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91-541: In the Prose Edda book Gylfaginning (chapter 44), the enthroned figure of Third reluctantly relates a tale in which Thor, Loki and Thor's servants, Þjálfi and Röskva are traveling to the east. They arrive at a vast forest in Jötunheimr , and they continue through the woods until dark. The four seek shelter for the night and discover an immense building. Finding shelter in a side room, they experience earthquakes through

182-445: A diurnal tide—one high and low tide each day. A "mixed tide"—two uneven magnitude tides a day—is a third regular category. Tides vary on timescales ranging from hours to years due to a number of factors, which determine the lunitidal interval . To make accurate records, tide gauges at fixed stations measure water level over time. Gauges ignore variations caused by waves with periods shorter than minutes. These data are compared to

273-406: A being named Logi to consume a trencher full of meat but loses. Útgarða-Loki asks what feat the "young man" can perform, referring to Þjálfi. Þjálfi says that he will attempt to run a race against anyone Útgarða-Loki chooses. Útgarða-Loki says that this would be a fine feat yet that Þjálfi had better be good at running, for he is about to be put to the test. Útgarða-Loki and the group go outside to

364-556: A collection known as the Poetic Edda . The Prose Edda consists of four sections: The Prologue , a euhemerized account of the Norse gods; Gylfaginning , which provides a question and answer format that details aspects of Norse mythology (consisting of approximately 20,000 words), Skáldskaparmál , which continues this format before providing lists of kennings and heiti (approximately 50,000 words); and Háttatal , which discusses

455-677: A day were similar, but at springs the tides rose 7 feet (2.1 m) in the morning but 9 feet (2.7 m) in the evening. Pierre-Simon Laplace formulated a system of partial differential equations relating the ocean's horizontal flow to its surface height, the first major dynamic theory for water tides. The Laplace tidal equations are still in use today. William Thomson, 1st Baron Kelvin , rewrote Laplace's equations in terms of vorticity which allowed for solutions describing tidally driven coastally trapped waves, known as Kelvin waves . Others including Kelvin and Henri Poincaré further developed Laplace's theory. Based on these developments and

546-525: A development "would have had to have taken place gradually", and Edda in the sense of 'poetics' is not likely to have existed in the preliterary period. Edda also means 'great-grandparent', a word that appears in Skáldskaparmál , which occurs as the name of a figure in the eddic poem Rigsthula and in other medieval texts. A final hypothesis is derived from the Latin edo , meaning "I write". It relies on

637-512: A few days after (or before) new and full moon and are highest around the equinoxes, though Pliny noted many relationships now regarded as fanciful. In his Geography , Strabo described tides in the Persian Gulf having their greatest range when the moon was furthest from the plane of the Equator. All this despite the relatively small amplitude of Mediterranean basin tides. (The strong currents through

728-496: A given day are typically not the same height (the daily inequality); these are the higher high water and the lower high water in tide tables . Similarly, the two low waters each day are the higher low water and the lower low water . The daily inequality is not consistent and is generally small when the Moon is over the Equator . The following reference tide levels can be defined, from

819-447: A gravitational field that varies in time and space is present. For example, the shape of the solid part of the Earth is affected slightly by Earth tide , though this is not as easily seen as the water tidal movements. Four stages in the tidal cycle are named: Oscillating currents produced by tides are known as tidal streams or tidal currents . The moment that the tidal current ceases

910-403: A large, gray cat in the hall but finds that it arches his back no matter what he does, and that he can only raise a single paw. Thor demands to fight someone in the hall, but the inhabitants say doing so would be demeaning, considering Thor's weakness. Útgarða-Loki then calls for his nurse Elli , an old woman. The two wrestle but the harder Thor struggles the more difficult the battle becomes. Thor

1001-419: A level-grounded course. At the course, Útgarða-Loki calls for a small figure by the name of Hugi to compete with Þjálfi. The first race begins and Þjálfi runs, but Hugi runs to the end of the course and then back again to meet Þjálfi. Útgarða-Loki comments to Þjálfi that he will have to run faster than that, yet notes that he has never seen anyone who has come to his hall run faster than that. Þjálfi and Hugi run

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1092-400: A powerful stench rolled over the bystanders that they had to smother their nostrils in their cloaks and could scarcely breathe. As a proof of their accomplishments, the men bring back a hair pulled from the giant's beard, stinking so harshly that several men drop dead on smelling it. Apart from the name of the giant there is little that reminds of Snorri's Útgarða-Loki. The bound giant figure

