The Olive Tree (Romans 11)

Introduction

Paul used the illustration of an olive tree in Romans 11 to disclose one of Scripture’s most important doctrines. Understanding what Paul taught by this illustration is critical for the serious student of the Bible. By the olive tree example, Paul revealed God’s sovereign plan for Israel and Gentiles. He revealed Israel’s place in God’s plan (past, present, and future) and how Gentiles have received a new relationship with God.

According to God’s prophetic, Old Testament program, outlined in Psalm 2, Gentiles were to be blessed through God’s covenant with Abraham (Genesis 12.1-3). Gentile blessing in the Old Testament was, therefore, dependent upon Israel’s obedience to God. After Israel’s rejection of their Messiah (Acts 2.22-24, 3.13-15, 7.51-53) and the offered kingdom of God, God commissioned Saul of Tarsus, who became Paul the Apostle. The ascended Lord revealed to Paul a new plan of blessing for Gentiles. This new plan was not based upon Israel’s obedience but was a result of their disobedience. Instead of pouring out His wrath according to the Old Testament prophetic program (cf. Joel 2, which Peter had quoted on the Day of Pentecost), God poured out His mercy through the salvation of Paul. The risen Lord commissioned Paul as “the Apostle to the Gentiles” (Romans 11.13) and Paul proclaimed the “gospel of the grace of God” (Acts 20.24; 1 Corinthians 15.1-4). Paul explained that despite Israel’s disobedience, God’s dealings with the nation had not ended. Their being set aside and God’s disapproval was temporary. God would fulfill all His promises at the proper time despite their disobedience.

The Context

Romans 11 concluded Paul’s dissertation on Israel which he began in Romans 9. The three chapters of Romans–9, 10, and 11–interrupt Paul’s main argument in his epistle. One can place chapter 12 next to chapter 8 and not miss a beat. Having said this, these three chapters are critical to understand God’s overall plan for Jews and Gentiles. In other words, while Romans 9-11 is parenthetical to Paul’s main argument, it provides a framework and the context for his main argument (Romans 1-8 and 12-16).

Paul began his argument in Romans 9 in the following manner:

¹ I am telling the truth in Christ, I am not lying, my conscience testifies with me in the Holy Spirit, ² that I have great sorrow and unceasing grief in my heart. ³ For I could wish that I myself were accursed, separated from Christ for the sake of my brethren, my kinsmen according to the flesh, ⁴ who are Israelites, to whom belongs the adoption as sons, and the glory and the covenants and the giving of the Law and the temple service and the promises, ⁵ whose are the fathers, and from whom is the Christ according to the flesh, who is over all, God blessed forever. Amen.

We notice the following from these verses:

1. Paul was brokenhearted over Israel’s unrelenting attitude of rejection of their Messiah (λύπη μοί ἐστιν μεγάλη καὶ ἀδιάλειπτος ὀδύνη). Paul was distraught to the point that if it were possible he would suffer hell to save Israel.¹
2. Paul’s subject was racial Israel.²  He expressed this fact as “his kinsmen according to the flesh” (ἀδελφῶν μου τῶν συγγενῶν μου κατὰ σάρκα). Paul declared that to racial Jews belonged:

a. The adoption as sons
b. The glory and the covenants
c. The giving of the Law, temple service, and the promises

They were the fathers from whom Christ had come according to the flesh. Jesus the Christ was a racial Jew. None of these blessings pertained to Gentiles. God gave them exclusively to Israel. This point is essential to establish, understand, and keep in mind throughout the three chapters. Without this foundation, one cannot understand Paul’s argument or progress further into the text.

The Text: Romans 11

God Preserves a Remnant

¹ I say then, God has not rejected His people, has He? May it never be! For I too am an Israelite, a descendant of Abraham, of the tribe of Benjamin. ² God has not rejected His people whom He foreknew Or do you not know what the Scripture says in the passage about Elijah, how he pleads with God against Israel? ³ “Lord, THEY HAVE KILLED YOUR PROPHETS, THEY HAVE TORN DOWN YOUR ALTARS, AND I ALONE AM LEFT, AND THEY ARE SEEKING MY LIFE.” ⁴ But what is the divine response to him? “I HAVE KEPT for Myself SEVEN THOUSAND MEN WHO HAVE NOT BOWED THE KNEE TO BAAL.” ⁵ In the same way then, there has also come to be at the present time a remnant according to God’s gracious choice. ⁶ But if it is by grace, it is no longer on the basis of works, otherwise grace is no longer grace (Romans 11.1-6).

