As in the case of the "first moved," the uniform unceasing rotation of each "sphere" is explained by the influence on it of an unchanging immaterial "form," which is to its own "sphere" what God is to the universe as a whole. In the Aristotelianism of the mediæval church these pure forms or intelligences which originate the movements of the various planetary spheres are naturally identified with angels. It is _e.g._ to the angelic intelligences which "move" the heaven of Venus, which comes third in order counting outward from the earth, that Dante addresses his famous Canzone, _Voi ch’ intendendo il terzo del movete_. The mediæval astronomy, however, differs in two important respects from that of Aristotle himself. (1) The number of "spheres" is different. Increasing knowledge of the complexity of the paths of the planets showed that if their paths are to be analysed into combinations of circular motions, fifty-four such rotations must be an altogether inadequate number. Aristotle’s method of analysis of the heavenly movements was therefore combined with either or both of two others originated by pure astronomers who sat loose to metaphysics. One of these methods was to account for a planet’s path by the introduction of _epicycles_. The planet was thought of not as fixed at a given point on its principal sphere, but as situated on the circumference of a lesser sphere which has its centre at a fixed point of the principal sphere and rotates around an axis passing through this centre. If need were, this type of hypothesis could be further complicated by imagining any number of such epicycles within epicycles. The other method was the employment of "eccentrics," _i.e._ circular movements which are described not about the common centre of the earth and the universe, but about some point in its neighbourhood. By combinations of epicycles and eccentrics the mediæval astronomers contrived to reduce the number of principal spheres to _one_ for each planet, the arrangement we find in Dante. (2) Also real or supposed astronomical perturbations unknown to Aristotle led some mediæval theorists to follow the scheme devised by Alphonso the Wise of Castille, in which further spheres are inserted between that of Saturn, the outermost planet, and the "first moved." In Dante, we have, excluding the "empyrean" or immovable heaven where God and the blessed are, nine "spheres," one for each of the planets, one for the fixed stars, and one for the "first moved," which is now distinguished from the heaven of the stars. In Milton, who adopts the "Alphonsine" scheme, we have further a sphere called the "second movable" or "crystalline" introduced between the heaven of the fixed stars and the "first moved," to account for the imaginary phenomenon of "trepidation."[#] In reading Dante, Shakespeare, and Milton, we have always to remember that none of these reproduces the Aristotelian doctrine of the "spheres" accurately; their astronomy is an amalgam of