Prof. Dr. S.V. Zagraevsky. About the scientific basis of “Azimuth method” (the method of determination of dates and dedications of ancient Russian temples by the azimuth of their altars) / Sergei Zagraevski, Zagrajewski, Zagraewski, Zagraewsky. On the basis of statistical material and historical-architectural analysis Professor S. V. Zagraevsky shows the lack of research significance of the topic related to the determination of dates, dedications and other attributes of ancient temples by the azimuth (orientation to cardinal points) of their altars.

Prof. Dr. S.V. Zagraevsky

About the scientific basis of “Azimuth method”

(the method of determination of dates and dedications of ancient Russian temples

by the azimuth of their altars)

Published in Russian: Заграевский С.В. О научной обоснованности «азимутального метода» (метода определения дат и посвящений древнерусских храмов по азимуту их алтарей). В кн.: Архитектор. Город. Время. Материалы Ежегодной международной научно-практической конференции (Великий Новгород – Санкт-Петербург). Объединенный выпуск XIII и XIV конференций. СПб, 2011. С. 69–74.

Annotation

On the basis of statistical material and historical-architectural analysis Professor S. V. Zagraevsky shows the lack of research significance of the topic related to the determination of dates, dedications and other attributes of ancient temples by the azimuth (orientation to cardinal points) of their altars.

Attention!

The following text was translated from the Russian original by the computer program

and has not yet been edited.

So it can be used only for general introduction.

RUSSIAN VERSION

The purpose of this study - review and assessment of the scientific value of the themes, connected with the determination of the dates and dedications of ancient temples in azimuth¹ (orientation to the horizon) of their altars.

What the altars of Orthodox churches must be oriented to the East, was universal and mandatory rule in every period of the formation of the ancient Russian architecture from the times of Byzantium². Before was invented and became widespread compass direction to the East was seen by an overwhelming majority of the people as the direction of the sunrise.

And the sun because of the tilt of the earth rises exactly in the East only twice a year, at the spring and autumn equinox, when the azimuth of sunrise - 90 degrees. In General, the evolution of azimuth sunrise can be described as follows: the vernal equinox (March 21), the sun rises exactly in the East, then as the length of the days it rises closer and closer to the North (and thus moves across the sky through the South more and more the way), then reaches its northernmost point in the summer solstice (June 22), then, as the shortening of the day it goes back farther and farther to the South, again goes East

The azimuth of the sun rising in the days of the summer and winter solstice - the extreme South and extreme North - different for different latitudes areas (see Table. 1)³.

Table. 1

The azimuth of the sun rising in the days of the summer and winter solstice

(LS and CS - summer and winter solstice)

City	Latitude	Azimuth in the LS, the first beam, deg.	Azimuth in the LS, full drive, deg.	Azimuth in the AP, the first beam, deg.	Azimuth in the AP, full drive, deg.
Kiev	50,4	50,1	50,9	127,3	128,1
Moscow	55,8	43,2	44,3	133,3	134,3
Novgorod	58,5	38,3	39,6	137,5	138,7
Petersburg	59,9	35,1	36,6	140,2	141,5
Arkhangelsk	64,5	17,4	20,6	153,3	155,7

So, in Moscow (latitude 55,8º) azimuth sunrise at the summer solstice is about 44º (exact figures are given in Table. 1 and depend on the first beam of the sun to navigate or full disk), the winter is about 134º. In Novgorod (latitude 58,5), respectively 39º and 138º. Consequently, in Moscow twice a year the sun rises at one of the points of the horizon between 44º and 134º, in Novgorod - between 39º and 138º, etc.

The azimuths of the sunrise on the first day of each month during the year are given in Table. 2.

Table. 2

The azimuths of the sunrise on the first day of each month during the year

Date	The azimuth of the sun, grad.
1 January	113
1 February	121
March 1	102
April 1	82
1 may	63
June 1	48
1 July	45
August 1	57
1 September	75
1 October	95
1 November	116
1 December	130

In the middle-second half of the twentieth century some scientists have suggested that the orientation of the temple altars for a particular azimuth can give information on what day the built a Church (at least with accuracy up to two times a year, as the sun during the year rises in a particular azimuth two times), and what you can do some conclusions related to the history of the Church, primarily to his dedication. Such studies have been conducted in the West⁴ in the USSR this subject was developed first B.A. Rybakov⁵then R.M. Garyaev⁶ and P.A. Rappoport⁷.

The main idea of these researchers can be described as: because they assumed that the builders usually focused on sunrise on the day of inception of the temple, and that the day of Foundation of the Cathedral, in their opinion, usually coincided with the corresponding Church holiday, they thought possible with sufficient accuracy to determine the date of Foundation of the Cathedral and its primary dedication in azimuth its altars. B.A. Rybakov and gave the name to this method - "azimuth"⁸.

In fairness, we note that by p. A. Rappoport has made various reservations and is not considered "factorization method" universal panacea⁹. But since these reservations were accompanied by a General perception that certain results this method can give, many modern scholars, including S.A. Gavrilov¹⁰, D.A. Petrov¹¹, A.V. Podosinov¹², O.M. Rapov¹³found this method grounded in their works tried to apply it in the scientific field. And in some cases the azimuth of the sanctuary was given and sacred meaning¹⁴.

