his Opus 500, is almost entirely free from the _à priori_ theory. He transfers mechanics to music. With good results he treats individual cases, as for example, when he appends to the beginning of passages a finger-exercise not given in the scale; he designs immediately to return to the usual fingering in order to arrive duly at the extreme notes with the extreme fingers, and to avoid unnecessary underpassing. It was reserved for a later time not merely to bring the note-material lying before us into harmony with economic fingering, but also to make execution, which with Czerny has but a loose dependence on the finger-exercise, re-act upon the fingers. Bülow, for example, is fond of unusual fingering, in which the execution forbids any too easy playing, and a too loose rendering is prevented by irregularities in the succession of the fingers. * * * * * The mechanics of the fingers formed the first part of piano-instruction; touch and execution were the second. Their importance as means to the mechanism of music was fully seen; and in the “Technical Studies” of Plaidy, or in Köhler’s “Methode für Klavierspiel und Musik” (1857), they are as exhaustively handled as before had been the “manieren” or the thorough-bass. The former contents himself with the simple terms, Legato, Staccato, Legatissimo, and Portamento; the latter gives a more mechanical division, always according to the use of the fore-arm, the finger-joints, the wrist, or the elbow. Neither is complete, neither supplies a systematic advance on the lines of his predecessors; and we should be astonished at these divergences if we set the numerous schools of these times, from a theoretical point of view, over against one another. Practically considered, however, they agree well enough. The holding of the hand as enjoined by Philip Emanuel Bach has remained on the whole unaltered down to the present day. With trifling differences, which concern the relation of the extreme fingers to the middle finger, and the profile of the back of the hand, Bach, Türk, Müller, Hummel, Logier, Kalkbrenner and the rest, are at one as to the support of the arm which carries the hand, and of the hand which carries the fingers as they descend. In Paris Logier constructed an instrument to hold the hand in practice, in shape like a bracket, which he named “chiroplast.” Kalkbrenner, in his “Guide-mains,” introduced some modifications on the chiroplast; but such mechanical contrivances gained no general acceptance. Logier’s speciality was his prefatory note that the finger must remain in continual touch with the key. With this was allied that special kind of sensuously charming touch which differentiated the Parisian school from the brilliant playing of the Viennese and the emotional style of the English. That _carezzando_, or stroking of the keys, was a favourite practice of Kalkbrenner and Kontski in Paris.