O.S. Reuter, Skylore of the North, Part 4

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IV. Constellations and cosmology. Ocean navigation

Earth I pray, and heaven above …
and heaven’s might and halls on high.
Anglo-Saxon [23]

At the end of the 10th century Oddi Helgason (see Section II.10) was named Star Oddi, because “he made a practice of observing the stars”. In the Sagas he is not the only person to be so engaged: at almost the same time as Oddi, and also in northern Iceland, lived Einar Eyolfsson (brother of Gudmund the Mighty) who was renowned for his observations and wide knowledge of the constellations. In Sweden the farmer Randulf had a similar reputation, and his sons inherited his knowledge of the stars.

Of all this, nothing remains. With all the more care, then, must we follow up the smallest clue to ancient astronomy, which was doubtless not restricted to those named above. There are more of these clues than one might have dared to hope, and some of them are of such a kind as to give an idea of what has been lost.

1. On the nature of the stars

For as far back as historical sources reach, the Germanic concept of the stars has been different from the Babylonian one. Babylon looked upon the stars as gods, just as Augustine saw them as angels. The north Germanic creation myth, which is of high antiquity and probably springs from the earliest Germanic roots, sets the gods as creative forces above the sky and the star world. From the skull of the primeval giant, whose body became the material universe, the gods built the sky. The free-moving glowing darts hurled out from the hostile southern fire world were placed by them as stars in their present places and paths.

Caesar’s brief remark [24] that the Germans worshipped the sun god and moon god (along with a god of fire) was not taken up by Tacitus, with his closer knowledge of Germany, when describing Germanic religion 150 years later. Nor is there any mention of star worship among the Germanic peoples in the reports of Christian missionaries, even in the informative letters to Boniface from the Anglo-Saxon bishop David of Winchester. Worship is reserved for “Heaven’s might and majesty”, that is, the work of the gods themselves.

The stars are fiery by nature: their light is their own. The Germanic opinion that the stars shine by their own light, which seems self-evident to us now, was also argued by Sisebut, king of the West Goths, in his didactic poem written at Toledo in 614 [25]; but the most important spokesmen for the western Middle Ages did not share his view. The 7th-century Spanish bishop Isidore of Seville, and Rabanus Maurus in Germany in the 9th century, two of the most respected doctors of the church in their times, taught with the elder Pliny that the stars receive their light from the sun. By the 13th century this upside-down doctrine had reached Iceland.

2. The lode star

Introductory note. The hub of the circling sky does not remain close to the same stars, but (as a result of the precession of the earth’s axis around the pole of the ecliptic) traces out a circle in the sky, which does not bring it back to the same star until 26,000 years later. In Neolithic times the pole lay near Alpha Draconis; in the time of Arminius (0 AD/BC) it was already near the star which, around 800 AD, it approached within the moon’s apparent diameter; since 1400 AD it has been in the neighbourhood of our present pole star.

The Germanic term “lode star” denotes a conspicuous star near the hub of the sky, used as a visible direction marker instead of the invisible hub itself. The Middle Ages knew as the “mariners’ star” only the bright star at the end of the Little Bear’s tail, that is, our present north star or pole star, which in 800 AD stood about 7 degrees, or 14 times the moon’s apparent diameter, from the turning-point.

In a medieval Icelandic manuscript, which often blends native ideas with a medieval outlook, two lode stars are given for Iceland: a bright one, most likely our own pole star, and a “not bright” one that traces out only a small circle. Around 800 AD the 26,000-year movement of the turning-point had brought it close to the star 32 Camelopardi Hevelii [26], which although only of 4th of 5th magnitude is easily picked out in the centre of a wide and apparently star-free area. In fact the Chinese at this time used the same star as their Thien Shu (“heaven point”) [27]. Since no star besides 32 Camelopardi, the star in the head of the Giraffe, need be considered for early Germanic times, we may interpret the “not bright” second lode star of the Icelandic account as the Vikings’ lode star, to which ocean navigation at that time owed its extraordinary achievements. (See the star-map.)