We begin our analysis of "azimuth method" with a review of its mathematical parts. The calculation of the azimuth of the sun rising on any date for any latitude is expressed by a simple formula¹⁵:

Cos A = Sin In / Cos With,

where A is the azimuth of the points of sunrise on that date In the declination of the sun to date on the latitude of the observation place, With the latitude of the observation place.

Therefore,

A = ArcCos (Sin / Cos ).

This formula does not take into account the refraction of the atmosphere and implies that the angular dimensions of the lights are negligible, which gives a margin of error of plus or minus 1 degree. There is a more accurate formula that takes into account these indicators:

Cos A = (Sin In + 0.015 x Sin ) / Cos C.

But in the future we will see that in reality error of calculations according to the formula so great that any mathematical and astronomical inaccuracies (refraction of the atmosphere, the angular size of the sun, rounding etc) negligible, and for simplicity, we can use the first formula.

Accordingly, if we know the azimuth of sunrise, you can get the value of the declination of the sun in the day of such azimuth according to the following formula:

Sin = Cos A x Cos S.

Therefore,

B = ArcSin (Cos A x Cos ).

But the declination of the sun and the date of its sunrise at each latitude we can get from the astronomical tables of conjugations¹⁶. To compute trigonometric functions suitable scientific calculator¹⁷.

Calculating the date for the ancient temples, do not forget to take into account the old and new style. The difference between the Julian and Gregorian calendars are shown in Table. 3.

Table. 3

The difference between Gregorian and Julian calendars

Period, century	The difference, days	The beginning and the end of the period
X and XI	6	6 March 900-6 March 1100
XII and XIII	7	7 March 1100-7 March 1300
XIV	8	March 8 1300-8 March 1400
XV	9	9 March 1400-9 March 1500
The XVI and XVII	10	10 March 1500-10 March 1700
XVIII	11	11 March 1700-11 March 1800
XIX	12	12 March 1800-12 March 1900
XX and XXI	13	March 13 1900-13 March 2100

So, the calculation date on the azimuth of the sun is a relatively simple task. But her decision may give researchers of ancient Russian architecture?

In order to answer this question, first of all, we present data on the orientation of the altars 127 ancient temples (Table. 4).

The author collected the data during the 2000-ies in several regions of Russia, tentatively identifying the azimuth of the altars of the compass, and with the advent of the computer program "Google Earth" has the opportunity to adjust the orientation of a number of temples and down it. Unlike compass, this program takes into account the magnetic declination, and the results more accurate. However, the author, given the inaccuracy of a breakdown plans temples, rounding out the results obtained up to 5th, as we will soon see that this error when working with azimuthal method" is very small.

Data were collected randomly (especially the temples is not selected), which provides a representative sample.

