Smith:
1) The Priestly Office of Christ is that office in both natures whereby He makes an atonement. In the same priestly office and in virtue of his atoning work his Intercession is maintained. Intercession belongs to Christ as priest: it includes his constant application of his sacrifice; or, generally, all his agency in redeeming mankind, in his glorified state. Of the two parts of Christ’s work as Priest Atonement and Intercession we speak here only of The Atonement.
I. Usage of the word, and of certain terms which cluster about it.
1. Of the terms Redemption and Atonement. Redemption implies the complete deliverance from the penalty, power, and all the consequences of sin: Atonement is used in the sense of the sacrificial work, whereby the redemption from the condemning power of the law was insured.
2. Of the terms Reconciliation and Atonement. Reconciliation sets forth what is to be done: Atonement, in its current theological sense, likewise involves the idea of the way, the mode, in which the reconciliation is effected that is, by a sacrifice for sin. Henry B. Smith, System of Christian Theology, 2nd ed., (New York: A.C. Armstrong and Son, 1884), 437. [Some reformatting; italics original; footnotes not included and underlining mine.]
2) [T]he truth of General Atonement says: The Atonement made by Christ is made for all mankind, is such in nature and design, that God can save all men, consistently with the demands of holiness, on condition of faith and repentance.
1. The distinction is to be made between Atonement and Redemption. Atonement is the provision. Henry B. Smith, System of Christian Theology, 2nd ed., (New York: A.C. Armstrong and Son, 1884), 478. [Some reformatting and underlining mine.]
[Brief biographical notes: 1) In the decades after 1840 New School theology became more conservative. Its proponents widely criticized Finney’s prefectionism. They attacked Darwinism, early biblical criticism, and German philosophy and theology. Henry B Smith of Union Theological Seminary emerged as the leading spokesman. His defense of systematic theology and biblical infallibility and his perceptions that New Schoolers had become more orthodox were influential in the reunion of the Presbyterian Church in 1869. W. A Hoffecker (Elwell Evangelical Dictionary). 2) What most impresses the student of Warfield’s writings—apart from his deeply religious spirit, his sense of complete dependence on God for all things including especially his sense of indebtedness as a lost sinner to His free grace—is the breadth of his learning and the exactness of his scholarship. Caspar Wistar Hodge, his immediate successor at Princeton Seminary and long his associate, in his Inaugural Address after referring to the illustrious men who had given the institution fame throughout the world for sound learning and true piety, such as Archibald Alexander, Charles Hodge and Archibald Alexander Hodge, spoke of Warfield as ‘excelling them all in erudition.’ John DeWitt, long the professor of Church History in Princeton Seminary and himself a man of no mean scholarship, once told the writer that he had known intimately the three great Reformed theologians of America of the preceding generation— Charles Hodge, W.G.T. Shedd and Henry B. Smith—and that he was not only certain that Warfield knew a great deal more than any one of them but that he was disposed to think that he knew more than all three of them put together. Samuel G. Craig. 3) Upon Smith’s death, W.G.T. Shedd succeeded him in the chair of Systematics. 4) See also the brief Wiki entry on Smith.]