O.S. Reuter, Skylore of the North, Part 2

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II. Observation and measurement

Gazing at the sky, bedecking it with constellations, worshipping it, still fall short of astronomy; this first shows itself in the observation and measurement of celestial phenomena, whether some material benefit (for example, finding times of directions) is to be achieved, or whether this observation and measurement are ultimately motivated by some inkling of natural law. With this last object in view, observation and measurement set out on the road towards science.

1. The midnight sun at the North Cape

(See Fig. 4)

In the 9th century the Norwegian Ottar sailed round the North Cape, in order to find out how far the land extended to the north. He penetrated into the White Sea as far as the mouth of the Dvina (Archangel). In the detailed account of his journey that has come down to us [5], the stretches of coast are so accurately described in terms of the astronomical directions that these, the compass being unknown, must have been found by observation. Now in those latitudes the stars are invisible throughout the summer on account of the permanent brightness of the sky; the sun itself circles constantly above the horizon. The only way of finding direction would have been by the highest or lowest elevation of the sun above the south or north point. Ottar’s direction finding was based on observing the sun at the lowest point in its path. The gap between the lower edge of the sun and the visible horizon at midnight on the summer solstice at the North Cape (71° 11′ N) amounts to about 4.5° (that is half a handbreath with the arm outstretched); by means of this observation Ottar determined the middle of the northern sector, that is the true north. Since the coastal explorer is reported to have waited some time at the head of the North Cape for a “westerly or somewhat northerly wind” (probably in the shelter of Horn Bay) he will have repeated his observation several times to check the result.

2. The sun’s height at midday and midnight in north Greenland

On 25th July 1267 (Old Style) some fishermen of south Greenland were driven north by a storm from their home port of Gardar. At the end of their journey they established:

  1. the sun at midday stood so low, that a man lying athwart the ship could just gauge the sun above the ship’s side;
  2. the sun at midnight stood “as high as in their home port in the northwest (on the longest day)”.

(Regarding 1): The practice of using the ship’s side or a raised portion of the rail (sun board) to cast a shadow, or in dull light as a backsight, is often attested in the old North. With a more southerly position of the ship the shadow was cast nearer, and with a more northerly position further. Notches in the seat of the boat could mark the shadow position for the home port and for every other known position of the ship, thus allowing the distance north or south to be estimated.

(Regarding 2): The height of the midnight sun in a distant place was compared with a known elevation in the home port Gardar (61° N). In Gardar the sun on the longest day stood 3° 41′ high in the northwest; if at the more distant spot on 25th July (Old Style) the sun stood 3° 41′ high at midnight (that is when true north) then, making the necessary calculation, we find for the ship’s position a latitude of 74° 34′ north, a point on the coast of Baffin Bay, north of Upernavik.

Somewhat further south (73° N), northwest of Upernavik on the island of Kingigtorssuaq, a rune stone was found in 1824, dated on linguistic grounds to about 1300. The journey into those high latitudes was thus not unique. The astronomical method of finding position, garbled though it is in this account, rests on comparisons of the sun’s height. The height of the midnight sun could not be compared with the same phenomenon at the home port Gardar, since there (61° N) the midnight sun just passes below the horizon. The citing of the “sun’s height in the northwest at Gardar” is thus an expedient, and is a splendid testimony to the astronomical experience and schooling of the men concerned.

3. The “shaft height” of the sun

(See Fig. 5)

The time marker “eykt point” (WSW) was permanently fixed and recognizable for every farmstead by a landmark on the horizon. On journeys, however, the astronomical directions were not so easy to find, at least not in the summer months, when the brightness of the nights prevented the stars from being seen. From preChristian times there comes a popular method for announcing an agreed time to stop work, or any other time, by using the height of the sun instead of its direction. For instance, the law defined the “shaft height of the sun”; this occurred in the afternoon when

“the lower edge of the sun appears to rest on the point of a spear set up nine feet from the observer”.

The law expressly provides that this shall be the observer’s own spear, and that he shall have set up the spear so that he can still reach comfortably with a “shaft hand” (that is the thumb held out from the fist) up to the socket of the iron spear head; in other words, that in all circumstances the same sighting angle shall be ensured.

The spear’s length stands in a fixed practical ratio to its owner’s bodily proportions. The sighting angle “shaft height” is thus guaranteed independently of both standpoint and reach.