Table. 4

Data on the orientation of the altars of ancient temples

Town, temple	Azimuth altars, deg.
Borovsk, the Cathedral Pafnutiev monastery	65
Borovsk, the refectory and the bell tower Pafnutiev monastery	80
Vladimir assumption Cathedral	60
Vladimir, St. Demetrius Cathedral	60
Vladimir assumption Cathedral of the Knyaginin monastery	100
Vladimir, the Church of deposition of the robe in Golden Gate	70
Vladimir, the Church of our Saviour	50
Vladimir, the Church of St. George in the court Dolgoruky	60
Vologda, St. Sophia Cathedral	35
Vologda, Sretenskaya Church	45
Vologda, St Nicholas Church in the Bishop's Sloboda	45
Moscow, the Kremlin, Uspensky Cathedral	70
Moscow, Kremlin, Cathedral of the Annunciation	70
Moscow, the Kremlin, the bell tower of Ivan the Great	70
Moscow, the Kremlin, the Cathedral of the Archangel	85
Moscow, Cathedral of the Intercession on the Moat	60
Moscow, the Church of Nikita for Yauza	80
Moscow, Cathedral of the Andronikov monastery	105
Moscow, the Church Trifon Naprudnom	55
Moscow, the Church of Gregory of Neocaesarea	70
Moscow, the Church of the Trinity in Vorobyev	85
Moscow, the Church of the Conception of Anne in the Corner	100
Moscow, the Church of our Saviour in Tushino	100
Moscow, the Church of St. Nicholas in Wads	95
Moscow, the Church of Ivan the Warrior	90
Moscow, the Church Antipov at carriage yard	40
Moscow, the Church of St. Nicholas in the Old Vagankovo	50
Moscow, the Church of the Sign on Sheremetevo the yard	40
Moscow, the Resurrection Church in Uspensky Vrazhek	40
Moscow, St. Volodymyr's Cathedral of the Sretensky monastery	85
Moscow, the Church of Archangel Michael in Troparevo	120
Moscow, the Church of the exaltation of the Altufyevo	110
Moscow, the Church of the Trinity in the Leaves	90
Moscow, "Menshikov tower	45
Moscow, the Church of Sofia by the Cannon court	55
Moscow, the Church of St. George in Archer	55
Moscow, the Church of St. Nicholas in Blindekuh	75
Moscow, the Church of St. Vladimir in Old discussing	55
Moscow, the Church of St. Nicholas in Podkopaeva	100
Moscow, the Church of the Three hierarchs in the neighbourhood of Kulishki	110
Moscow, the Church of the Nativity of the virgin in Old Simon	85
Moscow, the Church of the Trinity in Khoroshevo	120
Moscow, the Church of St. Nicholas in Khamovniki	45
Moscow, the Church of the Trinity in nikitniki	65
Moscow, the Church of the Nativity of the virgin in Putinki	70
Moscow, the Church of deposition of the robe in Donskaya street	85
Moscow, the Church of Peter and Paul at the Yauza gates	70
Moscow, the Church of the Icon of the Mother of God of the Sign in Sacharine	30
Moscow, the New Cathedral of the Donskoy monastery	75
Moscow, the Old Cathedral of the Donskoy monastery	70
Moscow, Cathedral of the Fathers of the Seven Ecumenical councils of the Danilov monastery	95
Moscow, Cathedral of the Smolensk icon of the Mother of God of the Novodevichy convent	120
Moscow, the Novodevichy monastery bell tower	120
Moscow, the Novodevichy monastery refectory	120
Moscow, Cathedral of the Nativity monastery	95
Moscow, refectory Church of John Chrysostom Nativity monastery	95
Moscow, the Church of the ascension in Kolomenskoye	105
Moscow, the Church of St. John the Baptist in Djakova	90
Moscow, Cathedral High-Petrovsky monastery	60
Moscow, Bogolyubsky Church Highly-Petrovsky monastery	65
Moscow, refectory Church of St. Sergius of Radonezh High-Petrovsky monastery	60
Moscow, the Church Pachomius over the Southern gate of High-Petrovsky monastery	45
Moscow region, the Church of St. Nicholas in Pushkin	90
Moscow region, Trinity Church in Chashnikovo	50
Moscow region, the Church of the Nativity of the virgin in Pojarkova	35
Moscow region, Znamenskaya Church in Dubrovica	90
Moscow region, Church of the Transfiguration in the Island	70
Moscow region, Church of the Transfiguration in Large Vyazemy	50
Moscow region, the Church of the Nativity in Conversations	55
Moscow region, Arkhangelsk Church in Arkhangelsk	110
Moscow region, the Church of Michael the Archangel Cathedral in Khotkovo	105
Moscow region, the Church of the Vladimir icon of the Mother of God in Kurkina	90
Moscow region, the temple complex in the New Jerusalem	85
Moscow region, the Trinity-Sergius Lavra, Troitsky Cathedral with Nikon's chapel	60
Moscow region, the Trinity-Sergius Lavra, the Cathedral of the assumption	85
Moscow region, the Trinity-Sergius Lavra, the Refectory Church	75
Moscow region, Sergiev Posad, Pyatnitskaya Church on Podol	65
Moscow region, Sergiev Posad, Vvedenskaya Church on Podol	65
Moscow region, Zvenigorod, the assumption Cathedral on the Gorodok	125
Moscow region, Zvenigorod, the virgin Nativity Cathedral Savino-Storozhevsky monastery	100
Moscow region, Serpukhov, the Cathedral of the Vysotsk monastery	75
Moscow region, Serpukhov, the Bishop's Cathedral of the monastery	95
Moscow region, Serpukhov, Vladychna monastery Refectory	90
Moscow region, Kolomna, Uspensky Cathedral	90
Moscow region, Kolomna, the Church of the Resurrection	85
Moscow region, Kolomna, the Church of St. Nicholas	90
Moscow region, Kolomna, Church of Nikola Posadsky	110
Moscow region, Kolomna, the Church of John the Baptist in the Settlement	65
Moscow region, Kolomna, the Cathedral of the Brusensky monastery	95
Moscow region, Kolomna, Old Cathedral, monastery Golutvina	85
Moscow region, Kolomna, the Church of St. Sergius of Radonezh of the Old monastery Golutvina	85
Kazan Annunciation Cathedral	80
Kazan, the Church of Paraskeva Pyatnitsa	80
Kazan, the exaltation of the cross Cathedral	85
Kazan, the Church of the Epiphany	50
Kazan, the Church of St. Varvara	100
Kyiv, St. Sophia Cathedral	50
Kiev, Uspensky Cathedral of Kievo-Pecherskaya Lavra	65
Kiev, St. Andrew's Church	50
Novgorod, St. Sophia Cathedral	110
Novgorod, the Church of Peter and Paul in the tanners	85
Novgorod, the Church of the Trinity spirit monastery	110
Novgorod, the Church of Boris and Gleb in the Carpenters	85
Novgorod, the Church of St. Simeon the God-receiver	60
Nizhny Novgorod, the Church of the assumption	60
Nizhny Novgorod, the Church of John the Baptist	90
Nizhny Novgorod, joy of all who sorrow Church	125
Pskov, the Cathedral of the Mirozhsky monastery	80
Pskov, Troitsky Cathedral	80
Pskov, the Church of the assumption of the Ferry	90
Pskov, the Cathedral Snetogorsky monastery	75
Pskov, the Church of the miraculous image with Toad Levity	80
Pskov, the Church of Elijah Wet	60
Pskov, the Church of Varlaam of Khutyn on Zvanite	45
Pskov, the Church of Epiphany with Zapskovye	70
The Smolensk Cathedral of the assumption	45
Smolensk, Peter and Paul Church	85
Solotcha, the Cathedral Solotchinskoe monastery	60
Solotcha, Church of St. Spirit Solotchinskoe monastery	60
Solotcha, Kazan Church	100
Suzdal, the virgin Nativity Cathedral	50
Suzdal, the Church of the assumption in the Kremlin	50
Suzdal, Paraskeva Church for the Gostiny Dvor	105
Suzdal, the Cathedral evfimiev Saviour monastery	55
Suzdal, the Dormition refectory evfimiev Saviour monastery	55
Suzdal, the Cathedral of the intercession monastery	85
The Yaroslavl Church of Elijah the Prophet	50
The Yaroslavl Church of Michael the Archangel	60
Yaroslavl, Cathedral of Sudarium-Transfiguration monastery	80
Yaroslavl, the Refectory of the Spaso-Preobrazhensky monastery	95
Yaroslavl, the Epiphany Church	90
Yaroslavl, the Church of Dmitry Solunsky	75
Yaroslavl, the Church of the presentation of the	60
Yaroslavl, the Church of the Nativity of Christ	50
Yaroslavl, the Church of St. Nicholas Chopped	55
Yaroslavl, the Church of St. Nicholas Wet	85
Yaroslavl, the Church of the Annunciation	85