The above-mentioned (see Section II.4) observation of the lode star in a foreign land, but made by lying on the back in native Icelandic style, was intended to find the height of the pole so as to compare it with that at home. In 1500, according to an account by Olaus Magnus of Uppsala, the northern country people were observing the pole (polus arcticus), as distinct from the lode star, in “a wonderful manner”. On the terms nail star and navel star, that is, axle star, see below. The distinction between the true pole and the lode star is apparent throughout the religious myths, and also in the mythology of the sky.

3. The mythology of the sky

The northward gaze up to the hub of the sky, as the apparent turning-point of the universe, called forth, in Germanic sacred and astronomical myths, poetic and religious images of great power and grandeur. We cite only a few:

1. The world pillar, Irminsul. The ancient Saxons worshipped a wooden pillar of no small size set in the open air and “representing the supporting post of the universe”. The word “representing” in this account by Rudolf of Fulda [28] frees the Saxons from the reproach of idolatry and establishes the macrocosmic meaning of the concept. This pillar was not itself the support of the universe, but only its symbol. The name Irminsul thus originally belonged to the basic concept, not its copy the visible world pillar. The national sanctuary destroyed by Charlemagne in 722 AD was not the only one of its kind. The original was indestructible.

2. In the northern sacred myths of the Edda the pillar is replaced by, among other things, the symbol of the world tree. It is described as a world ash, but evergreen above the heavenly sea (Urd’s well), a leafy tree rising through all the worlds, even the roof of Valhalla, the starry hall of the sky. Eagle and hawk, that is sun and moon, nest in its branches. It may tremble, but will remain standing, in the coming holocaust, and being itself immortal, it protects the life of the new and perfect creation.

3. At the same time the world pillar is seen as a sword, on whose point the universe turns. The gods have placed it in the foaming jaws of the primeval wolf (Fenrir) so that it rises up from the earth to the sky. This is called “gagging the wolf” who, chained down, “evermore gazes on the throne of the gods”. The world axis is a symbol of divine order.

4. In connection with the sky’s rotation, which is seen as the rightward turning upper millstone of the handmill, the world pillar appears as the upright axis of the lower millstone, or of the heavenly mill; agreeing with the ancient Romans, the Hellenes and the Indians in an image of Indo-European origin.

5. In another very old image the circling universe is likened to a spindle constantly turning rightwards in the hands of the divine mother. The yearly rotation of the spindle, like the mill, is known in many Germanic customs. The distaff belonging to the vertical spindle staff is depicted in the northern sky as “Frigg’s distaff” (see the next subsection).

These and many other images, like that of the world mountain, the “earth’s hazel wand”, etc., do not refer to a visible star, but the invisible “centre of the moon’s hall”, from which the Edda poem says the Norns cast their ropes of fate; not the lode star, but the true turning-point of the sky.

Stars and constellations

The word “star”, whose root is common to all Indo-European languages, appears to have meant originally “the scattered, strewn” (cf. Latin sternere = strew).

The traditional star names do not refer only to single stars; the Germanic peoples, like all others of the world, brought the profusion of stars, scattered seemingly at random and yet moving in regular paths, into patterns of constellations.

1. The Lode Star (32 Camelopardis) common Germanic; in Anglo-Saxon Tir (= Old Norse Tyr), name of the old sky god (Old Saxon Saxnote).

2. The Lady’s Wain (or Wagon) (Ursa Minor), old Icelandic; probably connected with the sky mother, as the great wagon was connected with Woden; east Swedish, North Wagon.

3. Woden’s Wain (Ursa Major), Old Dutch; in Old High German, Anglo-Saxon and Old Norse, Charles’s (i.e. Woden’s) Wain.

4. Day Star (Arcturus), Old Norse; for telling the time.

5. Orendel’s (Aurvandil’s) Toe (probably Corona Borealis); Old Norse. According to the Edda, placed in the sky by Thor himself as a memorial to his divine power.

6. South Star (Vega), Old Icelandic; probably used in navigation.

7. Frigg’s Distaff (Orion’s belt), old in Sweden, Denmark and Norway. In Old High German: the Rake, the Three Reapers, the Plough. In Norway, mostly the Three Fishers. Seasonal and nightly time marker.