With a greater height of observation (for example from a hilltop) the sun’s disk stands higher above the visible horizon. If the sun’s height were measured from the visible horizon, then observation from a hilltop would give a different time than observation from the shore.

The legal rule, aimed at getting the same time value for observations made at any height, whether from the seashore or from a mountain, removes the horizon from the determination of height, and expressly requires the reference level to be the actual eye level, regardless of the ground height or the edge of the sky; in other words it requires the so-called apparent horizon.

Calculation gives for the “shaft height of the sun” an angle of about 10 degrees.

4. Finding the height of the pole by lying on one’s back

In 1150 the Icelandic abbot Nikolaus completed a pilgrimage to the Jordan. At the spot where Christ is said to have been baptized, Nikolaus at once noted in true Icelandic style that the Jordan flows “from northeast to southwest”, and he also noted how high the Lode Star appeared there.

“If you go down to the Jordan and lie in a flat field, raise your knee, place your fist on top of it and lift your thumb straight up from the fist, the Lode Star can be seen above it, so high and no higher.”

The fist with the raised thumb is once again the old Germanic measure of the shafthand. By the Lode Star we must understand, as we shall establish in the section on the constellations, the star 32 Camelopardis in the head of the Giraffe, which we may suppose the Icelander had kept under observation on his outward journey; at that time our modern Pole Star was still far from the pole. To the Icelander it was important to compare the height of the pole at his journey’s end with that at his home village in northern Iceland.

Observations while lying on one’s back was another Icelandic practice, appropriate because in northern Iceland the celestial pole lies only 24 degrees from the zenith. On the other hand, lying down seems pointless on the Jordan, because the Lode Star there was only 32 degrees above the horizon. The reason for using the Icelandic practice on the Jordan was to avoid the high horizon of that mountainous district, and to set up an artificial apparent horizon (the horizontal eye level) independent of the height of the eye, such as was also required by law when fixing the “shaft height”.

A repetition of this folk method gives an angle, consistent with that latitude, of about 32 degrees.

5. The sun’s position as a year marker

(See Fig. 2)

In 930 the solar year was made the exclusive form of calendar in Iceland. The first day of summer was defined to be the day on which the sun in spring rose ENE, the summer “rising” eykt point (rismál). The first day of winter was to be when the sun in autumn set WSW, the eykt point for stopping work (eyktar staðr). But in addition the Icelanders wanted to count a whole number of weeks in their year, and forgot (in the unrest of the settlement period) the 365th day, although a knowledge of this is already in evidence among the Norwegians 400 years before. They soon noticed for themselves that the legal first day of summer no longer arrived as it should, and it was Thorstein Surt who advised the Icelanders to insert a week (later named after him) every seven years or so, after which they could investigate more carefully how to bring the year into harmony with the sunrise.

It is not known in what way the “sunrise” was defined; the practice of beginning the year from a certain sun position, and the custom of observing this every year, is of old Norse origin (see Section III on the calendar).

6. Finding position from the sun: the site of Vinland

(See Fig. 6)

In 986 the Norwegian Bjarni Herjolfsson became the first European to set eyes on the American continent. The first to land in the New World was Leif Eiriksson in the year 1000. The most southerly stretch of coast that he reached, named Vinland, was identified by Leif through an astronomical report. He states:

  1. that the winter they spent there was quite free of frost;
  2. that the days and nights there were more equal in length than in Greenland;
  3. that on the shortest day the sun had the eykt point and the dagmál point.

These last two eykt markers we already know as the WSW and ESE points. Leif is comparing astronomical phenomena in the new land with those in his homeland. On Eirik’s farmstead Brattahlid, the family settlement in southern Greenland (61° N), the sun set on the shortest day in the direction S 37.4° W, that is roughly 33° south of the WSW point, or eykt point.

The further south we go, the further north the sun sets on the shortest day, and the closer sunset on the day approaches the eykt point; but even on the equator it does not quite get there. On the horizon of Cuba (21° N) the difference is still 2.7 degrees; on the horizon in Georgia (31° N), about 5 degrees. Leif’s description of the country in the saga rules out the possibility that he penetrated further south than Florida; however, on this coast the sun on the shortest day still almost reaches the eykt and dagmál points. The difference amounted to 33° in southern Greenland, in Vinland 3 to 4 degrees, which were no doubt observed, although they have dropped out of the report, which was written down only after three centuries of oral tradition.