1183-426: A second race. Þjálfi loses by an arrow-shot. Útgarða-Loki comments that Þjálfi has again run a fine race but that he has no confidence that Þjálfi will be able to win a third. A third race between the two commences and Þjálfi again loses to Hugi. Everyone agrees that the contest between Þjálfi and Hugi has been decided. Thor agrees to compete in a drinking contest but after three immense gulps fails. Thor agrees to lift

1274-464: A smooth sphere covered by a sufficiently deep ocean under the tidal force of a single deforming body is a prolate spheroid (essentially a three-dimensional oval) with major axis directed toward the deforming body. Maclaurin was the first to write about the Earth's rotational effects on motion. Euler realized that the tidal force's horizontal component (more than the vertical) drives the tide. In 1744 Jean le Rond d'Alembert studied tidal equations for

1365-514: A system of pulleys to add together six harmonic time functions. It was "programmed" by resetting gears and chains to adjust phasing and amplitudes. Similar machines were used until the 1960s. The first known sea-level record of an entire spring–neap cycle was made in 1831 on the Navy Dock in the Thames Estuary . Many large ports had automatic tide gauge stations by 1850. John Lubbock was one of

1456-808: A wide landscape remains. In Gesta Danorum a ship meets strong winds and sacrifices are made to various gods to obtain favorable weather, including to one called Utgarthilocus . With vows and propitiations to him a beneficial spell of weather is obtained. Later an expedition to the land of the giants comes upon this figure. Ex qua item atrum obscenumque conclave visentibus aperitur. Intra quod Utgarthilocus manus pedesque immensis catenarum molibus oneratus aspicitur, cuius olentes pili tam magnitudine quam rigore corneas aequaverant hastas. Quorum unum Thorkillus, adnitentibus sociis, mento patientis excussum, quo promptior fides suis haberetur operibus, asservavit; statimque tanta foetoris vis ad circumstantes manavit, ut nisi repressis amiculo naribus respirare nequirent. From here

1547-465: Is "unlikely, both in terms of linguistics and history " since Snorri was no longer living at Oddi when he composed his work. Another connection was made with the word óðr , which means 'poetry or inspiration' in Old Norse. According to Faulkes, though such a connection is plausible semantically, it is unlikely that "Edda" could have been coined in the 13th century on the basis of "óðr", because such

1638-455: Is a useful concept. Tidal stage is also measured in degrees, with 360° per tidal cycle. Lines of constant tidal phase are called cotidal lines , which are analogous to contour lines of constant altitude on topographical maps , and when plotted form a cotidal map or cotidal chart . High water is reached simultaneously along the cotidal lines extending from the coast out into the ocean, and cotidal lines (and hence tidal phases) advance along

1729-422: Is at once cotidal with high and low waters, which is satisfied by zero tidal motion. (The rare exception occurs when the tide encircles an island, as it does around New Zealand, Iceland and Madagascar .) Tidal motion generally lessens moving away from continental coasts, so that crossing the cotidal lines are contours of constant amplitude (half the distance between high and low water) which decrease to zero at

1820-561: Is based on the Útgarða-Loki story from the Prose Edda . Útgarða-Loki serves as the villain and Elli is described as his mother. In the Marvel Comics continuity, Utgard-Loki is an enemy of Thor . He had attempted to lead a cadre of Frost Giants against a weakened Asgard but was defeated by a small force of its defenders. Utgarda-Loki also makes an appearance as the final boss in the video game Ragnarok Odyssey . Skrymir also appears in

1911-418: Is called slack water or slack tide . The tide then reverses direction and is said to be turning. Slack water usually occurs near high water and low water, but there are locations where the moments of slack tide differ significantly from those of high and low water. Tides are commonly semi-diurnal (two high waters and two low waters each day), or diurnal (one tidal cycle per day). The two high waters on

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2002-426: Is called Edda. Snorri Sturluson has compiled it in the manner in which it is arranged here. There is first told about the Æsir and Ymir, then Skáldskaparmál (‘poetic diction’) and (poetical) names of many things, finally Háttatal ('enumeration of metres or verse-forms') which Snorri has composed about King Hákon and Earl Skúli . Scholars have noted that this attribution, along with that of other primary manuscripts,

2093-454: Is called the spring tide . It is not named after the season , but, like that word, derives from the meaning "jump, burst forth, rise", as in a natural spring . Spring tides are sometimes referred to as syzygy tides . When the Moon is at first quarter or third quarter, the Sun and Moon are separated by 90° when viewed from the Earth (in quadrature ), and the solar tidal force partially cancels

