Here at Thy Cross, my dying God. I. Watts. [Salvation in the Cross.] First published in his Hymns & Sacred Songs, 1707, Book ii., No. 4, in 5 stanzas of 4 lines. It is in common use in its original form, and as: "Here at Thy Cross, my dying Lord"; "Here at Thy Cross, incarnate God"; and "Here at Thy Cross, my Saviour God," in various American hymn-books, the aim of these alterations being to remove the objection that might be made to the clause my dying God, in the opening line.
--John Julian, Dictionary of Hymnology (1907)