The reason why this astronomical method of fixing position must be of Germanic origin and not borrowed from the south (as Frithjof Nansen still maintained) is that it depends on the broad spread along the horizon of sunrise and sunset points: a feature which results from the flattish angle of the sun’s path and is found only in northern latitudes. In the Mediterranean regions the sunrise and sunset show little variation with latitude, so that observation and measurement to determine one’s position are made more difficult. In Germanic seas and lands the method provides the possibility of measurements up to five times better. The northern practice is never mentioned in southern antiquity; it developed independently from the seafaring experience of the North, and is peculiar to it.

7. A country rule for predicting new and full moon

Introductory note. When the moon passes between the earth and sun it usually disappears in the sun’s glare and cannot be seen. Nevertheless, it is visible from time to time in this position, if its journey brings it exactly in front of the sun, so that the latter is eclipsed behind it. The time of appearance of the first delicate crescent, once the moon has passed through, is irregular. In southerly latitudes the month began with the new light, whose first sighting was proclaimed. In Germanic latitudes the time of, appearance of the first crescent varies, even in a clear sky, between 1 and 3 days; reason enough to fix the beginning of the month by other means.

The great Germanic military king Ariovistus, Caesar’s opponent, was advised by the matrons following the army not to give battle before the new moon [6]. Since this was a highly important decision, these matrons must also have been in a position to advise Ariovistus as to the day when new moon fell – assuming that he was unable to find it himself. If the sky was overcast this could only be done by calculation. When Tacitus, 150 years later, reports that the Germans assemble on certain days, namely at new or full moon, he is therefore correct when he adds that they calculate the number of the day [7]. In Section III on the Germanic Calendar, we shall show from further evidence that the Germanic lunar reckoning started neither from the first sighting nor from new moon, but generally from full moon.

A Swedish popular rule, first recorded in the 17th century, but lying as far from Christian practice as does the primestave, asserts: “All the moon’s appearances are dated from full moon. Full moon occurs when the moon stands in the centre of the nightring.” Nightring is their name for the cast shadow of the earth, which shows up in the east at sunset, and in the west at sunrise, as a low, broad, dark curve on the horizon opposite the sun, getting larger and larger in the evening till it covers the whole sky and passes into night, and in the morning getting smaller and smaller before the daylight and sunlight rising up opposite, until it is turned to full day. Since the full moon occurs when the moon stands exactly opposite the sun (which happens every 29 or 30 days on average), the country rule is quite correct when it states: “Full moon is when the moon stands at the centre of the nightring.”

For predicting the time of new or full moon the country people used the short handspan between the tip of the thumb and the index finger, which marks off some 13 degrees in the sky. Very early on, even back in the primitive Germanic period, as can be verified among all western and northern Germanic peoples, the moon was compared with a cock, which appeared to throw its tail (German “wedel”), the new and old crescents, on the east side of the sun during one half of the month and on the west side during the other half. The metaphor was thus derived from the full moon; today people in southern Germany still say “es wädelt” when it is full moon. They speak of the bad tail, “böser wedel”, meaning the waning moon.

From this metaphor of a cock the expression “cock stride”, found within the above-mentioned Germanic regions, is used for the amount of sky which the moon can be seen to cover from night to night in its true path eastwards among the stars. This true eastward movement (as distinct from the apparent westward movement reflecting the earth’s rotation) can easily be traced hour by hour among the stars at night. The moon returns to the same star (though not exactly the same phase) after about 27.3 (in round figures 27 or 28) nights. This marks the end of the moon’s true circuit, used for reckoning the thirteen-month year as described below. The cycle of shape (that is from phase to phase) is not completed till 2½ days later, because to arrive back at the same shape (determined by the light of the sun) the moon must catch up with the sun which has also been moving eastwards in the meantime.

From night to night the moon therefore covers, in its true circuit, 360 degrees divided by 27 or about 13 full degrees. This distance corresponds to the short span and shares with it the name “cock stride”, because it is the cock in the sky, the moon, that makes a complete circuit in 27 or 28 of these strides. With practice one can obtain a quite accurate measure.

