The criticism that the doctrine of limited atonement prevents the free offer of the gospel rests upon a profound misapprehension as to what the warrant for preaching the gospel and even of the primary act of faith itself really is. This warrant is not that Christ died for all men but the universal invitation, demand and promise of the gospel united with the perfect sufficiency and suitability of Christ as Saviour and Redeemer. What the ambassador of the gospel demands in Christ’s name is that the lost and helpless sinner commit himself to that all-sufficient Saviour with the plea that in thus receiving and resting upon Christ alone for salvation he will certainly be saved. And what the lost sinner does on the basis of the warrant of faith is to commit himself to that Saviour with the assurance that as he thus trusts he will be saved. What he believes, then, in the first instance is not that he has been saved, but that believing in Christ salvation becomes his. The conviction that Christ died for him, or in other words that he is an object of God’s redeeming love in Christ, is not the primary act of faith. It is often in the consciousness of the believer so closely bound up with the primary act of faith that he may not be able to be conscious of the logical and psychological distinction. But nevertheless the primary act of faith is self-committal to the all-sufficient and suitable Saviour, and the only warrant for that trust is the indiscriminate, full and free offer of grace and salvation in Christ Jesus.(source)
There is more of value in the article, to be sure, such as this:
That the non-elect, those who do not become the actual partakers of salvation and are therefore finally lost, are not included within the scope of the redemption purchased by Christ, we may and must even from that which we have already quoted infer to be the teaching of the Confession. But it is interesting to observe that not only does the Confession imply this; it also expressly states it. "Neither are any other redeemed by Christ, effectually called, justified, adopted, sanctified, and saved, but the elect only." (III.vi.) The Confession is using the phrases "redeemed by Christ" and "purchased redemption" synonymously. Here it is said that redemption by Christ or the purchase of redemption is for those who as a matter of fact are saved and for those only. It is exclusive of those who are not called, justified, adopted, sanctified, and saved. Redemption is defined not only extensively but exclusively.
If we may recapitulate then, the teaching of the Confession can be summed up in these three propositions. (1) Redemption is purchased for the elect. (2) Redemption is applied to all for whom it is purchased. (3) Redemption is not purchased for those who finally perish, for the non-elect.
Atonement is defined therefore in the Confession in terms of sacrifice, reconciliation, redemption, satisfaction to divine justice, discharge of debt, and states clearly that atonement thus defined is for those whom God hath predestinated to life, namely the elect. They are saved because Christ by his redemptive work secured their salvation. The finally lost are not within the embrace of that salvation secured, and therefore they are not within the embrace of that salvation secured, and therefore they are not within the embrace of that which secures it, namely the redemption wrought by Christ. It is just here that the difference between Arminianism and Calvinism may be most plainly stated. Did Christ die and offer Himself a sacrifice to God to make the salvation of all men possible, or did He offer Himself a sacrifice to God to secure infallibly the salvation of His people? Arminians profess the former and deny the latter; our Standards in accordance, as we believe, with Holy Scripture teach the latter.