In order to find the corresponding morphological polarity in the animal kingdom, we must realize that the animal, by having the main axis of its body in the horizontal direction, has a relationship to the gravity-levity fields of the earth different from those of both man and plant. As a result, the single animal body shows the sphere-radius polarity much less sharply. If we compare the different groups of the animal kingdom, however, we find that the animals, too, bear this polarity as a formative element. The birds represent the spherical (dry, saline) pole; the ruminants the linear (moist, sulphurous) pole. The carnivorous quadrupeds form the intermediary (mercurial) group. As ur-phenomenal types we may name among the birds the eagle, clothed in its dry, silicic plumage, hovering with far-spread wings in the heights of the atmosphere, united with the expanses of space through its far-reaching sight; among the ruminants, the cow, lying heavily on the ground of the earth, given over entirely to the immensely elaborated sulphurous process of its own digestion. Between them comes the lion - the most characteristic animal for the preponderance of heart-and-lung activities in the body, with all the attributes resulting from that. Within the scope of this book it can only be intimated briefly, but should not be left unmentioned for the sake of those interested in a further pursuit of these lines of thought, that the morphological mean between radius and sphere (corresponding to Mercurius in the alchemical triad) is represented by a geometrical figure known as the 'lemniscate', a particular modification of the so-called Cassinian curves.2 1 For further details, see the writings of G. Adams and L. Locher-Ernst who, each in his own way, have made a beginning with applying projective geometry on the lines indicated by Rudolf Steiner. Professor Locher-Ernst was the first to apply the term 'polar-Euclidean' to the space-system corresponding to levity. 2 For particulars of the lemniscate as the building plan of the middle part of man's skeleton, see K. König, M.D.: Beitrage zu einer reinen Anatomic des menschlichen Knochenskeletts in the periodical Natura (Dornach, 1930-1). Some projective-geometrical considerations concerning the lemniscate are to be found in the previously mentioned writings of G. Adams and L. Locher-Ernst. CHAPTER XIII 'Radiant Matter'