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represents the structure of each into the other. The general formula 

 for any radiated animal is that it is made up of a number of spherical 

 wedges, arranged round a vertical axis, having two poles, the actinal, 

 at which stands the mouth, and the abactinal, opposite to it. This gen- 

 eral formula can be changed to stand for a Polyp by making the 

 spherical wedges a number of chambers, separated by partitions radia- 

 ting toward a digestive cavity, which is only the prolongation of the 

 outer wall turned in, thus making an opening commonly called the 

 mouth, — some of the partitions reaching the wall of this digestive 

 cavity, and others only extending a short distance from the outer wall 

 of the Polyp. The upper part of each one of these chambers is sur- 

 mounted by a hollow tentacle, which is nothing but the prolongation of 

 the chamber itself. Along the sides of these radiating partitions are 

 attached the bunches of eggs, one on each side of the partition, at the 

 extremity nearest the digestive cavity. This would be the general 

 formula for radiation carried out in a special manner so as to apply 

 to the class of Polyps. Next comes the formula for Acalephs. Here 

 we have a central cavity from which radiate tubes hollowed out of the 

 solid mass, on each side of which are placed the ovaries, running 

 toward the circumference, where they are either united by a circular 

 tube, or by numerous anastomoses. The digestive cavity is not, as in 

 the case of Polyps, formed by the turning in of the outer wall ; it is 

 cut out of the solid envelope, and around its edge hang down fringes 

 or lobes. Oj)posite each one of the radiating tubes we have a tenta- 

 cle, which may be hollow or not. In this connection the presence of 

 tentacles along the edge of the circular tube need not be taken into 

 consideration, since they are only a feature of a later growth. 



How can we transform the formula for Polyps, as it is given above, 

 into this Acaleph formula ? Let us take that formula as made up of 

 a number of chambers, separated by thin walls. Increase the thick- 

 ness of these walls, the chambers become gradually smaller and 

 smaller, until they may be reduced above and below to such an extent 

 as to change them into tubes. These tubes will open into a central 

 cavity. But where are the appendages of the mouth of Acalephs ? 

 Supposing that we take what we have called the digestive cavity of 

 our formula for Polyps, and turn it inside out like the finger of a 

 glove, cutting it open at the same time into as many lobes as there 

 are radiating tubes, we shall have a series of fringes surrounding 

 the opening of a cavity scooped out of a hollow mass, from which 

 tubes radiate toward the circumference. The tentacles will be placed 

 in a similar position at the end of the radiating tubes, as we find them 

 in Polyps in the prolongation of the chambers which are homologous 

 to the radiating tubes. The only thing wanting now is the circular 

 tube to connect these radiating tubes. In Polyps there is a hole in 



