Chapter XII of Loraine Boettner’s The Reformed Doctrine of Predestination is called “Limited Atonement.” Here’s Boettner:
“The question which we are to discuss under the subject of ‘Limited Atonement’ is, Did Christ offer up Himself a sacrifice for the whole human race, for every individual without distinction or exception; or did His death have special reference to the elect? In other words, was the sacrifice of Christ merely intended to make the salvation of all men possible, or was it intended to render certain the salvation of those who had been given to Him by the Father? Arminians hold that Christ died for all men alike, while Calvinists hold that in the intention and secret plan of God Christ died for the elect only, and that His death had only an incidental reference to others in so far as they are partakers of common grace” (p. 150).
Note Boettner’s phrase: “…or did His death have special reference to the elect?” If Christ died ONLY for those whom He represented at the cross (and no others), then why speak of a “special reference” of Christ’s death towards those whom He did NOT represent (i.e., the non-elect or reprobate)? In his polemic against the damnable heresy of “common grace” Marc Carpenter writes the following:
In fashionable Calvinism, “common grace” (the grace that is shown to everyone without exception) is contrasted with “special grace” (the grace that is shown only to God’s people). In fact, whenever you hear or read of the “special grace” of God, the heresy of “common grace” is usually not far away, either lurking in the shadows or brazenly trumpeted. For if God’s grace were always special and never universal, then the phrase “special grace” would be a redundancy.
Likewise when fashionable Calvinists like Boettner use the phrase “special reference” in speaking of Christ’s atonement the heresy that Christ “died in some sense for the non-elect” is usually not far away, either lurking in (relatively) subtle shadows or boldly and brazenly trumpeted. Boettner (somewhat vaguely) indicates what this other than “special reference” entails when he asserts that Christ’s death has “only an incidental reference to others in so far as they are partakers of common grace.”
Evidently for Calvinist heretics like Boettner, an “atonement” of “incidental reference” supposedly composed of mere “common grace” is NOT sufficient to make the non-elects’ salvation “certain” but IS sufficient to make the non-elects’ salvation “possible.” The ingenuous question to ask those who profane the efficacious cross-work of Jesus Christ is this:
“How can you maintain without any trace of disingenuousness, that the non-elects’ salvation is made ‘possible’ by an ‘atonement’ that has a mere ‘incidental reference’ that merely includes so-called ‘common grace’?”
I’m not saying that Loraine Boettner and A.A. Hodge are in particular agreement about this convoluted Calvinist teaching regarding how Christ’s atonement relates to the non-elect or in what “sense” Christ is blasphemously asserted to “die for” those who ultimately perish, but here is Hodge’s explication:
“2nd. He is, in the complete and permanent and saving sense, the Priest only of his own people, his sheep, those from the beginning given him by the Father, those who believe on him through the effectual call of his Spirit. Nevertheless, it is true that in a very important sense he has always been the Priest of the whole historic human race. He is the second Adam. He took upon himself human nature, the seed of Abraham. He was made under the law, and fulfilled the obligations, preceptive and punitive, which rest upon all men alike. He arrested, in behalf of the whole race as a body, the immediate execution of the legal penalty. The whole course of human history, of all peoples and nations, of all religions and civilizations, has been evolved under the shield of his cross, under a dispensation of arrested judgment or forbearance secured through his mediation. He, by his expiation, removed utterly out of the way of all men alike the objective hindrances in the justice of God and in the judgment of the law which rendered their salvation absolutely impossible. In this general sense, Christ, as the man whom God has appointed Priest, is the common bond of the whole human race, and his meritorious service the common basis of all human history.
3rd. But while he, in his priestly work, has made the salvation of all men possible on the condition of their accepting it, he has made the salvation of those whom the Father has given him certain by purchasing for them that faith which is the condition of their personal participation in his work” (A.A. Hodge, Evangelical Theology, pp. 218-219).
A.A. Hodge does not specifically mention the phrase “common grace” but the wicked teaching of it is clearly implied in such statements as “He arrested, in behalf of the whole race as a body, the immediate execution of the legal penalty.” Though many “common grace” and “dualist atonement”  Calvinists (Boettner included) may disagree with the particular way A.A. Hodge enunciated the “sense” in which Christ can be said to be a “Mediator” and “High Priest” for the “historic human race,” they nevertheless must agree in general since they all wish to maintain that the non-elect partake of “common grace.” And since they all wish to assert the heresy of “common grace” they must all answer the question: From whence cometh this grace?
 “Dualist atonement Calvinist” is a phrase I’ve chosen to employ to describe Calvinists who believe that Jesus Christ “died” in “some sense” for the non-elect (i.e., reprobate). This God-hating, Christ-dishonoring, precious-propitiatory-blood-profaning “some sense” garbage is seen in Calvinists who assert that Jesus Christ actually bore the sins of the reprobate, as well as those Calvinists who might vehemently deny that Jesus Christ bore the reprobates’ sins but who nevertheless maintain that Christ “died for” them.
Despite the somewhat confusing variations and permutations of the wicked Calvinistic doctrine of “common grace” (and related doctrine of the non-elects’ supposed relation to Christ’s atonement), this remains clear:
“[Those] who have adopted this term [“common grace”–CD] and who advocate and promote universal grace are the unwitting agents of Satan to destroy the gospel. The true gospel is the gospel of grace — the one and only grace of God as manifested in the work of His only begotten Son, Jesus Christ. Those who hold to ‘common grace’ must either believe that God shows grace at the expense of His justice or that Jesus Christ’s death in some way merited grace for everyone without exception.”
More from Boettner:
“The meaning might be brought out more clearly if we used the phrase ‘Limited Redemption’ rather than ‘Limited Atonement.’ The Atonement is, of course, strictly an infinite transaction; the limitation comes in, theologically, in the application of the benefits of the atonement, that is in redemption. But since the phrase ‘Limited Atonement’ has become well established in theological usage and its meaning is well known we shall continue to use it” (p. 150).
Many people lose sight by focusing too much on what has been called “the extent of the atonement.” The focus needs to be on the nature — the EFFICACY of Christ’s atonement. The essential (or main) point is that the atonement actually saved, that the atonement actually atoned for ALL whom Christ represented. That’s the key. Next Page (22)