8. The [Little] Wolf’s Jaws (Hyades), Old Icelandic. Directly on the sun’s apparent path (ecliptic); see the star-map.

9. The [Great] Wolf’s Jaws (Andromeda, Milky Way, surrounding branching point, that is, the great semicircle of stars through Pegasus to Cygnus), old Icelandic. The opening of the jaws is turned towards the pole of the sky. See item (15) below.

10. Battle of the Æsir (Auriga with Capella), old Icelandic. On the Milky Way.

11. The Torch Waver (Procyon), old Icelandic; near the Milky Way, the precursor of:

12. Loki’s Brand (Sirius), Icelandic; at the foot of the Milky Way.

13. Seven Stars (Pleiades); common Germanic, Cluck Hen and Evening Hen with seven (also twelve) chicks; perhaps old European. Herd of Boars (old Saxon, Anglo-Saxon), along with Hen perhaps the oldest Pagan description of the year marker (see Section III under “star year”).

14. Thiazi’s Eyes (probably Castor and Pollux); according to the Edda placed in the sky by Thor as “the greatest memorial to his deeds”.

15. Iring’s Way (Milky Way), Old Saxon, Anglo-Saxon, Old High German. Its two streams of saliva falling from the Wolf’s Jaws are Wan and Wil; the “evil Wan” as Hell’s stream and road of the dead, Old High German. In the Edda, Bifrost = shaking bridge, that is, road of the dead, and Fenrir = Wan’s Wolf, wolf of the river Wan. The Milky Way is at the same time the “god’s bridge” leading from earth to highest Heaven, and thence to Hell.

5. Distribution and meaning of the constellations

Apart from a few star names like South Star (Vega), nearly all the stars named are found in the winter half of the sky, probably because of the brightness of summer nights in the North. At the winter solstice, that is, at the astronomical new year of Oddi Helgason and the mark day of the German solilunar year (Mothers’ Night), nearly all the constellations are simultaneously visible in an area of the sky occupying only 1/8 of the whole. At midnight on the shortest day (see star-map), Loki’s Brand at that time stands exactly at its culmination in the southern end of the Milky Way, scarcely 10 degrees, that is, a handbreadth, above the horizon. The Great Wolf’s Jaws and Orwandil’s Toe stand opposite each other as spring and autumn constellations.

There can be no question of chance in the distribution of the constellations. Although handed down from widely separated sources, they are for the most part connected with religious myths. The Edda itself teaches that the two ancient names “Thiazi’s Eyes” and “Orwandil’s Toe” were not read off from the sky but placed within it to keep the great creative acts of the gods alive in peoples’ memories.

The Little Wolf’s Jaws stood at that time immediately in the track of the sun and moon, and circled round with them; the Edda tells of wolves descended from the primeval wolf Fenrir, constantly following the sun and moon. The Great Wolf’s Jaws open their mighty gape immediately opposite the divine seat where the north star Tir, in Anglo-Saxon tradition, “never flinches”. Concerning this shackled wolf, the magnificent song of Eirek (c. 950) makes Odin say: “Evermore the wolf, the grey one, gazes on the throne of the gods”.

When autumn is over, in the middle of the winter solstice night, Loki’s Brand, preceded by his torch bearer, steps onto the shining bridge of the gods, which at that time leads from the southern horizon to he north seat of the sky and then descends again towards Niflhel. But already the battle of the Æsir has begun on the bridge. It is the Edda’s great prophecy of the final battle between gods and giants, between creation and destruction, whose outcome is to free Baldur and bring creation to perfection.

This setting of religious myth among the stars, which we find consistently among the south, west and north Germanic peoples, contrasts with the purely descriptive and unmythologized picture of the sky among (say) the Arabs or Chinese. Its closest analogue is the Greek ornamentation of the sky with legendary star figures, but even in its ruined form it far superior to the latter both in spiritual greatness and in poetic and descriptive beauty and splendour.

6. Cosmology

We must distinguish between the sky and its movements seen as a subject for research and practical use, and the heavenly vault seen as a theme of joy and faith; between scientific and mythic cosmology. The latter, the world of thoughts and images, belongs to the contemplative and creative spirit; the former, the image and concept of the world, to the intellect.

