Madeline the mare
The lines of seemingly nonsensical verse that Stephen imagines as he marches rhythmically ("Crush, crack, crick, crick") along the strand—"Won't you come to Sandymount, / Madeline the mare"—do not appear to quote any preexisting literary text, though perhaps one will eventually be discovered. More likely, Stephen is playing with sounds to make a little poetic composition, as he will do later in Proteus when he dwells on the sounds of "mouth to her mouth's kiss." The second line refers punningly to either of two French visual artists, and the punning continues as Stephen thinks about the lines he has just brought into consciousness.
Thornton notes that "This seems to be an Irish song or poem, but I have not been able to locate it. D. Daiches calls it 'popular verse,' but does not identify it." Both scholars appear to be responding to the fact that Stephen's lines sound like ballad meter (iambic tetrameter alternating with iambic trimeter), which is commonly used in English and Irish popular songs and poems.
Regardless of whether Stephen is recalling a popular song in the first line or making one up, his imagination is clearly at work in the second line. Madeleine Lemaire, Gifford notes, was a watercolor painter known for portraits, illustrations, and floral compositions in the last decades of the 19th century and the first of the 20th. Sometimes called The Empress of the Roses, she was a fixture of the artistic salons in Paris and was one of Marcel Proust's high-society intimates. If Madeline the mare is Madeleine Lemaire, then Stephen—who perhaps encountered her works or her reputation in Paris—may be wishing that this elegant French artiste would come to Dublin and lend some class to the local literary scene.
Alternatively, Gifford notes, the mare could be Philippe Joseph Henri Lemaire, known as Henri, a sculptor who fashioned the relief of the Last Judgment on the pediment (tympanum) of l', or church of the Mary Magdalen, in Paris in the 1830s. If Madeline the mare is Lemaire who did the Madeleine, then Stephen, Gifford observes, may be wishing that this impressive sculptor could have come to Sandymount and improved the façade of Mary, Star of the Sea, the church that he has just passed in Leahy's Terrace on his walk to the strand.
Of course, it is entirely possible that Stephen is thinking of both Lemaires; nor do the verbal acrobatics stop there. His linguistic imagination is still romping as he contemplates the "Rhythm" of the lines, fancying that his "catalectic tetrameter of iambs" is "marching. No, agallop: deline the mare." Lemaire is now fully a mare, galloping along the shore of the mare (Latin for sea).