General Nelson Monroe was a veteran of the Civil and Mexican-American Wars. In 1893, he published a book of “reminiscences of the days of dark secession 1861 and 1865” entitled The Grand Army Button: A Souvenir. It can be viewed in full at archives.org.
The finale of the book is a poem called “The Dead Line” at Libby Prison about the horrors of internment at the Confederate Libby Prison in Richmond, Virginia. It can be read here.
The inscription on the back of the monument can be viewed at Pictures of Arlington’s facebook page.