Mythic cosmology

According to the younger Edda, in which Snorri Sturluson tries to teach the bardic arts by accurate renderings of old creation poems, the earth, made from the giant’s body, stands firmly in the centre of cosmic space (Ginnungagap); circular in shape, it rises like a mountain (Midgard), sloping down to the north. Around Midgard flows the deep ocean.

Over the Earth, or Irmin’s ground, the sky is arched like a round skullcap, placed on the four dwarf corners – north, south, east and west. The sky and stars, like the earth, are originally made from the giant; the ordering, the work of creation, is of divine origin.

In the middle of the universe, that is the pole of the sky, is Asgard, citadel of the gods; at its centre is placed Odin’s high seat, from which he oversees all worlds and fates. It is the same “centre of the moon’s hall” from which the Norns spin the fate of the world, and even of the gods.

From the depths of the earth, rising above Irmin’s ground, the world tree grows through all the worlds, breaking through the gods’ starry hall with its golden foliage. Eagle and hawk, probably sun and moon, live in its branches.

It is Ida’s whirling meadow, washed around by the stars’ circling tracks, yet immortal, in whose centre Asgard is set; the centre of the moon’s hall, and the reason why prayers are addressed to the north.

Scientific cosmology

The fragmentary nature of the tradition does not prevent us from cautiously sketching in a few lines of the scientific cosmology.

We recognize the pre-Copernican world view: the earth is fixed; it is the sky that moves. To the wheel cross and the swastika of the rock carvings there correspond in historical times the hub and sky wheel for turning point and rotation. The axis points to the north. The “sky wheel” is the wide track travelled by the sun and moon, north and south of the celestial equator; in the Menglöð [29] myth the latter is depicted as the “wall of the sacred enclosure”, which the young sun crosses in spring.

In Christian times the Arctic circle went by a name coming directly from Paganism, the “wheel-nail-circle” (hjól-gadds-hringr). The nail fastens the wheel to its axle. The old Icelandic (probably age-old) term “world nail” likewise refers to the north star (originally 32 Camelopardis), and in the form “nail star” still extends as far as the Chukchi people of the Bering Strait. The terms “nail” and “hub” are not current in the south, while the Babylonian and Greek “navel of the earth” is lacking in the north.

The fixed stars are fastened to the “upper sky”; beneath, in the lower sky, move the “loose stars” or planets, in regular paths despite their striking looped movements. The stars’ motion, the whirling meadow, is supported by the hub; “post and stars” go together in old Norse idiom. This may be compared with the ropes of the Norns, fixed to the centre of the moon’s hall.

In ancient India the stars were thought to be fastened to the pole star by “wind ropes”. The rotation of the heavenly vault results from the “star wind”. For the rotation of the swastika see Section I.2.

The sun’s motion, as far as we can tell from the surviving theory of Star Oddi, is seen as regular; the winter and summer halves of the motion are considered to be the same length. Instead of our familiar concept of equal days and nights (equinox), we find in spring and autumn the fixing of “the midpoint between the solstices”. This concept is derived from the sun’s motion, not, as with the equinox, the brightness of the sky. In winter the solstice invariably takes place at the north point of the lowest path (middle of the longest night), and in summer at the south point of the highest path (middle of the longest day). The universe has a concentric motion.

The “sky wheel” is divided into 8 or 16 sectors when referring to the sun, and 27 or 54 sectors when referring to the moon.

The daily path of the sun, as well as its yearly path and the monthly path of the moon, lies in a broad zone of the sky which can be divided by the sun of moon, as one wishes. The Babylonian and Greek 12-fold division of the sun’s yearly path (every night the rising or setting sun conceals from the southern observer the stars in 1/12 of the sky), along with the signs of the zodiac, cannot be observed in the Germanic region owing to the longer twilight and the bright summer nights. However, the 8-fold and 16-fold division of the sun’s daily path were observed and were transferred to the sky wheel.

The moon’s circuit in 27 nights divides the sky wheel into 27 star groups. In old Norse terminology the 27 nights are to be counted as 54 half days.