As noted above, Paul’s subject was national Israel (“His people”). Paul confirmed this fact with his statement that he was an Israelite (a Jew), a descendant of Abraham from the tribe of Benjamin. Paul answered his question of whether God had rejected the Jews with the strongest negative he employed (μὴ γένοιτο). Paul used this negative twice in this passage to make this point (vv. 1, 11). Despite the nation’s rejection of their Messiah, God had a future plan for national Israel independent and apart from His work of forming the Church, the body of Christ. Thus, Paul emphatically stated, “God has not rejected His people whom He foreknew.” One may ask why Paul keep hammering the point that his subject was racial Jews, national Israel? Through the guidance of the Holy Spirit, Paul anticipated the rise of false teachings which maintain the Church is the new Israel or that all blessings to Israel (present and future) now come through the Church. Paul made this point so strongly that one has to exert great effort and wrestle the text to get a different meaning. Those who maintain God has no future plan for national Israel have done just this. The greatest theological tragedy in the past 1,900 years is that most of Christendom has rejected Pauline theology and declared exactly the opposite what Paul wrote: Israel is independent from the Church and that God has a future plan for Israel as a national entity.³

Paul reminded his readers of God’s faithfulness to Israel by the example of Elijah. Elijah’s ministry to Israel made him angry, frustrated, and lonely. Depressed at the unfaithfulness of his people, Elijah thought he was the only believer in the entire nation. He faced 450 of Baal’s prophets and 400 prophets of the Asherah alone (1 Kings 18.19). This was tough odds for any contest. But God assured him He had 7,000 believers who had not bowed to Baal. Thus, even in this time of great spiritual darkness and decline (Ahab was king and Jezebel queen), God preserved a faithful remnant. Paul’s point was that God always has a remnant. In Paul’s day, a remnant of Jews believed Jesus was the promised Messiah (cf. Romans 9.6). This remnant was according to “God’s gracious choice” and was a result of grace rather than works.

⁷ What then? What Israel is seeking, it has not obtained, but those who were chosen obtained it, and the rest were hardened; ⁸ just as it is written, “GOD GAVE THEM A SPIRIT OF STUPOR, EYES TO SEE NOT AND EARS TO HEAR NOT, DOWN TO THIS VERY DAY.” ⁹ And David says, “LET THEIR TABLE BECOME A SNARE AND A TRAP, AND A STUMBLING BLOCK AND A RETRIBUTION TO THEM. ¹⁰ “LET THEIR EYES BE DARKENED TO SEE NOT, AND BEND THEIR BACKS FOREVER.”

Paul used the above verses to fortify his point. National Israel had not obtained their Messiah because they refused to repent and come to Him. However, individual Jews had obtained their Messiah for they had believed in Him. The majority of the nation became hardened. Paul used the aorist, passive, indicative of πωρόω which means to harden by reason of a callus. Metaphorically, it means they had become dull of understanding.

¹¹ I say then, they did not stumble so as to fall, did they? May it never be! But by their transgression salvation has come to the Gentiles, to make them jealous. ¹² Now if their transgression is riches for the world and their failure is riches for the Gentiles, how much more will their fulfillment be! ¹³ But I am speaking to you who are Gentiles. Inasmuch then as I am an apostle of Gentiles, I magnify my ministry, ¹⁴ if some how I might move to jealousy my fellow countrymen and save some of them. ¹⁵ For if their rejection is the reconciliation of the world, what will their acceptance be but life from the dead?

Verse 11 is a parallel of verse 1. Here, for the second time, Paul employed his strong idiomatic negative (μὴ γένοιτο) in response to his question. In the latter part of the verse, Paul explained the result of Israel’s stumbling. The first reason was so salvation might come to Gentiles. What did Paul mean by this statement? With God’s call of Abraham, God laid the foundation for the creation of a new race, the Jews. From that time forward He dealt with them exclusively (with a few exceptions). In this new plan, Gentiles were blessed through Israel on the basis of the Abrahamic covenant. This was God’s revealed plan to bless Gentiles. God had revealed no other plan in which Gentiles could be blessed apart from the favored nation. What Paul revealed in these verses was that God had now created a new plan in which Gentiles could be blessed apart from national Israel. Thus, Paul wrote, “by their transgression salvation has come to the Gentiles” and “if their transgression is riches for the world and their failure is riches for the Gentiles.”⁴ Notice Paul’s words: transgression (παράπτωμα) and failure (ἥττημα) had resulted in riches (πλοῦτος) for Gentiles. This was impossible under the Old Testament, covenant program.