Now the Swedish country people, when the moon is waxing, use this handspan to measure the distance between the sun and the moon to the east of it, and find out how many “spans” the moon has progressed from the sun, its position at new moon; that is, how many days have elapsed since new moon. At sunset the distance between the moon and the nightring indicates how many days are left until full moon. During the waning moon, that is when the moon is west of the sun and moving towards it, the number of spans between moon and sun (measured in the morning) indicates how many days are left until new moon; the number of spans (measured before sunset) between the nightring and the moon shows how many days have elapsed since full moon.

This handspan rule can only be used by day, since at night the sun and the nightring are lacking. At night, if the stars are visible, the span allows one to read off immediately the number of days since the moon was at a certain star.

The “cock stride” measure has been known by this name among the Germanic races from the earliest times. The word “tail” indicates the full moon among both the north and the south Germanic peoples. We shall later come across the number of cock strides, 27 or 28, as a basic parameter of the moon’s motion, that is as an astronomical unit.

8. Observations in the polar night

(See Fig. 7)

About 550 AD some Norwegians from the Lofoten Islands reported, on being questioned by the Greek historian Procopius [8], that in their homeland people counted off days during the sun’s upper course, that is, during the period of the midnight sun, by noting how often the sun crossed over the direction of its first rising. This sunrise takes place after the polar night every year at midday in the south point. We may thus safely assume – since the informants are described as especially trustworthy – that this observation was made by using a fixed standpoint and a landmark.

The counting of days in the 40-day polar night was so advanced, according to this report, that the length of the day could be kept track of by observing the moon and stars as they crossed the south point.

The first sunrise in this south point is by custom predicted “somehow” from a mountain summit by special observers. They announce that the sun will become visible again in five days. What kind of observations these were cannot be determined from the “somehow” of the account; we may, however, recall the twilight observations by Star Oddi (see below) in Iceland, which can be shown to rest on Norwegian practice. The account also states explicitly that the five days “that were left of the darkness (twilight)” were kept as a great feast. Some sort of twilight observation must therefore have been in use.

Incidentally, during the 40 days when the sun is invisible the moon goes through 1½ cycles; so the northerners in this report, who calculated the sun’s return by the moon’s cycles and by counting the days, must have got to know the number of days needed for the moon’s own cycles – both the 27 to 28 days of its true course through the stars, and the 29 to 30 days of its constantly varying phase.

(On the Nordic solar year, see Section III on the calendar.)

9. The circumpolar moon

Introductory note. Whilst the sun, as seen north of the 66th parallel near the summer or winter solstice, remains above or below the horizon for 24 hours at a time, the moon (whose declination varies between 18.5 and 28.5 degrees every 18.6 years) shows the same behaviour over a cycle of 19 years; and also, irrespective of its phase, in each of its 27.3-day circuits among the stars. North of the Lofoten Islands, in the years of greatest declination, the moon remains above or below the horizon for an average of 7 days at a time; between these two periods there are some 14 days during which the moon rises and sets somewhere between the north and south points of the horizon. As the declination decreases, these periods of permanent visibility or invisibility also decrease, and then, for every latitude north of 61 degrees, begin to increase again in a 19-year cycle.

These phenomena are reported by the Greek historian Diodoros [9]: that in the land of the Hyperboreans the god Apollo visits the earth every 19 years, and dances a round dance without stopping from the spring equinox to the earliest rising of the Pleiades, playing on the cithara and amusing himself on his festival days. In this Greek legend the god himself is made to represent the body that was sacred to him in Greece. The Greeks knew of the 19-year calendar cycle devised by Meton of Athens; this was founded on the 19-year revolution of the moon’s nodes. But what the Greeks and other Mediterranean peoples could never experience, or even deduce, was the phenomenon of the circumpolar moon, that is, the permanent circling of the moon above the horizon.

Homer’s Greeks had already heard of the bright nights and the circumpolar sun [10]. News of the circumpolar moon could also have reached them along the ancient routes, if indeed they had not brought this Doric legend with them into the south from their more northerly homeland. But only a first-rate astronomer, who also knew the so-called Great Metonic Year of 19 ordinary years, could recognize and describe the connexion between this and the appearance every 19 years of the circumpolar moon in the high north.

One such notable astronomer was the Greek Pytheas, who visited Norway around 330 BC to see the midnight sun for himself. His object was purely scientific, and the conversation he is reported to have held with the Norwegians of the Trondheim district will have touched not only upon the sun but upon the moon and its behaviour. Probably it was Pytheas himself, in his travelogue “On the Ocean” (now unfortunately lost) who brought an account of the circumpolar moon and its 19-year cycle from the North back to Greece, where it seems to have met with strong disbelief.