2184-455: Is finally brought down to a single knee. Útgarða-Loki said to Thor that fighting anyone else would be pointless. As it is now late at night, Útgarða-Loki shows the group to their rooms and they are treated with hospitality. The next morning the group gets dressed and prepares to leave the keep. Útgarða-Loki appears, has his servants prepare a table, and they all merrily eat and drink. As they leave, Útgarða-Loki asks Thor how he thought he fared in

2275-431: Is more reminiscent of the bound Loki who likewise lies chained and tortured in a cave. Gabriel Turville-Petre notes that "Utgardilocus appears to be Loki, expelled from Ásgarð into Útgarð" and expresses an opinion that "Snorri appears to be retelling a folktale, which has changed from the original myth in which Útgarðaloki must have been Loki himself". The Danish animated film Valhalla (Peter Madsen and others, 1984)

2366-446: Is never time for the fluid to "catch up" to the state it would eventually reach if the tidal force were constant—the changing tidal force nonetheless causes rhythmic changes in sea surface height. When there are two high tides each day with different heights (and two low tides also of different heights), the pattern is called a mixed semi-diurnal tide . The changing distance separating the Moon and Earth also affects tide heights. When

2457-403: Is not clear whether or not Snorri is more than the compiler of the work and the author of Háttatal or if he is the author of the entire Edda . Faulkes summarizes the matter of scholarly discourse around the authorship of the Prose Edda as follows: Whatever the case, the mention of Snorri in the manuscripts has been influential in a common acceptance of Snorri as the author or at least one of

2548-408: Is not necessarily when the Moon is nearest to zenith or nadir , but the period of the forcing still determines the time between high tides. Because the gravitational field created by the Moon weakens with distance from the Moon, it exerts a slightly stronger than average force on the side of the Earth facing the Moon, and a slightly weaker force on the opposite side. The Moon thus tends to "stretch"

2639-456: Is not the case due to the free fall of the whole Earth, not only the oceans, towards these bodies) a different pattern of tidal forces would be observed, e.g. with a much stronger influence from the Sun than from the Moon: The solar gravitational force on the Earth is on average 179 times stronger than the lunar, but because the Sun is on average 389 times farther from the Earth, its field gradient

2730-519: Is often considered to have been to some extent written, or at least compiled, by the Icelandic scholar, lawspeaker , and historian Snorri Sturluson c. 1220. It is considered the fullest and most detailed source for modern knowledge of Norse mythology , the body of myths of the North Germanic peoples , and draws from a wide variety of sources, including versions of poems that survive into today in

2821-402: Is shorter than average, and stronger tidal currents than average. Neaps result in less extreme tidal conditions. There is about a seven-day interval between springs and neaps. Tidal constituents are the net result of multiple influences impacting tidal changes over certain periods of time. Primary constituents include the Earth's rotation, the position of the Moon and Sun relative to the Earth,

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2912-479: Is the last section of Prose Edda . The section is composed by the Icelandic poet , politician, and historian Snorri Sturluson . Primarily using his own compositions, it exemplifies the types of verse forms used in Old Norse poetry. Snorri took a prescriptive as well as descriptive approach; he has systematized the material, often noting that the older poets did not always follow his rules. The Prose Edda has been

3003-419: Is the time required for the Earth to rotate once relative to the Moon. Simple tide clocks track this constituent. The lunar day is longer than the Earth day because the Moon orbits in the same direction the Earth spins. This is analogous to the minute hand on a watch crossing the hour hand at 12:00 and then again at about 1: 05 + 1 ⁄ 2 (not at 1:00). The Moon orbits the Earth in the same direction as

3094-719: The Buffy the Vampire Slayer novel Spike and Dru: Pretty Maids All In A Row . Utgard-Loki appears as a supporting character in Rick Riordan 's Magnus Chase and the Gods of Asgard series. He is stated to be king of the mountain giants and the most powerful sorcerer in Jotunheim. In Thomas Hardy 's 1884 short story, Interlopers at the Knapp , a breeze 'brought a snore from the wood as if Skrymir

3185-589: The Coriolis effect , is generally clockwise in the southern hemisphere and counterclockwise in the northern hemisphere. The difference of cotidal phase from the phase of a reference tide is the epoch . The reference tide is the hypothetical constituent "equilibrium tide" on a landless Earth measured at 0° longitude, the Greenwich meridian. In the North Atlantic, because the cotidal lines circulate counterclockwise around