In the latter part of verse 12, Paul introduced the future hope of Israel. Israel’s stumbling had resulted in Gentiles being blessed through God’s call of the Apostle Paul as “the apostle of the Gentiles” (Romans 11.13) But God had not forgotten Israel. He would fulfill His covenant promises to the nation. They would become what God intended for them (e.g., Exodus 19.4-6). God is sovereign and His plans cannot be overturned. Thus, Paul wrote that if Israel’s transgression (disobedience) had resulted in Gentile blessing, imagine what would happen when they obeyed God (πόσῳ μᾶλλον τὸ πλήρωμα αὐτῶν). Paul’s phrase was, “how much more the fullness of them” and in verse 15, τίς ἡ πρόσλημψις εἰ μὴ ζωὴ ἐκ νεκρῶν, “what will their receiving (πρόσλημψις) if not life from the dead?” The Greek noun πρόσλημψις is a ἅπαξ λεγόμενον and is related to the verb προσλαμβάνω. Paul’s used this word to mean “accept” or “receive” those who were formerly estranged (cf. Romans 14.1, 3, 15.7; Philemon 1.17).

Paul’s second explanation of how good had come from Israel’s stumbling was his hope that as “the apostle of the Gentiles” (Romans 11.13) he might cause Jews to become jealous of and long for the blessings Gentiles were receiving in Christ. Paul hoped Israel’s jealousy would lead them to Christ.

Gentiles Grafted into the Olive Tree

¹⁶ If the first piece of dough is holy, the lump is also; and if the root is holy, the branches are too. ¹⁷ But if some of the branches were broken off, and you, being a wild olive, were grafted in among them and became partaker with them of the rich root of the olive tree, ¹⁸ do not be arrogant toward the branches; but if you are arrogant, remember that it is not you who supports the root, but the root supports you. ¹⁹ You will say then, “Branches were broken off so that I might be grafted in.” ²⁰ Quite right, they were broken off for their unbelief, but you stand by your faith Do not be conceited, but fear; ²¹ for if God did not spare the natural branches, He will not spare you, either (Romans 11.16-21).

Paul began his analogy of the olive tree with an example of a lump of dough. Just as a piece of dough from the lump shares the properties of the whole lump, the branches of a tree share the properties of the root. If a lump of dough is holy, a piece of the lump is holy. If the root is holy, so too the branches.

The olive tree represented God’s place of blessing. The Abrahamic covenant is the olive tree. The Jewish nation acquired their place of blessing from the Abrahamic Covenant. Paul likened Israel as natural branches of a cultivated olive tree (Romans 11.24). God’s subsequent covenants with them (Land, Mosaic, Sabbatical, Davidic, and New) were the “cultivation.” Gentiles, on the other hand, were wild branches. Gentiles had no covenants (Ephesians 2.11-12) and God had set Gentiles aside when He called Abraham. The Abrahamic Covenant ended God’s direct dealing with Gentiles. All God’s dealings with Gentiles from that point going forward were mediated through Israel.

Due to their unbelief (stumbling, transgression) God broke off national Israel (natural branches) from the tree. God then grafted Gentiles (wild olive tree branches) into the place of blessing. Gentiles now occupy the place of blessing previously held by Israel.

Notice Paul did not mention the Church, the body of Christ, in his illustration. This place of blessing is for ALL Gentiles, not just the Church. This is an important point to apprehend and requires some reflection. In God’s covenant program, Israel occupied God’s special place of blessing. Were all Jews saved? No, most were not saved. Yet they occupied the position of blessing. In the same way, God has placed Gentiles into his special place of blessing. Are all Gentiles saved? No, most are not saved.