A division into 8, 16, and 27 can already be seen in the ritual disk of the Bronze Age sky chariot from Trundholm in Denmark, while the numerous wheel crosses on the Swedish rock carvings show similar divisions. In historic times this division appears in an astronomical fragment of the Edda, describing the celestial Valhalla with 540 and gates, each with 800 warriors, 43,200 in all, who are to be sent out against the oncoming destruction. Since multiplication by 10 and 100 is attested elsewhere as a Germanic artistic device, the basic astronomical numbers of the sky circle are 54 and 8; they divide up the tracks of the sun and moon through the common multiple 432,000, which is found with the same meaning in ancient India, and explains at last the Aryan-derived numerology in the so-called “Revelation to St. John”. The symbolic hall Valhalla is built on astronomical foundations.

A similar division is lacking in Babylon, which divided the moon’s path into 24 sectors. These first became known in Iceland through the works of Bede in the 13th century, when the 27-fold division of the moon’s true circuit had long been superseded in the calendar there by a count of 28 nights (four seven-day weeks).

The northward dip of the earth’s vault, mentioned in the mythic cosmology (north = downwards), explains the rising of the turning-point (increase in the pole’s height) as one travels north, and its lower position in the south. However, we hear nothing about a spherical shape for the earth. Nevertheless, the following observations will have brought the open-minded northern mariner at least to the threshold of understanding the true shape of the earth, with which the West Goth Sisebut was familiar in 614 AD.

The shift in sunrise and sunset directions with latitude, used to find the ship’s position; likewise the height of the sun; the regular alteration in the height of the pole and of the stars as a whole (Vega); the need to measure the height of the stars, etc., not against the visible horizon but against eye level, and even to make this a legal requirement; observation of the circumpolar (midnight) sun and also, at longer intervals, the circumpolar moon; the speeding up and slowing down in the direction of sunrise and twilight relative to the horizon (certainly not by Oddi alone); the important and often recorded distinction, used by navigators for recognizing land and setting course (heiti), between full sight and half sight of a mountain, which decreased with increasing distance and grew as one went nearer.

The causes of solar and lunar eclipses were correctly stated by Sisebut, probably on a Gothic-Greek basis. In the Germanic north, information is lacking. The stars shine by their own light.

As reference planes for fixing astronomical directions and altitudes there existed:

  1. the clear edge of the sky (sea horizon) with the zenith vertically above it; the horizontal plane (apparent horizon);
  2. the (theoretical) plane of the “sky wheel” (track of the sun and moon), with the world pillar as axis.

These correspond to the Greek and modern systems of the true horizon and celestial equator.

Of the Greek angular grid system there is no trace. In its place stand natural units: the sun’s diameter and radius, the moon’s daily travel (span), the distance between zenith and pole, etc. However, the stability of these natural units makes them very suitable for recording natural laws, as we see from the surviving number sequences.

8. Ocean navigation

Thus it resounded, when smote together
The long keel and Kolga’s sisters (the waves),
As if crag and surf were cleft asunder.
Higher still hoisted Helgi the sail,
The Vikings flinched not before the surge,
Although angrily Aegir’s daughter
Tried to overturn the oarsman’s steed.

The practice of making ocean voyages in the North Atlantic, across 40 degrees of latitude from the North Cape and Spitzbergen down to Morocco and to Vinland on the east coast of North America, has heretofore been considered a mystery because it was thought that Germanic methods were confined to the flight of birds, magic, and a knowledge of ocean currents. In view of the supposed lack of astronomical traditions, reputable researchers have explained away the old accounts of Vinland and Greenland as fables. (See Fig. 10 in the June issue.)

But the use of astronomical phenomena is already apparent in the narrative of the Icelander Bjarni Herjolfsson, who, driven before a storm, became in 968 AD the first European to sight the coast of America. “As soon as they saw the sun again, they were able to mark out the quarters of the sky.” But how did Bjarni make his way from this unknown coast to his destination, namely Greenland? There exist sailing directions from a time before the compass was known, according to which the south Greenland mountain range Hvarf (Cape Farewell) lies “due west” of Bergen in Norway, and indeed both lie on the 60-degree parallel. How did the seamen work out this position and bearing?

