How do I say the word “bow” in the sentence “I set my bow in the clouds...”?

Arches and arcs, bows and rainbows

This one is actually spelled the way it’s said! It has the GOAT vowel, so it rhymes with the English words snow and no. That’s bow as in a bow-tie or even the elbow of your arm, so it’s pronounced /boʊ/ written in the International Phonetic Alphabet (sometimes also transcribed /bow/ phonemically).

That’s because your quote from Genesis 9:13 refers to the arc of a bow, the one that’s used by hunters. The KJV translation for that verse reads:

I do set my bow in the cloud, and it shall be for a token of a covenant between me and the earth.

^{_{Image Credit: Eric Rolph’s photo of a double rainbow in Wrangell–St. Elias National Park Alaska on Wikipedia}}

Indeed, a rainbow is itself the arc of a circle:

The arc is the round part, the chord (string) would be the line connecting the endpoints — which is why in Spanish they call a rainbow an arcoíris, meaning Iris’s arc. It was so named after the Greek goddess of the rainbow, Iris, who was Hera’s handmaiden and messenger.

Even English has used Iris to mean the rainbow. Caxton back in 1490 wrote that:

Yris..is the rayen bowe wyth hir fayr cote of dyuerse fygures.

(Read: Iris..is the rainbow with her fair coat of diverse figures.)

Shakespeare himself used Iris this way, something of a Hellenistic personification to refer to the rainbow, when in 1609 he wrote in Troilus and Cressida:

His crest that prouder then blew Iris bends.

Later in All’s Well That Ends Well he wrote of Iris in a more figurative sense as a halo of prismatic colors:

What's the matter, That this distempered messenger of wet? The manie colour'd Iris rounds thine eye?

Historical associations

The rainbow has ancient associations with divine messages, both in English and elsewhere. A Middle English reference from the 1300s speaks of the rainbow as Juno’s (Roman for Greek Hera’s) messenger. In the Theoi Project’s article on the goddess, they write:

For the coastal-dwelling Greeks, the rainbow’s arc was most often seen spanning the distance beteween cloud and sea, and so the goddess was believed to replenish the rain-clouds with water from the sea.

Indeed in Spanish, Genesis 9:13 runs something like this:

Mi arco pondré en las nubes, el cual será por señal de convenio entre mí y la tierra.

The Latin Vulgate for that verse also used arc as in an arch or a bow, reading:

Arcum meum ponam in nubibus et erit signum foederis inter me et inter terram.

The use of the word arc for a curve in the sky was not unique to the Romance languages. Geoffery Chaucer writing in Middle English referred to the heavenly arc in his Merchant’s Tale from around 1386:

Parfourmed hath the sonne his ark diourne.

That’s Middle English for what we might today write “The sun has performed his diurnal arc.” That’s in fact the first citation of the word used for celestial courses in English per the OED. The word bow had for ages been used for the rainbow itself, for even more anciently in Old English Ælfric translated a bit of that part of Genesis that you reference as:

Æteowþ min boᵹa on ðam wolcnum.

In other copies of the verse translated into Old English, we find renboᵹan used for rainbow instead:

Ic sette minne renboᵹan [L. arcum meum] on wolcnum.

(Wolcnum in Old English was the dative plural of a word meaning the heavens or skies.)

As you see, Old English spelled it boᵹa but that G was weak, so this developed first into Middle English’s boȝe, bouwe, boghe and then into Modern English bow. That original G from Old English can still be seen in some of English’s Germanic cousins: German has Bogen for it, Dutch boog, and Norwegian boge, but Danish like English has lost the G leaving Danish with only bue in that language.

The rain- part of rainbow came later; as just shown above, Old English just had (its spelling of) bow to mean rainbow, a use still sometimes found even in later versions of English. Poets have historically used bow to mean rainbow:

• 1667 Milton Paradise Lost xi. 865 — A dewie Cloud, and in the Cloud a Bow .
• 1728 J. Thomson Spring 13 — Bestriding Earth, the grand ætherial Bow.
• 1850 Tennyson In Memoriam cxx. 189 — Every dew-drop paints a bow.