In the program God revealed to Israel, Gentiles could be blessed only through a relationship or association with Israel. In God’s program of the Church, the body of Christ, both Jews and Gentiles are blessed by believing the gospel of grace (1 Corinthians 15.1-4). Peter’s remarkable statement at the Council of Jerusalem confirmed this fact (cf. Acts 15.7-12). Such a statement would have been impossible in the Jerusalem church before the Council. Two things are noteworthy:

1. One plan operates at a time. When natural branches were on the tree, wild branches were not. Wild branches were grafted in when the natural branches were broken off.
2. Most of those blessed by God in the Old Testament program were Jews. That was the status quo for 2,000 years. Since the time of Paul, most who have been blessed by God are Gentiles–the new status quo for the past 2,000 years.

In verse 17, Paul issued a warning to the wild branches (Gentiles):

• Warning to Gentiles: Do not boast against (κατακαυχάομαι) the natural branches (Israel).
• Question: Why not?
• Answer: Because the wild branches (Gentiles) do not support the root (God, the Abrahamic covenant, the source of blessing)–the root supports the branches.
• Objection: But the natural branches, (i.e., Israel) were broken off so that I, the wild branches (i.e., Gentiles) might be grafted in.
• Rebuttal: Correct–but remember–the natural branches (Israel) were removed because of unbelief. The wild branches (Gentiles) stand only by faith. Don’t be conceited but fear. If God broke off the natural branches (Israel) do you think He would not remove wild branches (Gentiles)?

²² Behold then the kindness and severity of God; to those who fell, severity, but to you, God’s kindness, if you continue in His kindness; otherwise you also will be cut off. ²³ And they also, if they do not continue in their unbelief, will be grafted in, for God is able to graft them in again. ²⁴ For if you were cut off from what is by nature a wild olive tree, and were grafted contrary to nature into a cultivated olive tree, how much more will these who are the natural branches be grafted into their own olive tree? (Romans 11.22-24)

The kindness of God was grafting wild branches (Gentiles) into the olive tree. His severity was breaking off the natural branches (Israel) from this place of blessing. God’s kindness is experienced upon response (faith) to His kindness. Paul warned Gentiles, like Israel, only stand by faith.

Both verses 22 and 23 are third class conditional sentences, “more probable future condition” (ἐὰν plus the verb in the protasis in the subjunctive mood). The “if” is assumed to be probable or true. Thus, Paul assumed Gentiles, in particular, the Church, would continue in faith (v. 22), just as he assumed Israel would not continue in unbelief (v. 23) but would be regrafted into the olive tree. Paul had more to write on this matter in the following verses but suffice to say at this point that He understood and relied upon God’s sovereignty from passages such as Zechariah 12.10, 13.5-6, and Matthew 23.37-39 to make his point.

Paul ended this section with the statement in verse 24: “For if you were cut off from what is by nature a wild olive tree, and were grafted contrary to nature into a cultivated olive tree, how much more will these who are the natural branches be grafted into their own olive tree?” In this statement, “if” is a first class condition (εἰ plus the indicative) and the condition is assumed to be true. Gentiles, likened as wild olive branches, were grafted “against nature,” i.e., without covenants, into a cultivated olive tree (the place of blessing). If this was so (and it was), Paul asked how much more likely would it be that the natural branches would be regrafted into their own tree.

²⁵ For I do not want you, brethren, to be uninformed of this mystery–so that you will not be wise in your own estimation–that a partial hardening has happened to Israel until the fullness of the Gentiles has come in; ²⁶ and so all Israel will be saved; just as it is written, “THE DELIVERER WILL COME FROM ZION, HE WILL REMOVE UNGODLINESS FROM JACOB.” ²⁷ “THIS IS MY COVENANT WITH THEM, WHEN I TAKE AWAY THEIR SINS.”

As noted above, God provided Paul with the revelation that Israel’s present condition of unbelief would end. Paul knew the Old Testament promises and the words of the Lord Jesus during His earthly ministry. But the ascended Lord had revealed to him a “secret” about Israel’s blindness. Paul revealed “this secret” (τὸ μυστήριον τοῦτο) to ward off any inclination by the Church (composed chiefly of Gentiles) to be “wise in your own estimation,” i.e., the temptation to “boast against the branches” (Israel) that had been cut off. This secret was “a partial hardening has happened to Israel until the fullness of the Gentiles has come in; and so all Israel will be saved.” The partial hardening (πώρωσις ἀπὸ μέρους) was/is national Israel’s present condition of unbelief. It is partial for not every Jew is hardened by unbelief. Thus, the hardening affected national Israel, not individual Jews. Paul also revealed the secret of how long this condition would afflict the nation. It would continue until “the fullness of the Gentiles has come in” (ἄχρις οὗ τὸ πλήρωμα τῶν ἐθνῶν εἰσέλθῃ).