3276-692: The Euripus Strait and the Strait of Messina puzzled Aristotle .) Philostratus discussed tides in Book Five of The Life of Apollonius of Tyana . Philostratus mentions the moon, but attributes tides to "spirits". In Europe around 730 AD, the Venerable Bede described how the rising tide on one coast of the British Isles coincided with the fall on the other and described the time progression of high water along

3367-518: The North Sea . Much later, in the late 20th century, geologists noticed tidal rhythmites , which document the occurrence of ancient tides in the geological record, notably in the Carboniferous . The tidal force produced by a massive object (Moon, hereafter) on a small particle located on or in an extensive body (Earth, hereafter) is the vector difference between the gravitational force exerted by

3458-537: The Poetic Edda . The etymology of "Edda" remains uncertain; there are many hypotheses about its meaning and development, yet little agreement. Some argue that the word derives from the name of Oddi , a town in the south of Iceland where Snorri was raised. Edda could therefore mean "book of Oddi." However, this assumption is generally rejected. Anthony Faulkes in his English translation of the Prose Edda comments that this

3549-440: The lunar theory of E W Brown describing the motions of the Moon, Arthur Thomas Doodson developed and published in 1921 the first modern development of the tide-generating potential in harmonic form: Doodson distinguished 388 tidal frequencies. Some of his methods remain in use. From ancient times, tidal observation and discussion has increased in sophistication, first marking the daily recurrence, then tides' relationship to

3640-518: The Codex Upsaliensis: The other three manuscripts are AM 748; AM 757 a 4to; and AM 738 II 4to, AM le ß fol. Although some scholars have doubted whether a sound stemma of the manuscripts can be created, due to the possibility of scribes drawing on multiple exemplars or from memory, recent work has found that the main sources of each manuscript can be fairly readily ascertained. The Prose Edda' remained fairly unknown outside of Iceland until

3731-426: The Earth rotates on its axis, so it takes slightly more than a day—about 24 hours and 50 minutes—for the Moon to return to the same location in the sky. During this time, it has passed overhead ( culmination ) once and underfoot once (at an hour angle of 00:00 and 12:00 respectively), so in many places the period of strongest tidal forcing is the above-mentioned, about 12 hours and 25 minutes. The moment of highest tide

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3822-419: The Earth slightly along the line connecting the two bodies. The solid Earth deforms a bit, but ocean water, being fluid, is free to move much more in response to the tidal force, particularly horizontally (see equilibrium tide ). As the Earth rotates, the magnitude and direction of the tidal force at any particular point on the Earth's surface change constantly; although the ocean never reaches equilibrium—there

3913-570: The Earth's accumulated dynamic tidal response to the applied forces, which response is influenced by ocean depth, the Earth's rotation, and other factors. In 1740, the Académie Royale des Sciences in Paris offered a prize for the best theoretical essay on tides. Daniel Bernoulli , Leonhard Euler , Colin Maclaurin and Antoine Cavalleri shared the prize. Maclaurin used Newton's theory to show that

4004-609: The Giant were sleeping there'. The short story appears in Hardy's short story collection, Wessex Tales . Saturn's moon Skrymir is named after him. Prose Edda The Prose Edda , also known as the Younger Edda , Snorri's Edda ( Icelandic : Snorra Edda ) or, historically, simply as Edda , is an Old Norse textbook written in Iceland during the early 13th century. The work

4095-427: The Moon and its phases. Bede starts by noting that the tides rise and fall 4/5 of an hour later each day, just as the Moon rises and sets 4/5 of an hour later. He goes on to emphasise that in two lunar months (59 days) the Moon circles the Earth 57 times and there are 114 tides. Bede then observes that the height of tides varies over the month. Increasing tides are called malinae and decreasing tides ledones and that

4186-459: The Moon is closest, at perigee , the range increases, and when it is at apogee , the range shrinks. Six or eight times a year perigee coincides with either a new or full moon causing perigean spring tides with the largest tidal range . The difference between the height of a tide at perigean spring tide and the spring tide when the moon is at apogee depends on location but can be large as a foot higher. These include solar gravitational effects,

4277-462: The Moon on the particle, and the gravitational force that would be exerted on the particle if it were located at the Earth's center of mass. Whereas the gravitational force subjected by a celestial body on Earth varies inversely as the square of its distance to the Earth, the maximal tidal force varies inversely as, approximately, the cube of this distance. If the tidal force caused by each body were instead equal to its full gravitational force (which

