penrose on the Results of an Examination of the
Orientations of a Number of Greek Temples.' Transactions of the Royal Society of
London, vol. 184. Royal Society, editor. London: The Society.
(1897). 'On the Orientations of certain Greek Temples and the Dates of their
Foundation derived from Astronomical Considerations, being a Supplement too a
Paper on the same subject published in the Transactions of the Royal Society in
1893.' Transactions of the Royal Society of London, vol.190, series A. Royal
Society, editor. London: The Society.
Petsas, Photios (1981). Delphi: Monuments and Museum. Athens: Krene Editions.
Plutarch, Numa, 14,4 (Dinsmoor 100)
Preziosi, Donald and Louise A. Hitchcock, (1999). Aegean Art and Architecture.
Oxford, New York: Oxford University Press.
Rutkowski, Bogdan, (1986). The Cult Places of the Aegean. New Haven and London:
Yale University Press.
Sacs, E. (1917). Die fiinf Platonischen Koper (Berlin).
107
Samuel, Alert E. {1972), Greek and Roman Chronology. Calendars and Years in
Classical Antiquity. Mfechen: C.H. Beck'sche Verlagsbuchhandlung.
Schaefer, Bradley A. (2001). 'New Methods and Techniques for Historical
Astronomy and Archaeoastronomy.' Archaeoastrommy, Vol. XV. Austin, Texas:
University of Texas Press.
Scully, Vincent (1969). The Earth, the Temple, and The Gods. New York, London:
Frederick A, Praeger.
Scranton, Robert L., (1960). 'Greek ArcMtecturai Inscriptiom as Document.' Harvard
Library Bulletin, Vol. XIV, No. 2. Cambridge, MA: Harvard University Library.
Scranton, Robert L., (1969). 'Greek Building.' The Muses at Work, edited by Carl
Roebuck. Cambridge, MA: The MIT Press; pgs 2-35.
Sesti, Giuseppe Maria, (1987). The Glorious Constellations: History and Mythology.
New York: Harry N. Abrams, Inc., Publishers.
Shaw, Ian, and Paul Nicholson, (1995). The Dictionary of Ancient Egypt. London:
British Museum Press.
Suunto Instruments (2001). Clinometer manual for the PM-5/360 PC. Finland.
Supplementum Epigraphicum Graecum, found in: Scranton 1960; pg. 163.
Thales to Euclid, Greek Mathematical Works. Loeb Classical Library (1939).
Translated by Ivor Thomas. Cambridge, London: Harvard University Press.
Reprint: 1998.
Thurston, Hugh, (1922). Early Astronomy. New York: Springer-Verlag. Reprint,
1996.
Toomer, G.J. (1996). 'Ptolemy and his Greek Predecessors.' Astronomy Before the
Telescope, Editor: Christopher Walker. Great Britain: British Museum Press.
Vermeule, Emily, (1964). Greece in the Bronze Age. Chicago and London: The
University of Chicago Press.
Vision S.R.L. (©1997). Ancient Greece: the famous monuments. Athens: The Muses
Publishers.
108
VitruviiK, De Architectura, Books I-V. Loeb Classical Library: translated by Frank
Granger; edited by, G.P. Gould. Cambridge: Harvard University Press, 1931;
reprinted with corrections: 1998.
————, De Architectura, Books VI-X. Loeb Classical Library: edited and translated
by Frank Granger; Cambridge; Harvard University Press. 1934; reprint,1999.
Voyatzis, Mary E. (1990). The Early Sanctuary of Athena Aha at Tegea: and other
Archaic Sanctuaries in Arcadia. Gdteborg, Sweden: Paul AstrCms Forlag.
Wheelwright, Phiiip, ed., (1966). The Presocratics. New York: Macmilian Press.
White, Raymond E. (2001). Accounting for the Change in Rising Azimuth of a
Celestial Object due to an Opaque Mask in the Direction of View. Tucson, Arizona.
White, Raymond E. (2001). Computing the Slope and Zeropoint of a Straight Line
between Two Known Points. Tucson, Arizona.
— (2002). The Length of a Shadow Cast by a Solid Object. Tucson, Arizona.
Wilkinson, Richard H. (2000). The Complete Temples of Ancient Egypt. New York:
Thames and Hudson.
