"If the Atonement be limited in Design, it must be restricted in the Offer.There is still another ground on which it is urged that Augustinians cannot consistently preach the gospel to every creature. Augustinians teach, it is urged, that the work of Christ is a satisfaction to divine justice. From this it follows that justice cannot condemn those for whose sins it has been satisfied. It cannot demand that satisfaction twice, first from the substitute and then from the sinner himself. This would be manifestly unjust, far worse than demanding no punishment at all. From this it is inferred that the satisfaction or righteousness of Christ, if the ground on which a sinner may be forgiven, is the ground on which he must be forgiven. It is not the ground on which he may be forgiven, unless it is the ground on which he must be forgiven. If the atonement be limited in design it must be limited in its nature, and if limited in its nature it must be limited in its offer. This objection again arises from confounding a pecuniary and a judicial satisfaction between which Augustinians are so careful to discriminate. This distinction has already been presented on a previous page (470). There is no grace in accepting a pecuniary satisfaction. It cannot be refused. It ipso facto liberates. The moment the debt is paid the debtor is free; and that without any condition. Nothing of this is true in the case of judicial satisfaction. If a substitute be provided and accepted it is a matter of grace. His satisfaction does not ipso facto liberate. It may accrue to the benefit of those for whom it is made at once or at a remote period; completely or gradually; on conditions or unconditionally; or it may never benefit them at all unless the condition on which its application is suspended be performed. These facts are universally admitted by those who hold that the work of Christ was a true and perfect satisfaction to divine justice. The application of its benefits is determined by the covenant between the Father and the Son. Those for whom it was specially rendered are not justified from eternity; they are not born in a justified state; they are by nature, or birth, the children of wrath even as others. To be the children of wrath is to be justly exposed to divine wrath. They remain in this state of exposure until they believe, and should they die (unless in infancy) before they believe they would inevitably perish notwithstanding the satisfaction made for their sins. It is the stipulations of the covenant which forbid such a result. Such being the nature of the judicial satisfaction rendered by Christ to the law, under which all men are placed, it may be sincerely offered to all men with the assurance that if they believe it shall accrue to their salvation. His work being specially designed for the salvation of his own people, renders, through the conditions of the covenant, that event certain; but this is perfectly consistent with its being made the ground of the general offer of the gospel. Lutherans and Reformed agree entirely, as before stated, in their views of the nature of the satisfaction of Christ, and consequently, so far as that point is concerned, there is the same foundation for the general offer of the gospel according to either scheme. What the Reformed or Augustinians hold about election does not affect the nature of the atonement. That remains the same whether designed for the elect or for all mankind. It does not derive its nature from the secret purpose of God as to its application."
Charles Hodge, Systematic Theology (Grand Rapids: Eerdmans, 1993), 2:557-558.