4368-457: The Moon's altitude (elevation) above the Earth's Equator, and bathymetry . Variations with periods of less than half a day are called harmonic constituents . Conversely, cycles of days, months, or years are referred to as long period constituents. Tidal forces affect the entire earth , but the movement of solid Earth occurs by mere centimeters. In contrast, the atmosphere is much more fluid and compressible so its surface moves by kilometers, in

4459-449: The Moon's tidal force. At these points in the lunar cycle, the tide's range is at its minimum; this is called the neap tide , or neaps . "Neap" is an Anglo-Saxon word meaning "without the power", as in forðganges nip (forth-going without-the-power). Neap tides are sometimes referred to as quadrature tides . Spring tides result in high waters that are higher than average, low waters that are lower than average, " slack water " time that

4550-449: The Moon. Abu Ma'shar discussed the effects of wind and Moon's phases relative to the Sun on the tides. In the 12th century, al-Bitruji (d. circa 1204) contributed the notion that the tides were caused by the general circulation of the heavens. Simon Stevin , in his 1608 De spiegheling der Ebbenvloet ( The theory of ebb and flood ), dismissed a large number of misconceptions that still existed about ebb and flood. Stevin pleaded for

4641-663: The Northumbrian coast. The first tide table in China was recorded in 1056 AD primarily for visitors wishing to see the famous tidal bore in the Qiantang River . The first known British tide table is thought to be that of John Wallingford, who died Abbot of St. Albans in 1213, based on high water occurring 48 minutes later each day, and three hours earlier at the Thames mouth than upriver at London . In 1614 Claude d'Abbeville published

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4732-532: The Prologue in the Prose Edda . Gylfaginning deals with the creation and destruction of the world of the Nordic gods , and many other aspects of Norse mythology . The section is written in prose interspersed with quotes from eddic poetry. Skáldskaparmál (Old Icelandic 'the language of poetry' ) is the third section of Edda , and consists of a dialogue between Ægir , a jötunn who is one of various personifications of

4823-450: The Sun and Moon, the phase and amplitude of the tide (pattern of tides in the deep ocean), the amphidromic systems of the oceans, and the shape of the coastline and near-shore bathymetry (see Timing ). They are however only predictions, the actual time and height of the tide is affected by wind and atmospheric pressure . Many shorelines experience semi-diurnal tides—two nearly equal high and low tides each day. Other locations have

4914-518: The Sun and moon. Pytheas travelled to the British Isles about 325 BC and seems to be the first to have related spring tides to the phase of the moon. In the 2nd century BC, the Hellenistic astronomer Seleucus of Seleucia correctly described the phenomenon of tides in order to support his heliocentric theory. He correctly theorized that tides were caused by the moon , although he believed that

5005-517: The Two Chief World Systems , whose working title was Dialogue on the Tides , gave an explanation of the tides. The resulting theory, however, was incorrect as he attributed the tides to the sloshing of water caused by the Earth's movement around the Sun. He hoped to provide mechanical proof of the Earth's movement. The value of his tidal theory is disputed. Galileo rejected Kepler's explanation of

5096-423: The amphidromic point, the high tide passes New York Harbor approximately an hour ahead of Norfolk Harbor. South of Cape Hatteras the tidal forces are more complex, and cannot be predicted reliably based on the North Atlantic cotidal lines. Investigation into tidal physics was important in the early development of celestial mechanics , with the existence of two daily tides being explained by the Moon's gravity. Later

5187-429: The amphidromic point. For a semi-diurnal tide the amphidromic point can be thought of roughly like the center of a clock face, with the hour hand pointing in the direction of the high water cotidal line, which is directly opposite the low water cotidal line. High water rotates about the amphidromic point once every 12 hours in the direction of rising cotidal lines, and away from ebbing cotidal lines. This rotation, caused by

5278-530: The atmosphere which did not include rotation. In 1770 James Cook 's barque HMS Endeavour grounded on the Great Barrier Reef . Attempts were made to refloat her on the following tide which failed, but the tide after that lifted her clear with ease. Whilst she was being repaired in the mouth of the Endeavour River Cook observed the tides over a period of seven weeks. At neap tides both tides in

5369-496: The authors of the Edda . The Prologue is the first section of four books of the Prose Edda , consisting of a euhemerized Christian account of the origins of Norse mythology : the Nordic gods are described as human Trojan warriors who left Troy after the fall of that city (an origin which parallels Virgil's Aeneid ). Gylfaginning (Old Icelandic 'the tricking of Gylfi ') follows