What did Paul mean by the “fullness of the Gentiles?” In light of the context of Paul’s argument, the phrase must refer to the completion of the body of Christ, the Church. No distinction in this age exists between Jew and Gentile in the body of Christ (Romans 10.12; Colossians 3.11) yet the Church is composed primarily of Gentiles. Thus, Paul employed the phrase, “fullness of the Gentiles” to refer to the Church which is composed mainly of Gentiles. God alone knows when He will complete His body but completion will occur when the last person trusts in Christ by believing Paul’s gospel of grace (1 Corinthians 15.1-4). When the body of Christ (the Church) is complete, God will remove it from the earth.

Once God removes the Church from earth He will restart His covenantal plan with national Israel and Israel’s blindness will begin to be lifted. Luke’s account in Acts 13.6-12 of Paul’s confrontation with Elymas, the Jewish the magician, was a prophetic anticipation of this truth. Paul told the false prophet he would “not see the sun for a time” (μὴ βλέπων τὸν ἥλιον ἄχρι καιροῦ). John revealed God will use the events described in the book of Revelation to convince the Jews that Jesus is the true Messiah, not the Beast. At the mid-point of the Tribulation, after 3 ^1/2 of the 7 years have passed, Jesus instructed the Jews to flee to the mountains when they saw the abomination of desolation (Matthew 24.15-16; Daniel 9.27, 12.11). As Jews see the words of Scripture being fulfilled, their spiritual eyes will begin to see (1 Corinthians 1.22). Some will began to recognize the one they accepted as Messiah is a pretender (John 5.43). At the end of the seven years (the end of Daniel’s 70th week–the Tribulation, the Day of the Lord, Revelation 1.10) every Jew will be saved (Romans 11.26), “all Israel will be saved”).⁵

When Paul stated “all Israel” (πᾶς Ἰσραὴλ) he meant “all Israel,” i.e., every Jew who is alive at the time. Peter had declared this same message to the nation on the Day of Pentecost. He told the nation, “let all the house of Israel know” (Acts 2.36). He told them they had killed their Messiah. When they asked him what they must do Peter replied,

“Repent, and each of you be baptized in the name of Jesus Christ for the forgiveness of your sins; and you will receive the gift of the Holy Spirit” (Acts 2.38)

The word “each” is ἕκαστος which means “each” or “every.” Every Jew had to repent (cf. Acts 4.10, 13.24). Peter’s message at Pentecost was a repeat of Jesus’ teaching:

³⁷ “Jerusalem, Jerusalem, who kills the prophets and stones those who are sent to her! How often I wanted to gather your children together, the way a hen gathers her chicks under her wings, and you were unwilling. ³⁸ Behold, your house is being left to you desolate! ³⁹ For I say to you, from now on you will not see Me until you say, ‘BLESSED IS HE WHO COMES IN THE NAME OF THE LORD!’” (Matthew 23.37-38)

In a future day, every single Jew will repent and verbalize (either aloud or in his heart) Jesus’ words. When these words are spoken, the prophecy will be fulfilled. Jesus will return and fulfill His promise as Israel’s Messiah. Thus, “all Israel” will be saved (cf. Isaiah 66.8; Ezekiel 39.25-29).

To demonstrate God’s faithfulness to save all Israel, Paul quoted the prophets:

²⁶ and so all Israel will be saved; just as it is written, “THE DELIVERER WILL COME FROM ZION, HE WILL REMOVE UNGODLINESS FROM JACOB.”” ²⁷ “THIS IS MY COVENANT WITH THEM, WHEN I TAKE AWAY THEIR SINS.” ²⁸ From the standpoint of the gospel they are enemies for your sake, but from the standpoint of God’s choice they are beloved for the sake of the fathers; ²⁹ for the gifts and the calling of God are irrevocable. ³⁰ For just as you once were disobedient to God, but now have been shown mercy because of their disobedience, ³¹ so these also now have been disobedient, that because of the mercy shown to you they also may now be shown mercy. ³² For God has shut up all in disobedience so that He may show mercy to all.