109
APPENDIX A
GPS Reduction Graph: The Temple of Apollo at Corinth
By
Erin Ann Nell
Raymond E. White, Distinguished Professor Emeritus
GPS Observations—Full Sequence,
Teaiple of Apollo, Corinih, Greece. Jmie27,2001. ErinNeli
il Suiuiiiu' su'"v»'\ pomts
.sre 5 ]riUtii.oxit,vaiJ liom ixsiijiteial Uanjjle ('jell's CeUaasifl (. jntci Setiuence surest ix)iuib(#17-24) are directly above temple fffuas (0 meters oulwjBd).
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0.01958192
0.01914124
0.00464124
0.28124859
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0.01443432
0.05650424
0.05619915
0.0559322
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0.05586864
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0.01468856
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0.01241808
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0.00758475
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0,00119492
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7.1672E-07
5.392E-06
1.4094E-05
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1.8696E-06
I.0474E-09
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1.7509E-06
4.5499E-10
3.9002E-06
7.9774E-08
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0.02787394
0.01054061
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0.00055692
0.00023622
0.00020099
-0.0004291
-0.0007342
1.6266E-05
6.5844E-06
2.1185E-06
2.4142E-06
7.0674E-06
1.3141E-05
1.9426E-05
1.4863E-05
1.0746E-07
2.8628E-05
1.0868E-05
1.3431E-05
1.0269E-05
1.0483E-06
7.4534E-07
8.0802E-06
3.873iE-06
2.8628E-05
9.1234E-06
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0.00019706
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Plot-X (1,e) Plot-Y ((j>N)
»
H
NW
iHiiiii
global
46.54
46.46
45.42
44.45
44.21
44.00
43.83
43.95
44.93
45.95
46.22
46.38
46.18
45.01
44.60
44.17
44.36
45.95
46.10
44.52
16.93
16.71
16.38
16.05
16.13
16.49
16.85
17.07
17,41
17.74
17.62
17.28
17.19
16.86
16.72
16.57
16.87
17.33
16.94
16.43
X
Y
If
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45.1625
16.8785
centroid of
virtual walls 45.1967388 16.8814101
AQ= 0.03423882 0.00291006
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6
SW
12
13
16.49
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44
46.38
46,18
14
CellaBack
45.01
16.86
15
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44.6
44.17
16.72
16 57
270.34
101.11
NE
16
E=
6
N - nnn6
17.28
17.19
X
D = den6 ~
725.56
801.4464
793.8342
1936
2151.1044
2132.5924
758.8686
745.712
731.8969
2025.9001
1989.16
1950.9889
4557.3181 12185.7458
Q
Y
30,7592
271.9201 -0.0239368 0.00057297
298.5984 0.00537192 2.8858E-05
295.4961 -0.0207044 0.00042867
284.2596 0.02324885 0.00054051
279.5584 0.01429231 0.00020427
274.5649 0.00172813 2.9864E-06
1704.3975 3.0983E.11 0.00177827
V
variance = 0.00044457
s - ± 0.02108475
s.e.m.y.
= ± 0.00860781
Plot-Y
U
%-error
- aaa6 =
0.319618196
= bbb6 =
2,45073617
K = 0,998306537
±
0.003801726 1.18945867
Plot-X
0.171329159 6.99092627
43
47
16.1943186
17.4727914
y = Ax + B
Central Sequence
18
> 17.5
^
16
43
43,5
44
44,5
45
45,5
46
46.5
47
E. Long. - 22° 52' {"J
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72,2751744
E-SE
S-SE
N = niiSs
D = dn3s 6.0626
A== aa3s = 0.32822551
B-bb3s = 1.46433857
K=
0.99979792
46.46
45.42
44.45
136.33
16.71
16.38
16.05
49.14
776.3466
743,9796
713.4225
2233.7487
2158.5316
2062.9764
1975.8025
6197.3105
U
279.2241