5460-421: The bars of the gate, and continue to a large hall. Inside the great hall are two benches, where many generally large people sit on two benches. The four see Útgarða-Loki, the king of the castle, sitting. Útgarða-Loki says that no visitors are allowed to stay unless they can perform a feat. Loki, standing in the rear of the party, is the first to speak, claiming that he can eat faster than anyone. Loki competes with

5551-410: The coast. Semi-diurnal and long phase constituents are measured from high water, diurnal from maximum flood tide. This and the discussion that follows is precisely true only for a single tidal constituent. For an ocean in the shape of a circular basin enclosed by a coastline, the cotidal lines point radially inward and must eventually meet at a common point, the amphidromic point . The amphidromic point

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5642-417: The composition of traditional skaldic poetry (approximately 20,000 words). Dating from c. 1300 to 1600, seven manuscripts of the Prose Edda differ from one another in notable ways, which provides researchers with independent textual value for analysis. The Prose Edda appears to have functioned similarly to a contemporary textbook, with the goal of assisting Icelandic poets and readers in understanding

5733-412: The contests. Thor says that he is unable to say he did well, noting that he is particularly annoyed that Útgarða-Loki will now speak negatively about him. Útgarða-Loki, once the group has left his keep, points out that he hopes that they never return to it, for if he had had an inkling of what he was dealing with he would never have allowed the group to enter in the first place. Útgarða-Loki reveals that all

5824-475: The daily tides were explained more precisely by the interaction of the Moon's and the Sun's gravity. Seleucus of Seleucia theorized around 150 BC that tides were caused by the Moon. The influence of the Moon on bodies of water was also mentioned in Ptolemy 's Tetrabiblos . In De temporum ratione ( The Reckoning of Time ) of 725 Bede linked semidurnal tides and the phenomenon of varying tidal heights to

5915-565: The drafting of the Edda of Snorri), and so the Poetic Edda is also known as the Elder Edda. Seven manuscripts of the Prose Edda have survived into the present day: Six copies from the medieval period and another dating to the 1600s. No one manuscript is complete, and each has variations. In addition to three fragments, the four main manuscripts are Codex Regius, Codex Wormianus , Codex Trajectinus, and

6006-747: The fact that the word "kredda" (meaning "belief") is certified and comes from the Latin "credo" , meaning 'I believe'. Edda in this case could be translated as "Poetic Art". This is the meaning that the word was then given in the medieval period. The now uncommonly used name Sæmundar Edda was given by the Bishop Brynjólfur Sveinsson to the collection of poems contained in the Codex Regius , many of which are quoted by Snorri. Brynjólfur, along with many others of his time incorrectly believed that they were collected by Sæmundr fróði (therefore before

6097-531: The first to map co-tidal lines, for Great Britain, Ireland and adjacent coasts, in 1840. William Whewell expanded this work ending with a nearly global chart in 1836. In order to make these maps consistent, he hypothesized the existence of a region with no tidal rise or fall where co-tidal lines meet in the mid-ocean. The existence of such an amphidromic point , as they are now known, was confirmed in 1840 by Captain William Hewett, RN , from careful soundings in

6188-419: The forest and "there is no report that the Æsir expressed hope for a happy reunion". The four travelers continue their journey until midday. They find themselves facing a massive castle in an open area. The castle is so tall that they must bend their heads back to their spines to see above it. At the entrance to the castle is a shut gate, and Thor finds that he cannot open it. Struggling, all four squeeze through

6279-420: The highest level to the lowest: The semi-diurnal range (the difference in height between high and low waters over about half a day) varies in a two-week cycle. Approximately twice a month, around new moon and full moon when the Sun, Moon, and Earth form a line (a configuration known as a syzygy ), the tidal force due to the Sun reinforces that due to the Moon. The tide's range is then at its maximum; this

6370-577: The horn and thought it slow to sink, I dare say that was a miracle I had not expected to be possible; the far end of the horn was submerged in the sea, but you did not see that. Now, when you come to the shore, you will see what kind of sip you drank from the sea; there is now a sandy beach where there used to be water." The contests, too, were an illusion. Útgarða-Loki reveals that Loki had actually competed against wildfire itself ( Logi , Old Norse "flame"), Þjálfi had raced against thought ( Hugi , Old Norse "thought"), Thor's drinking horn had actually reached to

