Odin and Billing's Daughter 

None should mock    what many have felt,
Should never blame another;
The wise may fall    while the fool remains
Unmoved by a beautiful body.

What many feel    mock not at all;
The condition is all too common.
The wisest men    are made into fools
By lust for a lovely form.

That I learned    when I lay in the reeds,
And hoped for my heart's desire.
Body and soul    she seemed to me,
But none-the-less I lost her.

Billing's daughter    in bed I saw
Asleep, the sun-white maid.
A noble's pleasure    seemed nothing then
Unless I lay with her.
"Wait, Odin    till after dark,
If you'd win a woman's heart.
It's best that none    know what we do--
Shameful they'd surely think it."

So back I went    to wait my joy,
Though wild with wanting her,
But certain that she    would soon be mine
For love and lustful play.

When next I came,    night had fallen,
But the warriors I found awake
With burning lights    and torches ablaze.
I'd walked a woeful path.

Almost at dawn,    once more I came,
When all inside were sleeping.
Tied to the bed    a bitch I found,
And the lovely girl had gone.

Many a fair maid,    when more you learn,
Is found to be fickle at heart.
I soon learned that    when the subtle maid
I tried to lure to love.
That time she heaped    my head with shame,
And nothing I had from her.
                                              trans. Jack Hart
 This little story from the Havamal is my own translation, and may be used freely.  The meter is ljodahattr, as is the case with the whole Havamal.   This passage covers stanzas 93, 94, 96-102 in Hollander's translation, and is part of a larger section dealing with relations between men and women, and the untrustworthiness of both.  Hollander observes of the story, beginning with stanza 96, "There is hardly any connection to be found with the preceding stanza" (The Poetic Edda 28).  Hollander is correct, but he apparently does not notice that stanzas 96-102 are a perfect fit with the two stanzas before that and, leaving out that one stanza, what remains is a clear, and very tight poem.               
     The purpose of this story is to illustrate that anyone can be made a fool of by love.  One might suspect that the story was simply made up for that purpose.  The detail about hiding in the reeds, however, is totally mysterious, and implies a more elaborate myth than now survives.  The story is self-explanatory, though various scholars have tried to find more than is there.  John Lindow (Norse Mythology 80) has some exceedingly odd comments, starting with "Odin ought not to come up short in any of his encounters, and for that reason it is useful to to speculate on how Odin's failure to seduce Billing's girl may in fact be a success."  None of the gods are infallible, not even Odin.  Odin is especially noted for cleverness, but in the story of how the Langobards got their name, he is bested by Frigga.  Odin is also a god of battle, but at Ragnarok Odin will lose to Fenris.  Probably a little thought would turn up other examples.  It is hardly surprising, therefore, that he should lose once at love as well.  Besides, the story would lose much of its point if Odin was not almost inevitably expected to succeed.  Remember, the point is that ANYONE can be made a fool of by love, and so what better a case in point than Odin, himself?
      Lindow's effort to protect Odin's reputation as a stud, however, take a far stranger turn with the suggestion that not having his way with the dog saves him from committing an act of bestiality, which would be more likely out of the giants.  This poem is not about whether one should or should not sleep with dogs; it is about being tricked by a girl.  There is not the slightest sense of self-congratulation in the fact that he does not, only chagrin about being tricked by the girl.  Equally implausible is the idea of a "magic binding" by Odin which the girl manages to deflect onto the dog.  Obviously it is the girl who does the binding, not Odin.  There is nothing here which suggests a plan to take her by force.  Besides, there is no mystery about any of this.  Put yourself in Odin's place.  You go to a girl's bedroom on what you thought was an invitation, and found that she has tied a dog to the bed--I think you'd get the point.  It is a pie in the face.  It is saying something like, "Hey, Mr. Super-Stud, if you think you're so hot, try this female on for size."    
     There is a far more offensive version of this story, though as far as I can tell it is to some extent modern.  It begins with Saxo's History of the Danes.  Saxo is no friend of the Aesir, and no very faithful respecter of sources.  (It is possible that Saxo does have alternate sources for some of his material, but so much of it seems so clearly designed to make the Northern gods look bad that I tend to agree with Dumazil's view that Saxo freely rescripts his material to suit his own agenda.)  According to Saxo Odin makes three tries to seduce Rinda, the daughter of the King of the Rutenians, and is violently rebuffed each time.  Finally, disguised as a woman by magic he makes her insane and tends her, though he gets no opportunity to do more than feel her up until she also gets sick.  At that point he provides medicine so bitter, he claims, that she will only take it if tied up.  While she is bound, he rapes her.  The Rutenians are an actual people, not dwarves, giants, or gods, but Saxo's Odin is also more or less human.  Viktor Rydberg adds that the King's name is Billing.  Finally, we have H.A. Guerber's Myths of the Norsemen.  This version from 1909 both elaborates and softens the story, and is the source of most modern references and retellings. 
      Why this need to tie this small story of failed seduction to Rind and the birth of Vali?  I think for the same reason that so many writers are determined that Odin be successful, even though in defending his reputation on one count they make him thoroughly offensive on another.  Odin must succeed, and no fragment can be left unaccounted for.  (Hollander, without explaining why, suggests the possibility that Billing's daughter might be Gunnloth.)  If we know almost nothing of Billing and his daughter, then their story must be hooked to something we do know.  But it is clear from the poem above that Odin is not interested in Billing's daughter because only she can provide an avenger for Baldr.  He sees her, he lusts for her, and he tries to seduce her.  He fails, but is not so petty and small minded (Unlike so many gods who go ballistic if anyone crosses them) that he can't use his own embarrassment as an illustration for the point he is making.  As a final note on this issue, I know of no serious modern scholar who connects Billing's daughter with Rind.        
    Other Translations