Around 1150 AD the compass (lode stone) became known in the Germanic North, where, however, because of the extreme differences in magnetic variation (from 10 degrees in Norway to 45 degrees in Iceland and 80 degrees in Baffin Bay, and then back to 10 degrees in Vinland (as opposed to plus or minus 5 degrees in Iceland) it was useless for keeping track of one’s direction. For this reason Columbus still sailed by the North Star.

As an aid to Germanic navigation only the sky need be considered. The art is already referred to in an Anglo-Saxon runic poem from the 7th or 8th century: by day the seamen travel by the sun, at night by the north star. And it was easy to set sail by the latter; with the sun, it was more difficult to keep the prow facing (say) due west. We get some idea of the methods from Oddi’s number sequences for the annual movement of the last twilight along the horizon, at his latitude of observation in northern Iceland. A prerequisite for this kind of navigation is to count off the days of the year, which as we have seen was done in the Norwegian calendar around 550 AD. As shown by the determination of the sun’s altitude in Baffin Bay, sailors knew such number sequences by heart. Counting off the days, so that the seasonal change in the sun’s position could be allowed for, meant that one could find the angle between daybreak (an arc of light of defined size) and due north, and thus find due north itself; in other words, astronomical directions could in practice be worked out from the number sequence. If the sailor in a starry night could easily keep his course by the lode star, so as the stars faded, his course could be kept by the direction of twilight; and then the sunrise position (as laid down in a similar number sequence) continued the process. At midday the sun’s altitude provided, via another number sequence, a new means of orientation; towards evening the direction of sunset and finally the disappearance of twilight handed the ship back to safe steering at night by means of the lode star. The altitudes and rising positions of certain stars (such as “Frigg’s Distaff”, due east) could help the ship’s journey in a similar way, in so far as they had been found by nightly observations on shore. Even the moon’s position, whose constant changes had been observed, could help to make these techniques more reliable.

It is clear that sailors waited for favourable winds and weather, not only for the obvious reason, but so that they could also see the stars. Because the stars were invisible in the bright summer nights, spring and autumn were preferred in higher latitudes; the evidence shows that long journeys were undertaken not in summer but in spring. Naddodd, one of the first Norwegians to see Iceland, travelled back from there to the Faroes in autumn; but it must have been late autumn, for it is reported that on his voyage back he saw snow falling on the island, and we may infer that he had waited for a favourable northwest wind, which brought snow to the island but not to him. A Norwegian law, designed to keep people on the land for the summer farmwork, states explicitly that anyone can travel as they choose in spring, autumn, and winter. Nevertheless, it was the custom in winter to lay up the largest trading ships at least.

It is no accident that we possess fragments of astronomical position-finding from the extremes of this vast region, that is, from Vinland and north Greenland; these are basically the determination of latitude, by various techniques, which however can all be proved to be of independent Germanic origin. The result of comparing these distant observations with astronomical phenomena at home was reported, and is the secret of fixing the ship’s position and course. How the necessary observations were carried out in the homeland, Star Oddi has already shown us.

With the heavens as their ally – on which they could rely absolutely – exultant daring, tireless energy, scorn of hardship and death-defying willpower were able to bring about an achievement that was not only unique in its own time, but has no parallel in the cultures of the South.

Summary and prospects

To evaluate what remains of Germanic astronomy, archaeological science will call upon, after the astronomer, the ethnologist, the Germanist, the mythologist, and the student of religious and cultural history. If the astronomical argument is convincing (as we believe it to be) then a road into the spiritual history of the Germanic races is opened, and a useful technique has been acquired for investigating religious and spiritual history.

We must discover whether any so-called “primitive peoples” have arrived at an eight-year rule, such as we find among the Germanic races, probably as early as the beginning of our era; whether the recorded number sequences (along with those hinted at by such astronomical fragments as the Baffin Bay observation) have analogs among other early cultures, for instance the ancient Romans. If the use of the solar year or bound lunar year (see introduction) is denied to the Germanic races, on the grounds that they did not have the astronomical and mathematical knowledge required, then either the proofs given here for both forms of calendar, or else the prejudice prevailing till now, must be overthrown.