6461-415: The idea that the attraction of the Moon was responsible for the tides and spoke in clear terms about ebb, flood, spring tide and neap tide , stressing that further research needed to be made. In 1609 Johannes Kepler also correctly suggested that the gravitation of the Moon caused the tides, which he based upon ancient observations and correlations. Galileo Galilei in his 1632 Dialogue Concerning

6552-464: The interaction was mediated by the pneuma . He noted that tides varied in time and strength in different parts of the world. According to Strabo (1.1.9), Seleucus was the first to link tides to the lunar attraction, and that the height of the tides depends on the moon's position relative to the Sun. The Naturalis Historia of Pliny the Elder collates many tidal observations, e.g., the spring tides are

6643-412: The month is divided into four parts of seven or eight days with alternating malinae and ledones . In the same passage he also notes the effect of winds to hold back tides. Bede also records that the time of tides varies from place to place. To the north of Bede's location ( Monkwearmouth ) the tides are earlier, to the south later. He explains that the tide "deserts these shores in order to be able all

6734-514: The more to be able to flood other [shores] when it arrives there" noting that "the Moon which signals the rise of tide here, signals its retreat in other regions far from this quarter of the heavens". Later medieval understanding of the tides was primarily based on works of Muslim astronomers , which became available through Latin translation starting from the 12th century. Abu Ma'shar al-Balkhi (d. circa 886), in his Introductorium in astronomiam , taught that ebb and flood tides were caused by

6825-425: The night. The earthquakes cause all four to be fearful, except Thor, who grips his hammer in defense. The building turns out to be the huge glove of Skrýmir, who has been snoring throughout the night, causing what seemed to be earthquakes. The next night, all four sleep beneath an oak tree near Skrýmir in fear. Thor wakes up in the middle of the night, and a series of events occur where Thor twice attempts to destroy

6916-420: The obliquity (tilt) of the Earth's Equator and rotational axis, the inclination of the plane of the lunar orbit and the elliptical shape of the Earth's orbit of the Sun. A compound tide (or overtide) results from the shallow-water interaction of its two parent waves. Because the M 2 tidal constituent dominates in most locations, the stage or phase of a tide, denoted by the time in hours after high water,

7007-671: The ocean and with his drinks he lowered the ocean level (resulting in tides ). The cat that Thor attempted to lift was in actuality the world serpent, Jörmungandr , and everyone was terrified when Thor was able to lift the paw of this "cat", for Thor had actually held the great serpent up to the sky. The old woman Thor wrestled was in fact Old Age ( Elli , Old Norse "old age"), and there is no one whom old age cannot bring down. Útgarða-Loki concludes by telling Thor that it would be better for "both sides" if they did not meet again. Upon hearing this, Thor takes hold of his hammer and swings it at Útgarða-Loki but he disappears and so does his castle. Only

7098-408: The problem from the perspective of a static system (equilibrium theory), that provided an approximation that described the tides that would occur in a non-inertial ocean evenly covering the whole Earth. The tide-generating force (or its corresponding potential ) is still relevant to tidal theory, but as an intermediate quantity (forcing function) rather than as a final result; theory must also consider

7189-621: The publication of the Edda Islandorum in 1665. The text is generally considered to have been written or at least compiled by Snorri Sturluson . This identification is largely based on the following paragraph from a portion of Codex Upsaliensis, an early 14th-century manuscript containing the Edda : Bók þessi heitir Edda. Hana hefir saman setta Snorri Sturluson eptir þeim hætti sem hér er skipat. Er fyrst frá Ásum ok Ymi, þar næst Skáldskaparmál ok heiti margra hluta, síðast Háttatal er Snorri hefir ort um Hákon konung ok Skúla hertuga. This book

7280-412: The reference (or datum) level usually called mean sea level . While tides are usually the largest source of short-term sea-level fluctuations, sea levels are also subject to change from thermal expansion , wind, and barometric pressure changes, resulting in storm surges , especially in shallow seas and near coasts. Tidal phenomena are not limited to the oceans, but can occur in other systems whenever

7371-553: The rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun ) and are also caused by the Earth and Moon orbiting one another. Tide tables can be used for any given locale to find the predicted times and amplitude (or " tidal range "). The predictions are influenced by many factors including the alignment of

7462-583: The sea, and Bragi , a skaldic god, in which both Norse mythology and discourse on the nature of poetry are intertwined. The origin of a number of kennings are given and Bragi then delivers a systematic list of kennings for various people, places, and things. Bragi then goes on to discuss poetic language in some detail, in particular heiti , the concept of poetical words which are non-periphrastic, for example "steed" for "horse", and again systematises these. This section contains numerous quotes from skaldic poetry. Háttatal (Old Icelandic "list of verse-forms" )