268.3044
257.6025
805.131
V
%
0.00381025 1.16086235
0.17317854
11.8264
Plot-X
Plot-Y
15.9062612
16.8909377
South Line
tan 0 - aaa6 --> 0 ~ tan"^(aaa6) ~> AzimuA == 90° - 0 =
71.8288444
-0.0036959
0.0076586
-0.0039627
4.9738EI12
vaiianc®=
s4±
s.e.m.y. =±
1.366E-05
5.8654E-05
1.5703E-05
8.8017E-05
8.8017E-05
0.00938172
0.00541654
8
W-NW
9
NW
10
N-NW
3
EN = niiBn
D = dn3n 6.0008
A = aa3n = 0.33492201
B--=bb3n = 2.35415511
K = 0.99979672
43.95
44.93
45.95
134.83
X
17.07
17.41
17.74
52.22
Y
750.2265
782.2313
815.153
2347.6108
Q
291.3849
303.1081
314.7076
909.2006
V
1931.6025
2018.7049
2111.4025
6061.7099
U
%
-±
±
0.00389948 1.16429495
0.17528456 7.44575218
Plot-X
43 •
47
Plot-Y
16.7558016
18.0954896
-0.003S775
0.0077f896
-0.0038215
9.5213E-12
varianee =
s«=±
s.e.in.y.|= ±
1.582E-05
6.0824E-05
1.4604E-05
9.1248E-05'
9.1248E-05
0.00955237
0.00551507
North Line
18.5
4
18
5:
17.5
(Yj
i
17
16.S
16
43
43.5
44
44.S
45
45,S
46
46.S
E. Long. -22°52' f"J
tan: i = aaa6 ==>B: == taii"'(aaa6) -> Azmutli - 90° - 0 -
71.4831682^
47
'•
ME/SW Orientation
Seq: 11x275174^
•
North Line:
South Line
71.48316822
71.8623Q567
Average:
71873.57941
APPENDIX B
Computing the Slope and Zeropoint of a Straight Line
By
Raymond E. White, Distinguished Professor Emeritus
Department of Astronomy
University of Arizona
121
Computing the Slope and Zeropoint of a Straight Line
betw^n Two Known Points
Raymond E. White, Ph.D.
1 November 2001
General Discnssion
Suppose that there are two points in the Cartesian plane with known
coordinates: Point A {xa , Va) and Point B {xb , Vb)- The problem is to
compute the slope, m , and zero-point (or "intercept"), z , of the straight line
connecting these two points. Begin with the general expression for a straight
liner
y
=
mx + z .
Therefore, we know that, whatever the values of rn and of z may be,
the following expressions for the two points in the line, A and B, may be
represented by the folowing expressions:
VA = mxA + 2 ,
V B = mxB + z .
We see that we have two expressions in two unknowns, m and z, so there
should be a unique solution for m and z. Subtracting the ys-expression from
the y^-expression algebraically obtain ...
Va - Vb = m { x A - x b ) + Q
Ay
m = -Y— , where Aq = qs — QA , for any variable q .
Ax
The geometric identification of m is; m = tmi&, where $ is the angle
increasing counter-clockwise from the x-axis to the Ine betwen the two
points. The distance, s , between the two points is given by the Pythagorean
Theorem, towit:
— Ax^ + Ay^ ... or ...
s = yAx2 -f Ay^
The calculation for the zeropoint, ^ , goes a little differently ...
- = V a - rnxA
122
ys - mxB
iVA
+ fe) - "1 (x^ +
to
Xb)
(x ^ + s s ) |
...or...
= < y > — m < X > , where
1
< q > = ~ { q .A + q s ) ,for any variable q
'Ay"
Practical Example
Point A (4,10) ; Point B (20.20)
Point
B
A
Aq
<q >
X
20
y .
20
4
10
=
10 _ 5
16
8
0.625
lU
iA
16 10
12 15
tan'
s
m
= 32° DO ^ 19.4
O
•
= 19.20937 units-
yj{l2)^ + (fef =
15 — 7.5 = 7.5 units.
2 = 15
Therefore, the final expression for the line betecn Points A and B
y = 0.625
X
+ 7.5 .
APPENDIX C
Accountingfor the Change in Rising Azimuth of a Celestial Object due to an Opaque
Mask in the Direction of View
By
Raymond E. White, Distinguished Professor Emeritus
Department of Astronomy
University of Arizona
124
Accounting for the Change in Rising Azimuth
of a Celestial Obj^t due to an Opaque Mask
in the Direction of View
Raymond E. White, Ph.D.