It is important here that this report can be derived only from an observation in the Germanic North. But since Pytheas himself spent only a few weeks in summer among the Trondheimers, he cannot have obtained the period of this phenomenon from his Northerners themselves, on whose astronomical knowledge he relied in other cases, as shown by a surviving fragment of his book [11].

Probably Diodorus, as was his custom, took this account from a reputable author, who can only have been Pytheas. We may conclude that the 19-year cycle of the circumpolar moon lay within the knowledge of the Norwegians whom Pytheas questioned.

10. Oddi Helgason

At the end of the tenth century AD, back in Pagan times, Oddi Helgason lived on the farmstead Muli in northern Iceland as one of farmer Thord’s workmen. The Reikiadal valley, above whose northern entrance the farmstead lay on a spur of rock, was settled about 900 by a Norwegian family from Hardanger; Thord and Oddi were probably cousins. This explains why Oddi, though not a skilful worker and – coming from a large family – without means (but on the other hand described as very loyal and truthful, and skilled in time reckoning beyond anyone else at that time) was well treated by Thord. All this is reported in a short ancient saga, “Star Oddi’s Dream” [12]. From it we learn his nickname, also that he looked after Thord’s fishery on the island of Flatey on the north coast (66° 10′ N), and that he was in the habit of observing the stars on clear nights.

A few astronomical reports by this Thor-worshipping Icelander are preserved in a 12th-century church manuscript on time reckoning, under the name “Oddi’s calculations” (Odda tala).

The first of these traditions (O I) compares the church’s new calendar of 365¼ days with the Icelandic-Norwegian year, and explains how the true divisions of the year (solstices and equinoxes), current in the North and correctly observed by Oddi, move about within the new Julian leap year cycle of 4 years. The discussion is shrewd and correctly thought out. The problem to be solved is without any foreign analogue, for it could only arise and have any meaning in the clash between these two particular calendar systems.

The second tradition of Oddi (O II) concerns the increase and decrease of the sun’s height at midday; the third tradition (O III), the northward and southward movenient of the twilight zone on the horizon.

It is quite clear that the star observations from which Oddi got his nickname have not been preserved; even about the moon we hear nothing. The three traditions that have been preserved deal with the sun’s motion; all three of them are attempts to find natural laws.

The sun’s height at midday

Around 1000 AD the sun at noon on the shortest day (winter solstice), as seen from Flatey, stood only 0° 35′ above the southpoint on the open horizon; at noon on the longest day (summer solstice), 47° 20′. Oddi expressed this increase in terms of an arithmetic progression; he measured not with a grid but with the natural units of the sun’s diameter and radius. Since Oddi gave to each of the 26 weeks between the solstices an increase that was either 1 radius larger or 1 radius smaller than in the previous week, he established the total increase as 182 radii. The tradition states:

“The sun’s path increases to the sight by ½ a sun wheel in the first week after the (winter) solstice; in the second week, 1 wheel; in the 3rd week, 1½; in the 4th, 2 wheels; in the 5th 2½; in the 6th 3; in the 7th 3½; in the 8th 4; in the 9th 4½; in the 10th 5; in the 11th 5½; in the 12th 6; in the 13th 6½; in the 14th likewise 6½. In these two weeks the sun’s course increases the most, because here is the midpoint between the solstices (and the weeks join up four nights before St. Gregory’s Day, that is, 16th March Old Style). In the 15th week the sun’s course increases by 6 wheels, in the 16th by 5½; in the 17th 5; in the 18th 4½; in the 19th 4; in the 20th 3½; in the 21st 3; in the 22nd 2½; in the 23rd 2; in the 24th 1½; in the 25th 1; in the 26th ½ a wheel. There the summer solstice has been reached, and by the same amounts as it has counted during its increase, the sun’s course now decreases. (In autumn the midpoint between the solstices is Holy Cross Day, that is, 14th September Old Style).”

A comparison with the true situation around the year 1000 AD results in the accompanying graph (Fig. 8), which shows a good approximation. The reason why complete agreement is lacking probably lies not in mistakes of observation but in Oddi’s theory, for which it was necessary to assume perfect regularity in the sun’s motion (as still with Eudoxos among the Greeks).