7553-445: The sense of the contour level of a particular low pressure in the outer atmosphere. In most locations, the largest constituent is the principal lunar semi-diurnal , also known as the M2 tidal constituent or M 2 tidal constituent . Its period is about 12 hours and 25.2 minutes, exactly half a tidal lunar day , which is the average time separating one lunar zenith from the next, and thus

7644-487: The sleeping Skrýmir with his hammer. Skrýmir awakes after each attempt, only to say that he detected an acorn falling on his head or that he wonders if bits of tree from the branches above have fallen on top of him. After the third attempt, Skrýmir gives them advice; if they are going to be cocky at the castle of Útgarðr it would be better for them to turn back now, for Útgarða-Loki's men there won't put up with it. Skrýmir throws his knapsack onto his back and abruptly goes into

7735-559: The subject of numerous translations. The most recent ones into English have been by Jesse Byock (2006), Anthony Faulkes (1987 / 2nd ed. 1995), Jean Young (1954), and Arthur Gilchrist Brodeur (1916). Many of these translations are abridged; the technical nature of the Háttatal means it is frequently excluded, and the Skáldskaparmál often has its more Old Norse thesaurus aspects abridged as well. Translations into English Translations into other languages Tide Tides are

7826-418: The subtleties of alliterative verse , and to grasp the meaning behind the many kennings used in skaldic poetry. Originally known to scholars simply as Edda , the Prose Edda gained its contemporary name in order to differentiate it from the Poetic Edda . Early scholars of the Prose Edda suspected that there once existed a collection of entire poems, a theory confirmed with the rediscovery of manuscripts of

7917-489: The tides. Isaac Newton (1642–1727) was the first person to explain tides as the product of the gravitational attraction of astronomical masses. His explanation of the tides (and many other phenomena) was published in the Principia (1687) and used his theory of universal gravitation to explain the lunar and solar attractions as the origin of the tide-generating forces. Newton and others before Pierre-Simon Laplace worked

8008-475: The truth, now you are out of my castle, and if I live and have a say, you shall never enter it again, and I would indeed never have let you in if I had known your strength beforehand, and you were very close to bringing us a great disaster. You see, I cast delusions on you, so that it was I who met you at first in the forest; and when you tried to untie the food bag, I had tied it with a magic wire, and you did not find out how to untie it. [...] And when you drank from

8099-400: The visitors could see a murky, repulsive chamber, inside which they descried Utgartha-Loki, his hands and feet laden with a huge weight of fetters. His rank-smelling hairs were as long and tough as spears of cornel -wood. Thorkil kept one of these as a more visible proof of his labours by heaving at it with his friends till it was plucked from the chin of the unresisting figure; immediately such

8190-475: The work " Histoire de la mission de pères capucins en l'Isle de Maragnan et terres circonvoisines ", where he exposed that the Tupinambá people already had an understanding of the relation between the Moon and the tides before Europe. William Thomson (Lord Kelvin) led the first systematic harmonic analysis of tidal records starting in 1867. The main result was the building of a tide-predicting machine using

8281-1133: Was not what it seemed to the group. Útgarða-Loki was in fact the immense Skrýmir, and that if the three blows Thor attempted to land had hit their mark, the first would have killed Skrýmir. In reality, Thor's blows were so powerful that they had resulted in three square valleys. "Nú skal segja þér hit sanna, er þú ert út kominn or borginni, at ef ek lifi ok megak ráða, þá skaltu aldri optarr í hana koma; ok þát veit trúa mín, at aldri hefðir þú í hana komit, ef ek hefða vitat áðr, at þú hefðir svá mikinn krapt með þér, ok þú hafðir svá nær haft oss mikilli ófœru. Enn sjónhverfingar hefi ek gert þér, svá at fyrsta sinn, er ek fann þik á skóginum, kom ek til fundar við yðr; ok þá er þú skyldir leysa nestbaggann, þá hafðak bundit med gresjárni, enn þú fannt eigi, hvar upp skyldi lúka. [...] Enn er þú drakkt af horninu, ok þótti þér seint liða; en þát veit trúa min, at þá varð þat unðr, er ek munda eigi trúa at vera mætti; annarr endir hornsins var út i hafi, enn þat sáttú eigi; enn nú, er þú kemr til sjávarins, þá muntú sjá mega, hvern þurð þú hefir drukkit á sænum; þat eru nú fjörur kallaðar." "I shall tell you

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