We see that the orientation of the altars of ancient temples is located in a very wide range - from 30 to 120. At 122 127 churches, are presented in Table. 4, azimuth altars keeps within the limits of a direction on the sun rising above the horizon at any given time of the year (see Table. 1)although there are exceptions¹⁸as Saint Sophia Cathedral in Vologda (azimuth altars 35º), the Church of the Nativity of the virgin in Pojarkova, Moscow region (35º), the Moscow Church of the Mother of God of the Sign in Sacharine (30), Antipov at carriage yard (40'c), the Resurrection, in Uspensky Vrazhek (40'c), Signs on Sheremetevo yard (40'c)¹⁹.

The conclusion from this we can do the following: as a rule, old Russian builders oriented altars of churches in the direction of the horizon where the sun rises.

But this is the positive part of our research ends and begins negative, as any other conclusions about the link bearing the sanctuary with their dedication, the date of the Foundation or more or less precise orientation to the sun rising in a given day is impossible.

We illustrate this with examples.

Exact azimuths successive Assumption Cathedral in the Moscow Kremlin: the 1326-1327 period - 82,2; Cathedral Myshkin and 1472-1474 years - 76,8; the Cathedral, Aristotle Fioravanti 1475-1479 years - 72,5th²⁰.

As we can see, these churches are oriented not parallel, i.e. their builders each time took a separate decision on the azimuth of the altar. Maybe they focused on the azimuth of the sunrise on the day of inception of the Cathedral?

But we know the date of inception of all these temples (new style, in brackets old style): 1326-1327 period - 13 (4) of August, the Cathedral Myshkin and Krivtsov - may 9 (30 April), the Cathedral Fioravanti - 21 (12) June²¹. These days the azimuth of the sun, respectively, was: August 13 - 64º, may 9 - 59º, 21 June - 51º. No connection with the orientation of the altars of any of the churches is not seen.

The azimuth of the sun rising on the feast of the assumption (August 28, new style) - 73º. It's fairly close to the orientation of the altar of the Cathedral Fioravanti. But if we assume that the architect at the inception of the Church in June somehow was able to calculate the azimuth of the sun rising in the end of August and focused on him, then it is unclear why this was not done by the builders of previous councils.

And since almost parallel to the Cathedral Fioravanti oriented nearby Cathedral of the Annunciation, which by that time was already almost a century²² it becomes clear that Aristotle was just built his temple in a single ensemble. Orientation as the Annunciation Cathedral is not connected with the feast of the Annunciation (April 7, new style, azimuth sunrise 87 º).

And if we look at the other churches of the assumption of approximately at the latitude of Moscow, we can see that the azimuth of the altar of assumption Cathedral in Vladimir is about 60 degrees, the assumption Cathedral of Vladimir Knyaginin monastery is about the same assumption Church in Suzdal Kremlin - about 50'c, the Dormition refectory Church in the Spaso-evfimiev monastery - 55'c, the assumption Cathedral in Smolensk - 45º, the assumption Cathedral of the Trinity-Sergius Lavra - 85º, the Dormition Cathedral in Kolomna - 90 degrees, the assumption Cathedral on the Gorodok in Zvenigorod - 125º, the Dormition Church in Nizhny Novgorod - 60 degrees. No system is seen.

P.A. Rappoport, exactly determine the true azimuth of the altar of assumption Cathedral in Vladimir - 62º, assumed that the temple, judging by its azimuth, could be laid on 21 April or August 9, old style. Assuming that the location of the building on a high hill above the flood plain lowland gives shift azimuth to the North for about 8-9°, he calculated that the sunrise coincides with the chronicle date of Foundation of the Cathedral - on P.A. the Rappoport, 8 may²³.

We don't know how made his calculations by p. A. Rappoport and in its conclusions crept so annoying inaccuracies, but in fact, the assumption Cathedral in Vladimir was laid not on 8 may and 8 April²⁴ (new style - 15 April)and the azimuth of the altar 62º match or may 7, or 5 August new style. And if we assume that a rise above the Klyazma really gives such a significant shift azimuth North - 8-9 degrees (which is also doubtful), the azimuth of the altar 53º match on 2 June or July 10, according to the new style.

As we can see, no link given dates and azimuths here too.