Yet to this early period of the Germanic races have been denied not only mathematical concepts, but even the possibility of conceiving large numbers. Against that opinion I have already noted (in the journal Mannus, 1939) a particular feature of an old Nordic number system, which immediatley leads to the formation of large numbers, and I have also proved that such numbers were actually used. From the difficulties that Bede, the great Anglo-Saxon doctor of the church, had with simple arithmetic, it has been decided that his race as a whole were incapable of mathematical reasoning – a fallacious generalization from the particular. To create the Uppsala rule, and to develop the various forms of calendar, needed not only simple arithmetic, but also the calculation of a mean value from various kinds of observation. The sum of a number sequence, which for every week between the solstices alters the increase or decrease of the sun’s height at midday by half its apparent diameter, is converted by the observer Oddi into a number sequence that tries to represent the slowing down and speeding up of the sun’s motion, and does so to a good approximation. That is a proof of mathematical insight, admittedly of the kind normally found only in a few talented people. Yet the whole Greek achievement too reached world importance only in isolated instances. The same arithmetical insight that we find in the above-mentioned number sequences, and clear geometrical thinking, are also shown in Oddi’s formula for the shifting of the solstice in the Julian leap year cycle, a question that could only arise in the meeting between Pagan and Christian-Julian calendars, that is, about the year 1000 AD with the angrily disputed but voluntary subjection of Pagan Iceland to the Norwegian Church. We shall refrain from any final judgement. Perhaps there existed higher knowledge than we can establish today; but until further witnesses are called we must rest content with what has been proved so far.

In this short summary we have, of course, barely touched upon such important topics as techniques for finding position on the unknown coasts of America and northern Greenland, the old Faroese instrument for finding latitude and longitude, the sun board and the shadow plank, the water clock in the eykt division, the sunstone, the fine didactic poem of the West Gothic king Sisebut dating from 614 AD, the explanation through Nordic astronomy of the Greek Hyperborean question, and much else. The extent of the destruction amid the mass of significant details is apparent from the sources and texts, the calculations and techniques, set down in my book Germanische Himmelskunde.

Beyond these traditions, our gaze recedes into the depths of prehistory. The Germanic orientation of the grave, the house, the moot hill, developed independently on an ancient European foundation older than Babylon, at a time when the oldest Germanic concept of the directions also developed from observations of the sun’s circular path. Thanks to new professional surveys by the astronomers J. Hopmann and Rolf Müller, the more important instances of prehistoric orientation, such as the stone circles at Odry in West Prussia, discovered and explained by Paul Stephan as early as 1914, the sun window in the Externstein rock tower, with which the name of Wilhelm Teudt is associated, similarly the orientation of Stonehenge towards the solstice, can be taken as proved and their significance as probably established. The orientation theories about Hof Gierke have on the other hand been disproved by the brilliant excavations of Professor H. Reinerth.1

Comparision of these prehistoric stone monuments with written traditions shows a rich and progressive development of astronomy on Germanic soil in the face of severe climatic difficulties, and at times, despite the destruction of historical records, masterly observation and thinking for such early times. The complete independence of Germanic astronomy from southern and eastern antiquity is proved.

1 See Paul Stephan, Mannus 1914, 213 f. – W. Teudt, Germanische Heiligtümer, 1926 f. – H. Röhrig, Heilige Linien durch Ostfriesland, Aurich 1930. – J. Andree, “Die Grabungen an den Externsteinen im J. 1934”, Nachr. f. Deutsche Vorzeit 1935, H. 1. – J. Hopmannn, “Die Ortung an den Externsteinen”, Mannus 1935, 143 ff. “Methodisches zur vorgeschichtlichen Sternkunde I, II”, Mannus 1934, 261 ff; 1935, 373 ff. – H. Reinerth, Excavation report at the Prehistoric Conference in Bremen, 1935. – Rolf Müller, Himmelskundliche Ortung auf nordisch-germanischem Boden, Curt Kabitzsch Leipzig 1936. – For mathematical understanding and for the introduction of the subject into school lessons, see Jos. Hogrebe, Himmelskunde bei den Germanen, Anwendungen und Aufgaben nebst Lösungen, Verlag Otto Salle Frankfurt a. M. 1936: Mathematisch-Naturwissenschaftlich-Technische Bücherei, Band 30.