The clear implication of the quotation “remove ungodliness from Jacob” is that the removal will be total: the entire nation. To men, events often seem out of place and without reason. But not to God. Paul concluded God will sovereignly bring all things to their proper end. No one received greater persecution from his kinsmen than Paul. Yet he concluded, “they are enemies for your sake” but “beloved for the sake of the fathers.” Paul knew God was sovereign. His statement, “the gifts and the calling of God are irrevocable” is the strongest statement possible to acknowledge that God has not forgotten the Jewish nation. He created her and will keep His promises. This statement should make ashamed any who hold to replacement theology.

Paul reminded his Gentiles readers they too had been disobedient to God but that God had shown them mercy. God’s mercy came not from Israel’s obedience but because of their disobedience. As God had shown mercy to Gentiles through Israel’s disobedience, He would show mercy to Israel when they believe. He concluded: “God has shut up (συγκλείω–to entrap completely like fish in a net) all in disobedience so that He might have mercy to all.” We are all sinners (Romans 3.22-23). We all require God’s mercy. No exceptions.

³³ Oh, the depth of the riches both of the wisdom and knowledge of God! How unsearchable are His judgments and unfathomable His ways! ³⁴ For WHO HAS KNOWN THE MIND OF THE LORD, OR WHO BECAME HIS COUNSELOR? ³⁵ Or WHO HAS FIRST GIVEN TO HIM THAT IT MIGHT BE PAID BACK TO HIM AGAIN? ³⁶ For from Him and through Him and to Him are all things To Him be the glory forever. Amen.

Paul concluded his treatise with a paean of praise to God for his wisdom. God inhabits eternity. He is above all. Who can know His thoughts? He is the Alpha and the Omega and all things are by Him and for Him.

Conclusion

In this tremendous discourse, Paul taught that Gentiles had been brought into a place of blessing and mercy, not through Israel’s obedience as the Old Testament covenantal program had indicated, but through the nation’s disobedience. This blessing was wholly a result of God’s grace. He warned Gentiles not to become arrogant against Israel since their place of blessing was held by faith alone. As God had shown Gentiles mercy in grafting them into the olive tree by breaking off national Israel, He would again show mercy to them and regraft them into the place of blessing. Israel’s blindness and temporary stumbling was a secret: no one before Paul knew about it. The ascended Lord revealed this secret to Paul. Paul communicated the gospel of the grace of God to Gentiles, who are enjoying God’s blessing.

¹ Paul’s attitude parallels Moses’ after Israel worshiped the golden calf while Moses was on Mt. Sinai receiving the Law from God. This event occurred shortly after God miraculously had delivered them from Egypt. Moses asked God to forgive their sin but if not to blot him out of his book, i.e., the book of life (Exodus 32.7-12, 30-32).
² The term “Israel” is a technical term used only of the Jewish people. Neither Gentiles nor the Church is included in the term. See the author’s study, “Israel” as a Technical Term for more information.
³ During the Reformation, significant portions of Christendom returned to Paul and regained an accurate knowledge of soteriology. Tragically, the Church did not recover Pauline teaching in other areas of theology. Great error and confusion continues to exist in ecclesiology, eschatology, and pneumatology. The Church began to abandon Paul’s theology while the great apostle was alive (2 Timothy 1.15, 4.3-4) and this has continued until today.
⁴ Paul assumed the role of Israel in blessing Gentiles as “the apostle of the Gentles.” This is what the great apostle meant by his statement of being “untimely born” in 1 Corinthians 15.8. Representing the nation according to the Abrahamic covenant, Paul became proxy Israel of God’s blessing to Gentiles. In the Millennium, Israel will again assume this role (cf. Zechariah 8.20-23).
⁵ The “gospel of the kingdom,” not the “gospel of the grace of God,” (Acts 20.24) i.e., Paul’s gospel (Romans 16.25; 2.16; 2 Timothy 2.8) will be preached after the Church has been removed (cf. Matthew 24.14). This time, this gospel of repentance (Matthew 3.1-2; 4.17; Mark 1.15; Acts 2.36-38) will result in Israel’s repentance so the Lord can return and establish His kingdom on the earth (Matthew 6.10, 23.37-39 cf. Romans 11.26).

©2011 Don Samdahl. Anyone is free to reproduce this material and distribute it, but it may not be sold.

Updated April 16, 2012