Here are two other translations of this passage.  The one on the left is by Henry Adams Bellows, the one on the right by Benjamin Thorpe.  Both are in the public domain.
Fault for loving    let no man find
Ever with any other;
Oft the wise are fettered,    while fools go free,
By beauty that breeds desire.

Fault with another    let no man find
For what touches many a man;
Wise men oft    into witless fools
Are made by mighty love.

This found I myself,    when I sat in the reeds,
And long my love awaited;
As my life the maiden    wise I loved,
Yet her I never had.

Billing's daughter    I found on her bed,
In slumber bright as the sun;
Empty appeared    an earl's estate
Without that form so fair.
"Othin, again    at evening come,
If a woman thou wouldst win;
Evil it were    if other than we
Should know of such a sin."

Away I hastened,    hoping for joy,
And careless of counsel wise;
Well I believed    that soon I should win
Measureless joy from the maid.

So came I next    when night it was,
The warriors all were awake;
With burning lights    and waving brands
I learned my luckless way.

At morning then,    when once more I came,
And all were sleeping still,
A dog I found    in the fair one's place,
Bound there upon her bed.

Many fair maids,    if a man tries them,
False to a lover are found;
That did I learn    when I longed to gain
With wiles the maiden wise;
Foul scorn was my meed    from the crafty maid,
And naught from the woman I won.
At love should no one
Ever wonder
In another:
A beauteous contenance
Oft captivates the wise,
Which captivates not the foolish.

Let no one wonder at
Another's folly,
It is the lot of many.
All-powerful desire
Makes of the sons of men
Fools even of the wise.

That I experienced,
When in the reeds I sat,
Awaiting my delight.
Body and soul to me
was that discreet maiden:
Nevertheless I possess her not.

Billing's lass
On her couch I found,
Sun-bright, sleeping,
A prince's joy
To me seemed naught,
If not with that form to live.
"Yet nearer eve
Must thou, Odin, come,
If thou wilt talk the maiden over;
All will be disastrous,
Unless we alone
Are privy to such misdeeds."

I returned,
thinking to love,
at her wise desire.
I thought
I should obtain
Her whole heart and love.

When next I came
The bold warriors were
All awake,
With lights burning,
And bearing torches:
Thus was the way to pleasure closed.
But at the approach of morn,
When again I came,
The household all was sleeping;
The good damsel's dog
Alone I found
Tied to the bed.

Many a fair maiden,
When rightly known,
Towards men is fickle:
That I experienced,
When that discreet maiden I
Strove to seduce:
Contumely of every kind
That wily girl
Heaped upon me;
Nor of that damsel gained I aught.
designed with Homestead
Odin I:  a page dealing with the god, Odin.
Odin II:  a continuation of the previous page.
Rune I:  The surving ancient rune poems.
Rune  II:  Modern rune poems.
Rune III:  Odin's rune poem from the Havamal, my translation