"Christ is an ALMIGHTY Savior, and a Savior for all mankind. He "takes away the sin of the world." He did not die for the Jews only, but for the Gentile as well as the Jew. He did not suffer for a few people only, but for all mankind. The payment that He made on the cross was more than enough to make satisfaction for the debts of all. The blood that He shed was precious enough to wash away the sins of all. His atonement on the cross was sufficient for all mankind, though efficient only to those who believe. The sin that He took up and bore on the cross was the sin of the whole world." (Comment on John 1:29).
I think those who claim J. C. Ryle was an Amyraldian are wrong because five point Calvinists believe everything Ryle has said here. Christ DID die for the sins of the whole world AND His death is sufficient for the sins of the whole world. But it is only "efficient" for those who believe. Unless you can show that Ryle does not believe in predestination, unconditional election and irresistible grace, it would be very difficult to paint him as an Amyraldian simply on the basis of this comment.
In fact, I checked Ryle's sermon on predestination and election and he says that only the elect will believe:
"Those men and women whom God has been pleased to choose from all eternity, He calls in time, by His Spirit working in due season. He convinces them of sin. He leads them to Christ. He works in them repentance and faith. He converts, renews, and sanctifies them. He keeps them by His grace from falling away entirely, and finally brings them safe to glory. In short, God’s eternal Election is the first link in that chain of a sinner’s salvation of which heavenly glory is the end. None ever repent, believe, and are born again, except the Elect. The primary and original cause of a saint’s being what he is, is eternal God’s election." (From, "Election," by J. C. Ryle.).
It is very clear that Ryle has borrowed from Article XVII in formulating his understanding of the biblical doctrine of election:
Of Predestination and Election
"Predestination to life is the everlasting purpose of God, whereby, before the foundations of the world were laid, He hath constantly decreed by His counsel secret to us, to deliver from curse and damnation those whom He hath chosen in Christ out of mankind, and to bring them by Christ to everlasting salvation as vessels made to honour. Wherefore they which be endued with so excellent a benefit of God be called according to God's purpose by His Spirit working in due season; they through grace obey the calling; they be justified freely; they be made sons of God by adoption; they be made like the image of His only-begotten Son Jesus Christ; they walk religiously in good works; and at length by God's mercy they attain to everlasting felicity."
"As the godly consideration of Predestination and our Election in Christ is full of sweet, pleasant, and unspeakable comfort to godly persons and such as feel in themselves the working of the Spirit of Christ, mortifying the works of the flesh and their earthly members and drawing up their mind to high and heavenly things, as well because it doth greatly establish and confirm their faith of eternal salvation to be enjoyed through Christ, as because it doth fervently kindle their love towards God: so for curious and carnal persons, lacking the Spirit of Christ, to have continually before their eyes the sentence of God's Predestination is a most dangerous downfall, whereby the devil doth thrust them either into desperation or into wretchlessness of most unclean living no less perilous than desperation."
"Furthermore, we must receive God's promises in such wise as they be generally set forth in Holy Scripture; and in our doings that will of God is to be followed which we have expressly declared unto us in the word of God."
There are many inconsistent Anglicans out there who reject the solid Augustinian, five point Calvinist views espoused in the 39 Articles and in the Lambeth Articles of 1595. However, they are inconsistent with the English Reformers and with later Reformed Anglicans like J.C. Ryle. The Reformed Anglican theology is Protestant, Reformed, Augustinian, and Calvinistic, which would include all five points of the Canons of Dordt.
It is interesting to note that even those opposed to Calvinism admit that the Lambeth Articles reflect the teaching of the Canons of Dordt in 1618-19:
"The Lambeth Articles were accepted at the 1615 Convocation of Dublin and consequently engrafted on the Irish Articles (written by James Ussher). One can find the basis of the Five Points of Calvinism, contained in the Canons of Dort (1618-19) in the Lambeth Articles." (From, "Lambeth Articles," at Wikipedia.
In an article on the Church Society website on the Lambeth Articles, it is pointed out that Bishop Ussher utilized the Lambeth Articles in formulating the Irish Articles of Religion of 1615, which also reflect the solid five point Calvinism of both the Lambeth Articles 1595 and the Canons of Dordt 1619. Thus, those who try to force Amyraldian views into the historical context of the English representatives at Dordt are tendentious. Obviously, Archbishop James Ussher of Ireland was a five point Calvinist and in favor of the decision at Dordt.
For a thorough critique of the Amyraldian view see, "The Amyraldian View Undone." Another excellent resource is Lee Gatiss' paper on limited atonement, "Limited Atonement: A biblical, theological, and practical investigation." While I disagree with Gatiss' assessment of J. C. Ryle as an Amyraldian, his paper is otherwise an excellent assessment of both views. I would disagree with him, however, that Amyraldianism is not a heresy since the Lambeth Articles 1595, the Irish Articles of Religion, and the Thirty-Nine Articles all seem to hold to a five point Calvinist position. Amyraldianism is a secondary heresy within the church. While holding Amyraldian views does not necessitate excommunication or disfellowship, it is nevertheless a heresy or division in doctrinal issues which leads back in the Arminian and semi-pelagian direction. If Amyraldians were consistent they would either become five point Calvinists or they would go back to the Arminian view for the Amyraldian view is simply a compromise with Arminianism and is not Calvinist at all.