guarded by no such Cerberus as the disciples of Plato encountered at the entrance of the groves of the Academy,-- "[Greek: Oudeis ageometraetos eisito]," "Let no one ignorant of Geometry enter here"; but the divine Aphrodite welcomed all mankind to the tender teachings of the Wild Acanthus, the Honeysuckle, and the Sea-Shell, and all the deep utterances of boundless Beauty. Truly, it is sad and dispiriting to the artist to find that all modern aesthetical writings limit and straiten the free walks of highest Art with strict laws deduced from rigid science, with mathematical proportions and the formal restrictions of fixed lines and curves, nicely adapted from the frigidities of Euclid. The line A B must equal the line C D; somewhere in space must be found the centre or the focus of every curve; and every angle must subtend a certain arc, to be easily found on reference to the tables of the text-books. "The melancholy days have come" for Art, when the meditative student finds his early footsteps loud among these dry, withered, and sapless leaves, instead of brushing away the dews by the fountains of perpetual youth. I am aware of no extant English work on Greek Lines which does not aim to reduce that magnificent old Hellenic poetry to the cold, hard limitations of Geometry. Modern Pharisees nail that antique Ideal of loveliness and purity to a mathematical cross. Now it is capable of distinct proof, that abstract Lines of Beauty, even in a greater degree than any other expressions of Art, are born and baptized in Love. Because parabolic curves frequently _coincide_ with these lines, it is no proof that they _created_ them.