In The Second Spring, the widely published author Joseph Bottum pens what may be the most original cultural undertaking in decades - an attempt to heal the damaged poetry of our time with an infusion of music, and an effort to strengthen the weak music of our age with an injection of poetry.     Ten years ago, in the pages of the Atlantic Monthly, Bottum published an essay called "The Soundtracking of America," a much-attacked account of the misuse of music in contemporary culture. Now, with The Second Spring, he comes at the problem from the other side, as a lyricist rather than a critic. Selecting twenty-four haunting melodies, from a 13th-century Galician-Portuguese cantiga to a modern country/western tune, Bottum composes new verses that both stand alone as poems and reach deep into the roots of the musical genres in which they stand.     Hymns, lullabies, folk tunes, pop songs, dirges, shape-note spirituals, broadsides, and Renaissance Italian dances - The Second Spring explores all these without sarcasm or mockery, allowing each genre to express itself within its natural form.      The Second Spring contains the lyrics, melodies, and new piano arrangements (with guitar chords) for twenty-four songs: new words to old music. With an introduction and, as an appendix, the text of "The Soundtracking of America," this book is a vital and significant event in the nation's artistic culture.