30 October 2001
Calculating the Azimuth of a rising (or setting) celestial object with re­
spect to the featureless Astronomical Horizon (simply "Horizon," for short)
is a relatively straight forward process using spherical trigonometry. The socalled "Astronomical Triangle" is compostxi of three sides (the Oteerver's colatitude, (j)' , the object's co-declination, 6' , and zenith distance, Zo = 7r/2),
and three angles {Zo , opposite 6'; opposite 2^ = 7r/2; 7|„ oppceite —^but
is rarely used). Then, applying the cosine law of spherical trigonometry to
the side opposite to, obtain ... [Notation: for any angle, k , k' =
|
— k]
cos Zo = COS (p' COS 6'
4-
sin 4>' sin S' cos to
= sin^sin<5 + cos ^ cos 5 cos
= cos7r/2 = 0
cos to = — tan^tan^
cos (x — £o) = tan
tan 5
Applying the cosine law again to the side opposite
cos 5'
=
cos (f> cos Zo + sin
Zq
...
sin Zo cos Zo
sin <5 = 0 4- (cos (p) (1) (cos Zo)
„
sin 5
cosZo =
7
cos<p
Suppcse, now, that there is an obstruction to the view of the rising object
so that it is not seen rising above the Horizon but, instead, appearing to rise
above the mask. Unl^ the Observer is located at the terrestrial Equator,
where the object's diurnal circle is precisely perpendicular to the Horizon,
the predicted Azimuth of the rising point of the object will be affected by
the angular height, 9 , of the mask at the apparent rising point. The zenith
distance of the apparent rising point is
= 0'. Neither the latitude of the
Observer nor the Declination of the object are affected by the mask; however,
125
the hour angle,
are affected.
^ and the azimuth of the apparent rise point, Zg , definitely
cos
CQStg
= cm 0 = cos (j)' cos 5' + sin
sin 6 — sin 6 sin S
=
cos <f> COS 6
sin S' cos 4
^
tan (p tan S
cos 4> cos S
sin 0
cos% =
;
- + costo or,
cos <p COS 0
sin0
COStg— COS to
=
,
COS <p COS o
For the modified Azimuth, [email protected] ...
COS S'
=
COS 9'
+ sin 4>' sin $' cos
sin 6 — sin 0 sin 6
cos Zn =
cos (j) cos 9
COS
sin 6
_
0 tan 0
COS <l> COS 9
cosZe =
COS Z5— COS Ze cos 9
—
cos Z _ ^
;;p—tan^tan^ or.
q
COS0
tan <t> sin 9
APPENDIX D
The Length of a Shadow Cast by a Solid Object
By
Raymond E. White, Distinguished Professor Emeritus
Department of Astronomy
University of Arizona
The Length of a Shadow Cast by a Solid
Object
R.E. White, Ph.D.
31 January 2002
1
Introduction
Without loss of generality, and because it's easier to draw, consider the "solid
object" to be a gnomon (a straight, vertical, pole, mounted perpendicular
to the groTund). First, consider the special case of the shadow cast by the
Sun at Local Apparent Noon (LAN); then, second, the general situation of
shadows cast at arbitrary times during the day.
2
The Shadow Cast at LAN
At LAN, the Sun is, by definition, directly on the observer's meridian (the
North/South line through the Celestial Poles and the observer's Zenith),
which is not the same thing as being overhead (in the Zenith) which wiU
produce no shadow. Sketches of the geometric situation ha^been provided
in the accompanying two diagrams. In Figure 1, the observational geometry
in the meridian plane has been illustrated; in Figure 2, the geometry of the
gnomon and the cast shadow have been ilustrated.
2.1
The geometry in the meridian plane
The included angle between the Zenith ( Z ) and the Equator Point (J^) is,
by definition the same as the latitude, (f> , of the observer at O. The angle
between
the Sun (in meridian transit) is its declination (5©); the
altitude of the Sun is denoted
. Since the line connecting the Zenith and
Nadir is a pole of the Hoiizon System, the angle between the Astronomical
Horizon and the Zenith is 90°. Therefore, see that ...
[ H q — 8 Q ) + (j}
L
flQ
—
=
2 ~
C
OQ
+ — — 0'
^
H
q
—
50 + ^
where the "prime" notation is used here to denoted a complementary angle,
i.e., (f> (j) = 7r/2 = 90° .
2.2
The geometry on the ground
The gnomon has height Jf, and casts a shadow, at LAN; the angle of the
Sun (the interior angle between the shadow and the top of the gnomon) is,
as above, its altitude, /iq From plane trigonometry, we have ... jp
H
tan(/io) = —
5 =
Notice that when /I q
3
=
7r/4 = 45°
or
H
^—r
tan (/Iq )
H
.
4
, then S = H •, which might be useful.
The Shadow Cast at Arbitrary times of the
Day
... working on it ... and ail of the figures ...
129
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