In spite of this shortcoming, which is to be charged less to Oddi the observer than to Oddi the theorist, the resulting error in the theoretical maximum declination is only 0.7 degree. To put it another way., assuming the declination to be correct, the mean value for the apparent radius comes to 15.5′, which approximates well to the true value of 15.8′ in the summer and 16.0′ in winter. Medieval Europe at that time (Bede, Honorius) estimated the sun’s apparent diameter three times too large (1° 40′).

The comments in “Oddi’s calculations” referring to the saints’ days do not belong to him, but to the church’s transcription of an oral tradition.

Movement of the twilight direction

Introductory note. When the sun is at a certain depth below the horizon, it sends a first, scarcely noticeable arc of light of a certain size up over the horizon: this we call, in the evening, the end of twilight, and in the morning, the beginning. The centre of this arc stands directly above the sun’s position, and, for a given depth of the sun, always has the same size. As the sun’s daily path moves north towards the summer, these arcs of light also move northwards day by day; then back south towards the winter.

Oddi Helgason observed on Flatey when a twilight arc of a certain size appeared in the 16 astronomical directions, and thus how many days were needed to move from one of these directions to the next. He established the speeding up towards the summer, and the slowing down towards the winter. Oddi took this fixed size of the twilight arc as the definition of daybreak. The report (O III) states:

“Oddi (worked out that St. Andrew’s day [30th November] and the fifth day of Yule were the same length. He) places daybreak on those days in the ESE, its setting in WSW. (From the fifth day of Yule) he counts off 43 nights until daybreak in the E and nightfall in the W (that is on St. Scholastica’s day [10th February]). Then there are 25 nights until daybreak (nightfall) in ENE (WNW), (that is 5 nights before St. Gregory’s day [12th March]); then 18 nights until daybreak in the _NE and nightfall in NW (that is on Lady Day [25th March]). Then 10 nights go by until daybreak in NNE and nightfall in NNW. The 5 nights go by until daylight no longer vanishes (that is 5 nights before Sts. Tiburtius and Valerianus [14th April]). Then 134 nights go by until daylight almost vanishes (that is 6 nights after the Assumption [15th August]), and the nights begin to lengthen in the same way as was counted for their shortening; that is 1 ætt in 5 nights, the second in 10, the third in 18, the fourth in 25, and the fifth ætt in 43 nights (thus arriving at St. Andrew’s day).”

The Julian dates (here parenthesized) place the beginning of the year, that is, the winter solstice, for that period between St. Andrew’s day and the fifth day of Yule, that is, between 30th November and 29th December Old Style, and thus at midnight on 14/15th December. In the middle of the 134 bright nights lies the summer solstice on 15th June. Calculation shows that the twilight directions apply to a position of the sun about 14 degrees below the horizon in 66° 10′ north, that is, the latitude of Flatey and Oddi’s observation point.

It is not a question here of measuring brightness or the visibility of stars, but fixing the centre of the very small twilight arc – a method of fixing the twilight direction which is meaningful only if applied to the same size of arc throughout the year. Oddi’s results are so exact that they correspond to an error in time of only about plus or minus 5 minutes. At the same time, this proves the exactness of his astronomical directions, especially the N–S axis (the meridian).

While the results for the first sequence, used for finding the sun’s height at noon throughout the year, were marred by theoretical influences, the movement of the twilight remains within the realms of observation. All three traditions in “Oddi’s Calculations” serve the investigation of natural law.

All three traditions work with a year of 365 days, which is compared with the new Julian year of 365¼ days in the first sequence only. Oddi always begins his counting and observations with the winter solstice, which he consistently places in the middle of the night; thus making it take place at the north point, the sun’s lowest point on the shortest day. In Oddi’s time (1000 AD) this fell on 15th December Old Style and did not pass into 14th December until about 1100.

Meanwhile the western Middle Ages long continued to calculate with the Julian year points, which had become more and more inaccurate since Caesar’s time. More accurate determinations began to appear from time to time within the church in the 11th century, and then, in the two known instances (Wilhelm von Hirschau, Hermann the Lame), only under GraecoArabic influence. Iceland remained untouched by this influence until 1173.

Oddi Helgason stands at the close of a preChristian astronomy; the accuracy of his observations, even in the fragmentary traditions, appears wonderful.