Similar situation takes place with temples dedicated to the Nativity of the virgin (celebrated on September 21 by new calendar). The azimuth of the sun rising in the day - almost 90 degrees (autumnal equinox), the altars of the Suzdal Nativity Cathedral of the virgin oriented approximately 50 degrees, Cathedral of the Nativity monastery is at 95 degrees, the Nativity Cathedral of the Savvino-Storozhevsky monastery - 100º, Church of the Nativity of the virgin in Old Simon - at 85 degrees, in Putinki - at 70 degrees, in Pojarkova - 35 degrees.

And in the feast of the Intercession (October 13 new style) the azimuth of sunrise - 103 degrees, the altars of the Cathedral of the Intercession on the Moat oriented approximately 60 degrees, Suzdal Cathedral of Holy protection monastery - 85 degrees.

UD Krasilnikov²⁵ made accurate measurements of azimuths altars 57 churches of Ivanovo region (the results are given in Table. 5).

Table. 5

Data on the azimuths of the altars of churches of Ivanovo region, collected UD Krasilnikov

Temple	Azimuth altars, deg.
Church of great Martyr Varvara in Novo-Chalitzah	122
The Church of the presentation of the virgin in the Temple in Rotnicka	69
The Church of exaltation of the cross in Ploskova	80
The Church of the Resurrection in Semilova	75
The Church of the resurrection of Christ on the jakovlevsky Pogost	57
The Church of St. George in the St George-in-Uvodi	70
The Church of the Icon of the Mother of God of Vladimir in Khrapunovo	115
The Church of the Icon of the Mother of God of Vladimir in Fiandino	76
The Church of the Icon of the Mother of God Joy of All who sorrow in Sotnitsa	83
The Church of the Icon of the Mother of God Joy of All who sorrow on Dmitrovka, Ivanovo	75
The Church of the Icon of the Mother of God of the Sign in Linevo	48
The Church of the Icon of the Mother of God of Kazan in Linevo	65
The Church of the Icon of the Mother of God of Kazan in Rotnicka	65
The Church of the Icon of the Mother of God of Kazan in Sadikova	86
The Church of the Icon of the Mother of God of Kazan in Khomutovo	86
The Church of the Icon of the Mother of God of the burning Bush in Borodino	113
The Church of the Icon of the Mother of God of Smolensk in Rumyantsevo	85
The Church of the Icon of the Mother of God of Smolensk in Semenovo	77
The Church of the Icon of the Mother of God of Smolensk on Mitrofanievskoe Pogost	82
The Church of Elijah the Prophet in Vorobyev, Ivanovo	88
The Church of St. John the theologian in Paneevo	65
The Church of St. John the theologian in Stepacheva	95
The Church of John the Baptist in Maslovo	132
The Church of Archangel Michael the Archangel (Island)	70
The Church of Archangel Michael in afanasovo	104
The Church of Archangel Michael in Borodino	112
The Church of Archangel Michael in Pronino	116
The Church of Archangel Michael in Cachtice	70
The Church of St. Nicholas in Linevo (nazarievo)	70
The Church of St. Nicholas the Wonderworker in Mytishchi	115
The Church of St. Nicholas in Nikolskoye	96
The Church of St. Nicholas the Wonderworker in Novo-Chalitzah	125
The Church of St. Nicholas in Petrovo-Gorodische	66
The Church of St. Nicholas the Wonderworker in Cachtice	70
The Church of St. Nicholas in Fiandino	95
The Peter and Paul Church at the cemetery in Balino, Ivanovo	92
The Church of the Intercession of the Holy virgin in Bryuhovo	123
The Church of the Intercession of the Holy virgin in Bulgakova	74
The Church of the Intercession of the Holy virgin in Zlatoust	78
The Church of the Intercession of the Holy virgin in Kochneva	88
The Church of the Intercession of the Holy virgin in Linevo (nazarievo)	82
The Church of the Intercession of the Holy virgin in the Small Davydovskaya	112
The Church of the Intercession of the Holy virgin on the Peter and Paul Pogost	76
The Church of the Intercession of the most Holy Theotokos at the monastery of Ivanovo Svyato-Uspensky monastery	74
The Church of the Transfiguration in Khomutovo	86
The Church of the Nativity of the blessed virgin Mary in Podolia	113
The Church of the Nativity in Komsomolsk	88
The Church of the Nativity in Linevo	67
The Church of St. Sergius of Radonezh at the metochion of the Nikolo-shartunski monastery in Ivanovo	87
Cathedral Church of the most Holy Theotokos in Berezniki	101
Church of the Savior all-merciful in Klementieva	86
The Church of the Vernicle in Novoselki	112
The Church of life-giving Trinity in the Bogatyryovo	115
The Church of life-giving Trinity in Smerdova	104
The Church of life-giving Trinity in the Monks	30
The Church of the beheading of John the Baptist in Kiberkino	112
Church of the assumption of the blessed virgin Mary in Sotnitsa	77

Of these churches to Intercession Church dedicated in Brjuhove (azimuth 123 degrees), Bulgakov (74 degrees), Zlatoust (78 degrees), the Kochnev (88 degrees), Lezhneva (82 degrees), Small Davydov (112 degrees), the Peter and Paul parish Church (76 degrees) and the Ivanovo monastery of the Holy assumption monastery (74 degrees). The system here is also a no-no.

