In Zechariah 9, God refers to Ephraim as His arrow and Judah as His bow. Given that Ephraim had been scattered for some 200 years at the time the prophecy was written, what could this mean?

First consider Zechariah chapter 9 as a whole:

 - The first eight verses describe Alexander's conquest of Syria, Tyre and Philistia in 331BCE; events some 200 years future from Zechariah.

 - Verses 9-10 describe the entry of Messiah riding on a donkey, an event almost 500 years future from Zechariah. They also describe the millennial reign of the Messiah.

 - Verses 11-12 describe the return of Joseph from exile which has not yet happened.

 - Verse 13 is the Maccabean revolt against Greece which is over 300 years future to Zechariah.

 - Finally verses 14-17 appear to foretell the Messianic Kingdom which is yet future today.

That's quite a span of time contained in just 17 verses of Scripture.

The interesting part is that the chapter seems not to be chronologically consistent. Consider:

          9:11 As for you also, because of the blood of my covenant with you,

          I will set your prisoners free from the waterless pit.

          9:12 Return to your stronghold, O prisoners of hope;

          today I declare that I will restore to you double. (ESV)       

Here is the return of Joseph from exile. Joseph was the brother thrown into a waterless pit by his brothers and then sold into exile in Egypt. So God remembering His covenant, redeeming Joseph and restoring double to him refers to the Northern Kingdom which was exiled by the Assyrians. Further, Joseph was elevated to the position of first born by Jacob and so would get a double portion. In itself this is not remarkable; other prophets also foretell the return of Ephraim. What makes this strange is the next verse:

          9:13 For I have bent Judah as my bow;

                   I have made Ephraim its arrow.

                   I will stir up your sons, O Zion,

                   against your sons, O Greece,

                   and wield you like a warrior’s sword. (ESV)

The second sentence of the verse predicts the Maccabean rebellion against Greece. Ephraim had no identifiable part to play in that event; it was actually led by Levi. One may assume that since Judah had led the return from Babylon, they were enthusiastic participants, but Joseph is not mentioned.

It is the first sentence that is of interest. The word 'for' indicates that this is a continuation of the previous thought and the verbs are in the past tense. So paraphrasing verses 11-13: "Because of my covenant and because I used you as an arrow, I will return your descendants to their land and restore to you double."

The metaphor of bow and arrow fits the historical events. Not to put too fine a point on it, the arrow flies toward its target while the bow remains in the archer's hand. Ephraim was sent out while Judah remained in the Land for another century and a quarter. This was even though the contemporary prophet Isaiah described the sins of Judah as being pretty much on a par with those of the House of Israel (Isaiah chapters 1-5).

Consider also that the division of Israel into two kingdoms was instituted by God Himself. 1 Kings 11:26-39 explains how He intended to take ten tribes away from the 'hand of Solomon' and give them to Jeroboam. Thus the plan to shoot Ephraim as an arrow into the gentile nations seems to have been put into motion at least two centuries before the actual Assyrian dispersion. Going back to the blessing of Jacob in Gen 49 it is possible to see these same themes:

          Ge 49:22 “Joseph is a fruitful bough,

                   a fruitful bough by a spring;

                   his branches run over the wall.

          23 The archers bitterly attacked him,

                   shot at him, and harassed him severely,

          24 yet his bow remained unmoved;

                   his arms were made agile

                   by the hands of the Mighty One of Jacob (ESV)

Joseph's branches running over the wall could indicate his spreading beyond the land and nation of Israel. In the Egyptian exile Joseph was the first son to leave the land of Israel. Similarly, Joseph (the ten northern tribes lead by Ephraim) was the first to be expelled from the Land in the current dispersion.  In the Egyptian exile, although it was Joseph’s ten brothers who wanted to get rid of him, the idea to sell him to Egypt was Judah’s. Hence, Judah was the archer who shot Joseph out of the Land and into Egypt. In the case of the Assyrian exile, God describes Himself as the archer who shot Ephraim out of the land, but He used Judah as the bow. So the metaphor is used consistently.

In the metaphor of Ephraim’s being God's arrow shot into the dispersion, what is His target? To answer this, consider first the call of Abraham:

          Ge 12:1 Now the Lord said to Abram, “Go from your country and your kindred and your father’s house to the land that I will show you. 2 And I will make of you a great nation, and I will bless you and make your name great, so that you will be a blessing. 3 I will bless those who bless you, and him who dishonors you I will curse, and in you all the families of the earth shall be blessed.”

It has always been God's intention that His Kingdom extend to the whole earth, not just to Israel. This theme is repeated in Exodus:

          Ex 19:5 Now therefore, if you will indeed obey my voice and keep my covenant, you shall be my treasured possession among all peoples, for all the earth is mine; 6 and you shall be to me a kingdom of priests and a holy nation. These are the words that you shall speak to the people of Israel.”

It is the function of a priest to:

Le 10:10 ...distinguish between the holy and the common, and between the unclean and the clean, 11 and you are to teach the people of Israel all the statutes that the Lord has spoken to them by Moses.

By that definition, it was always God’s intention that Israel go to the nations and teach them how to live in His Kingdom. When Israel sinned at Sinai with the Golden Calf, the priesthood became the province of Levi instead of the entire nation.

Historically the effect of the various dispersions has been to 'seed' the region from Egypt to Greece and from Spain to India with people who knew of God and His Scriptures. Some of those seeds that God scattered are identifiable as the House of Judah – Jews; others have lost their identity over the centuries, but at the time of Christ many were still identifiable as Israel.

        Jas 1:1 James, a servant of God and of the Lord Jesus Christ,

To the twelve tribes in the Dispersion: Greetings.  (ESV)

This seeding of Hebrews throughout the ancient world greatly facilitated the rapid spread of the Gospel. So it appears that the nations were God’s intended target when He shot Ephraim as an arrow.