On the whole Table. 5 we see that in the Ivanovo region is not even a tendency to focus on the sun in the April-may, the General trend - East of plus or minus 30 degrees. Almost one third considered the churches (20 of 57) is the azimuth 95 degrees and more, i.e. in accordance with azimuthal method" they would be laid from October to mid-March, which is highly unlikely. And since most of the temples are considered in the villages, the town planning situation in the orientation of their altars, too, could not influence.

From the statistics of other Russian regions, collected by the author (see Tab. 4), it follows that the azimuth of 95 degrees is about a quarter of a random sample of ancient churches (from 32 to 127). Extrapolating these data to Russia as a whole, we receive many hundreds of ancient temples. Of course, the Foundation and (or) beginning of construction of such a large number of Church buildings could not be made in late autumn, in winter or early spring.

Thus, the statistics do not confirm that the ancient builders in any way connected dedication of the temple, the date of its inception and azimuth of its altars.

There are many other reasons why it is impossible to link the azimuth of the temple altars from the date of its inception, initiation or place of occurrence over the horizon of the first sun rays.

The second reason (if the first reason to believe the statistics). We have no information of ancient sources that the builders in any way associated date, dedication and azimuth.

For the third. It is not proved that the builders were catching the first rays of the sun and it positioned the temple. And if, for example, the day of Foundation of the Cathedral was a cloud? And if to the East from the construction site was located the forest, any building, wall, or at least a high fence? Statistics show only that the builders knew which side the sun rises, and more accurately not targeted.

Reason four. Plans ancient churches were divided so inaccurate that the measurement of azimuth for different walls often gives an error of a few degrees. And the error of plus or minus 1 degree gives serious scatter date sunrise: spring and autumn are the two or three days, and in the summer - up to 10 days.

Reason five. Even the difference in azimuth at the time of occurrence of the first rays of the sun and at the time of the full lifting of light over the horizon gives variation: to Kiev, Moscow and Novgorod - about 1 degree, for Arkhangelsk - about three. And these degrees provide a mistake back in a few days, or even weeks (see above).

The reason for sixth. P.A. Rappoport noted that the location of the temple on a hill azimuth shifted to the North few degrees, and all spring dates should be considered later than the normal horizon, and all the dates fall, contrary to earlier. Under reduced the location of the temple or Suzanna the horizon picture is reversed²⁶. Hence, the measurement error in such places as Kolomna, Zvenigorod, the center of Vladimir and Kiev, is even higher.

The reason for seventh. Of great importance for the orientation of the temples had urban development (wrote about it and R.M. Garyaev²⁷and P.A. Rappoport²⁸), but to define, where the old Russian builders were guided by it, and where not focused, it can be very difficult, because the streets are frequently changed direction or completely disappeared. And, for example, in Kargopol temples, standing along October Avenue, focused almost the same, but not to the East and South-East (i.e. not lined Avenue)²⁹.

The reason for eighth. In many cases, the builders of stone temples guided by previous wooden, and in this case, any conclusions at all impossible to determine in what cases oriented, and in which not.

The reason ninth: the same applies to the numerous cases of orientation of the neighboring churches (as in many Moscow monasteries - Donskoy, Novodevichiy, the Danilov, Novospasskoye, and others), while in many cases neighboring temples were not focused (the most striking example is the construction of New Aleviz the Archangel Cathedral in the Moscow Kremlin).

The reason tenth. If questions more or less precise orientation of the altar on the East or any other azimuth at all worried construction, in the XVIII-XIX centuries, when everywhere there appeared an opportunity to use the compass, temples would be targeted very precisely - as, for example, the azimuth of the altar of the Temple of Christ the Savior is not 90 degrees, and 125º.

The reason for the eleventh. Even in the absence of the compass there are no problems precise directions to the East: it is enough to drive in the earth's pole, in any Sunny day to note the direction of the shortest shadow (North), and then to postpone this direction at right angles to the East. This confirms that the issues more or less accurate orientation altars to the East of the builders didn't care.

The reason for the twelfth. Do not mix layout plan of the temple (when we determined the azimuth of the altar) and its founding, usually understood by historians as a solemn divine service "at the base". These actions are not identical and not simultaneously.

There is a tradition of laying the temples, cities and other buildings on the "zero cycle". This is the modern "Chin on the basis of Church": "...the Foundation of the Church is made the following way: if the Church is stone, dig ditches prepared the stones and lime, and one rectangular stone depicts or cut out the cross. Under the cross to prepare a place for attachment of the Holy relics and relies following code... the Foundation of the temple can be done without the provisions of the relics of the Holy and mortgage labels, but the presence of rectangular stone necessarily. ³⁰. In antiquity the solemn divine service on the base of the temple" was done primarily on the Foundation ditches or insertion of foundations on the ground level, as in the Moscow Uspenie Cathedral 1475-1479 years.

But the digging of Foundation ditches, and especially the elimination of the basement on the ground level, is a long process that begins only after the plan of the temple marked. Consequently, between markup and laying could not take at least several weeks.

Many times there have been cases, when between the Foundation and the beginning of construction took place many years (for example, the stone walls of Novgorod were laid in 1302, and construction - with the re-founding - began only in 1331).

Apparently, even more frequent (even mass) was to conduct religious services "on the basis of Church" at a time when the building was already partially built. So, Novgorod's Church of the Annunciation in Arkaah was laid on 21 may and ended on August 25, the Church of the Annunciation on Machine laid on 21 may and ended on 25 August 1179 year, the Moscow Church of St. Nicholas the Hospitable was laid on June 21 and built 9 weeks, Church of the Savior in Staraya Russa laid on 21 may and ended on 31 July.

The Foundation of the temple was made most often in may-June³¹, despite the fact that construction is unlikely to begin later than March-April (to have time to finish it before the fall). And this shift of the date of inception is quite justified: muddy spring the soil was not always possible carrying out of the solemn divine service, when bishops and priests, clothed in ceremonial clothes, they were accompanied by the clergy, take a procession around the construction site.

Probably (although statistically not proven and documented)that the inception of the possibility of trying to coincide with the celebration of the saints, which were dedicated to temples. But in these cases, the time lag between the actual start of construction (respectively, determine the azimuth of the altar) and the service "on the basis of Church" could be even greater. However, P.A. Rappoport rightly argued that much more with the day of the patron of the Church coincided not its inception, and sanctification³².

It is necessary to take into account the fact that the inception of stone temples are usually made bishops - very busy people, and their participation in divine services could be delayed for a few weeks, or even months. Participation in the founding of the temple of the king, princes and boyars could also lead to multiple transfer ceremony. At the same builders, contractors related to the contract, should have to work regardless of the date of solemn worship.

From all the above reasons, it follows that no connection between the azimuth of the altar of ancient temples, on the one hand, and their dates of inception or the beginning of construction and dedication of their thrones, on the other hand, is not seen. No construction practice nor the Church rules did not provide for more or less accurate orientation at sunrise on a given day, and the azimuth of the altars was just about to withstand the Eastern direction. ³³).

Thus, "factorization method" cannot be considered scientifically valid, and all the practical results obtained by researchers with it, do not correspond to reality either due to random coincidences.

Topic specific dates and dedications temples in azimuth their altars should assume closed.

NOTES

1. In surveying the azimuth is the angle between the direction to the North (in the southern hemisphere - South) and direction on any remote object. Rotates clockwise and is measured in degrees from 0 to 360.

2. Unlike Byzantine tradition in Western European architecture orientation of the sanctuary to the East is not so universal and compulsory. For example, the Cathedral of St. Peter in Rome facing the altar in the West, and in Worms Cathedral two altars in the East and the West, and architectural expressed altar apse faces West.

3. Table azimuth of the sun rising in the days of the summer and winter solstice composed UD Krasilnikov and presented at the forum web sitewww.sobory.ru".

4. Cave With.J.P. The orientation of churches. - The Antiquaries Journ. 1950. Vol. 30. P. 49; Hawkins J., J. White. The answer to the mystery of Stonehenge. M., 1984. With. 214-220; Firnis M. und Ladenbauer-Orel H. Studien zur Orientierung mittelalterlicher Kirchen. - ] Der Österreichischen Arbeitsgemeinschaft fur Ur- und Frühgeschichte. 1978.

5. In particular, B.A. Rybakov wrote: "Historians of architecture, publishing plans of medieval Russian churches usually do not indicate their orientation. This is particularly unfortunate in cases where the published excavation plans nameless residues. If there was a precise indication of the azimuth of the longitudinal axis of the Church of the East-West, the definition of patron of the temple would be facilitated. This method was developed empirically to me preserved medieval churches of Chernigiv, whose name we know, and tested on a number of other objects.

As it follows from the above quotation, B.A. Fishermen claim to authorship of this development, but PS Klein convincingly demonstrated the existence of earlier Western counterparts (Klein PS Resurrection Perun. SPb., 2004. C. 71).

6. R.M. Garyaev believed that the builders of ancient temples to direct them to external objects, which could be adjacent churches, the river, the topography, street and road network. But in most cases a factor, according to the researcher, it was the position of the sun (Garyaev P.M. To the question about the orientation of Russian churches. In Proc.: XIA, 1978. Vol. 155. C. 42).

7. P.A. Rappoport, after a series of calculations of azimuths temples, wrote that the mapping of written sources and these calculations gives the basis for some General conclusions about what day of the Foundation of the temple usually fell in the spring or the first half of the summer, but often fall; that the day of bookmarks for the most part did not coincide with the day of the patron of this Church, though this, apparently, is sometimes sought; that occasionally, in order to combine these events, bookmark tolerated even in winter time (Rappoport P.A. Orientation of ancient churches. In Proc.: XIA. 1974. Vol. 139. C. 43; Rappoport P.A.

As we will see in this study, these findings it is just really were made on the basis of calculations of azimuths, and the experience and intuition of the scientist.

It should be noted that, according to YOU T.G. Shevchenko and Bogomazova (Shevchenko YU, Bogomazova this YEAR the Oldest surviving Christian Church of Russia. Scientific electronic library "Rusarh", 2007), in the development of "azimuth method" by p. A. Rappoport was based on earlier studies G.Y. Petrash, artist of the Chernihiv historical Museum, which was a temple of some kind of hours of sunshine (Petrash G.Y. Sundial Saviour Cathedral (3 books and 19 fotol.). Funds NAISU. SC-1032/DF-801. 1971; Petrash G.Y.

No reference to the works G.Y. Petrash by p. A. Rappoport has not done.

8. Fishermen B.A. Paganism of ancient Russia. M., 1987. C. 267.

9. So, P.A. Rappoport wrote: "With what degree of accuracy, you can define a name date? To measure the orientation of the longitudinal axis of the Church with the precision more than 1-2° difficult, because it usually prevents some uncertainty splitting themselves ancient monuments. Axis deviation of 2 degrees results in a difference of about three days, and for the summer months - even up to 10 days. In addition, the calculations are made for the geometric horizon, while the roughness of the relief often make real, visible horizon somewhat narrowed or advanced.

10. S.A. Gavrilov ABOUT the beginning of construction of Church of the ascension in Kolomenskoye (hypothesis). Scientific electronic library "Rusarh", 2009.

11. Petrov D. A. Targeting churches in Novgorod and its surroundings. In the book: Medieval architecture and monumental art. SPb, 1999. C. 101-105 .

12. Podosinov A.V. TO the question about the orientation of ancient churches. In the book: Church archeology. Materials of the First all-Russian conference. The Pskov. 20-24 November 1995. Part 2. Christianity and Russian culture. - Archaeological investigations. Vol. 26. SPb., 1995.

13. Rapov O.M. Official christening of Prince Vladimir Svyatoslavich and its citizens. In the book: "The Russian Church in the IX-the first third of the XII century the Adoption of Christianity". M., 1988.

14. For example, on the basis of data on the azimuth of the temple altars studies related to the alleged ideas of architects aimed at passage of sunlight on the frescoes of the Church in a sacred manner (roznyatovskii V.M. Astronomical information in the methodology of system research daylight Mirozhsky Cathedral. In the book: Novgorod and Novgorod region. History and archaeology of Novgorod. Vol. 19. Novgorod, 1995).

That ancient builders allegedly oriented altars of churches on the first beam of the sun, and the sun fell on the altar in the day that Holy, which temple dedicated, see, for example, the Internet sites "http://h.ua/story/16430/", "http://www.mag-i-a.ru/library/symbol/symbol_424.html", "http://kazan.eparhia.ru/conference/secondconf/abstracts2/" etc.

Parallels and temples of Ancient Egypt (the website "http://fortification.ru/library/savarenskaya/101.html".

And article V. Orlov, "the Inheritance of the blind" there are such words: "once the name of Raisa Dugashev Garyaev will be inscribed in the Pantheon of great scientists, along with the name of Champollion. Or maybe even higher, because opening Garyaev unlike bigger. If Champollion just read Egyptian hieroglyphs, Garyaev broke the code inherent in the architecture of Russian churches" (Internet site http://www.history-ryazan.ru/node/7967?page=0%2C4).

15. The author would like to thank UD Krasilnikov for introducing these mathematical formulas on the forum web sitewww.sobory.ru".

16. For example, for Moscow (latitude 55,75 º), such a table is on the web-site "http://hea.iki.rssi.ru/~nik/ak/sun.htm".

17. Online inverse trigonometric functions can be calculated on the website "http://www.planetcalc.ru/326/".

18. The author expresses his gratitude to the participants of the forum web sitewww.sobory.ru", assisted in the compilation of these exceptions.

19. From the temples of the New time, the azimuths of the altars which is even less fall within the range azimuth sunrise at any given time of the year, it is necessary to note the Cathedral of the Nativity of Christ in Riga (315º), the Church of the beheading of John the Baptist in Riga (350º), the Moscow Church of the Resurrection in Sokolniki (150º), the Cathedral of St. Nicholas Chernoostrovsky monastery in Maloyaroslavets (175º) etc.

20. Exact azimuths see: V.I. Fedorov assumption Cathedral: the study and conservation of the monument. In the book: Assumption Cathedral of the Moscow Kremlin. Materials and research. M., 1985. C. 57.

Clarification of some of the cathedrals in V.I. Fedorov's actually going on, see: Zagraevsky SV Architecture of North-Eastern Russia the end of the XIII-the first third of the XIV century. M., 2003. C. 41.

21. Detailed analysis and reconciliation of these dates, see: Kloss BM, Nazarov E Chronicles of XV century on the construction of the Moscow Cathedral of the assumption. In the book: The history and restoration of monuments of the Moscow Kremlin. The state museums of the Moscow Kremlin. Vol. VI. M., 1989. C. 20-42.

22. On the Dating of the Annunciation Cathedral, see: Zagraevsky SV Decree. back With. 22.

23. Rappoport P.A. Construction output... S. 111.

24. PSRL 1:348.

25. Presented at the forum website "www.sobory.ru".

26. Rappoport P.A. Construction output... S. 136.

27. Garyaev P.M. To the question about the orientation of Russian churches. In Proc.: XIA, 1978. Vol. 155. C. 42.

28. Rappoport P.A. Construction output... S. 113.

29. Reported by Igor Demin forum website "www.sobory.ru". At fair opinion of Sergey Popov, expressed at the same forum, that the churches are not focused along the Avenue, because the prospect was built much later. Fire 1765 in Kargopol was destroyed almost three quarters of the city. After the fire, according to the decree of Empress Catherine II, the city received regular planning, preserved until today, and in no way associated with the orientation of the temples.

30. Information gleaned on the website "www.liturgy.ru".

31. For more information, see: Rappoport P.A. Construction output... S. 110-113.

32. Ibid. C. 113.

33. Cm. note. 19.

Moscow, 2010.

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